Experimental Biology

Experimental Biology BSC 3402L Table of Contents Chapter 1 Introduction to Experimental Biology 4 Chapter 2 What is Science? 5 Chapter 3 Plant Reproductive Biology 9 Chapter 4 Pollen Vectors and Pollination Syndromes 16 Chapter 5 Foraging Ecology of Pollinators 26 Chapter 6 Experimental Design and Data 31 Chapter 7 Statistics--Distributions and Differences Between Means 37 Chapter 8 Statistics--Measures of Association 44 Chapter 9 Using the Library and Biological Literature 51 Chapter 10 Scientific Communication Proposals 55 Chapter 11 Scientific Communication Papers and Presentations 60 Chapter 12 Lab Exercise - Floral Morphology and Pollination Systems 65 Chapter 13 Lab Exercise - Costs and Benefits of Foraging 71 Chapter 14 Selected References on Pollination Ecology 77 Appendix 1 Hazards of the Wild 81 Appendix 2 Statement of Voluntary Consent The purpose of this course is to provide students with first-hand experience in experimental research. We really want you to learn what the whole process of biological research is like: coming up with a question, properly stating and designing experiments to try to address the question, executing "the experiment," analyzing the experiment, and, finally, organizing and writing your results in an acceptable fashion. As you will note, the experiment itself is actually only a small part of this process. Therefore, our emphasis in this course will be not the experimental system itself (pollination biology), but the whole process by which we "do Science." Given these goals, the system in which the research is actually carried out is of secondary importance. As evidenced by the depth and breadth of research conducted at Florida State University, we could have chosen innumerable systems for you to investigate. So, why pollination biology? Well, basically because we find it to be very interesting and diverse, even occasionally bizarre. We expect this course to be challenging, but we also want it to be enjoyable. Plus, it allows those of us who are teaching the course to get outside where we really want to be. Pollination in angiosperms consists of three phases: (1) the release of pollen from the "male" part of a flower, (2) transfer from the male to the female part, and (3) successful placement of pollen on the recipient surface of the female portion of the flower, followed by germination of the pollen grain. These steps ultimately lead to fertilization, seed production, and eventual propagation of the individual plant, none of which we will directly consider in this course. However, any portion of the three phases of pollination is open to investigation by you in your experiment. Further, don''t feel restricted to working from a "plant perspective"; as insects, bats, and even mice can be involved in pollination, we encourage you to look at the process from an animal perspective if you wish. Just remember: this course in not really about pollination biology; it''s about how to conduct experimental research. We will give you just enough background in pollination biology to get through the course. We also hope to convince you that it is an interesting and fun subject. Consider the analogy of someone studying how we swallow. Why not use ice cream during the study? We hope that pollination biology is your ice cream What is science http://bio.fsu.edu/~winn/3402L/WinnCH2.html Science is the investigation of rational concepts that can be tested by observation and experimentation. The analytical method, which involves a pattern of observation, experimentation, and both inductive and deductive logic, is what distinguishes science from other disciplines. Biology is the science of life on earth. The process of acquiring scientific information involves postulating and testing hypotheses. Hypotheses are possible explanations for observed phenomena. This process is just a formalization of one we carry out all the time. Construction of hypotheses itself does not constitute science: the hypotheses must be testable in the physical world. For example, if one morning your roommate turns an interesting shade of green, a possible hypothesis is that this is just fate, something the gods of late-night partying have wished to happen. Because this hypothesis is not testable, however, it lies outside the scope of science. Plant Reproductive Biology http://bio.fsu.edu/~winn/3402L/WinnCH3.html ch3 Higher plants have alternation of generations, with a gametophyte generation being reduced to the status of a short-lived parasite on the sporophyte generation. What most of us think of as a "plant" and its flowers are actually parts of the diploid, sporophytic generation (Figure 3.1). Most of the flower itself consists of evolutionarily specialized structures of the sporophyte. However, hidden within the ovary of the flower, specialized cells undergo meiosis to create the haploid megaspore mother cells. The megaspore divides three times to produce the embryo sac, which is the female gametophyte and will produce female gametes, eggs (Figure 3.1). Meanwhile, inside the anthers other cells under go meiosis to produce haploid microspores. Microspores also undergo mitosis to produce pollen grains, which are the male gametophyte. The single celled pollen grain has two nuclei. When a pollen grain is transferred to the stigma (part of the sporophyte), one of the nuclei divides to produce two sperm nuclei, which are the male gametes. The pollen grain itself "germinates" to grow a long tube down the stigma and style to the ovary. Here one of the sperm nuclei fuses with an egg to produce a diploid zygote, which divides mitotically many times to produce an embryo. The other sperm nucleus fuses with other nuclei in the ovule to produce the triploid endosperm, which acts as food for the embryo and germinating seedling. The two fusions of nuclei are referred to, appropriately enough, as "double fertilization." A brief note on how we use words like "adaptation" when discussing evolution: It is unfortunate that a wide gap often exists between common parlance and scientific terminology. Many biology students are confused by evolution because we discuss how a species is "adapted" to a specific environment. When we say that a person adapts well to adverse circumstances, we are obviously referring to a short-range, dynamic process--something that happens in the lifetime of the person involved. However, in an evolutionary context, "adaptation" most commonly describes a state rather than an action of an individual. That is, when we say that a flower has evolved or is adapted for wind pollination, we are talking about a process that has taken millions of years and involved changes to the species, not to individuals. And, of course, no suggestion is ever intended that the process involves effort or volition on the part of the plant. Outcrossing and Selfing The flower is so highly specialized or adapted for pollination that it is the dominant characteristic by which Linnaeus, and now all the rest of us, differentiate species. Why has evolution by natural selection led to the extremely complex and diverse array of flowers we see around us? Of several apparent reasons, the most important is the desirability of outcrossing; much of floral diversity appears to be related to getting the pollen from one plant to the stigma of another plant, rather than allowing self-pollination (also called "selfing"), reproduction involving pollen and ovules from the same plant. The primary benefit of outcrossing is the avoidance of inbreeding depression which is a decrease in the fitness of offspring resulting from breeding between close relatives. Most species are either predominantly self-pollinating or predominantly outcrossing, not intermediate in strategy (Schemske and Lande, 1985). Selfing, where it exists, appears to be a secondarily derived condition. That is, ancestors of these species were outcrossing and then evolved self-pollination. As evidence, many plants produce colorful flowers, lots of nectar and pollen, and attract significant numbers of pollinators, yet are entirely selfing and require no pollination. It is clear that, in these cases, ancestral species that required outcrossing were involved in the evolution of the flower. Selfing can occur through pollination of an ovule by pollen from the same flower, which is called autogamy. Pollination between different flowers is called allogamy. Allogamy that occurs when pollen is carried from one flower to another on the same plant is called geitonogamy. True outcrossing, in which pollen is carried from a flower on one plant to a flower on a different plant is called xenogamy. Evolution by natural selection has apparently acted to promote outcrossing in many ways. These are all very important to keep in mind when looking at any given flower, as much of its structure is likely to be the result of past selection for allogamy. Let''s consider some of the most common ways in which plants prevent pollination from occurring within a flower. Separation in Space The simplest way for plants to prevent autogamous self-fertilization is to separate the anthers physically from the stigma. In flowers that are hermaphroditic (i.e. those that produce both male and female gametes), this separation virtually always occurs. When the bud opens, the two structures will physically separate themselves before the pollen is released and the stigma becomes receptive. Having flowers that contain both male and female parts separated in space is termed herkogamy. Extreme examples of herkogamy can be found in orchids and milkweeds (Asclepiadaceae, butterfly weed is a good example). In both these groups, all the pollen is packed into fairly hard masses with a wax-like appearance, called pollinia (singular, pollinium). These pollinia are usually located in a kind of "key" mechanism in the flower so that they are only removed from the flower when the pollinator is leaving and only deposited onto the next flower when the pollinator arrives. It is very difficult for them to be deposited in the flower of origin. Of course, herkogamous flowers are still susceptible to transfer of pollen within a flower by pollinators, or even by the wind or other disturbances. A more effective arrangement is actually to have separate male and female flowers. Monoecious species have both male and female flowers on the same plant. In this case, autogamy is impossible, yet the genetically equivalent geitonogamy is still likely, as pollinators frequently move between flowers on the same plant (Table 3.1). Some species avoid this problem by only having a small number of flowers open at a time. Dioecious species actually have plants of different "sex." Recognize that we are using a convenient short-hand: the sporophyte plants themselves are sexless but produce gametophytes which are male or female. Although dioecy enforces xenogamy, it does so at the expense of half the population not bearing seeds and creates a risk of nonpollination (Table 3.1). For example, species that persist by colonizing new habitats are not likely to be dioecious, as both a male and a female plant would have to be lucky enough to colonize a new area at the same time. An interesting way in which the male and female function can be separated in plants is a form of heteromorphy (literally, different shapes), distyly and tristyly. Heteromorphy is simply the condition in which some individuals in the population have a structure different from that of others, and in this case it has to do with the relative locations of the stigma and anthers in different flowers (Figure 3.2). For example, in distyly, there are two forms of the plant. One produces flowers in which the stigma is located high in the flower and the stamens somewhat lower, and the other produces the opposite arrangement, the stigma low and the stamens high. This strategy discourages pollination within a flower and encourages pollen transfer between flowers. In our area, heterostyly occurs in many species, including several Oxalis species and species in the coffee family, as well as in purple loosestrife (Lythrum salicaria) and pickerel weed (Pontederia cordata). Charles Darwin was one of the first to recognize the significance of the different locations of stamens and pistils in his wonderful book The Different Forms of Flowers on Plants of the same Species. pictires http://educationally.narod.ru/exbiophotoalbum.html Plant Reproductive Biology:Separation in Time http://bio.fsu.edu/~winn/3402L/WinnCH3.html ch3 We define anthesis as beginning when the anthers or the stigmas become exposed to the pollinating agent(s), either because the flower opens or because the organs protrude from a closed flower in such a manner as to expose themselves to the same agent. When pollen grains are fully mature, the anthers often split open and begin to shed the pollen. When the stigma is mature and can accept pollen, we say it is receptive. The stigma may not be continuously receptive during anthesis and, in fact, self-pollination can be prevented by careful timing of stigma receptivity relative to pollen maturation within the same flower Dichogamy describes the case in which the stamens and pistil of a flower mature at different times, thereby preventing autogamous self-pollination. There are two types of dichogamy: Protandry, in which the anthers mature and release pollen before the stigmas are receptive, and protogyny, in which the stigmas become receptive before pollen release. Protandry is found in most composites (Asteraceae) and also in many mints (Lamiaceae) and figworts (Scrophulariaceae). In both cases, the temporal separation of the sexes enforces allogamy, can encourage xenogamy, and can allow each sexual function to occur at a time that may be more advantageous to the plant (Table 3.1). Good examples of protandry are often provided by species with columnar or spike inflorescences, such as the bumblebee-pollinated foxgloves (Digitalis purpurea) and fireweed (Epilobium angustifolium). Both the opening of the flower buds and the production of nectar in the flowers follow a very strict time pattern, geared to the foraging strategy of the pollinators. The inflorescences of these plants bloom from the bottom up, and each flower lasts several days. Therefore the lowest flowers on an inflorescence with many open flowers are female, having gone through the male stage already. These flowers are also the richest in nectar, and foraging bumblebees nearly always visit them first, with the result that any pollen deposited on their stigmas is likely to have come from another plant. The bumblebees then work their way up the inflorescence, visiting several flowers in succession until the nectar reward is no longer commensurate with the energy they have to expend in order to get it. They then fly off, usually to the lowest flowers of another inflorescence, where the pollen they have picked up from the higher-placed flowers may be deposited on the stigma. The result is usually cross-pollination. Protogyny is very pronounced in a number of families commonly regarded as primitive, for example, water lilies (Nymphaeaceae) and magnolias (Magnoliaceae). Very common plants that demonstrate protogyny are the plantains (Plantaginaceae). These species have flowers arranged on spikes and flower from the bottom up, just as do foxglove and fireweed. However, in these species older flowers are male rather than female. Therefore, in an inflorescence with many open flowers, it is the bottom ones that are male, whereas those higher up are female. Because plantains depend on the wind for pollination, the likelihood of pollen traveling upwards is very low, and the situation favors cross-pollination. Autogamy and Apomixis Many species do not avoid autogamy. In some flowers, self-pollination is spontaneous, so that even if no external pollination agent (biotic or abiotic) touches the flower, its own structures cause the transfer of pollen from anthers to stigma. The evolution of such pollination methods is thought to be a "retrograde" development; that is, that it has evolved from outcrossing ancestors, perhaps as compensation for poor chances for allogamous pollination. Weedy species present special problems with regard to allogamy. It has even been suggested that autogamy is a prerequisite for the successful establishment of long distance migrants, perhaps because long-distance dispersal isolates plants from their normal pollinators. Evolutionarily, there are two options: (1) a generalized flower form that attracts many different types of pollinators and/or (2) autogamy. Another mechanism to insure fertilization found in weedy species is apomixis--the development of a sporophyte from a gametophyte without fertilization, the equivalent of parthenogenesis in animals. In this case, there is no self- or outcrossed fertilization. Apomixy can occur in several ways. In many apomictic species, the megaspore mother cell goes through meiosis to produce the egg, but the egg chromosome number at some time simply doubles. In other species, there is no meiosis at all; the so-called "egg" is produced by mitosis and already has the diploid chromosome number. Clearly, apomictic species do not require pollination. Now, if a flower is already pollinated before it opens, and there is no likelihood of later pollination having any effect, the whole anthesis is functionally redundant, and could be done away with. Cleistogamous (from two Greek words together meaning a secret marriage) flowers never open and have a marked reduction (or elimination) in portions of the flower affecting advertisement and pollinator rewards. Generally, the anthers and number of pollen grains are also reduced in accord with the greater efficiency of this pollination process. Cleistogamous species are distributed worldwide: well-known examples include violets, rushes, wood sorrel, and some rice species. Practically all cleistogamous plants can also produce normal open or chasmogamous flowers. Cleistogamy appears to be related to environmental conditions: when the environment is harsh, plants are more likely to produce cleistogamous flowers. The classic example is jewel weed (Impatiens capensis), an annual species that in moist, high-light environments produces many large and beautiful chasmogamous flowers, which offer large amounts of nectar to pollinating bees. However, on unfavorable sites, the plants are stunted and produce only cleistogamous flowers. The main advantage of cleistogamy is that it is a cheap method. Producing and maintaining large, nectar-rich open flowers is biologically expensive. The cost of producing a seed through cleistogamy is only about two-thirds of that for one formed through chasmogamy. Another interesting point is that well-developed jewel weed plants that would normally form a number of chasmogamous flowers will make only cleistogamous ones after they have been grazed by deer or when the ends of the branches have been cut off--a quick response to an emergency situation. Self-Incompatibility Separation of male and female flower parts in time and space are prepollination mechanisms to reduce selfing. That is, they act to reduce the probability that self-pollination will occur. There are also postpollination mechanisms of reducing selfing. An example is self-incompatibility. In a self-incompatible species, self pollen that reaches a stigma does not produce viable seed. Self-incompatibility often supplements other mechanisms promoting outcrossing, so a species may demonstrate herkogamy and also be self-incompatible. Self-incompatibility is not invariably absolute; in fact, it varies from 100% to a very slight advantage for foreign pollen. Incompatibility is a prerequisite for allogamous pollination in many flowers in which pollen and receptive stigma inevitably come into contact with each other (i.e. in which there is no herkogamy). Incompatibility can take several forms. Pollen grains may not grow on self-pollinated stigmas or may only grow slowly relative to foreign pollen, perhaps as a result of stigmatic secretions that harm the pollen. In some species, a chemical barrier on the stigma can only be broken down by foreign pollen. It has been shown in these cases that wounding the stigma mechanically, electrically, or chemically can remove the chemical barrier and allow self-pollination. Another common artificial way around this incompatibility is "bud pollination," in which the flower is carefully dissected before it opens and a self-pollination is performed. This method works because the chemical barriers are generally incompletely formed before the flower opens. It is interesting to note that in situations where self-incompatibility is due to slow pollen-tube growth, self-fertilization is likely to occur when no other pollen is available. That is, it appears to be a "last-chance" way of producing seed. If any foreign pollen arrives on the stigma, it will win the race down the style and fertilize the ovule, but if no such pollen arrives, then the race goes to the slow self pollen. It has been suggested that this screening out of potential pollen by the stigma may also allow "competition" between different sources of foreign pollen. Perhaps plants that are genetically "good fathers" will have pollen tubes that grow faster. Another way in which incompatibility may operate is through gametic incompatibility. In this case, the male and female gametes unite but do not form viable offspring. This mechanism is costly to the plant because it "loses" the ovule involved in gametic incompatibility. Similarly, endosperm incompatibilities (in which the embryo in the seed has no stored food) and production of sterile offspring, lead to wasted ovules. It seems unlikely that these mechanisms have evolved in response to selection for self-incompatibility. Instead, these are likely consequences of inbreeding and the increased probability of the expression of deleterious recessive genes. To reiterate, mechanisms that prevent selfing are not mutually exclusive and two or more may occur together, as I have noted in several cases above. Such apparent redundancy is likely to represent relics from the pollination mechanisms of ancestral species, left in the course of further evolution. To understand properly the avoidance of self-pollination, one should take into account not only the fact that (in many species) the resulting seed is poor, but also that the wrong pollen may have immediate negative effects, in extreme cases resembling poisoning. In the evolution of pollination, economy plays a large role. Prevention of waste of pollen and especially eggs seems to be a legitimate consideration. The devices listed above therefore affect not only the pollination process proper but, even more prominently, the economy and prevention of nonsense or even deleterious pollination. Pollen Vectors http://bio.fsu.edu/~winn/3402L/WinnCH4.html ch4 Pollen Vectors and Pollination Syndromes Pollen-transfer problems have widely different aspects depending on whether the vector is an animal or an inanimate physical force. Pollination by a living agent can result in coadaptation and the so-called "evolutionary chase." Whatever the pollination vector, it is apparent that natural selection has resulted in extreme floral diversity and specialization. Each part of each flower functions in its own way, but functions of various parts within a blossom are correlated. We know that certain combinations of floral traits appear more frequently than others, thus producing definite flower or inflorescence types. Further it is generally found that these types are characterized by specific pollination mechanisms. For example, red tubular flowers that produce large amounts of nectar are almost always hummingbird pollinated. We refer to these flower types as syndromes. Note that not all the "typical" features are present in all cases; rather each syndrome represents a set of characteristics that are commonly found in flowers pollinated by a particular mechanism or vector. The two most prevalent forms of pollination are wind pollination, or anemophily, and insect pollination, or entomophily. Both anemophilous and entomophilous flowers seem to be present in the earliest fossil records of flowers, which has made it very difficult to determine which evolved first. It is generally thought that modern anemophilous species are mostly secondarily derived from entomophilous species, but exceptions may occur in the palms (Palmae) and a few other families. Indications that anemophily is derived from entomophily can be found in the occurrence of nectaries in the flowers of many anemophilous species (including marijuana and nettle). Abiotic Vectors Wind pollination is the dominant type of abiotic pollination and is especially prevalent in several plant families, including the grasses (Poaceae) and sedges (Cyperaceae). Most gymnosperms (including pines, firs, spruces, etc.) are also wind-pollinated. Abiotic pollination is, with few exceptions, a wasteful process. The plant must release as much pollen as possible, given the low probability that wind or other physical forces can effect transfer of grains of that pollen to a receptive stigma. To this end, anemophilous plants have morphological adaptations that increase pollen dispersal and capture. Modifications of the flowers include a highly reduced perianth (no need to be showy) and green to dark brown to reddish bracts and perianth. It has been suggested that dark red is important for the temperature conditions of the blossom, especially of the bud. The flowers of anemophilous species are often found above or outside the leaves which may increase their access to wind currents. Some species flower before the leaves are out, which allows maximum wind speed around the flowers. Flowers of anemophilous species are generally unisexual (either monoecious or dioecious species) and are often temporally or spatially separated from flowers of the opposite sex. This separation not only prevents self-fertilization and increases outcrossing but prevents stigmas from being clogged by self pollen. One common arrangement of anemophilous flowers is for the female flowers to be located higher on the plant than male flowers so that pollen will not just fall down onto stigmas of the same plant. Because of the high inefficiency of wind pollination, anemophilous species produce huge numbers of pollen grains. Filaments are frequently very long, causing the anthers to extend outside the surrounding perianth. Some species even have "explosive" anthers. The filaments are under strong tension in the bud stage and spring out, throwing pollen into the air, after the flower has opened. Anthers generally do not open unless the weather is favorable, i.e. warm and dry, because pollen is rapidly washed out of the air in rain. Pollen grains of anemophilous species are usually very small (diameter of 10-20 mm), which increases their buoyancy. Some relatively large conifer pollen grains solve the problem of buoyancy by the addition of one or more air-sacs, which give a larger surface area without appreciably increasing weight. Great quantities of pine pollen have been found hundreds of kilometers away from the nearest forests. The typical rate of fall for wind pollen in calm air is of the magnitude of a few centimeters per second. Also contributing to buoyancy is the tendency of grains of anemophilous species not to adhere to each other but to be smooth and dry. Conversely, in entomophilous species, the pollen grains are usually highly ornamented and/or sticky, increasing the probability of their attaching to insects. The female portion of anemophilous flowers has evolved to capture and utilize wind-born pollen. In contrast to the large number of pollen grains, the number of ovules per flower is generally rather low in anemophilous species; many species have but one ovule, so each flower only produces one seed. To capture wind-borne pollen, anemophilous flowers usually have greatly enlarged stigmas. For example, feather-like stigmas are often found in grasses and brush-like stigmas are found in cattails (Typha spp.), both of which increase the ability of the plant to "capture" pollen. Several common plants use both anemophily and entomophily. Several species of Plantago, a common roadside weed, have inconspicuous, green flowers that produce massive numbers of pollen grains. These plants have been shown to be pollinated by wind in some circumstances, but they are also frequently pollinated by honeybees and flies. Other evidence comes from the loads of pollen-collecting bees; these frequently contain pollen from anemophilous species, sometimes exclusively. Another much rarer form of abiotic pollination is hydrophily, or water pollination, which can occur through a variety of mechanisms. In some flowers, the pollen is released into the water and floats to the water surface. The female flowers emerge onto the surface, receive pollen, and are then withdrawn back under the water. The most famous case is of Vallisneria in which the whole male flower is released instead of individual pollen grains; the pollen itself therefore does not touch the water surface. The female flowers create small depressions in the surface tension of the water. These depressions cause nearby floating male flowers to slide down allowing the anthers to contact the stigma of the female flower. In accordance with this effective mode of pollination, the number of pollen grains per male flower is drastically reduced. Biotic Vectors Biotic pollination introduces into the sequence of events a second organism, the pollination agent or the pollen vector. The common pollinating animals include bees, wasps, butterflies, moths, birds, bats, and flies. Most plant species have adopted one of two very different kinds of relationships with biotic pollen vectors. One option is to be a generalist and try to attract a wide variety of different pollinators. The other is to specialize (and often coevolve) with a single type of pollinator. Species that generalize can occur in a wide variety of habitats and survive conditions under which some of the pollinators cannot persist. On the other hand, they encounter a great deal of "foreign" pollen from other species, which can clog stigmas and prevent pollination. Good examples of generalists can be found in the parsley family (Apiaceae), in such plants as Queen Anne''s lace (Daucus carota). Flowers on these species are often grouped together in large showy, flat or gently rounded inflorescences. On their inflorescences one can usually find a motley crowd of insects--bees, wasps, flies and beetles of many kinds, and even some butterflies, although these are generally considered specialists. Specialists can adapt to have very specific and highly efficient pollination mechanisms but are restricted to cooccurring with their pollinators. It is these mutualists that draw the most attention in pollination biology with their intricate and sometimes outlandish mechanisms for pollination. Whether adapted as generalists or specialists, animal-pollinated plants share several characteristics. The pollen is sometimes larger than in anemophilous species, is often sticky and/or highly ornamented with spines and bumps, and sometimes adheres in clumps of several grains. The number of pollen grains, sometimes expressed as a ratio with the number of ovules, is much lower in biotic pollination than in anemophilous species. Stamens are located so as to contact the pollinators, rather than to be exposed to wind. However, much of the floral structure is related to attracting specific types of animals to act as pollinators. We will discuss some of the attractants used by plants, then discuss some of the more common pollinators and the floral syndromes associated with them. Attractants and Rewards for Biotic Pollinators Christian Sprengel (1750-1816) was one of the first to realize that bees and other flower visitors do not provide their pollen-carrying services free of charge. The plant must offer a reward in the form of something the pollinators need, either for their own survival or for that of their offspring. Alternatively the plant fool the pollinator into thinking it is getting some reward. Plants also must advertise these rewards. Flowers announce their rewards by being conspicuous in color, scent, size, or shape, making it easier for visitors to pick them out from their surroundings. Recognize that animals perceive flowers in many different ways, and certainly in different ways than do humans; what seems like an inconspicuous flower to us may be like a flashing neon sign to an insect or bird. The most common rewards are nectar and pollen. Pollen may have been the original bribe by which flowers began attracting insects in the Cretaceous period some 140 million years ago. Because pollen is the male gametophyte, it is obvious that some pollen must be transported and not consumed for fertilization to take place, but flowers always produce much more pollen than is necessary. Pollen is a highly nutritious and well-balanced food material containing protein, sizable amounts of starch, sugars, fat or oil, minerals, antioxidants, and vitamins such as thiamin. It is also rich in free amino acids. There can be no doubt therefore about its value as a food for insects and mammals. Plants that offer pollen as a reward often produce it in huge quantities In order to minimize the loss of viable pollen to pollinators, some plants produce, in the same flower, two types of anthers, normal ones, which produce healthy pollen, and others that yield sterile or at least less viable but still very nutritious and probably tasty pollen. Good examples of food stamens can be found in mullein (Verbascum thapsus) and partridge pea (Cassia spp.). In dayflower (Commelina sativa), the feeding anthers do not produce pollen, but offer a milky fluid instead. Some orchids have hit upon still another way to offer imitation pollen. They produce "food hairs" on the lower lip of the flower, which easily fall apart into individual cells, rich in starch. Orchids cannot offer pollinators some of their pollen for food because, as noted in the last chapter, all the orchid pollen within a flower comes in neat little packages called pollinia and any attempt to sacrifice a few grains would sacrifice the whole pollinium. Finally, it should be pointed out that not all the credit for pollen movement should be given to the insect pollinators. Pollen itself has been shown to "jump" from the stamens onto the insect, then from the insect onto a receptive stigma. It is known that electrostatic charges can build up on the body of a foraging honeybee and that these charges may reach a magnitude of several hundred volts. The bee is therefore flying at the center of its own highly charged electrostatic field. Most floral surfaces are well insulated, but the pistil is an exception: indeed a path of very low resistance leads from the stigma to the ground, almost like the earthing track of a lightning conductor. The result is that the bee''s electrostatic field is attracted to the stigma, and with it the pollen. Nectar is another important reward offered by many plants. Many scientists believe that nectar was already being produced before flowers first appeared on the scene. Primitive ancestral plants appear to have had many nectaries on their leaves, stems, and other non-floral areas. These nectaries may have been important for excreting excess sugars in maturing portions of plants. It is quite conceivable that these nectaries were simply incorporated into the structures we call flowers at the time those structures developed. Nectar is an ideal substance to offer as a reward. It is easily produced by plants, it can be produced quickly as demand requires, and, being a sugar solution, it is readily digested and quickly assimilated as a source of energy. However, nectar has been modified in some species to reward specific pollinators. One critical factor is the amount of nectar, as flowers "want" to reward pollinators without satiating them. If too much nectar is provided, the pollinator has no need to forage further, and pollen will not be transported. On the other hand, flowers of different species, and even within species, are competing with one another for pollinators, and those that provide the most nectar are likely to attract the most pollinators. Another way in which nectar can vary is in concentration and content. Bird-pollinated flowers usually have a fairly dilute nectar, with a sugar concentration between 20 and 30%. Birds simply cannot suck up a nectar that is too syrupy. On the other hand, horse-chestnut flowers may have a sugar concentration as high as 70 percent, with the results that bee visitors have to dilute it with their own saliva before they can suck it up. The observation that certain nectars,and consequently some honey, can be poisonous has received a great deal of attention. Some of Xenophon''s 10,000 soldiers were incapacitated on their epic homeward trek from Persia after consuming poisonous honey. In all likelihood, the culprit was Rhododendron ponticum. Other species are also known to produce poisonous nectar or pollen, although the reasons for doing so are not clear. Of course, nectar that is poisonous to one pollinator (or humans!) may not be poisonous to another. Many other types of rewards are offered in the great diversity of types of flowers. Some flowers produce fatty oils (glycerides) to offer visiting bees instead of a sugary nectar. The bees that pollinate these species have specialized hairs to colle Pollination Syndromes http://bio.fsu.edu/~winn/3402L/WinnCH4.html ch4 Pollination by bees: There can be no doubt that, on a global scale, bees (especially honeybees and bumblebees) are the most important pollinators. It has been calculated that in Germany alone, honeybees pollinate about ten trillion flowers in the course of a single summer''s day. To make 0.5 kg of honey, bees have to visit about ten million clover flowers, leading to the production of about 13.5 kilograms of clover seed. The pollen collected by a single honeybee colony may be more than 29 kilograms per year. The "intelligence" of pollinators (i.e. their ability to perceive, discriminate between, and remember the characteristics of flowers) reaches a peak in bumblebees and honeybees. The bees have a large range of relationships with flowers, from the rather simple ones in parasitic bees to the incredibly complicated ones of honeybees and other social bees, in which communication and temporal variation play a large role. Typical bee flowers are open in the daytime, have a minty fragrance, and offer their visitors nectar, pollen, or both. Bee eyes have trichromatic vision, and contain pigments sensitive to green, blue, or ultraviolet. Bees are blind to red. Thus, bee flowers are brightly colored (often yellow or blue), in order to attract insects from a distance, but are not red. For close-range guidance of pollinators, bee flowers often possess nectar-guides in the form of detailed color or smell patterns (which may include special UV reflection patterns), which direct the pollinator to places where the flower "wants" the pollinator to go. Many species provide the bees with a landing platform, usually in the form of a broad lower lip on which the visitor can alight before pushing its way deeper into the flower. Thus, bee-pollinated flowers are generally bilaterally rather than radially symmetric. Because bees can visit may types of flowers, it appears that there has been some selection for pollen to be deposited on different parts of the visitor''s body (e.g. the back, underside, or head), so as to increase the probability of the transfer of "correct" pollen. The pollen grains of bee-pollinated species are sticky and spiny or highly sculptured, so that they cling easily to the mouth-parts, legs, or bodies of the visitors. Because one animal may carry thousands of pollen grains, it is not surprising that the ovary of the receiving flower contains a great many ovules. Getting to that pollen may not be easy, especially for bumblebee flowers. Many bumblebee flowers have petals or other floral parts that must be pried apart to allow entry into the flower. This arrangement prevents undesirable insects from taking pollen or nectar. A number of bumblebee species "steal" nectar by piercing the corolla and removing nectar without properly entering the flower. These species generally do not pollinate the flower, and some plant species have adaptations that appear to be specifically designed to discourage robbers. These include hidden nectaries and thickened corollas. Some plant species have developed mutualistic relationships with ants, in which the plant produces small amounts of nectar on the outside of the flower, attracting ants. These ants, in turn, defend flowers from nectar robbers. Pollination by Butterflies: Butterflies are sun lovers that like to perch while feeding. They have long and slender probosces, can perceive a wide spectrum of colors, and have an excellent sense of smell. With few exceptions, they are nectar feeders. From these characteristics, we can easily deduce the characteristics of typical butterfly-pollinated flowers. They are open in the daytime, produce a goodly amount of nectar, possess a long, thin corolla tube (often with a "spur" or out-pocketing which contains the nectar), and are generally vividly colored (often red), although sometimes white. They also provide their butterfly visitors with a platform to land and walk on. The flat-topped inflorescences of verbena, lantana, red valerian, milkweeds, and various composites provide excellent examples of butterfly-pollinated species. The spike inflorescence of purple loosestrife and some violets represent yet another type of butterfly-pollinated flower. Pollination by birds: Birds that feed on nectar are highly specialized and feed on little else. Thus, they depend on flowers with large amounts of nectar available on a year-round basis. Plants in temperate areas cannot bloom year round and must therefore rely on migratory bird species which feed elsewhere during the winter. In the tropics, bird pollination of flowers is at least as important as insect pollination. At least 2,000 species of birds feed on nectar, flower-inhabiting spiders, and insects, or (rarely) pollen. Even some fruit-eaters among tropical birds will occasionally consume nectar. In New Zealand, which has no native bees pollination by birds is the rule rather than the exception. Many of these birds are highly specialized to feed on nectar. Their bills are long and narrow, and their tongues are tube-shaped or have brush-like tips. They include hummingbirds, sunbirds, honeyeaters, honey creepers, and brush-tongued parrots. One can often determine their food-plants by looking at the pollen attached to their bills and feathers. This method can work even with museum skins, and even in some cases with species that are now extinct. Most of these birds also have very high metabolic rates, so their caloric intake per gram body weight must be high. Although few people who watch hummingbirds flit from flower to flower are aware of it, these birds are constantly on the verge of starvation. To meet their energy needs they must visit thousands of nectar-rich flowers every day. Night provides severe problems: some hummingbirds have solved this problem by essentially going into hibernation every night. Their temperature drops, and their rate of metabolism may go down to about one-fifteenth of the peak daytime value, so they save a great deal of energy. Birds have excellent color vision and appear to favor red. In contrast, their sense of smell is very poor. These traits are reflected in the flowers they feed on. Bird-pollinated flowers have no odor. The amount of nectar produced can be quite large, up to a cupful a day in some cases. The colors of bird-pollinated flowers vary enormously. Many are red, but others are yellow or blue or almost any other color. Red flowers may be common simply because bees cannot see them well, so little nectar is lost to ineffective pollinators. To provide food during all active hours, bird pollinated flowers are generally open all day. Flower size and shape can vary, but corollas are often tubular (and are larger in diameter than butterfly flowers) and are sturdily constructed as a protection against the probing bills of their visitors. The ovules are usually below the perianth (that is, they have "inferior ovaries"), out of harm''s way. Usually, stamens are quite numerous and often stick out of the flower, in which case they are brightly colored and quite strong. The visiting bird is normally touched on the head or breast as it feeds. However, in some flowers the stamens are "explosive" and cover the bird with pollen. Hummingbirds, which are only found in the Americas, feed on the wing and so hummingbird flowers hang down or are downward-facing and lack a landing platform. In Asia and Africa, however, many of the flower-birds do not hover and, accordingly, the plants offer them a landing-platform or perch. Fly and Beetle Pollination: Both flies and beetles present a wide variety of pollinators and pollinator syndromes, making it difficult to generalize, but a number of flies and beetles should be specifically mentioned because they are not really adapted to flowers at all (although the flowers are adapted to them!). These are the carrion, dung, and mushroom flies and beetles that are trapped by various flowers or inflorescences. Species in this group are primarily attracted by smell. Some are looking for food, others are looking for egg-laying sites. In either case, they are tricked by the flower odor into thinking that they have found their normal prey. They enter the flower, eventually figure out that they have been fooled, then move on. Common traits of the flowers that use such pollinators include dull colors, often large, open flowers, (although some species instead have enclosures, which trap the pollinator for a time), and distinct odors, which are sometimes quite unpleasant to humans. The names of some of these flowers are can be equally unattractive. The world''s largest "flower" (really it''s an inflorescence) is the stinking corpse lily (Raflesia sp.). Ants and Pollination: Until recently, no beneficial role in pollination was attributed to ants: they were considered to be just thieves of nectar and pollen. At best, certain investigators were willing to concede that an "ant guard," provided with food by the plant in the form of extrafloral nectar, might keep potential flower robbers at bay. However, it is now recognized that there is a genuine ant-pollination syndrome. Because worker ants do not fly and therefore do not expend many calories on traveling, the whole system is low-energy. The nectaries are small and produce a quantity of nectar so modest that larger insects are not interested. The flowers, likewise, are small, sessile, and close to the ground, and exhibit minimal visual attractions. They produce only small quantities of sticky pollen grains, so the ants are not forced into intensive self-cleaning activities that would remove the pollen from their bodies. Outbreeding is promoted because on each plant only a few flowers are open at the same time and also because these low-growing plants occur in groups with their branches closely intertwining. It is believed that this syndrome is most often found in hot, dry habitats, which are certainly among those favored by ants. Pollination by Wasps: The wasps form a large and highly diversified group. Adults are generally predators or feed on carrion (sometimes just to feed their larvae), and for that reason nectar is important to them only as a source of carbohydrate for their own energy needs. As pollinators, they don''t begin to compare to honeybees. In fact, they may exert a strong negative influence on other pollinators by attacking honeybees, other wild bees, and butterflies. The question of whether or not there are flowers adapted specifically to pollination by wasps has been a hotly debated issue. The one well-known relationship is that of figs and fig wasps. Gall wasps are specialized pollinators of figs (Ficus, of which there are about 700 species, mostly tropical). Female wasps deposit eggs in specialized fig flowers, which are clumped together into an inflorescence. These eggs cause the flowers to change into galls, each with a larva inside. When a male larva matures and hatches, he chews his way out into the fruit, finds himself a female in the same inflorescence "prison," and mates. The female then enlarges the hole the male used to enter, crawls out of her gall, and leaves the fig in which she was born. In doing so, however, she must cross a region of male flowers near the fruit''s entrance, which have just opened. Powdered with their pollen, she now makes her way to the young edible figs that have just formed on the same tree or on another one close by. These contain a different type of specialized flowers, which are quite hard and resist the female wasp''s attempt to deposit eggs in them, but in the attempt, the flowers are pollinated. This fruit gradually matures and turns into the fleshy fruit we know as figs. Long before, however, the unsuccessful female has left the immature fig to continue her efforts in another fig of about the same developmental stage, but again in vain. She cannot satisfy her urge to deposit eggs in fig flowers until the type of flower in which she hatched again begins to develop in trees. These small, inedible flowers are generally found on the upper branches and are excellent incubators for the eggs and larvae of the female wasp. Thus the cycle starts all over. Pollination by Moths: Hawkmoths, also known as sphinx moths because of the peculiar position their caterpillars adopt when disturbed, are the nocturnal counterparts of hummingbirds. Like hummingbirds, hawkmoths normally feed on the wing, and, because they are usually quite large, fly at high speeds. In some ways, they operate rather like warm blooded animals, having higher energy requirements than most insects and thus high nectar needs. Some moths can consume a good teaspoon of nectar at a single sitting. Hawkmoths are highly specialized flower visitors, equipped with a long, thin, and very flexible proboscis, which is kept coiled up when the animal is not feeding but which can be stretched out to take nectar. The tongue is usually extended just as the moth reaches its floral target. Not surprisingly, flowers that cater to hawkmoths open in the evening and are extremely fragrant. They are snow-white or light-colored, offer no landing platform and may have fringed petals--possibly for guidance. Many have both visual and olfactory nectar guides. The corolla tube is long and narrow, a feature that discriminates against other, short-tongued, visitors, and nectar is abundant. Typical hawkmoth flowers are evening primrose (Oenothera biennis), some tobacco flowers (Nicotiana spp.), and most honeysuckle (Lonicera) species. Pollination by Bats: Certain bats have become pure "flower animals"--especially those in the Macroglossinae or "big-tongues," found in southern Asia and the Pacific. Their protein requirements are met entirely by pollen, which they deliberately collect and consume in great quantities, along with nectar. Several New World species have the same life-style. Of course, bats are most active at night. They have reasonably good eyesight but appear to be color-blind. They have a keen sense of smell, displaying a preference for odors that humans find definitely unpleasant: mouse- or urine-like, stale, musty or rancid, resembling butryric acid or sweaty feet. The sonar sense of flower-pollinating bats is not as well developed as is that of other bats. Most flower-pollinating bats are small, sharp-snouted animals with long tongues that can be stuck out very far and have special projections (papillae) and, in some cases, a soft brush-like tip--devices that enable them to rapidly pick up the copious pollen and nectar soup that bat flowers offer. Normally, it is a bat''s head that becomes dusted with pollen, transfer of the precious powder to the pistils of other flowers is no problem. Considering their extreme food specialization, it is not surprising that these ba Foraging Ecology of Pollinators http://bio.fsu.edu/~winn/3402L/WinnCH5.html ch5 Recently, studies of pollinator foraging behavior have shifted from descriptions to attempts to understand and predict behavioral patterns. One particularly useful approach developed in the 1960''s has been to consider foraging decisions in terms of their costs and benefits. The theory that developed is generally referred to as optimal foraging theory. The key assumption of all of these studies is that the animal maximizes some efficiency expression (usually stated as net caloric gain per unit time) because its reproductive output (i.e. fitness) is positively correlated with foraging efficiency. Bernd Heinrich was one of the first to test foraging theory using pollinators and has published many papers on the foraging of bumblebees. Since then, some of the most productive and enlightening studies of optimal-foraging theory have used pollinators as model animals. Among the reasons for this success are: (1) that food (usually nectar) can be easily manipulated (see, e.g., Waddington, 1979a); (2) that the movements of many pollinators are slow enough that the foraging path, time budget, and choice of flowers can be quantified; and (3) that other factors, such as predation and mate choice, usually do not influence observed behavioral patterns in important ways. Optimal-foraging approaches have proved "fruitful" for understanding and predicting foraging behavior of pollinators. Realize that we all act as foragers, so that this framework is one that is easily understood by humans. When we are choosing dinner from a restaurant menu, we are making some of the same decisions that bees are making in a field of flowers. At the beginning of their foraging careers, pollinators are naive. They have little or no information about where or when flowers occur. The benefits and costs of the various available flowers are, of course, unknown. Thus, resources must be searched for and "sampled" before economically prudent foraging decisions can be made. Little is known about the initial search behavior of any pollinator but it is likely that they employ strategies similar to those of other animals. Without specific information on the spatial distribution of floral resources, the most efficient strategy is to move straight ahead. Once visual or olfactory information indicates that a flower is nearby, a local search is started, utilizing a convoluted, looping path. Presumably, numerous flowers, perhaps in many local patches, are sampled before areas are chosen for repeat visits. The experienced pollinator, foraging within a patch of flowers containing one to many flowering species, is supposedly moving in a fashion closer to "optimal" and must make numerous complex decisions. What rules of movement do pollinators use when foraging within and between inflorescences? How are these decisions influenced by such factors as the abundance and distribution of food, floral arrangement, and plant density? How do foragers choose among the various floral types? Individuals that forage in the most efficient manner will produce the most offspring, perhaps passing on some of these abilities. Foraging Range The foraging ranges of pollinators vary in size and shape and are dependent on a number of factors, including resource density and distribution and the density of conspecifics and potential competitors. A honeybee may fly several kilometers to forage, but usually forages within 1 km of the hive when a suitable resource is available. Studies also indicate that individual honeybees exhibit considerable area fidelity. The bees return repeatedly (even over several days) to the same relatively small area of a field of flowers. This is probably not the strategy that yields the highest rewards, but it may be a low-variance strategy that minimizes the risk of doing very poorly in unknown areas. Bumblebees exhibit area fidelity under some conditions. It has been observed that bees are not only area specific but that they also repeatedly fly the same pattern among the same flower clumps. The bees "memorize" the spatial positions of the clumps and the flight paths among them. This foraging strategy is called traplining behavior, by analogy with the trapper who checks his traps in a set sequence on a regular basis. This strategy may be very important to the pollination of widely dispersed, long-blooming tropical shrubs and trees. Male bees of some species are territorial; a small area of flowers is used as forage and is defended against non-territorial flower visitors and other bees vying for territories. The foraging behavior of intruders (their choice of where and on what to forage) may be substantially influenced by territorial bees. Some nectivorous birds, under certain conditions, also exhibit territoriality. The recent conceptual framework for studying territoriality is "economic defendability"; the idea is that an animal should be territorial only if the gains accrued minus the costs of defense are greater than they would be if the animal were not territorial. Hawaiian honeycreepers have been used in tests of this theory. When the resource is small, the birds do not defend it, because the exclusion of other birds would not increase its worth enough to offset the additional costs of defense. However, when the resource is very plentiful, birds should also not defend it because energy needs are adequately met even when other birds are feeding in the area. Hummingbirds exhibit two foraging strategies that influence foraging range: territoriality and traplining. Traplining species, which spend more time in flight than territorial species, have longer wings relative to body size and have lower energy demands for flight than do territorial birds. Hummingbird behavior is also influenced by the density of competitors. When the number of competitors is relatively small, territoriality may be profitable; but when there are so many competitors that the time spent on defense becomes too large, individuals drop their territorial behaviors. Foraging Behavior Within a Floral Patch Once a pollinator arrives at an area with flowers, information must be received, processed, and recalled from memory, and decisions must be made. Let us first consider a forager in a single-species patch of flowers. If a pollinator chooses to feed in such a patch, its choice of floral species on each flight between plants is determined. However, decisions must be made regarding which flower of that species to visit next. Research has shown that the choice is not random, and we are learning the "rules" that some pollinators use to make choices. These rules are different for between and within-patch movements. Two parameters can be used to describe pollinator movements between flowers. The flight distance is the linear distance between two successfully visited flowers. This represents an underestimate of the true flight distance because the flight path is rarely linear. The change in direction is the angular difference between the direction of arrival at an inflorescence and the direction of departure from the inflorescence. These parameters will vary with certain conditions. The distributions of flight distances have a similar shape for a variety of pollinators (e.g. bumblebees, Pyke, 1978; honeybees, Levin and Kerster, 1969). In each case, the distributions are highly skewed to the right; most flights are made to a near-neighbor flower. Flights to occasional more distant neighbors may be exploratory flights looking for better areas; no one really knows. Flying to near-neighbor flowers minimizes flight costs, but a closer examination shows that bees adjust their flight distance in response to the volume of recently received nectar rewards. Waddington (1981) found that bumblebees departing inflorescences with high rewards flew short distances, whereas relatively long flights were made after visits to nectar-poor inflorescences. Bumblebees foraging at patches of nectar-rich white clover (Trifolium repens from which bees had been excluded to permit nectar to buildup) flew about half as far between flower heads as when foraging in nectar-poor depleted patches (Heinrich, 1979). The amount of nectar in flowers just visited can influence the direction as well as the distance of pollinator movements. Heinrich (1979), for example, found much greater change in direction in a nectar-rich area of clover heads than in a neighboring depleted area. Honeybees foraging on single flowers do not exhibit this pattern: the reasons for this behavior are not clear. The degree of change in direction can also influence the rate of returns from foraging. Two patterns have emerged from studies of pollinator movements. The most frequently observed pattern is a tendency to move straight ahead by exhibiting considerable unidirectionality on successive flights. A second pattern is frequent turning or foraging behavior that is apparently random with respect to changing direction. An increase in the degree of turning raises the probability of a revisit to a just-emptied flower, thereby lowering the mean reward per visit. On the other hand, frequent turning also tends to keep a forager in the same area, which may be desirable if it is an area of high floral rewards. Zimmerman (1979) argues that turning frequently enhances the energy gain when flower densities are so high that the probability of revisiting flowers is low. Bumblebees, for example, visit a very small proportion of the flowers each time they land on a Polemonium foliosissimum plant, so a return to a plant means few revisits. Some bees can even detect a recent visit (perhaps by odor) before alighting and pass by previously visited flowers. These bees are able to localize their movement by exhibiting no directionality and flying to the nearest neighbor whatever the direction, but still maintain low costs associated with repeat visits. Foraging Ecology of Pollinators http://bio.fsu.edu/~winn/3402L/WinnCH5.html ch5 Behavior on Individual Flowers or Inflorescences Numerous observations have been made of the behavior of pollinators on individual flowers; usually these behaviors have been viewed in terms of pollinator effectiveness. We are just beginning to understand the behavior of pollinators on multiple-flower inflorescences. A pollinator approaching an inflorescence must decide which flower to visit first. After the first visit and after each succeeding visit, the next flower must be chosen on the inflorescence, or the animal must decide to leave for another inflorescence. None of the details regarding how these decisions are made is known, but the decisions are known to depend on the distribution and abundance of rewards on the inflorescence and on the rewards expected at other inflorescences. Waddington and Heinrich (1979) constructed simple artificial inflorescences made up of five vertically arranged flowers. The distribution of rewards (nectar) was manipulated in an effort to learn how bumblebees decide where to arrive at and depart from an inflorescence and what they do in between. The bees move upward between the flowers and rarely fly by a flower to visit another one above it. This strong propensity to move upward did not change with the distribution of nectar rewards, but the start and departure points did. When rewards are biased toward the bottom of the inflorescence, bees learn to start on a low flower and usually depart before reaching the topmost flowers. When the rewards are greatest at the upper flowers, the bees tend to start near the middle of the inflorescence and depart from the top. An even distribution of rewards results in a start near the bottom and a departure near the top. In the field, bumblebees have been observed to start at the bottom on relatively nectar-rich flowers, to move upward, and to depart before reaching the top of the inflorescence. These behavior patterns are of interest in relation to the distribution of flower sex and probably important as mechanisms that enhance the likelihood of outcrossing. Bees carrying pollen from another plant first visit the female flowers at the bottom and then move up the inflorescence, picking up pollen from the male flowers before departing for another inflorescence. Pyke (1978) viewed inflorescences as patches and asked how many floral visits an efficient hummingbird should make at an inflorescence before flying to another inflorescence. He found that the decision to leave is a function of the number of flowers already visited, the number of flowers on the inflorescence (more visits at larger inflorescences), and the amount of nectar obtained from the last flower. Much of this result matches nicely with predictions of optimal foraging theory. Floral Choice in Mixed-Species Patches. How do pollinators choose from the myriad flowers seemingly available to them as forage? This question has been the subject of many studies that document the proportion of visits to different flowers by pollinators. In general, pollinators exhibit considerable fidelity to single species, going from flower to flower of the same species on any given foraging trip. Less is known about why they choose a particular floral species and when and why they switch from one species to another. The spatial and temporal distribution of flowers is an important factor influencing the sequence of visits among flowers. Plants often grow in single-species stands. Because pollinator flights are usually to neighboring flowers, the species choice is certain. Even when plants grow intermingled, pollinator fidelity may be high. This pattern may still be related to nearest-neighbor visitation, but on a vertical scale. Bees have been shown to exhibit horizontal flight paths between flowers (i.e. they tend to forage at the same height on successive visits). When flowers of different species occur at different heights, this behavior would promote successive visits to the same species (Waddington, 1979b). However, once again, a cost-benefit approach has proven to be a useful way to understand foraging behavior. Pollinators sample flowers and are thought to visit more frequently flowers that are perceived to provide the highest net intake of calories per unit time. Bees, for example, learn which flowers are best on the basis of (1) the magnitude of the floral reward they receive, (2) how long it takes to remove the reward from each flower, and (3) the time needed to fly between the flowers. The caloric value of nectar rewards depends on the volume and concentration of rewards. Preferences based on concentration are well known; pollinators forage on flowers that provide higher concentrations of sugars in their nectar. Variation in reward among flowers of each species has also been shown to affect foraging decisions. Briefly, it may be beneficial for an animal to minimize the uncertainty (due to reward variance) associated with a foraging decision in order to minimize the risk of doing very poorly in its foraging. Real (1981) discovered that bumblebees and paper wasps foraging on a patch of two colors of artificial flowers prefer the color with the lower variance in reward even though the expected rewards were equal for the two colors. The relationship between pollinator morphology and floral morphology affects the time needed to land on (or hover in front of) a flower to obtain the rewards and so will affect pollinator preferences. There is a correlation between proboscis length and time spent by different species of bumblebees on flowers. Bumblebee species with short tongues forage more rapidly on flowers with short corollas than do long-tongued bees and, conversely, long-tongued bumblebees forage more quickly than short-tongued bees on deeper flowers such as larkspur (Inouye, 1980). Hummingbirds likewise exhibit an inverse relationship between corolla length and the rate of nectar intake (Hainsworth and Wolf, 1976). Handling costs are also affected by many factors other than the ratio of tongue length to corolla depth. The width of a flower affects how quickly pollinators can gain access to nectar and pollen. The external floral structure can provide varying amounts of support for foragers as they land or take off. Some flowers have very sticky pollen, which may discourage some nectar foragers because of the extra time needed to clean themselves. Foragers must also consider costs related to flying or moving between flowers. In a mixed-species floral array, the probability that a flower of a particular species will be the closest flower to a forager increases with increased density. Honeybees repeatedly given a choice between a yellow and a blue artificial flower usually chose the flower closer to the previously visited flower, regardless of color. Usually, less-common flower colors are visited by fewer foragers than more common flowers, even if the floral rewards are identical. Bumblebees foraging on two subalpine species concentrated their foraging in dense patches (i.e. there was a positive correlation between per-flower visitation rate and density), perhaps as a response to lower flight costs (Thomson, 1981). In addition, competitive interactions among foragers are known to influence floral choice in some situations. Inouye (1978) studied the behavior of two species of bumblebees foraging on two floral species in the Rocky Mountains; each species of bumblebee had an apparent preference for one floral species. However, when nearly all of the individuals of either bumblebee species were removed from a local patch, individuals of the remaining bumblebee species would visit the other (previously unvisited) floral species. The introduction of honeybees into an area in Central America dominated by stingless bees resulted in a local reduction of foraging by the stingless bees. Finally, pollinators'' foraging behavior may be biased by certain inherent preferences. Honeybees are known to prefer certain shapes and colors, and hummingbirds may have an inborn preference for red. So we must consider the nature-vs.-nurture question when trying to understand foraging decisions. Experimental Design and Data http://bio.fsu.edu/~winn/3402L/WinnCH6.html ch6 Since science advances by tests of hypotheses, scientists spend much of their time devising ways to test hypotheses. There are two general kinds of hypothesis tests; observational tests and experimental tests. Observational tests are those in which two or more groups observed to differ naturally in some respect are compared. For example, If you wished to test the hypothesis that bees are more effective pollinators than ants, you might compare the numbers of seeds set by flowers that bees chose to visit with the seed set of flowers that ants chose to visit. You would be comparing seed set for two groups of flowers that differ naturally in the identity of the organism that pollinated them. Similarly, to test the hypothesis that pollinators prefer blue flowers in a species in which flower color is variable, you could compare the number of visits received by groups of flowers that differ naturally in their color. A second way to test a hypothesis is to construct an experimental test. In an experimental test, the experimenter causes two otherwise similar groups to differ in order to test predictions about the factor that now differs. For example, you might wish to test the hypothesis that pollinators are more likely to visit flowers that are higher from the ground. An appropriate experimental test would be to grow a set of similar plants in pots and when they are in flower, set them out in a field with half on the ground and half perched on cement blocks. You would then observe your two sets of plants (low and high) and determine if the tall plants receive more visits. A question you might ask at this point is "Why bother to grow the plants in pots and place them at different heights - wouldn''t it be easier to simply observe rates of pollinator visitation to naturally occurring plants of different height?". In other words, why not perform an observational test rather than an experimental test? In general, experimental tests provide more conclusive tests of hypotheses. Consider the following possibility; plants growing in wetter spots in a field may be taller and, many pollinating insects are susceptible to desiccation and therefore avoid areas of low humidity. Under these circumstances, taller plants may receive more visits but not because they are tall, but because they are in areas of higher humidity. The major weakness of observational tests of hypotheses is that groups being compared may differ in more than one aspect. From this, it is clear why an experimenter must only manipulate one factor at a time. In this way groups that differ in only one respect are compared. If, for example, one wished to test the hypothesis that both height and flower color affect pollinator visitation rates, one must perform two experiments; one in which only height differs between groups and one in which all flowers are presented at the same height and only flower color differs. Clearly, if the number pollinator visits to tall white flowers was compared to the number of visits to short blue flowers we would not know whether the difference was due to flower color only, to height only, or to both. Manipulations performed in the course of an experiment are referred to as treatments and the manipulated groups of subjects are called treatment groups. Although only one factor will differ among treatment groups, there may be more than two groups (e.g. tall, medium tall, midsize, and short). Some experiments are designed to compare a manipulated group with an unmanipulated group called a control. For example, one might hypothesize that bees are attracted to the smell of lemons. An experimental test of this hypothesis might involve a comparison of the frequency of bee visits to a set of flowers, half of which have been sprayed with lemon juice. Those flowers not sprayed are the control group and are identical to the treatment group in all respects except the treatment factor. Data All science is based on data of some kind (note that the word "data" is the plural of "datum"). The data may come from the results of experiments or from noting patterns in nature or it may even be purely theoretical, as in Einstein and Bohr''s famous letters on thought experiments in physics. Data are generally obtained as individual observations, in which a particular aspect or variable is quantified. Different observations of the same variable can constitute replicates. A sample then consists of a collection of replicate observations selected by a specified procedure from a larger population. Before we go any further, we need to distinguish between different kinds of data and discuss how you describe the samples you have collected and how you use samples of data to test specific hypotheses. Kinds of Data There are basically two types of data and the analysis of each requires its own statistical approach. Discrete data fall into distinct categories, such as types of insects. For example, the pollinators visiting a plant might fall into three categories: bees, butterflies, and wasps. Or flowers of a plant species might contain a variable number of petals: three, four, or five. Continuous data fall along a continuum or scale, like sizes or time measurements. For example, the four bees visiting a flower may be 8.2, 9.1, 9.2, and 10.3 mm in length and spend 2.3, 4.1, 6.0, and 3.2 seconds on the flower. The difference can be problematical and may depend on what type of data you wish to take. Consider our previous example of the greenish faces. Clearly there are two categories here: green faces and normal ones. However, there are equally clearly varying degrees of "greenness", including some cases in which it is difficult to determine whether the face is green or normal. You might have created a scale from 1 to 10, on which 1 is a normal complexion and 10 is brilliant green and proceed to collect continuous data on face color. If you are thinking while reading, you may have reason to pause here. Didn''t we just go from two categories (green and non-green) to 10 categories (1 through 10)? And, if so, aren''t the data still discrete but simply divided into more categories? The difference can be very subtle (to the point of invisibility), but an easy way of thinking about it is whether or not the data could potentially be divided further by use of better measuring tools. If your subjects truly form two groups, green and normal, then no matter how you measure individuals, they still come out either one or the other. However, in the more realistic case in which individuals vary more or less continuously from green to normal, the number of categories is limited only by the precision with which you measure the color. Discrete and continuous data are analyzed in very different ways. In fact, these data may be collected and graphically presented in different ways. Most of the remaining discussion in this chapter will deal with continuous data. We will return to discrete data when we discuss the chi-square procedure (Ch. 7). Describing Data Sets: Means and Central Tendencies One of the first things to do with a sample of data is to describe it in a simple fashion that will both give others some idea of its nature without their having to see the data themselves and allow it to be compared to other samples. For continuous data, the two simplest descriptors are some value indicating what an "average" value is (e.g. mean, median, or mode) and some measure of the amount of variation around that average. The most commonly used "average" value is the mean, the sum of all the data values (which we call "x"''s) divided by the number of values (symbolized "n"). mean = = Before we go further, let''s get a set of data to use as an example. Consider a population of bean plants. A scientist has noticed that the flowers are visited by both butterflies and bees (the observation). She knows that bees collect lots of pollen and so wonders whether they are better at pollinating the beans than the butterflies (the question), and she guesses that they do (an informal hypothesis). Formally stated, a single bee visiting a flower will pollinate with a higher efficiency than a single butterfly, thus producing a greater number of seeds in the bean pod (a hypothesis). As a test of the hypothesis, she removes all the open flowers on several plants, then covers the plants with pollinator-exclusion cages for three days. She then returns, removes the cages and watches pollinators visit the flowers. After a single butterfly or bee visits a flower, she bags that flower with a net bag to prevent further visitation. After several hours, she decides that she has sufficient data and goes home. Two weeks later she comes back and collects the developing pods from her marked flowers. She carefully dissects the pods and counts the number of developing seeds in each. In this fashion she obtains the following data: Number of seeds/pod Bee pollinated Butterfly pollinated 4 6 3 8 2 4 5 7 4 8 5 8 7 8 4 7 6 8 6 6 3 7 4 1 5 - 4 - mean () 4.43 6.50 sample size (n) 14 12 Experimental Design and Data http://bio.fsu.edu/~winn/3402L/WinnCH6.html ch6 First of all, note another descriptor of the two samples: the sample size. More bees were active, resulting in 14 observations, as opposed to 12 for the butterfly-pollinated flowers. Inspection of the means gives the simplest information about the data and suggests that butterflies are actually better pollinators than bees. But always remember that this kind of difference might be just due to chance events. In Chapter seven we will discuss how to determine whether these means are statistically significantly different using a t-test. For now, however, we are concentrating on describing rather than comparing our samples. After obtaining the mean of each sample, the next important descriptor is how the data are distributed around the mean, and the easiest way to observe this distribution is using a particular type of graph. Graphs are wonderful tools. Scientists, like everybody else, find it difficult to understand complex patterns in data just by looking at the numbers. They often have to sit back, graph out the data, and just stare at it for a while. The graph needed here is called a frequency histogram. Traditionally, the vertical axis (the y-axis) gives the frequency of occurrence of a particular measurement and the horizontal axis (the x-axis) represents your variable of interest (e.g., number of developing seeds). Figure 6.1 shows the frequency histograms for our scientist''s experiment. The frequency histogram in Figure 6.1 shows that the two samples not only have different means but that they also have very different distributions around the mean. The distribution for bees is symmetric about the mean and is called a normal distribution (symmetry is only one of several criteria for a normal distribution, see below). It is a version of the bell-shaped curve that you may have heard instructors mention in the past with respect to grades. In the butterfly distribution, most of the values are packed into the right-hand portion of the graph, and the data are spread over a slightly larger range of seeds/pod. This sort of distribution is "skewed" and, confusingly enough, in this case is left or negative-skewed (the direction of skewness is determined by the location of the tail of the distribution). Other types of distributions are also possible. For example, a uniform distribution would have an equal number of observations for each unit of measurement. For example, the sample might have been 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, and 6 (trying plotting this distribution, either on paper or in your head). A frequency histogram in which the data form two peaks is said to show a bimodal distribution. The data you collect are likely to be normal or somewhat skewed but will always be spread out on either side of a "central" point (the mean). When you analyze your data, you are often interested in this central point and that is why we calculate means. However, the mean is not necessarily truly the central point. In fact, the mean, reported alone, may not be very meaningful. If your plotted data were skewed or bimodal, the mean might be nowhere near the center of the range of the data. For example, the most common measurement for the butterfly data was eight, yet the mean is much less Frequency histograms for bean pollination data. Describing Data Sets: Dispersion about the Mean How the data are dispersed around the mean is most easily (although not most accurately) described by the range: the minimum and maximum values in the sample. However, the most frequently used measurement for describing the dispersion of data is the variance, symbolized s2. Without going into much detail, the variance is related to the "points of inflection" on a normal curve; that is, the "natural breaks" in a normal curve, the points at which the curve changes direction. Higher values for the variance indicate that the data are dispersed widely around the mean; lower values indicate that the values are all close to the mean. The variance is calculated as: s2 = It is important to note here that many statistical tests require that your data be normally distributed. The further your data deviate from normality, the less reliable the result of the test. Many statistical procedures can be used either to test for normality in your data or to transform your data to make them normally distributed (for example, taking the logarithm of each datum). Or, if your data are severely nonnormal, another whole class of statistics ("nonparametric" statistics) can be used. However, we are not going to study those tests here: if more sophisticated statistics are necessary for your analysis, your Teaching Assistant will help you. The Metric System A final note. The United States is virtually the last country on earth to switch over seriously to the metric system. The scientific community, on the other hand, is much less affected by national boundaries and switched nearly completely 20-30 years ago. No major scientific publication will consider research using anything but the metric system, and neither will we. All your units must be given in grams, meters, and liters, with the correct abbreviations where necessary. We don''t care about the units you use in the field. I have known scientists who forgot to bring equipment to the field and were forced to take data in "beer-bottle units," but, before the data are analyzed and presented in your paper, they must be converted to metric units. Statistics--Distributions and Differences Between Means http://bio.fsu.edu/~winn/3402L/WinnCH7.html ch7 In most experiments, a scientist compares two or more samples chosen from populations that have been treated differently in some way. The point is to discover whether these samples do indeed differ significantly with regard to some measured characteristic or property. For example, you might want to see whether flowers pollinated by butterflies and bees produce different numbers of seeds. Such decisions require the application of certain statistical rules and procedures. You may be thinking to yourself, "life is short and statistics is hard, so why should I learn statistics?" Statistics can be relatively simple. It is just a box of tools for saying what a sample "looks like" and how is it related to other samples (e.g. whether it is different from or correlated with other samples). This is not a course on statistics, so we are only going to provide you with some of the basic statistical tools with which to conduct simple analyses (Chapters 7 and 8). If your experiment requires more complex statistical analysis than what is presented here, your Teaching Assistant can help you further. Two statistical procedures commonly used in the analysis and evaluation of data, the t-test and chi-square test, are outlined below. Although the mathematical principles behind the procedures are rather complex, and will not be treated in any detail here (you may be forced to take a course in statistics one of these days), you should find it comparatively easy to apply the rules given to the analysis of many common experimental designs. Null Hypotheses and Significance First, a note on accepted conventions in statistics. Remember that in science we must disprove, rather than prove. So, instead of testing for differences between two samples, statistical tests are designed to test the hypothesis that there is no difference between groups. By convention, a hypothesis of no difference (or no effect) is called a null hypothesis symbolized H0. Let us consider the scientist studying bees and butterflies. Her hypothesis was that a single bee visiting a flower will pollinate with a higher efficiency than a single butterfly, thus producing a greater number of seeds in the bean pod. We will call this hypothesis H1 or an alternate hypothesis because it is an alternative to the null hypothesis. (Additional alternate hypotheses would be H2, H3, etc). To test for differences between the pods pollinated by bees and those pollinated by butterflies, we must first construct a null hypothesis of no difference between the groups. H0: There is no difference between bees and butterflies in the number of seeds produced by the flowers they pollinate. or H0: Bees and butterflies will, on average, produce the same number of seeds when pollinating a bean flower. or H0: # seeds/flower produced by bees = # seeds/flower produced by butterflies. Now we come to the philosophical question of the definition of a significant difference between two groups. That is, how different must two groups be before we state that they are "significantly different"? Most statistical tests determine the probability that the null hypothesis is correct, or stated in somewhat different terms, whether, the probability that two groups of data represent samples taken from the same population of data. Statistical tests, such as the chi-square and t-test, are methods used to test for significance, that is to determine whether some quantity differs from another quantity by an amount greater than that expected to arise from random variation (i.e. chance) alone. A problem then arises: What level of probability does one choose to decide whether two groups differ as a result of some treatment or simply because of chance variations? By tradition or convention, most scientists have decided that, if the difference between two groups is of such magnitude that it would happen by chance fewer than 1 out of 20 times (the probability or "P" < 0.05), then the two groups differ significantly. That is, the null hypothesis of no difference is rejected. Sometimes, when greater confidence in the results is desired, scientists will choose probability levels of less than 1 in 100 (P < .01) or 1 in 1000 (P < 0.001). Consider the common example of flipping a coin. You have a friend who always seems to win tosses with his lucky coin by choosing "heads." You wonder if this coin is "fair." You first check to see that it indeed has a head side and a tail side. Your hypothesis (H1) here is that this coin has a greater probability of coming up heads than tails. The null hypothesis would be that there is no preference for this coin coming up heads or tails, that it is a "fair" coin and your friend is just lucky. Experiment! Say that after one toss, you get a head. The probability of this result is 50/50 or P = 0.50. The probability of getting two heads in a row is 1 in 4 or 0.25. The probability of getting three heads in a row is 0.125. All this could still happen just by chance. Four heads in a row occurs with a P = 0.0625. A scientist would say that even this extreme result was probably just due to chance. On the other hand, five heads in a row occurs with a P = 0.03125. At this arbitrary point, because P < 0.05, a scientist might say that this coin is biased I would become concerned about the trustworthiness of the friend who owns the coin. Recognize that the 0.05 level is entirely arbitrary. It is just an accepted level of significance and has no magical meaning on its own. Also recognize that, by using such levels, scientists are possibly making errors in about one of every twenty conclusions! Think about it. T-test (Continuous Data) Statisticians use a technique called the t-test to compare the mean values of random samples of continuous variables. This test was described by W. S. Gossett, who first published it under his regular pseudonym "Student" (although I don''t know why he used a pseudonym, perhaps it was a good idea given the pain and suffering this test has caused students ever since). With this test, one can compare the means of two samples and determine whether any difference between the two samples is likely to be due to "normal" sampling variations (e.g. chance, measurement errors) or to the particular treatments the samples received. All statistical tests have certain restrictions which determine when they should and should not be used. The t-test requires that certain assumptions be met: 1. The distribution of observations is continuous. 2. The individual observations are independent of one another. 3. The observations are normally distributed. 4. If the variances of the samples differ significantly from each other, an alternate equation for the t value must be used. If you have widely different variances for the two samples you are testing, you should discuss this problem with your Teaching Assistant. see photos 3. When you have calculated your value of t, and your df, refer to Table 7.1. At the 0.05 probability level and at your approximate degrees of freedom, the critical t value is given in the table. If the t you have calculated is greater than the critical value for t in the table, you may reject your null hypothesis. Because you have rejected the null hypothesis that the means were equal, you may conclude that your H1 that they are unequal is probably true. If tcalculated is less than tcritical, then you have failed to reject your null hypothesis. Chi-square test (discrete data) When the data are made up of discrete variables, the chi-square (c2) test can be used to test the null hypothesis. The chi-square has two different uses: determining whether the distributions of two variables are independent of each other and testing a sample against an expected distribution. Statistics--Distributions and Differences Between Means http://bio.fsu.edu/~winn/3402L/WinnCH7.html ch7 Restrictions on the use of chi-square analysis include: 1. Data must be discrete. 2. When there are only two categories, no expected value may be < 5. When there are more than two categories, no more than 20% of the expected values may be < 5, and no expected value may be < 1. One use of the chi-square test is sometimes called a contingency test because it is used to determine whether the value of one discrete variable is contingent upon the value of a second variable. The null hypothesis for this kind of chi-square analysis is that variable one is independent of variable two. As an example, suppose that in a field of red and yellow flowers we observe that bees and butterflies appear to specialize on flowers of different colors. We might wish to test the hypothesis that these two pollinators selectively visit flowers of different colors. Our null hypothesis would be that pollinator type is independent of flower color (i.e., that pollinators do not visit flowers differentially on the basis of color). We could conduct an experiment by observing and recording what pollinators visit flowers of each color. Our data might look like this: see photos The procedure for a chi-square contingency analysis would be: 1. Determine the expected values for each combination (= cell) of flower color and pollinator type. The expected values for each cell are determined by the appropriate (row total x column total)/grand total. The expected values for our example are shown below in parentheses see photos. Determine the c2 value and your degrees of freedom using the following formulae:photos for the above bees/butterflies example photos Evaluate your chi-square value using Table 7.2. If the c2 value calculated is equal to or greater than the critical value given in Table 7.2, for your degrees of freedom, you should reject the null hypothesis. This is the case for our example, so we reject the null hypothesis that pollinator type is independent of flower color. A second use of c2 is to test what is called goodness of fit. The procedure for this test is similar to that for a contingency test except for the calculation of the expected values. The difference is that you are comparing an observed distribution of data with a specific distribution that you expect on the basis of additional information. In other words, you are asking "how good is the fit between the data I collect and the results I expect?" Your null hypothesis for a goodness-of-fit test is that there is no difference between your observed and your expected distributions. A simple example of a goodness of fit test is an experiment to determine whether a coin is fair (I.e. whether it is equally likely to turn up heads and tails in a toss). You can test the hypothesis that the coin is fair (in this case, this is your null hypothesis) by tossing it a number of times and recording the outcome. You then use a goodness-of-fit test to determine whether the distribution of heads and tails you observe is significantly different from what you would expect from a fair coin, that is, 50% heads and 50% tails. Let''s say you toss the coin 10 times, and it comes up heads 6 times and tails 4 times. 1. Determine expected values for each class (heads and tails) by multiplying the sample size (10) by the expected probability of an event in each class (50% or 0.5). For the coin toss, we would expect 10(0.5) = 5 heads and 5 tails. 2. Calculate c2 as for the contingency analysis and the degrees of freedom as the number of classes minus one. For our example: c2 = (6 - 5)2/5 + (4 - 5)2/5 = 0.4 df = (2 - 1) = 1 3. Compare your value of c2 with the critical value for one degree of freedom in Table 7.2. Your c2 is less than the critical value of 3.8, so you cannot reject the null hypothesis that the coin is fair. In other words, your 6:4 ratio is not statistically significantly different from a 1:1 ratio. A note on sample size: In general, the larger your sample size (in this case the number of times you toss the coin) , the less your observed distribution is affected by chance alone, and thus the more reliable your test of the hypothesis. To illustrate the effects of sample size, consider a data set in which the observed ratio of heads to tails is the same as in the above example, but the sample size is 100 rather than 10. The observed number of heads is 60 and of tails 40. The expected values (100 x 0.5) are 50 heads and 50 tails. For these data: c2 = (60 - 50)2/50 = (40 - 50)2/50 = 4 Comparing this value with the critical value in Table 7.2, you must now reject your null hypothesis and conclude that the coin is not fair. The effect of sample size on the reliability of statistical tests is general. It applies to continuous as well as discrete data, to both contingency and goodness-of-fit tests, and to regression analysis (described in the next chapter). A very rough guideline is that a total sample size of 50 to 60 observations (i.e. 25 to 30 per group for a t-test) is usually large enough to avoid undesirable effects of chance. Note that when you are comparing two or more groups, it is also desirable for the groups to be made up of approximately the same number of observations (i.e. for sample sizes to be equal). Statistics--Measures of Association http://bio.fsu.edu/~winn/3402L/WinnCH8.html ch8 We frequently want to know whether two measured variables are related in any fashion. The answer can most easily be seen in a graph of the two variables against one another and can be quantified statistically by means of correlation and regression. When you are looking for a relationship between two factors, data are presented differently than in the frequency histogram we have previously shown. Consider the experiment by our intrepid biologist watching bees and butterflies on bean plants. Suppose that she also measured the amount of time each pollinating insect spent on the flower. Her data for bees see photo It seems reasonable to suggest that a bee that spends more time on a flower might transfer more pollen to the flower. If so, # seeds/pod might be increase as time/flower increases. In other words, these two variables are not independent, the value of one depends on the value of the other. We can show the relationship between the two variables by plotting pairs of the two on a set of axes. By convention, the dependent variable (here viable seeds per pod) is measured on the y-axis and the independent variable (here time on flower) is measured on the x-axis. Figure 8.1 illustrates these data properly graphed. Note that as time per flower increases, so does the number of seeds per pod. These variables appear to be related. In fact, knowledge of the time spent per flower would help our scientist to predict the number of seeds per pod with some certainty. Note that one variable need not be dependent on the other. For example, if we plotted height against weight in humans, there is no reason to presuppose that one of these two variables is more causative than the other. Height does not cause weight nor weight cause height, although these variables are clearly related. Linear Regression Analysis Regression analysis tests whether or not a functional relationship exists between variables. In simple linear regression, we are dealing with only two variables and testing to see whether there is a functional relationship between the dependent variable Y and the independent variable X that can be described by means of a straight line. This type of analysis can be used to examine causal relationships between variables or to predict one variable given the value of the other. see photo The regression equation Y = a + bX describes a relationship in which Y is the dependent variable, X is the independent variable, and b is the slope of the straight line that describes the change in Y per unit change in X. The "a" is the point where the line crosses the Y axis, called the Y-intercept (i.e. the value of Y when X = 0). The null hypothesis to be tested is that the slope of the line, b in the equation Y = a + bX, is equal to 0. That is, H0: b = 0. A slope equal to zero would mean that knowing the value of the independent variable (e.g. time/flower) provides no predictive information about the dependent variable (e.g. number of seeds/pod). Restrictions on Use Include: 1. The test assumes that the values of X, the independent variable, are measured without error. (The values of X are fixed by the experimenter and only the values of Y are free to vary.) 2. The Y values must be measured on a continuous scale. The X values can be discrete or continuous. 3. The test assumes that values of Y are from a normal distribution 4. It also assumes that the variance around the regression line is the same for all XY pairs. Procedure: 1. Arrange the data by XY pairs and determine the following values: see photo 2. Compute the slope, b, by the following formula: Note that SX2 is different from (SX)2. 3. Compute a, the intercept where X = 0, by: 4. Place the values you have calculated into this equation 5. Compute the total sum of the squares of the Y values (SST) as: 6. Compute the sum of the squares due to regression (SSr) as: 7. Compute the sum of squares due to error (SSE) = SST - SSr 8. Now we need to divide the SSr and the SSE by the appropriate degrees of freedom to get the variance for each (the Vr and the VE). The degrees of freedom for SSr are always 1. Therefore, SSr = Vr. The degrees of freedom for SSE = n - 2. Therefore, the formula for the variance due to error is : 9. The last step is to calculate an F statistic using the formula:phptos Then compare your calculated F with the critical values for F in Table 8.1 on page 48. The critical value for F must be found for 1 degree of freedom in the numerator and n - 2 degrees of freedom in the denominator. If the F value you have calculated is equal to or greater than the critical value in the F table, you may reject the null hypothesis that b = 0 and conclude that the alternative hypothesis is probably correct, that your data can be explained by a simple linear regression with a slope of b describing the functional linear relationship between your values of X and those of Y. If the Fcalculated is less than the Fcritical on the table, you fail to reject your null hypothesis and cannot conclude that a linear relationship exists between your two variables. The data on seeds/pod and time/flower above produce the significant relationship seen in Figure 8.2. Statistics--Measures of Association http://bio.fsu.edu/~winn/3402L/WinnCH8.html ch8 practical Problems are 1. In an alpine meadow, four flower colors occur with equal frequency. You wish to determine if bees seen pollinating these flowers visit flowers differentially based on their color. a. State appropriate null and alternative hypotheses b. What data would you collect to test your hypothesis? c. What statistical test should you use to analyze these data? d. You collect the following data: #visits to: red yellow purple white 25 86 50 39 Show how you would set up your statistical test (get the correct formula(e) from your handbook). 2. Three kinds of pollinators, birds, butterflies, and bees are foraging in a field of flowers. There are many species of flowers that differ in their color and abundance. You wish to know whether birds tend to fly longer distances than bees between visits to flowers. a. State appropriate null and alternative hypotheses b. What data should you collect? c. Is this an observational or an experimental test of your hypothesis? d. What statistical test should be used to analyze the data? 3. A researcher happens upon a field containing two species of flowering plants but no pollinators. The researcher wishes to make a prediction about which species would be visited by an optimal forager that shows floral constancy (i.e. one that will only visit one species). YOU are the researcher. a. What data will you collect? (be specific) b. What calculations will you make? c. What will be the ultimate basis for your conclusion of which species an optimal forager should visit? 4. In the study of heliotropic (sun-tracking) buttercups described in lecture, the scientist wanted to know if flowers that tracked the sun better maintained higher temperatures than those that tracked less well. To test this idea, the scientist might have classified solar tracking ability into 10 groups with 1=poor tracking and 10=best tracking and measured the temperature in flowers with different tracking abilities. a. Is the scientist collecting continuous or discrete data? b. What are the appropriate null and alternative hypotheses? c. What statistical test should be used to analyze these data? d. Describe a possible experimental test of this same hypothesis. What would constitute treatments and controls and what data would you collect? 5. A pollination biologist finds a population of flowers in an alpine meadow. The flowers all look the same but each bears either a skunky odor or a sweet scent. The biologist proposes the hypothesis that pollinators will visit the flowers differentially based on scent, and collects the following data: Ants are observed visiting 25 skunky scented flowers and 25 sweet scented flowers. Bees are seen visiting 50 skunky and 150 sweet flowers. Moths are seen visiting 20 skunky and 80 sweet flowers. a. Summarize these data graphically with a single frequency distribution b. State the appropriate null and alternative hypotheses the biologist should use to answer his question. c. What statistical test should be used to analyze these data? d. The researcher calculates the appropriate test statistic and finds that it is less than the critical value for that statistic at the correct degrees of freedom. What has this analysis proved? e. The same researcher would now like to know whether plants with sweet-scented flowers have greater fitness when pollinated by bees or when pollinated by moths. What data should the researcher collect? f. What would be the best way to summarize these data? g. What data should he collect to test the hypothesis that ants selectively visit the shorter plants in the population? h. Is he collecting continuous or discrete data? Explain your answer. i. What statistical test should be used to analyze the data? j. How would the scientist use the calculated test statistic to decide whether to reject the null hypothesis? Using the Library and Biological Literature http://bio.fsu.edu/~winn/3402L/WinnCH9.html ch9 When you are looking for research ideas, one approach is to go out into the field and see what interests you. Alternatively, you can get an overview of the field by looking at general books on pollination biology. Usually, the pertinent chapters of the text will cite references that you can use to lead you to other literature. More specific articles on pollination ecology may also be useful in deciding on an experimental project. Finding the Scientific Literature Another quick way to get into the literature on some topic of interest is to browse through scientific literature. Acceptable scientific literature for this class includes many botanical and ecological journals, most published by different scientific societies from around the world. What is called the primary literature consists of journals in which scientists describe and interpret the results of their own original work. The primary scientific literature does not include handbooks, gardening and horticultural manuals, plant and animal identification books, or even this handbook. Information from web sites and homepages is definitely NOT primary literature, and should always be viewed with some caution. Just about anyone who knows how to can create a web site containing whatever they wish to include. As a fourth grade school assignment, my son constructed a homepage containing all the information he could find about tree frogs. Surely you would not want to use this information to guide your research! The Dirac Science Library displays recent (usually less than a year old) copies of most journals in the stacks in the east end of the entry floor of the library (the entry floor is the second floor). Most of these journals have their tables of contents on their covers. In a few minutes of browsing you should be able to locate recent articles that might be useful. We would strongly recommend the following journals: Ecology Oikos Oecologia American Journal of Botany Journal of Ecology Bulletin of the Torrey Botanical Club Evolution American Naturalist Each of the articles you might be interested in is likely to have an abstract at the very beginning. Scanning the abstract will help you determine whether the article is worth reading. Don''t worry too much at this stage about the technical terms; you can usually either figure out what they mean or get around them. Some journals, like older volumes of American Naturalist, do not include an abstract, but do provide some other type of summary section, usually at the end of each article. Look over the literature cited of any interesting paper for further leads into the literature. Once you have decided what you want to investigate, a more formal search of the published literature is necessary. When you know how to extract information from a library, you hold the key to all of humankind''s recorded experiments. The most fundamental aspect of a successful search strategy is that it start with a broad overview of a topic and gradually narrow in focus. The following strategy is recommended. 1. Start with a general source of background information. It can be found in textbooks, references, or review articles. The textbooks and other books can be located through LUIS and its search capabilities. Even if you haven''t already used LUIS, it really is easy, and the library staff can help. To locate review articles, you will need to make use of guides to the literature (see below) or An Index to Scientific Reviews. A review of the literature will save you a great deal of time in identifying appropriate papers, techniques, important work, and research workers in your field of interest, and as a dividend, the review will also provide you with a beginning bibliography for your own paper. Remember that there will be a lag of two to three years, or more, depending on the date of your review article, between the work reported and the current state of the literature. The library will also do a computerized index search for about $30. Such searches are inappropriate and unacceptable for this course. This type of search will probably not meet your needs and does not give you the hands-on experience we want you to have. 2. After you understand the general concepts of your topic, you can locate the primary literature through the abstracting and indexing periodicals. These are produced by companies that periodically (usually monthly or biweekly) release a listing of all the recent articles, along with very useful indices. The abstracting services provide brief summaries of the articles they list to help you choose only those that are the most relevant. The indices do not provide abstracts but rely solely on listing titles and authors; however, they appear with less of a time lag than do the abstracts. In particular, we recommend Current Contents, Science Citation Index, and Biological Abstracts. All three of these can be found on the south side of Dirac on the second floor. Because pollination biology is photogenic and often exotic, you may find many articles in popular journals. Some that we recommend you look through include: Natural History National Geographic Discovery Smithsonian Scientific American BioScience Articles in these popular journals cannot substitute for primary scientific literature, but they can often provide you with names, references, or just ideas. As you work, be sure to record properly all the books and articles you consult. A time-honored system is to use one 3x5 card for each reference. In addition to the factual material you may need for your paper, record all the bibliographical material you will need for the "literature cited" section of your paper. If you head the card with the last name of the first author, the cards will be easy to alphabetize when you are ready to type your literature cited section. Be sure that the information you collect includes the correct name of the author (or authors), the year of the publication, and the title of the article or book. For an article, you will also need the name of the periodical, the volume number, and the pages on which your article appears. For a book, you will need the volume number if there is more than one, the names of the editor(s) if any, and the name and location of the publisher. Some of the library tools you may want to use (ask a librarian for help, if necessary) are: Biological Abstracts: This is the major abstracting service in the English language. It is comprehensive, is cumulative every six months, and includes five indices: subject, author, biosystematic, generic, and concept. The service scans over 8,000 periodicals annually, reporting world research in all fields of biology. Biological Abstracts should be used with its companion periodical BioResearch Index, with A Guide to the Vocabulary of Biological Literature, and with the Serial Sources for the BIOSIS Previous Database. This last publication lists full and abbreviated titles for all the serials abstracted and indexed in Biological Abstracts. There is a lag time of about six months between article publication and appearance. Science Citation Index (SCI): This citation index provides access to articles in all branches of science. It covers periodicals, patents, government reports, books, meetings, and personal communications. This index is particularly useful if one knows a classic paper in the field. Such papers will be listed in Science Citation Index along with all the recent articles that have cited them, allowing you to track forward in the literature from appropriate papers. Once you learn to use it, the SCI is immensely useful. Current Contents/Life Sciences: This is neither an index nor an abstracting periodical. It presents the tables of contents of the current issues of biological journals and includes author and subject indexes. It serves as a prepublication announcement of current research, and there is little or no lag time between the appearance of the article and its listing in Current Contents. The primary literature search method of many scientists is to go first to Biological Abstracts and use the subject index. Start with more recent issues and work your way back to older issues as necessary. By reading the abstracts, find three to five potentially interesting articles. Then go find and read those articles. Those articles can then be used both to backtrack to older articles through the literature they have cited and to check on later literature through Science Citation Index. By combining Biological Abstracts with Science Citation Index, you can track subjects both forward and backward in time using key articles. Reading a Scientific Paper Most of you will be unfamiliar with reading scientific papers. They can be somewhat intimidating but get much easier to read with some experience. Two papers are included at the end of this manual as examples. We will discuss these papers in the laboratory, and you should consider them examples throughout this semester. Be organized while reading these and any other papers. First, each paper will begin with an abstract which provides a brief summary of the paper. Read it to determine whether this paper is an appropriate one for you to read further. If so, then read the remainder of the paper, noting important points as you go: Introduction: What questions or hypotheses are being addressed? How are they similar to yours? What alternate hypotheses are proposed? Check all other studies they cite that might be useful. Materials and Methods: These experiments are done by people who have experience with pollination ecology. This section can often provide some ideas about techniques. Considering their techniques may also help in avoiding problems with your own--always consider why they used a particular method that seems unusual or unnecessary to you. Note the experimental design and statistical analyses. The analyses they used may be way over your head--don''t worry. Ultimately all statistics really do the same thing, trying to distinguish patterns from one another or any single pattern from a random pattern. Results: Although it is apparently hard to understand, nothing goes in this section but results! No interpretation, no discussion, no comparisons, nothing but the results of the experiments, with appropriate statistical analyses and good graphics and tables where appropriate. If you are in a hurry, read the methods, then take a quick look at the figures and tables. But for relevant papers, take the time to be a careful reader: errors often show up in the results. For example, authors may say in the Methods that they sampled 100 flowers, but in the results they only present data for 65 flowers. What happened? Note reasons why their results may differ from yours. For example, very few pollinators except bumblebees are found at high altitudes. Thus a study done at high altitude may give results very different from those of one done in Tallahassee. These differences will become apparent with a careful reading of the results. It is especially useful to note how the authors present or analyze their data, as these methods could be very handy when you work on your own project. Discussion: This section is where the author is supposed to (1) interpret the results, (2) compare these results with those of other similar studies, and (3) put the research in some larger perspective by telling us what is important about this study. No new data should be presented here, and no statistics. Check to make sure the authors address all questions or hypotheses presented in the introduction. A particularly important flaw of many studies is failing to address alternative hypotheses that may be consistent with the results or the experiment (again, consider the example of the earth going around the sun or the sun around the earth). Literature Cited: All literature discussed or cited in the text of the paper should be cited here. This is a particularly useful place to look for related articles. Note that each journal uses its own format for citations (we prefer you use the format used in the journal Ecology), yet virtually all give the same information: names of the authors, year of publication, title, journal name, volume, and page numbers. When done, ask yourself what you learned from this paper. Be critical--I know of virtually no perfect papers in the scientific literature, and you can learn from their errors. Did they state their hypotheses clearly? Did they address them and alternatives sufficiently? Were their methods stated in enough detail that another scientist could replicate the experiment? Did they analyze all data statistically? Did they provide a comprehensive evaluation and discussion of their results? How well was the paper organized? Were their figures and tables understandable? Scientific Communication: Proposals http://bio.fsu.edu/~winn/3402L/WinnCH10.html ch10 To be perfectly honest, most scientists "do science" because it is fulfilling and enjoyable. Many would like nothing better than to be left alone just to satisfy their own curiosity. However, Science (with a capital "S") is a building process; each scientist builds on the knowledge garnered by earlier workers. This process requires that each scientist be able to communicate exactly what he or she did, how it was done, and what it means. To "do Science," it is of critical importance to be able to write science. We will put great emphasis on writing in this course. Research Proposals A proposal is a description of work that an investigator is planning to do. The proposal is written before the research is initiated and is often written for the purpose of obtaining funding for the research or permission to use resources needed for the research. A successful proposal must convince its readers that the research described is worthwhile and feasible. Funding agencies are unlikely to allocate scarce research funds to projects that are esoteric or that are not likely to be successfully completed. You will write a proposal describing the experiment you plan to conduct. Your proposal must convince your instructor and teaching assistant that your research topic is interesting and that your experimental approach is feasible. The format for your proposal is outlined below and an example of a research proposal is given at the end of this chapter. A worthwhile idea for research is any idea that will contribute something new to our current knowledge in a particular area. You should not propose to demonstrate a phenomenon that is already well understood, or to repeat exactly an experiment, merely to see if you will get the same results as a previous study. Developing a good idea for a research project requires fairly detailed knowledge of a particular area. The depth of knowledge you will need is greater than what was introduced in lecture. You will need to research your proposed topic in the library (Chapter Nine described how to research a topic in the library). Once you have developed an idea for your research project, you must formulate a testable hypothesis (or hypotheses) and design an experiment that will allow you to distinguish among competing hypotheses. Consider alternative designs for testing your hypothesis and choose the one that is most efficient and most practical. Keep in mind time constraints (your experiment must be completed and analyzed by the time you give your oral report) as well as the availability of materials and equipment. It is often a good idea to test your proposed methods in the field before proposing a specific experimental design. For example, if you need to construct artificial flowers, make some up and take them to your proposed field site to make sure pollinators recognize them as flowers. This sort of trial (sometimes called "pilot work") is very useful in helping your to fine tune your design and to make sure that you can successfully complete your experiment. Format for your research proposal Your research proposal should contain a clear description of your area of interest and of the specific question(s) being asked. An explicit statement of the null and alternative hypotheses is also required, along with a justification of the effort entailed. This usually includes an indication of why the question is important and how it fits into a broader picture of what is already known about the topic, in other words, the previously published literature on the subject. The proposal should outline the actual plan of experimental attack, mentioning specific equipment and techniques to be used (and referring to the literature if previously published procedures are to be followed). The organization of the experimental treatments and the envisioned sample sizes should be described. An actual day-by-day schedule of events and procedures is particularly useful. You must also specify what organism(s) you plan to work with and where you will do your research. Finally, the proposal should describe the statistical treatment that will be applied to the data collected. It is only with this type of careful planning that you can avoid collecting meaningless, inconclusive, or irrelevant data. Later, when you are writing the full report of your experiment, you will find that most of the material in your proposal will be useful. The justification in your proposal may be used in writing the introduction and possibly the conclusion of your final report; the description of methods and materials will be practically written; and the results section will follow logically from your statistical plan. The time spent on the research proposal will be well invested, insuring a logical experiment and an easily-written report. Your proposal must use the following format: TITLE QUESTION WHY THIS QUESTION EXPERIMENTAL LOGIC H0 (null hypothesis) H1 (primary alternative hypothesis) H2 (second alternative - if any) There may be even more alternative hypotheses. It is important that you present all reasonable hypotheses, carefully distinguishing among them. Then carefully delineate which hypothesis you expect to be correct and explain the basis for your expectation. EXPERIMENTAL DESIGN Note that your methods must distinguish among the possible hypotheses presented in the Experimental Logic. PROPOSED STATISTICAL TREATMENT Sometimes it is useful to make up some hypothetical data of the type you expect to collect and actually to try out the statistical test. This may reveal how much data would make an adequate sample. LITERATURE CITED See description below for correct format. Illustrative tables and figures should be inserted near where they are first cited in the text. No figure or table should be included unless it is cited. Citing the literature in a scientific paper Your proposal, like all scientific writing, should be properly documented by references to the scientific literature. Citations of the literature serve two purposes: they put your work in the context of current knowledge of a field and they fulfill your ethical and legal obligation to give credit to others for their ideas and work. You should use citations whenever you state the results of previously published work or the ideas of others. You should not cite references for what is considered common knowledge in a field. For example, you would not need to cite a reference to support the following text; "Because plants are sessile, they must employ mobile vectors to transport their pollen". This would be considered knowledge that is common to anyone reading the literature on pollination biology. As a general guideline, you do not need to cite references for any information you would expect your classmates to know. In most scientific writing, references are cited using the "name-and-year" method (sometimes called the Harvard method). To credit an idea or result to a published reference, you simply put the author''s name and the date of the publication you wish to refer to in parentheses following the text that refers to the work. For example: "Other studies have demonstrated that a hummingbird does not sneeze when it gets pollen up its nose (Werner 1979)." The author''s name may also appear as part of the sentence: "Werner (1979) demonstrated that a hummingbird does not sneeze when it gets pollen up its nose." Multiple references for the same point are listed in chronological order, separated by commas: "(Werner 1979, Johnson and Leibold 1992)." For multiple papers by a same author, the author''s name should not be repeated: "(Werner 1978, 1982)." In cases of three or more authors for the same paper, you may use "et al." in the text of your paper (e.g. Jones et al. 1972 rather than Jones, Smith, and Brown 1972). In the Literature Cited section, list your citations in order of the last name of the first author. Only list papers you have cited correctly in the text. Do not use "et al." in the literature cited section; all authors must be named in full. Journal titles may be abbreviated according to standard practices. Different journals have slightly different formats for citations. Some use more abbreviations, some include commas or periods where other do not, etc. But they all include virtually the same information, and each journal is internally consistent. We are asking that you use the format found in the journal Ecology. We have provided some examples here; for any unusual cases, look for examples in published papers. Standard Article Beare, M. H., and W. E. Perkins. 1982. Effects of variation in floral morphology on pollination mechanisms in Asclepias tuberosa L., butterflyweed (Asclepiadaceae). American Journal of Botany 69:579-584. Book Real, L. 1983. Pollination biology. Academic Press, Orlando, Florida, USA. Chapter in Book Waser, N. M., and M. V. Price. 1983. Optimal and actual outcrossing in plants, and the nature of plant-pollinator interactions. Pages 341-359 in C. E. Jones and R. J. Little, editors. Handbook of experimental pollination biology. Van Nostrand-Reinhold, New York, USA. A final note: Plagiarism or the use of literal material from the scientific literature is prohibited under most circumstances. Do not quote from articles: instead figure out what the author(s) has written and interpret it in your own words. Follow your interpretation with a proper citation. Even enclosing material in quotes is generally unacceptable unless, for some reason, you could not write this information in your own words. NOTE: We will require that your proposal cite at least two papers from the primary literature. Below is a sample research proposal of the sort you will write. You may use this example as a guide to the format and content we expect in your proposal. A Sample Proposal TITLE: The effect of flower age on self-incompatibility in Raphanus sativus QUESTION: Are older flowers that are still unpollinated more likely to allow selfing as a last chance way to produce seeds? WHY THIS QUESTION: Self-incompatibility has the advantage of preventing inbreeding depression that may result from selfing. However, it would seem that self-incompatibility would be less advantageous when the chances of cross-pollination are low. When there is a high probability of not being cross-pollinated, self pollination might be better than no pollination at all (Bookman 1983). I will investigate whether individual flowers that have not been pollinated can reduce their self-incompatibility so that they can have a last chance at producing seeds through selfing. EXPERIMENTAL LOGIC: H0: Flowers of different ages (times from opening) will exhibit the same degree of self-incompatibility, as measured by number of ovules matured following selfing. H1: Self-pollinated flowers that are older will produce more seeds than those that have just opened, due to a decline in the effectiveness self-incompatibility mechanisms. EXPERIMENTAL DESIGN: Raphanus sativus individuals will be identified in a population near Innovation Park. Two flowers on each of twenty plants will be covered with mesh bags before they open to exclude pollinators. Ten plants will be labeled "Day 1" and ten will be labeled "Day 4" using plastic stakes at the base of the plant. The plants will be checked daily to see which flowers have opened. When flowers open, they will be tagged with a paper tag that notes the day they opened. When the first flower opens on any given plant, I will toss a coin to determine if that flower is to selfed or outcrossed and the flowers will be tagged appropriately. Pairing selfed and outcrossed flowers on the same plant will help prevent other factors from affecting selfing, such as plant size (Geber 1985). If the flowers are on a plant marked Day 1, they will be pollinated on the first day they are open. Flowers on Day 4 plants will be pollinated on the fourth day after they open. Flowers marked for selfing will be pollinated with pollen from the same flower. Flowers marked for outcrossing will be pollinated by removing an extra flower from another randomly chosen plant and using it as a pollen donor. After pollination, the flowers will always be re-bagged. Two weeks after each pollination, I will remove the flowers and dissect the fruit to count the number of developing seeds. PROPOSED STATISTICAL TREATMENT: The data will consist of numbers of developing seeds, a continuous variable, in selfed and outcrossed flowers of different ages. I will first summarize my results in a bar graph showing mean number of seeds/flower for each flower age group separately for selfed and outcrossed flowers. I will then compare the number of seeds produced by selfing on Day 1 and Day 4 using a t-test (2 groups with 10 replicates per group). I will do the same thing for the outcrossed plants. If my hypotheses is correct, I will find that the Day 4 plants will have a higher seed set than the Day 1 plants for the selfed group, but not for the outcrossed group. Scientific Communication: Papers and Presentations http://bio.fsu.edu/~winn/3402L/WinnCH11.html ch11 Scientific Papers The organization of a research paper reflects the basic pattern of research design. The rigid format of scientific papers is extremely helpful to both writer and reader. Although the highly structured format will be new to many of you, you may find that writing a scientific paper is easier than writing a paper for a humanities course. Cleverness, beauty, originality, and style (although extremely important in the design of experiments) are not required in scientific writing. What is required is a clear, logical, orderly presentation of what your question was, how you planned to answer it, what your results were, and what you concluded. Needless to say, good grammar and precise wording are crucial to effective communication. Your scientific paper must have the following elements: TITLE ABSTRACT INTRODUCTION METHODS AND MATERIALS RESULTS DISCUSSION LITERATURE CITED Illustrative tables and figures may be inserted where appropriate. These actual words (Introduction, etc.) are to be used to head the appropriate sections of your paper. Each heading is centered on its line and followed by the text for that section. The abstract appears alone on a page, and the Literature Cited begins on a new page. Otherwise, you do not normally begin a new page for a section unless the preceding section completely filled the page. Illustrative tables and figures may be inserted where appropriate or placed at the end of the paper. These items must be fully labeled (not just "Figure 1" but an explanation of what is being shown) so that they can be understood by someone who has not yet read the paper. See Figure 8.2 in this manual for an example of a complete figure legend. Data or experimental results presented in a graph or table must also be summarized verbally in the text so that the text could be understood by someone who had not seen the table. Each of the sections of the scientific paper will be discussed in more detail. Examples of scientific writing can be found in the papers at the end of this manual. You can find many other examples by browsing through any of the journals previously discussed (Chapter Nine). Title: The title of a scientific paper should tell the reader what kind of work is being reported in as succinct a manner as possible. If possible, it should reveal the name of the organism studied, the particular aspect or system examined, and the variables manipulated. Abstract: The abstract is a one- or two-paragraph condensation of the entire article giving the main features and results of the work described more completely in the article. It helps the reader decide whether the material in the paper will be of interest (something to keep in mind when you survey the literature). Abstracts are often published separately from the paper in literature-searching services such as Biological Abstracts, so they must be able to stand alone. Reducing a long paper to a few paragraphs is not easy and may take several tries. If it gives you great difficulty, put it off until the very last, then give it several tries. Introduction: The introduction should present the question being asked and place it in the context of what is already known about the topic. Background information that explain why the topic is of interest and related findings by other scientists should be mentioned here, along with proper literature citations. Basically, you should introduce the general question and justify its importance. Then present the specific hypotheses being tested. For your paper, you must describe the findings of at least two related studies from the primary literature in the context of your system and hypotheses. Of course, these papers must be cited correctly in the text and in the Literature Cited. Methods and Materials: This section of the paper should describe the materials and procedures used in sufficient detail that others could repeat the research to see if they would get similar results. Previously, published techniques can be cited without a detailed description. The method of approach to the problem should be narrated in the past tense, telling what was done and not what the reader should do. Diagrams of the experimental apparatus or study areas are often helpful. Remember that statistics are a method and so you should describe your statistical analyses in this section (note examples from the literature during your survey). If you have not done so in your introduction, you should also briefly describe the species with which you are working in this section. At least once, you need to tell the reader the scientific name (Latin binomial) of the organism(s) you are working with. After you have provided the genus and species of each major organism involved in your experiment, you may then refer to them by common names. The following sentence illustrates the correct way to cite the Latin name of a species and to connect it to a common name; "My work examines the effect of formaldehyde on the length of stigma receptivity in the tropical lily, Rafflesia vulgaris, the stinking corpse lily. " Note that the genus is capitalized but the species name is not. Also note that Latin names, like any foreign words, should be underlined. In subsequent text, you may refer to your study organism as "the stinking corpse lily" or as "R. vulgaris". Results: The results of each experiment should be presented clearly, without comment, bias, or interpretation (that all goes in the discussion). Graphs, tables of data, and figures are often useful here (they are must be cited in the text), but do not replace a verbal summary of the findings. Also, never present only the raw data. It is your job to organize, summarize, and simplify the data for presentation to the reader. The most important features of tables and figures should be pointed out in this section. The results of statistical tests applied to your data are reported in this section, although conclusions about your original hypotheses are saved for the discussion section of the paper. Discussion: In this section you evaluate the meaning of your results in terms of the original question and hypotheses and point out their biological significance. In fact, it is a very good idea to reread your introduction while writing your discussion; you would be surprised how many published papers fail to address the hypotheses presented in the introduction. If the results are unexpected or contradictory, you should attempt to explain why and to point out avenues of further research. The discussion should describe the significance of your experiments in terms of other work without trying to review the entire field. We require that you compare your findings with at least one cited study from the primary literature, explaining similarities to and differences from your own work. Literature Cited: All published work mentioned in your paper must be cited correctly in the text and listed in the Literature Cited section at the end of your paper. You will have saved hours of pain and suffering if you are now working from well organized notes taken during your literature survey. The correct format for literature citation was described in the previous chapter on scientific proposals. Illustrative Material We expect that your scientific paper will be augmented by diagrams of study areas or apparatus, figures showing graphical or diagrammatic representations of the data, and/or tables of actual results. In all cases, the more complete the labeling, the more effective the presentation of information. Again, while doing your literature survey, note the presentation of information. These articles, especially those in papers closely related to your subject, should provide examples of good presentation of illustrative materials. A few guidelines: 1. All tables and figures must be cited in the text. As with references to literature, they are usually cited indirectly--"Anger level in bees is correlated with flower color (Figure 4)." but they can be referred to directly--"Figure 4 illustrates the relationship between anger level in bees and flower color." 2. Always provide an adequate legend. Be sure to define any symbols used in figures and any abbreviations used in tables or figures. The table or figure must be comprehensible without the text. 3. Use capital letters on the x- and y-axes, except when abbreviating measurements. Indicate the units (e.g. cm, seconds, gm) in which measurements are presented. Use lower case letters for any text inside the graph. 4. Many computers now offer programs with high quality graphics. Don''t get carried away. Simple graphs make clear, easily understood points. That is the primary purpose of the material. Oral Presentations Much of what we do in science involves verbal and visual communication. Many scientists participate in professional conferences or symposia that offer a forum for exchanging ideas, conveying information about new research methods, and reporting on research in progress. By talking, we paint mental pictures with words, try out ideas, convince people that our ideas are sound, and find out if our ideas are not sound. With pictures, we hope to present ideas and data in a way that is easy for people to understand. Good pictures and good conversation are an integral part of science. In this course, you are required to prepare an oral presentation of your experiment. There are many similarities between writing a paper and planning an oral presentation. Both activities require you to convey information clearly, accurately, and logically. Both also force you to examine your own understanding of the material and to use writing as a means of clarifying your thoughts. The organization of your talk should follow that of your final report, although you will present less detail in your talk. Start by introducing the general subject of your research and briefly summarizing results of related published studies. Your introduction should lead up to your hypothesis in a way that makes clear why the question you asked is interesting. After introducing your question, you should describe your experimental design and methods. Unlike your paper, your talk does not need to present enough detail to permit your audience to repeat the experiment you did. You need only summarize your methods sufficiently to convince the audience that they provide an adequate test of your hypothesis. Next, you should present a summary of your data in a graph or table. In general, you should not present your raw data unless you need to make a specific point about it. After you present your data summary, you should present the results of your statistical analysis, even if your results do not support your hypothesis! Last but not least, you should interpret your results in the context of your original hypothesis and of other studies form the literature that have addressed the same or similar issues. As you are composing your oral presentation, keep in mind that your audience for this presentation is your classmates, not your TA or your instructor. You should not assume that the audience is familiar with your research subject and the details of your experiment, even though you may have discussed them at length with your TA. You should assume that the audience is familiar with basic concepts in pollination biology and experimental design and analysis that were covered in lecture. The following are some practical suggestions for giving a successful oral presentation: 1. Write out the entire talk beforehand. Even if you are an accomplished speaker, putting everything down in writing will make your presentation more organized and coherent and will lessen the chance that you''ll forget an important point. As with a paper, first construct a rough draft, then revise, plotting your talk sentence by sentence. 2. Never read a prepared talk word for word. You will only distance yourself from your audience or put them to sleep. Instead, use the written version of the talk to make a brief list of key points or concepts; these can be put on a single sheet of paper or on file cards arranged sequentially. As you speak, use these key points to jog your memory and keep you on track. An effective talk--one that really engages the audience--strikes the proper balance between carefully structured wording and a spontaneous, informal delivery. 3. Organize your talk carefully. Tell the audience your hypothesis at least three times: at the beginning, in the middle and at the end. It is often good to write your hypothesis on an overhead to show at the beginning and end of your talk. Planning may be easiest if you think of the talk as having a distinct beginning, middle, and end. Use straightforward language, avoiding jargon. Save time at the end to summarize the most important points, offer conclusions, and discuss broader aspects of your work. 4. Watch your time limit carefully. Practice speaking your talk at least twice, including the use of visual aids. A very common problem is speaking too fast. Slow down! It is very rare that someone gives a talk too slowly, yet very common that a talk is given too quickly. It helps to pause briefly after important points and to repeat difficult material with a slightly different wording. Doing so allows listeners to time to digest everything they hear. 5. Establish eye contact with the audience. Doing so will actually help make you feel more relaxed and will certainly help make your audience more receptive. When practicing, concentrate on eliminating "um''s" and "ah''s". 6. Use simple, well constructed, visual aids. Graphs and tables can be put on overheads. You will not have time to put figures or tables on the board before (or during) your talk. Overheads should be simple to read (use large type) and clearly labeled: the ideal visual aid will stand on its own with no explanation. Even so, when you present a table or figure, take some time to orient your audience by describing the axes of your graph or the columns of your table. Remember, this is the first time they have seen this information! 7. Be prepared for questions. You cannot predict everything you will be asked, but you probably can anticipate some of the questions. Look at questions as an opportunity to improve your work, not as a threat. If you are asked a question for which you are unprepared, do not try to bluff your way through a reply. It is far better to say that you don''t know the answer. Lab Exercise: Floral Morphology and Pollination Systems http://bio.fsu.edu/~winn/3402L/WinnCH12.html ch12 The diversity of angiosperm flowers on earth is tremendous, there are over 300,000 different species, each with a unique flower. Yet, all flowers serve a similar function and evolved from the same common ancestor. Therefore, by understanding a few basic structures in a "general" flower, we can understand the structure and function of most flowers. In this lab you will be responsible for learning the structure of a typical flower, studying some examples of "typical" and atypical flowers, and determining the identity of the most likely pollinators of some flowers on the basis of the color and morphology of the flower. Remember that the plants we see around us are the sporophytic generation, while the sexual generations (gametophytes) are relatively hidden. The flower is where gametophyte and sporophyte generations co-occur. As you look at flowers, try to understand the function as well as the name of each part of the flower by remembering how each part of the flower fits into the whole life-cycle of the plant. Flower Morphology Your TA will provide you with what we will call a "typical" flower. Evolutionarily, floral parts are extraordinarily specialized leaves. These specialized leaves occur in groups or whorls, each with a different purpose. Starting at the outside we find a roughly circular whorl of sepals (Figures 11.1 and 11.2), which are usually green and fairly small in relation to the size of the flower as a whole. Before the flower opens, it is the sepals, collectively called the calyx, that enclose and protect the developing bud. Inside the sepals are petals, usually larger and more colorful. Note that in some species, for example in tulips, the sepals and petals look very much alike and act together to provide the color attracting pollinators. Together, the petals make up the corolla, and the calyx and corolla make up the perianth. Continuing in towards the center of the flower, we encounter one or more whorls of stamens, which are the flower''s male organs (Figure 11.1). Each stamen typically consists of a slender stalk or filament attached to the flower at its base and carrying on its free upper end a structure called an anther, which contains the pollen. Finally, in the center of the flower are the female organs, or carpels. Individual carpels, as well as fused carpels which make up a pistil, consist of a basal ovary containing the ovules, a slender column-shaped structure called a style, and on the end of the style the stigma, the function of which is to receive the pollen grains. All of these parts of the flower are "sporophyte" structures. The pollen grain is the adult male gametophyte. When a grain finds itself in the comfortable environment of a stigma, it sprouts a long, slender, tubular outgrowth that pierces the tissue of the stigma, worms its way down the length of the style, and finally delivers one of its two sperm cells (gametes) to an egg cell within the ovule (the female gametophyte). The ovule is the structure that, after fertilization, gives rise to a seed. All well and good. But in the real world this logical regular pattern of flower parts is not always so obvious. Three things can make flower structure a bit confusing: similarity of parts, absence of parts, and coalescence of parts or groups of flowers. You should try to look at examples of several different flowers in lab before you go on. The most common instance of similarity of parts is resemblance between the sepals and the petals, which has already been mentioned as occurring in tulips. Similarly, brightly colored leaves and bracts surrounding the flower may also be confused with the petals. Other instances of "mimicry" exist, including situations in which the style and stigma resemble a stamen. The best way to sort out similar parts is to look at the organization of the whorls and to remember that it should go sepals, petals, stamens, pistil. Many species have evolutionarily lost some parts of the flowers. The most obvious situation is that in which a plant or a species has male and female flowers. In this case, flowers have lost one sexual function, allowing them to specialize in the other. Many flowers have also lost petals or sepals. Cohesion and fusion are common both within and among flowers. The petals may be fused to make a tube, as in a petunia flower. Or the filaments may be fused, as in the beautiful Hibiscus flowers. Fusion can also occur between different types of parts; for example, filaments can fuse with petals. Flowers may combine to form what is called an inflorescence. In fact, one of the largest families of plants is the composites, which include sunflowers, dandelions, and a large number of what botanists call DYC''s (damn yellow composites). Each "sunflower" is in actuality many flowers joined together. The inner flowers have lost their sepals and petals and are called disk florets. The outer flowers produce the petals along the edge of sunflowers and are called ray florets. Other examples of inflorescences abound. When looking at each species, try to determine attractants and rewards offered by each flower. These may include, but not be limited to, color, nectar, odor, and pollen. Also, determine how the flower tries to "guide" the pollinators to specific locations in the flower in a particular order. In other words, try to think like a pollinator crawling around on the flower. Where would you go first? Make sure that you are comfortable with the diversity of flowers we provide you with in the lab. Some are small and can be looked at under the scope. Don''t worry about occasionally being fooled: we all are. Pollination Vectors Pollen is transferred from the anthers of one flower to the stigma of another (or the same flower) by a number of different agents. These include, but are not limited to, wind, beetles, flies, bees, butterflies, moths, birds, and bats. As might be expected, different species that require the same "type" of pollinator often share floral characteristics that act to attract that pollinator. For example, hummingbird pollinated flowers are usually tubular and red, because red is easily seen by birds and because tubular flowers are less accessible to bees and other insects that might take the rewards (usually nectar) without pollinating the flower. Below we have provided you with a floral key to pollination systems. Using this key, you will be able to determine how a particular plant is pollinated, or at least narrow it down to a few likely possibilities. Keep in mind that some plants use a variety of pollinators and therefore may have characteristics that are intermediate between, or a combination of, more than one system. The pollination systems addressed in this key are abbreviated as: Abiotic systems (water pollination is not addressed in this key) WI wind pollination Insects BT beetles F-M flies (myophily) F-S flies (sapromyophily) BE bees BU butterflies MO moths Vertebrates BI birds BA bats This key is used to eliminate unlikely pollinators. Use this key to determine the most likely pollination system for at least two flowers provided for this purpose by the Teaching Assistant. For each flower, start with a list of all the options.see exbiophotoalbum.html Costs and Benefits of Foraging http://bio.fsu.edu/~winn/3402L/WinnCH13.html ch13 This exercise is to be conducted in the Biology Computer Laboratory in Conradi 223. For a variety of reasons, we will not allow students to take copies of the program out of the lab to use elsewhere. All students must read and sign the Biology Computer Lab Agreement handed out in lecture before running this program. Be forewarned that there are more students in your lab section than there are computers in the lab. Although the program does not take long to run, do not put off this assignment until the last moment, as the computers are likely to be busy. "The computer lab was always busy" will not be accepted as an excuse for not turning in your assignment on time. NOTE: You may find it handy to have a calculator with you for this exercise. Background Chapter five in this manual provides background material on foraging ecology. You should read this chapter before attempting this exercise. Foraging ecology encompasses a large body of theory and experimental work aimed at understanding how organisms acquire resources. Foraging ecology considers all sorts of resources, such as nesting materials, food, and mates. We will specifically be concerned with the rules that govern how, where, and when pollinators visit flowers to collect rewards (and sometimes incidentally carry out pollen transfer). The basic premise of foraging ecology is that natural selection favors pollinators that are efficient, that is those that collect the most resources for the least amount of effort. Foragers do not collect resources haphazardly; rather, their behavior has been molded by natural selection to maximize their efficiency. The goal of this exercise is to allow you to explore foraging strategies that pollinators may use in maximizing their efficiency. Efficiency is usually quantified by the ratio of benefits obtained to costs incurred while foraging. A forager that achieves a greater ratio of benefits to costs is more efficient. For pollinators, the benefits can be measured by the amount of reward they collect. Their costs can be measured by the energy they must expend flying from flower to flower collecting this reward. As you complete this assignment, think about how you might explore some of these ideas in the real world. How could you measure costs and benefits? How could you figure out what cues and what rules are used by a pollinator in a field of flowers to decide what flower to visit next? Using the Foraging Program The program you will use for this exercise is called "Bee." It is accessible on the Macintosh computers in the computer lab. Using Macintosh computers is a cinch, but, if you have any problems at any time, just ask the helpful staff in the computer room or someone on the Mac next to you. If you have questions or problems with the program itself, get in touch with your TA or professor. If you have not used a Mac before, the only real trick is controlling the mouse, that little box with the button on it next to the computer. As you move the mouse around the tabletop, an arrow moves around in corresponding directions on the screen. You can run a Macintosh almost entirely by moving the mouse around to get the arrow to a particular point on the screen and then pushing the button ("clicking"). Some things require pushing the button on the mouse twice in quick succession ("double-clicking"). It does take a few seconds to get used to double-clicking. I should note here that all the computer cares about is where the tip of the arrow is. That is, you can''t actually point the arrow at an item on the screen and have the computer know what you want. You have to put the tip of the arrow on top of the item of interest, then click the mouse. To start our program, first sit down at a Macintosh computer in the Biology Computer Lab. If the screen is dark (the computer is off), push the button in the uppermost right-hand corner of the keyboard. If the screen has fish swimming on it, or some other such nonsense, first make sure that no one else is using the computer, then restart the computer (if you don''t know how, use a computer that is already turned off or ask the staff for help). The screen on the computer will now request that you enter your user ID and password to get onto the server (a set of files that are shared by all the Macs in the room). Type in the user ID and password from the white cards handed out in lecture using only lowercase letters. The computer asks for the password first. Enter it, then hit the tab key. Now enter your user ID. When you have entered your password and ID, click on the box labeled "OK." Again, if you have any problems such as having forgotten to record your user ID and password, contact the staff. To find the Bee program, put the arrow on the little figure labeled server found in the right-hand portion of the screen. Double-click. Numerous small boxes should appear, one of which is labeled "Classes." Put the arrow on this box and double-click. More boxes should appear, one of which is labeled "BSC 3402L" (our course number). Again, put the arrow on the box and double-click. Two last clicks on the bee should start the program and give you an introductory screen. Click on the box labeled "continue," and you should see something like the figure on the next page (the program may change slightly as we develop it further). On the right hand side of the screen is a bee in a field of flowers. To the left is a box labeled "Foraging Data." The program allows you to become the bee and to forage for nectar rewards on the flowers in the field. Each time you click on a flower, the bee will "fly" over and visit that flower and collect its reward (try it!). Each time you visit a flower, the box on the left side of the screen will show you how much of a reward you collected and how much it cost you to get that reward. The cost is determined only by how far you had to fly to reach the flower, not by the type of flower. The six types of flowers differ in the amount of reward they offer (1 to 10 units) and in their abundance. A given flower type always gives the same reward unless the flower has previously been visited. Once you visit an individual flower, its reward is gone, and if you revisit that same flower, you will not get a reward. You will still get a reward from other flowers of the same type. The basic problem you (in your role as a bee) are faced with is to decide which flowers to visit. That is, what is your "strategy" for choosing the next flower each time you leave a flower you have just sucked dry? If you have some previous knowledge of this flower community, you can consider a variety of important factors, including amount of nectar or pollen (related to benefit), how difficult it is to obtain that nectar or pollen (related to cost), distance to or density of your flower type (related to cost). Other factors may also be important in the real world, such as predation risk, temperature, distance from hive, etc., all of which we will not explicitly consider in this program. So, do you just go to flowers that have the greatest reward, no matter what the cost? Or do you just go to flowers that have the lowest cost, regardless of reward? These decisions can mean the difference between life and death for your poor bee. 1. In the lab sections, you will discuss how we construct and test hypotheses. Before conducting this lab, you need to "predict" what you think will happen by constructing your own set of hypotheses about how bees should forage. You need to construct three hypotheses: a. H1: The foraging technique you think would be best for the bee. Explain. b. H2: At least one alternate hypothesis. Explain. c. H0: A null hypothesis, used for statistical analyses (Chapter 7). 2. Go to the computer lab on your own time and try the program. Sample the different flowers available by visiting each kind and noting the reward that is offered. You should make some notes as you forage. Note that if you revisit a flower from which you have already collected a reward, the reward for the second visit will be zero because we are assuming that the flower will take a significant amount of time to replenish its nectar. Take as much time as you need to familiarize yourself with the bee, the flowers, the rewards, and the travel time. 3. A foraging bout will consist of 15 visits. For each visit, record the reward received and the cost in terms of travel time on the data sheet on page 70. At the end of the bout, total your rewards and travel time and determine the ratio of benefits : costs. After each bout, click on the box labeled "renew" to refill all the flowers for the next bout. a. Forage for one bout (fifteen flowers) visiting only the flower type with the highest reward. Calculate your benefit:cost ratio. Click on Renew. b. Now try a bout visiting only the most common flower. Compare the pattern of costs and benefits with those obtained by foraging only on the highest reward flowers. Calculate your benefit:cost ratio. Click on Renew. c. Forage for one bout in which you always visit the nearest flower (taking care not to revisit a given flower). Calculate your benefit:cost ratio. Click on Renew. Rerun the program three more times, repeating each of the three strategies (high reward, most common, nearest) once each. 4. Now that you are an experienced forager, use your own set of rules and forage in what you think is the optimal fashion. For three separate bouts of fifteen flowers, try to maximize your benefit:cost ratio. Is your strategy better than any of first three? Try to figure out why you are getting better (if you are). When you are finished with the computer, you should shut down your machine. To do so, click on the quit button in the lower right-hand corner of the field. Put the arrow on the word "Special" at the top of the screen and hold the mouse button down. Pull the mouse toward the edge of the table until the word "shut down" is highlighted. Now release the mouse button. The machine should turn itself off. Provide brief, written answers to the following four questions and hand them in WITH YOUR DATA : 1. Provide the three initial hypotheses you formulated before you ran the computer lab (from section 1 above). Remember that we do not necessarily expect these to be correct, so there is no reason to cheat and change them after you have run the program. 2. What "rules" did you follow when you were trying to forage optimally (section 4 above)? 3. If you were a real forager in an actual field of flowers, what circumstances might cause you to change the rules you use in foraging? Give three circumstances and for each case suggest how the forager would change its behavior. 4. Suggest several ways (other than increasing reward) in which a given plant species could increase the frequency with which it is visited by its optimally foraging pollinator. Selected References on Pollination Ecology http://bio.fsu.edu/~winn/3402L/WinnCH14.html ch14 Three general references on pollination biology have been placed on reserve in the Dirac Science Library. All are useful for background information, potential references, and ideas for projects. Barth, F. G. 1991. Insects and flowers. Princeton University Press, Princeton, NJ. Dafni, A. 1992. Pollination Ecology. IRL Press, New York, NY. Faegri, K., and L. van der Pijl. 1979. The principles of pollination ecology. Pergamon. Elmsford, New York. Kearns, C. A. and D. W. Inouye. 1993. Techniques for pollination biologists. University Press of Colorado, Niwot, CO. Meeuse, B. and S. Morris. 1984. The sex life of flowers. Facts on File, New York, New York. Real, L. 1983. Pollination biology. Academic Press, Orlando, Florida, USA. A selection of articles from the primary literature on pollination biology: Agren, J. 1989. Seed size and number in Rubus chamaemorus: between-habitat variation, and effects of defoliation and supplemental pollination. Journal of Ecology 77:1080-1092. Aizen, A., K. B. Searcy, and D. L. Mulcahy. 1990. Among- and within-flower comparisons of pollen tube growth following self- and cross-pollinations in Dianthus chinensis (Caryophyllaceae). American Journal of Botany 77:671-676. Beare, M. H., and W. E. Perkins. 1982. Effects of variation in floral morphology on pollination mechanisms in Asclepias tuberosa L., butterflyweed (Asclepiadaceae). Amererican Journal of Botany 69:579-584. Bookman, S. S. 1983. Effects of pollination timing on fruiting in Asclepias speciosa Torr. (Asclepiadaceae). Amererican Journal of Botany 70:897-905. Charlesworth, D. 1988. Evidence for pollen competition in plants and its relationship to progeny fitness: a comment. American Naturalist 132:298-302. Cruden, R. W. 1977. Pollen-ovule ratios: a conservative indicator of breeding systems in flowering plants. Evolution 31:32-46. Feinsinger, P. 1987. Effects of plants on each other''s pollination: is community structure influenced? Trends in Ecology and Evolution 2:123-126. Feinsinger, P., K. G. Murray, S. Kinsman, and W. H. Busby. 1986. Floral neighborhood and pollination success in four hummingbird-pollinated cloud forest plant species. Ecology 67:449-464. Fenster, C. B., and V. L. Sork. 1988. Effect of crossing distance and male parent on in vivo pollen tube growth in Chamaecrista fasciculata. Amererican Journal of Botany 75:1898-1903. Galen, C. and C. Plowright. 1985. Contrasting movement patterns of nectar-collecting and pollen-collecting bumble bees (Bombus terricola) on fireweed (Chamaenerion angustifolium) inflorescences. Ecological Entomology 10:9-17. Geber, M. A. 1985. The relationship of plant size to self-pollination in Mertensia ciliata. 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Kerster. 1969. The dependence of bee-mediated pollen and gene dispersal upon plant density. Evolution 23:560-571. Louda, S. M. 1982. Inflorescence spiders: A cost/benefit analysis for the host plant, Haplopappus venetus Blake (Asteraceae). Oecologia 55:185-191. Marshall, D. L. 1988. Postpollination effects on seed paternity: mechanisms in addition to microgametophyte competition operate in wild radish. Evolution 42:1256-1266. Price, M. V., and N. M. Waser. 1979. Pollen dispersal and optimal outcrossing in Delphinium nelsoni. Nature 277:294-297. Pyke, G. H. 1978. Optimal foraging: movement patterns of bumblebees between inflorescences. Theoretical Population Biology 13:72-98. Real, L. 1981. Uncertainty and pollinator-plant interactions: the foraging behavior of bees and wasps on artificial flowers. Ecology 62:20-26. Redmond, A. M., L. E. Robbins, and J. Travis. 1989. The effects of pollination distance on seed production in three populations of Amianthium muscaetoxicum (Liliaceae). Oecologia 79:260-264. Schemske, D. W. 1981. Floral convergence and pollinator sharing in two bee-pollinated tropical herbs. Ecology 62:946-954. Schemske, D. W., and C. C. Horvitz. 1984. Variation among floral visitors in pollination ability. A precondition for mutualism and specialization. Science 225:519-521. Schemske, D. W., and R. Lande. 1985. The evolution of self-fertilization and inbreeding depression in plants. II. Empirical observations. Evolution 39:41-52. Schmitt, J. 1983. Flowering plant density and pollinator visitation in Senecio. Oecologia 60:97-102. Sih, A., and M. Baltus. 1987. Patch size, pollinator behavior, and pollinator limitation in catnip. Ecology 68:1679-1690. Snow, A. A. 1982. Pollination intensity and potential seed set in Passiflora vitifolia. Oecologia 55:231-237. Snow, A. A. 1986. Pollination dynamics in Epilobium canum (Onagraceae): consequences for gametophytic selection. Amererican Journal of Botany 73:139-151. Stanton, M. L. 1987. Reproductive biology of petal color variants in wild populations of Raphanus sativus: I. Pollinator response to color morphs. Amererican Journal of Botany 74:178-187. Stanton, M. L. 1987. Reproductive biology of petal color variants in wild populations of Raphanus sativus: II. Factors limiting seed production. Amererican Journal of Botany 74:188-196. Stanton, M. L., and C. Galen. 1989. Consequences of flower heliotropism for reproduction in an alpine buttercup (Ranunculus adoneus). Oecologia 78:477-485. Stanton, M. L., A. A. Snow, and S. N. Handel. 1896. Floral evolution: attractiveness to pollinators increases male fitness. Science 232:1625-1627. Stanton, M. L., A. A. Snow, S. N. Handel, and J. Bereczky. 1989. The impact of a flower-color polymorphism on mating patterns in experimental populations of wild radish (Raphanus raphanistrum L.). Evolution 43:335-346. Thomson, J. D. 1981. Spatial and temporal components of resource assessment by flower-feeding insects. Journal of Animal Ecology 50:49-59. Thomson, J. D. 1985. Pollination and seed set in Diervilla lonicera (Caprifoliaceae): Temporal patterns of flower and ovule deployment. Amererican Journal of Botany 72:737-740. Waddington, K. D. 1979a. Quantification of the movement patterns of bees: a novel method. American Midland Naturalist 101:278-285. Waddington, K. D. 1979b. Divergence in inflorescence height: an evolutionary response to pollinator fidelity. Oecologia 40:43-50. Waddington, K. D. 1981. Factors influencing pollen flow in bumblebee-pollinated Delphinium virescens. Oikos 37:153-159. Waddington, K. D., and B. Heinrich. 1979. The foraging movements of bumblebees on vertical inflorescences: an experimental analysis. Journal of Comparative Physiology 134:113-117. Waser, N. M., and L. A. Real. 1979. Effective mutualism between sequentially flowering plant species. Nature 281:670-672. Willson, M. F., and B. J. Rathcke. 1974. Adaptive design of the floral display in Asclepias syriaca L. American Midland Naturalist 92:47-57. Wyatt, R. 1976. Pollination and fruit-set in Asclepias: a reappraisal. Amererican Journal of Botany 63:845-851. Young, H. J., and M. L. Stanton. 1990. Influence of environmental quality on pollen competitive ability in wild radish. Science 284:1631-1633. Young, H. J., and M. L. Stanton. 1990. Influences of floral variation on pollen removal and seed production in wild radish. Ecology 71:536-547. Zimmerman, M. 1979. Optimal foraging: a case for random movement. Oecologia 43:261-267.