* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Mechanistic Approaches to Community Ecology
Survey
Document related concepts
Island restoration wikipedia , lookup
Unified neutral theory of biodiversity wikipedia , lookup
Biodiversity action plan wikipedia , lookup
Overexploitation wikipedia , lookup
Habitat conservation wikipedia , lookup
Maximum sustainable yield wikipedia , lookup
Biogeography wikipedia , lookup
Storage effect wikipedia , lookup
Source–sink dynamics wikipedia , lookup
Landscape ecology wikipedia , lookup
Agroecology wikipedia , lookup
Ecological fitting wikipedia , lookup
Restoration ecology wikipedia , lookup
Soundscape ecology wikipedia , lookup
Deep ecology wikipedia , lookup
Reconciliation ecology wikipedia , lookup
Molecular ecology wikipedia , lookup
Transcript
AMER. ZOOL., 26:81-106 (1986) Mechanistic Approaches to Community Ecology: A New Reductionism?' THOMAS W. SCHOENER Department of Zoology, University of California, Davis, California 95616 SYNOPSIS. Mechanistic approaches to community ecology are those which employ individual-ecological concepts—those of behavioral ecology, physiological ecology, and ecomorphology—as theoretical bases for understanding community patterns. Such approaches, which began explicitly about a decade ago, are just now coming into prominence. They stand in contrast to more traditional approaches, such as MacArthur and Levins (1967), which interpret community ecology almost strictly in terms of "megaparameters." Mechanistic approaches can be divided into those which use population dynamics as a major component of the theory and those which do not; examples of the two are about equally common. The first approach sacrifices a highly detailed representation of individual-ecological processes; the second sacrifices an explicit representation of the abundance and persistence of populations. Three subdisciplines of ecology—individual, population and community ecology—form a "perfect" hierarchy in Beckner's (1974) sense. Two other subdisciplines—ecosystem ecology and evolutionary ecology—lie somewhat laterally to this hierarchy. The modelling of community phenomena using sets of population-dynamical equations is argued as an attempt at explanation via the reduction of community to population ecology. Much of the debate involving Florida State ecologists is over whether or not such a relationship is additive (or conjunctive), a very strong form of reduction. I argue that reduction of community to individual ecology is plausible via a reduction of population ecology to individual ecology. Approaches that derive the population-dynamical equations used in population and community ecology from individual-ecological considerations, and which provide a decomposition of megaparameters into behavioral and physiological parameters, are cited as illustrating how the reduction might be done. I argue that "sufficient parameters" generally will not enhance theoretical understanding in community ecology. A major advantage of the mechanistic approach is that variation in population and community patterns can be understood as variation in individual-ecological conditions. In addition to enriching the theory, this allows the best functional form to be chosen for modeling higher-level phenomena, where "best" is defined as biologically most appropriate rather than mathematically most convenient. Disadvantages of the mechanistic approach are that it may portend an overly complex, massive and special theory, and that it naturally tends to avoid many-species phenomena such as indirect effects. The paper ends with a scenario for a mechanistic-ecological Utopia. INTRODUCTION 1 ecology, and ecomorphology—as the basis constructing a theoretical framework Wlth w h l c h to interpret the phenomena of community ecology. The approach contrasts Wlth t h e "descriptive" one, in which community phenomena are represented by models with no lower-level derivations, but which have one or both of descriptive prowess and mathematical convenience. Of course, any given work may contain both mechanistic and descriptive elements, Hence m principle there exists a continuum of mixtures, although the distribution of actual studies may be bimodal. Somewhat informally, I will use "mechanistic" to to refer refer to to studies studies primarily primarily employing employing the the h, T-. h U dJ • .„ hi • • • for Community ecology is chronically among the most tumultuous and at the same time alluring of ecology's subdisciplines. Presently there is as much controversy over method as over fact (see symposia volumes by Strong et al, 1984; Price et al, 1984). During the past decade or so, a rather distinct methodology in community ecology, called the mechanistic approach, has been slowly coming into prominence. This approach can be most simply denned as the use of individual-ecological concepts— those of behavioral ecology, physiological , From the Symposium on Mechanistic Approaches to theStudyofNaJalCommunitiespresemedJLAnn^l Meeting of the American Society of Zoologists, 2730 December 1983, at Philadelphia, Pennsylvania. mechanistic approach. T h e designation mechanistic has been used in disciplines Other than ecology, inevitably with differ81 82 THOMAS W. SCHOENER ent meanings. For example, within behavior, it sometimes implies casting an explanation in terms of physiological or structural constraints rather than according to evolutionarily selected goals. Our usage of the term seems to have arisen gradually during the past decade or so, with independent roots in a number of the papers described in the examples section below. The movement appears to be one symptom of the increasing "particularization" of community ecology, in which biological differences (among others) between various systems are emphasized rather than ignored (Colwell, 1984; Schoener, 1985a). Disappointingly but not surprisingly, when the idea of this symposium was first exposed to the scientific public, there was substantial opposition. Two criticisms stood out. First, the mechanistic approach was deemed indistinguishable from the way ecology was normally performed; it had nothing new to offer—everyone did it as it was. Second, the mechanistic approach was pejoratively labeled "reductionist"; reductionist approaches have never worked in science, and they will not in community ecology either. No matter how cathartic, it is seldom wise to devote most of an article to rebutting one's grant reviewers. However, these two criticisms provide such excellent departure points for discussing the whole subject of mechanistic approaches that I have yielded to the temptation, as follows. The first part of this article describes in some detail a well-known approach to community ecology, that dealing with limiting similarity, which in original form is shown very close to the nonmechanistic end of the spectrum. This approach is contrasted in its procedures with the principal kinds of mechanistic approaches, using examples that include other papers in this symposium. Next, the question of reductionism is addressed. To do this, it is necessary to outline what philosophers of science mean by reductionism. To apply their conditions to ecology, it is useful first to decide upon what the various levels of ecology are, inasmuch as this is possible. The questions can then be asked, is the mechanistic approach reductionist, and to the extent that it is, is this a drawback or an advantage, or does it not matter? In performing this evaluation, I will be interested in what scientists and philosophers have said about reductionism in other areas of science, and whether characteristics of reductionism in general are usefully applied to issues concerning community ecology. Much discussion has already ensued over the question of whether biology can be reduced to physics and chemistry (e.g., papers in Ayala and Dobzhansky, 1974). More recently, a fair amount of discussion of the possible reduction of Mendelian and population genetics to molecular genetics has taken place (papers in Sober, 1984). However I think mine is the first paper considering in detail the possible reduction of community ecology, so that I am scouting new ground and will doubtless draw some fire. EARLY APPROACHES TO LIMITING SIMILARITY: A NONMECHANISTIC METHODOLOGY As the mechanistic approach has recently begun to infiltrate limiting-similarity concepts, we can obtain a purer example of nonmechanistic methodology by concentrating on relatively early papers. To this end, I will deal mainly with the 1967 paper by MacArthur and Levins (hereafter referred to as ML). The basic objective of ML is to specify, given a two-species community, whether a third species can invade; that is, whether its population will increase when initially rare to some stable equilibrium. The resident species are envisioned as being arranged along a single resource dimension with respect to the distribution (called the utilization) that describes how a species population uses resources. An example of a resource dimension is prey size, and the utilization can be thought of as a frequency histogram of population use for the various prey-size categories. The specific question of ML is whether or not the invading species can be sandwiched between the two residents. No changes of any kind in the utilizations are allowed; utilizations are taken as given. ML proposes that to answer this question it is sufficient to know a ratio of carrying capacities (specifically, that of the invader to that of either resident, the two COMMUNITY ECOLOGY latter being assumed identical) and a quantity labeled d/w. This quantity is the ratio of the distance between utilization peaks (assumed constant) to the niche width (the standard deviation of the utilization, again assumed identical for all species). Carrying capacities (K's) would be hard to measure in nature without an experiment, but in principle they can be measured. Where they are not measured, or for simplicity, they can be assumed equal for all species, in which case their ratio equals one. Utilizations are typically computed (as in Levins [1968]; also Mac Arthur and Levins [1967]) by observing a species population and noting the frequency of the population's aggregate use of resource items in the various resource categories. For example, if the resource dimension were prey size, one would observe (say by gut analysis) what food items a representative set of individuals from the population have eaten, then count the number of such items in each food-size category (say 1.1-2 mm, 2.1-3 mm, etc.) and divide by the total number of items to obtain the frequencies (the p's). In short, ML offers a very simple protocol to determine quantitatively the possibility of community invasion. To understand how this protocol can be so simple, we need to sketch its derivation. Assume that species are competing according to the Lotka-Volterra competition equations. Assume that the parameters a in these equations can be calculated as 2 (1) where pjh is the frequency of the utilization of Species i in Resource Category h. Then the Lotka-Volterra equations are used to calculate those combinations of a's and K's just allowing coexistence (the limiting similarity). With the use of eq. 1, those combinations can be related to the p's, which compose the utilizations. Finally, assuming that the utilizations are normally distributed, the p's in turn can be related to d/w, the ultimate unit in which limiting similarity is expressed. Note that this derivation, while using population-dynamical equations, does not 83 require that we draw on the data or theory of behavioral or physiological ecology. It is possible to justify eq. 1 in behavioral terms, but in fact the simplest such justification involves many more parameters than the p's (Schoener, 1974a); the p's occur as a kind of scaffolding around which these other parameters are placed (see below). Eq. 1 then is justifiable only as a limiting case, i.e., when all additional parameters are identical and cancel out. Moreover, it is possible to interpret the Lotka-Volterra equations in behavioral or physiological terms, but only at equilibrium for resource competition (see below), and in any event this was not done either in the equation's original derivation or in ML. Persons not familiar with community ecology may at this juncture have the impression that the ML protocol has been demonstrated to work enough of the time so that it can be called an "experimental law" sensu Nagel (1961; see below), or at least some assumptions used in its derivation can be called experimental laws. In fact, as is so often the case in community ecology, these are more nearly "hopeful laws" rather than laws; they are proposals about nature that remain, for the most part, to be supported with evidence. As we shall illustrate in part, they have sometimes not in fact been supported for particular systems—it is a matter of some debate whether they can even be called "statistical laws." Nonetheless, they do constitute theoretical concepts, and their lack of strong support does not prevent us from examining them from a philosophical standpoint. Five problems with the assumptions used in the derivation of the ML protocol may help explain its tenuous position with respect to nature (see also Abrams, 1983). 1. The assumption that utilizations are normal, when relaxed, can change radically the d/w just allowing coexistence (Roughgarden, 1974). 2. The assumption that all utilizations are identical, when relaxed, allows variation from the original predictions (McMurtrie, 1976). 3. The assumption that a can be calculated using eq. 1, when relaxed, can give quite different values of limiting d/w; there 84 THOMAS W. SCHOENER is a systematic tendency for sensible variation in eq. 1 to give smaller d/w's (Abrams, 1975). 4. During the process of competition, individuals may modify their per-unitresource consumption rates, so that utilizations will not be constant. 5. The Lotka-Volterra equations may not actually describe the population dynamics of competition, in which case there may be no "a" as such, and either a linear approximation only valid near equilibrium must be used or a whole new approach invented (see below and Abrams, 1980a). Although numerous other complications exist (see Abrams, 1983; Schoener, 19856, for reviews), I have listed the above five, in order of increasing potential for undermining the ML protocol, to set the stage for a demonstration of how behavioral and physiological information can be used to determine their seriousness. To evaluate Points (1) and (2), it would be essential to know something about the consumption of resources at the individual level—for example, when are utilizations leptokurtic (peaked, with thin tails) in terms of the feeding behavior of individuals? To evaluate Point (3), we would like to know what set of assumptions concerning how individuals use resources and how energy gained from that use is converted into offspring will give eq. 1 literally, and what will not. We need to know the same kind of information to evaluate Point (5). To evaluate Point (4), we need to know (say from foraging theory) whether the probability of consuming a unit of a particular resource kind changes as the number of such resource units is affected by the action of competing individuals. We shall now see to what extent mechanistic approaches to community ecology help avert these and similar problems characteristic of nonmechanistic approaches. MECHANISTIC APPROACHES: SOME EXAMPLES I would like to divide mechanistic approaches to community ecology into two groups, those which explicitly include population dynamics in their formulation and those which do not. As the latter are somewhat more straightforward than the former, I begin with them. Approaches that exclude population dynamics 1. Werner and Hall (1976, 1977, 1979; Werner, 1984). Ecologists have long observed that given species have different habitat distributions in the presence than in the absence of other species; in particular, habitats of sympatric forms are often less similar than those of allopatric forms (review in Schoener, 1985). This phenomenon has been investigated in two ways. First, habitat distributions from places where a given species does or does not coexist with one or more other species are compared (e.g., Crowell, 1962; Keast, 1970; Schoener, 1975; Lister, 1976). Second, experimental addition or removal of species is performed and subsequent habitat shifts noted (review in Schoener, 1983). The commonest explanation for habitat shift is that it results from some kind of competition, either consumptive (via resource depletion), pre-emptive (via passive competition for space), or some form of interference (e.g., territorial, encounter; all terms sensu Schoener, 1983). Such competition could act at the behavioral level or at some higher level. Patterns discovered by the comparative approach are typically the end result of ecological or even evolutionary processes. Most experimentally produced habitat shifts, in contrast, must necessarily be behavioral responses, given their short-term nature. Even for those, however, the exact mechanism of the competition, and a clear idea of how to predict the occurrence and degree of habitat shift, remained largely unknown until the work of Werner and Hall with sunfish. Werner and Hall related habitat shift to optimization of feeding intake by individual fish, as follows. First, they showed that individuals of each of three species when by themselves preferred the vegetated habitat. Then they placed individuals of the species together and found that those of one species shifted into open-water habitat, those of a second shifted into bottom COMMUNITY ECOLOGY habitat, and those of the third stayed in the vegetated habitat. They calculated the energetic gain per unit time of staying in the vegetated habitat with a competitor vs. moving to a new habitat. By assuming that individuals maximize their rate of net food energy intake per unit feeding time, they correctly predicted which species would shift out of the vegetation and the point (in terms of food density) at which each did so. These experimental results paralleled the habitat distributions of the species in unmanipulated field situations. Small discrepancies in the predictions were attributed to aggressive behavior between individuals. 2. Pulliam (1986). Pulliam is concerned with seasonal shifts in niche overlap among coexisting sparrow species. Such shifts have been explained from two intersecting theoretical perspectives. One perspective is behavioral: the compression hypothesis (MacArthur and Wilson, 1967) and related ideas of foraging theory predict, again on the basis of maximizing energy per unit time, the nature of diet and habitat shifts and expansions. The other perspective is evolutionary; the morphological and behavioral adaptations of individuals are constraints on their feeding abilities, in the sense that different phenotypes have different feeding costs over an array of food and habitat types. Given that such adaptations have evolved in response to conditions during one season rather than another, seasonal variation in ecological overlap can be given an evolutionary explanation (Schoener, 1982). By measuring certain behavioral quantities necessary to evaluate feeding profit, e.g., husking time, Pulliam was able to show that both theoretical perspectives contribute toward explaining niche overlap in sparrows. 3. Price (1986; Price and Waser, 1984, 1985). Price's work is similar to Werner and Hall's but is framed somewhat more generally. Various heteromyid rodent species show different habitat distributions in the North American Sonoran desert. These distributions can be hypothesized as resulting from 1) differential abilities to harvest resources in different habitats (as in Werner and Hall, 1979) or 2) differen- 85 tial abilities to avoid predators in different habitats. By a study of individual feeding abilities on types of seeds found in the various habitats, by creating artificially "seeded" habitats in nature and examining subsequent heteromyid preferences, and by detailed field observation of individual escape abilities in the various habitats, Price hopes to demonstrate which, if any, of the two hypotheses explains the heteromyid habitat distributions in nature. Results to date indicate that different species selected patches with different soil textures, in turn interpretable on the basis of rodent size and locomotory attributes. Predictable habitat shift by the rodents was induced by artificially altering soil-patch types (Price and Waser, 1985). 4. Moermond (1979, 1986). The ML approach as outlined above is not concerned with the question of why utilizations are placed where they are on the resource axis, or why they have the shape they do. To explore such questions, one can take a variety of tacks, some of which are nonmechanistic. For example, by using certain very general assumptions about how evolution works (e.g., it maximizes population density, Roughgarden, 1972), shifts and other changes in utilizations that are responses to competition can be modeled. Initial attempts in this direction (e.g., Roughgarden, 1976; Slatkin, 1980) did not use individual-ecological concepts to justify their assumptions; the latter were sometimes induced from observations, and in that sense were "experimental laws," albeit highly statistical ones. Other assumptions (e.g., like eq. 1) were simply assumptions, not well justified empirically or conceptually. More recent theoretical approaches to evolutionary changes in utilizations do use individual-ecological justification for certain assumptions (e.g., Case, 1982). None of the approaches just discussed, whether entirely or partly nonmechanistic, is concerned with the degree to which, independently of resource abundance, certain resource categories are more effectively used by consumers than others. Moermond's approach is to analyze habitat dimensions from a functional-morpholog- 86 THOMAS W. SCHOENER ical standpoint; he asks what sorts of habitat distributions for individuals are and are not likely, given functional-morphological constraints. For example, no matter what their special adaptations, arboreal lizards are able to jump so far and no farther; this limits how they get around in the vegetation, in turn constraining the degree of generalization possible. Moermond's approach identifies a number of locations in habitat-niche space that are relatively "easy" to occupy purely from the standpoint of locomotory abilities. These locations give an expectation of where in a noncompetitive niche space species utilizations are most likely to be found. This initial picture forms a mechanistically based null expectation to which competitive effects can then be added where necessary to produce the final community configuration. 5. Schluter and Grant (1984). Schluter and Grant's approach is very similar to Moermond's in its general objectives. Rather than lizards, however, Schluter and Grant studied finches, and rather than being concerned with habitat dimensions, they were concerned with the food-size dimension. They were able to show that variation in beak depth within and between species from one Galapagos island to another is predictable (with a few exceptions) from variation in the availability of differently sized seeds. The necessary calculations for such predictions involve behavioral data in a fundamental way: seedharvesting abilities of individuals having different beak sizes are measured (Schluter, 1982), and a particular sized individual is expected on a given island which can attain the highest population density (vide Roughgarden, 1972) for its particular spectrum of seed sizes. Schluter et al. (in preparation) were able to use these results as a basis with which to examine evolutionary effects of interspecific competition. Approaches that include population dynamics The preceding five approaches by and large do not include population concepts as major components in their theoretical accounting for community phenomena, a partial exception being the assumption Schluter and Grant make about density. In particular, no study explicitly employs population dynamics—the dynamics of birth and death, and of immigration and emigration—as part of a theoretical explanation. The major problem in not so doing is as follows. Individuals may optimize some aspect of their performance, e.g., maximize net food-energy intake per unit feeding time, yet not be able to maintain a population in the habitat of interest. Ultimately, what determines the abundance of a species in some place is how net food energy is converted into offspring, and how that energy can be used to promote survival in comparison to how survival is reduced by the increased exposure to predation or other risks that foraging entails. Because there are often very strong relationships between optimizing a behaviorally defined currency and maximizing individual fitness (Schoener, 1971), which itself can be related to population characteristics, this problem, while serious, is far from a fatal flaw. A second problem is that concentration on individual behavior and physiology emphasizes what has been called (Van Valen, 1965; Roughgarden, 1972) the within-phenotype component of population variability. Phenotypes are treated seriatim: they are compared with respect to their fitnesses but are essentially considered as alternatives rather than as possibly coexisting in a population. However, to understand completely why a population's utilization has a particular set of properties, one needs also to know the betweenphenotype variation, and the latter is very much of a population-ecological trait, determined by the scheduling of births and deaths as it affects age structure, by how constraints such as sexual reproduction affect the inheritance of phenotypic variability, and so on. A second class of approaches, the one we are about to discuss, explicitly includes population phenomena, particularly population dynamics, as a major theoretical tool. Approaches of this class, however, are not necessarily superior to those discussed in the last section; they too entail certain COMMUNITY ECOLOGY disadvantages, especially for higher organisms. Evolutionary aspects are often not considered of primary interest; rather, traits are plugged into ecological models with little interest in their evolutionary underpinnings. Moreover, such individualecological complexity typically must be subsumed into a limited number of population parameters—while the models used in population-dynamical approaches are based on mechanistic considerations, they still often simplify greatly. For example, the shifts in resource type (e.g., seeds, habitats), which are the fundamental phenomena certain of the above studies are trying to understand, are assumed not to occur in many of the population-dynamics approaches. Because extant differences between these two approaches are more a matter of emphasis than anything else, the two sorts of approaches might ultimately be combined, a union that has been mostly avoided up to now probably because of the increased complexity that would be entailed. As we shall see below, certain studies provide partial exceptions to this generalization. 6. Tilman (Titman, 1976;Tilman, 1977, 1982, 19866). Tilman's (Titman, 1976; Tilman, 1977) research with diatoms concerned the question of the coexistence of competitors, the same question attacked by MacArthur and Levins. Tilman's approach was quite different, however. He took advantage of the fact that growth of many microorganisms on specific nutrients can be represented by the Michaelis-Menten equation, a relatively simple model having only two parameters. By determining Michaelis-Menten parameters for each of two species of diatoms on each of two nutrients, he could predict under what combined nutrient regimes one or the other species would win in competition, and under what regimes the species would coexist. Coexistence occurs under combinations in which each diatom species has its growth limited by a different nutrient. In addition to verifying his predictions in laboratory experiments, Tilman could show that certain phenomena in the field are fairly consistent with them (but see Sell et al, 1984; Tilman et al., 1984). 87 Tilman (1982, 1986a, b) later extended his ideas to terrestrial herbaceous plants. He is engaged in testing the general proposition that spatial variation in the identity of the dominant species can be explained with mixed-nutrient models similar to those used for diatoms. So far in such models, only the equilibrium situation is considered: the dynamics leading to equilibrium are not made explicit. Nonetheless, the models approach community questions via population models in turn based on physiological considerations. 7. Schoener(1973, 19746, 1975, 1976, 1978). Over the past decade, I have developed a set of competition models that are alternatives to Lotka-Volterra models. Unlike the latter, the alternative models typically generate non-linear zero-isoclines. Using relatively simple terms, they attempt to represent the various components of competition more isomorphically than does the Lotka-Volterra model, used primarily because of simplicity and supposed descriptive prowess. For example, the simplest term for resource division is I/(N, + /3N2), where I is the amount of resource to be divided, N, and N2 are the number of individuals of Species 1 and 2, respectively, and /3 is the ratio of the resource consumption rates of an individual of each of the two species (Schoener, 19746). By contrast, interference is assumed proportional to terms in Nj, as would be the case for "encounter" competition, in which deleterious interactions between individuals occurred randomly. More complicated terms for resource division can be derived from submodels of how competitors consume resources. Other terms concerning how energy is converted into offspring also occur in the models, although these are very primitive. The models were initially tested in a study of habitat shift in Anolis lizards; more recently, they have been tested by Belovsky (1984a, b, 1986) and Rasmussen (1983), among others. Their common characteristic, concave zero-isoclines, is in qualitative agreement with most competition data from the literature (e.g., Ayala et al., 1973; Quinn, in preparation). A related set of models, in which inter- 88 THOMAS W. SCHOENER ference is the only form of competition, leads exactly to the Lotka-Volterra equations (Schoener, 1973, 19746). In the sense to be explained below, this constitutes a derivation of the Lotka-Volterra model and has as a by-product the decomposition of its parameters, r, K and a, in terms of microparameters describing feeding abilities and time budgets, themselves parameters of behavioral ecology. 8. MacArthur(1968), Schoener (1974a, b). In contrast to the models discussed in the last section, which all involve a single trophic level, MacArthur represented the dynamics of each consumer and resource by a separate equation. The behavior of such an equation system away from equilibrium can be very complex (Case and Casten, 1979), but as MacArthur showed, the equations can be collapsed at equilibrium into Lotka-Volterra form. In the same sense as just discussed, this is also a derivation of the Lotka-Volterra model, but at equilibrium only (see Schaffer, 1981, however, for conditions on its approximate validity elsewhere). Again, one may obtain expression for r, K and a in terms of microparameters, but these are valid only at equilibrium. The expression for a is of special interest. Schoener (1974a) later showed that it contained the utilizations (the p's) in exactly the same places as they occur in eq. 1, but in the company of various other parameters having to do with resource availabilities, overall rates of consumption by individuals, and conversion rates of food into energy. A similar collapse of another set of consumer-resource equations was performed by Schoener (19746); this yielded a derivation at equilibrium of some of the nonlinear-isocline equations discussed in the previous section. 9. Holt (1983). In an entirely theoretical treatment, Holt investigated the constraints that optimal foraging of individuals places on population models of predator-prey interactions. Holt assumed two prey and one predator and analyzed the shape of the predator isocline. This isocline is a curve connecting all values of the number of Prey Species 1 and the number of Prey Species 2 that give a fixed yield to the predator. Ecologists have generally assumed that this isocline has negative slope; when it has positive slope, curious effects can occur, such as one predator increasing its population size when another predator eats more of one of its prey. Holt concluded that while many assumptions about foraging behavior do lead to negatively sloped predator isoclines, predators that must spend much time discriminating between prey of unequal value or that show switching behavior (Murdoch, 1969) may give positive slopes. In short, Holt explicitly related feeding-behavior considerations to population-community models. 10. Abrams (1982); Sih (1984). The "functional response" describes the relationship between the number of prey consumed per predator and prey density. The form of the functional response has profound consequences for the stability of predator-prey interactions, and ultimately, for community composition (Murdoch and Oaten, 1975). Theoretical papers by Abrams (1982) and Sih (1984) explore how various feeding strategies affect the functional response curve. Abrams showed that the proportion of time spent feeding makes a great deal of difference to the shape of the functional response. Sih examined how variation in foraging area, foraging speed, overall foraging time, and time spent foraging in risky but energetically profitable places affects the functional response. In general, if these behavioral parameters increase with prey density, a functional response that stabilizes the predator-prey interaction is favored. Time minimizers (sensu Schoener, 1969) and certain classes of energy maximizers (e.g., those not near satiation) are argued likely to show this increasing relation and hence to contribute toward community stability. As in Holt's (1983) paper, explicit connections are made between behavioral parameters and those of population dynamics; the former are used to characterize variation in the latter. 11. Belovksy (1984a, 1986). Like Tilman, Belovsky was able to show that the outcome of competition could be quantitatively predicted using mechanistic equations in which the parameters were those expected from individual-ecological con- COMMUNITY ECOLOGY siderations. Unlike Tilman's diatoms, however, Belovsky dealt with organisms at the peak of the phylogenetic scale, i.e., mammals. Belovsky first fitted several of Schoener's (19746) resource-competition models, and the Lotka-Volterra model, to experimentally generated field data on competition between moose and hare. The free parameters were simultaneously adjusted by nonlinear regression to produce the best fit to the data, which comprised the population sizes of each species. He determined that the model having overlapping and exclusive resource terms was best. Using the empirically determined parameters of that model, he was able to obtain estimates of the amounts of overlapping and exclusive resource. Belovsky next calculated the same quantities from his model of food selection, a model which he had previously shown (Belovsky, 1978, 19846) to fit dietary data from individual moose and hare. The quantities calculated by this second, entirely independent, method were very similar to those obtained from fitting the population data, thereby providing a striking consistency. In a separate analysis, Belovksy (1986, in preparation) used similar models to predict the number and sizes of generalized herbivore species that can coexist in a community. Here, food quality and food size were the axes of resource separation, and limitations of an individual's physiology and morphology determined how much of the resource could be utilized by a given sized herbivore. In particular, large herbivores require large food items (large bulk per bite) but can get away with eating food of low quality (low digestibility); small herbivores are the opposite. The handling time of individuals, their metabolic requirements and their digestive rates are all relevant to determining each sized herbivore's position on the two resource axes. Here, behavioral and physiological quantities are related to community ecology in an entirely explicit way. 12. Abrams (19806, 1981a, 6). Another very detailed application of a mechanistic competition model was performed by Abrams on hermit crabs. These organisms use empty molluscan shells for protection, 89 and as such shells are generally scarce, they are often proposed as a limiting resource. To investigate this proposal precisely, Abrams (19806) first constructed a differential equation describing the dynamics of the shell resource. This expression at equilibrium was used to derive a "competition ratio," similar to the competition coefficient discussed above, which like the latter expresses the relative intensity of inter- to intraspecific competition, all taken percapita. The competition ratio was checked by marking shells and following their fate in the field (Abrams, 198 la); the two methods gave very similar results. Competition ratios were then calculated for species in various communities and found to be lower than those anticipated from previous studies on other organisms (Abrams, 1981a, 6). In short, this study used a mechanistic model, tailor-made for the hermit-crab system, in place of the ML protocol to determine relative competition intensity and thereby help explain the identities of coexisting species. 13. Spiller (1986). Very recently, Spiller was able to evaluate experimentally the simple ML expression (eq. 1) for the competition coefficient and the more complicated expression that Schoener (1974a) derived from the Mac Arthur (1968) consumer-resource equations (#8 above). Using field observations, Spiller separately evaluated each term in the two expressions for two syntopic spider species in a salt marsh. He then did a series of controlled manipulations in which he was able to measure directly the magnitude of the competition coefficient. The more complicated Schoener (1974a) expression matched the experimentally determined a's rather well, but the ML expression (eq. 1) failed even to match the relative magnitudes of the a's. Thus the more mechanistic expression was shown far superior in predicting the effects of competition. In conclusion, the above review (which is incomplete) shows that mechanistic approaches are used in a wide variety of systems, are mostly very recent, and can take on various specific methodologies. The discussion also makes clear that our meaning of the term "mechanistic" is in some 90 THOMAS W. SCHOENER ity, in which terms not in the to-be-reduced science must be related to terms in the reducing science. These relationships can take three forms: 1) logical connections between established meanings, 2) conventions, or definitions; and 3) facts, i.e., relations established empirically. The second condition is derivability, in which all laws of the to-be-reduced science, including those with terms not in the reducing science, must be derivable from the theoretical princiREDUCTIBILITY OF COMMUNITY ECOLOGY ples of the reducing science, using where Formal conditions for the reduction of necessary the connectability relationships. one area of science to another Various difficulties with Nagel's criteria While most philosophers (review in have been summarized by Wimsatt (1980a; Wimsatt, 1980a) now advocate a broader see also Hull, 1976). On the one hand, the concept of reductionism than did Nagel use of approximations makes a literal exe(1961) in his classic work, Nagel's formal- cution of Nagel's conditions problematical ism, because of its precision and primacy, (in what sense are they logical deductions?) is an attractive place for our discussion to and jeopardizes most conceivable realizabegin. In general, "a reduction is effected tions in actual science. On the other hand, when the experimental laws of the second- if such difficulties can be overcome, the inary science (and if it has an adequate the- principle satisfying of Nagel's conditions ory, its theory as well) are shown to be the may generally be possible, even though the logical consequences of the theoretical in-practice realization may be too complex assumptions . . . of the primary science" to be useful to science and may merely sat(Nagel, 1961, p. 352). By experimental law, isfy a philosophical desire for ontological Nagel means generalizations about the simplification. Because scientists seem often phenomena of the science in question, to show reductionist behavior, broadly whether they be absolute or statistical. An construed, Wimsatt (19766, 1980a) argues example of an absolute experimental law that rather than emphasizing Nagel's idealis "lead melts at 327°C." Nagel distin- ization, we should adopt a broader charguishes "theoretical laws" or "theories" acterization which corresponds more from experimental laws (I.e., p. 32) as state- closely to the actual practice of science. ments "whose basic terms are not associ- Toward this end, Wimsatt (1976a, b) proated with definite experimental proce- poses "explanatory" reduction, in which dures for applying them . . . so that a theory one has "an explanatory relation between cannot be put to direct experimental test" a lower-level theory or domain of phenom(I.e., p. 85). An example of a theoretical ena and a domain . . . of upper-level phelaw would be a statement dealing with the nomena" (Wimsatt, 19766, p. 220). Furatomic theory of matter. Nagel admits the ther, one "attempts to identify or explain distinction is in some ways not hard and the upper-level whole and its properties fast, and given the statistical and often with or in terms of a configuration of lowerweakly verified nature of "laws" in ecol- level parts and their known monadic or ogy, it is even looser here than it is in phys- relational properties" (Wimsatt, 19766, p. 208). A consequence of Wimsatt's modiics and chemistry. fication is that practical aspects of reducA problem with reduction can be that tionism, e.g., "research strategies," are the laws of the science to be reduced may emphasized over formal aspects; if the contain terms not found in the reducing lower-level characterization becomes too science. Under such circumstances, reduc- intricate or cumbersome, it is no longer tion can be said to be effected formally explanatory. when the following two conditions are met (I.e., pp. 353-354). The first is connectabil- My tactic in this section is to evaluate ways quite different from its other meanings in biological parlance (as in Nagel, 1961, p. 428 ff). Advantages to the above approaches are already obvious simply from their descriptions, but I will defer coalescing them into a summary until the penultimate section, after the issue of reduction is dealt with formally. Those uninterested in philosophical issues will not miss much by going directly to that section. COMMUNITY ECOLOGY how closely Nagel's conditions might be met by a mechanistic approach to community ecology. I will try to show that, while of course community ecology has not been reduced in toto, some prototype reductions exist for certain of its aspects that appear explicitly to satisfy Nagel's conditions in most major ways. In so doing, I will be trying out the notion that to the degree Nagel's conditions are met by extant mechanistic approaches without excessive postulation of links and deductions not now existing, and without excessive complexity, the reduction is usefully explanatory. The existence and success of such prototype reductions, I will argue, makes a much broader reduction at least plausible. Levels of ecology To attempt application of Nagel's conditions, we must first decide what the various subdisciplines of ecology are; each of these will then be considered a separate "science" in the above terminology. Moreover, as reduction proceeds from "higher" to "lower" sciences in some sense (Medewar, 1974), we need to arrange the subdisciplines, inasmuch as possible, into a hierarchy of levels. Hierarchies are perhaps best defined with respect to objects, such as organisms or populations, which are in fact the "parts" composing the various levels. I am going to assume in what follows that these "parts" are the objects of principal focus with respect to a particular subdiscipline, rather than being any kind of object that is mentioned in the phenomenology or theory of the subdiscipline. Hence, "term" is obviously a more inclusive label than "part." Beckner (1974) has stated the formal conditions for a perfect hierarchy as follows: (a) every part P; is assigned to exactly one level L;; (b) every part Pj (except those of the highest level) is a part of exactly one part at each level above L(; and (c) every part P; (except those of the lowest level) is exhaustively composed of parts at each level below L,. I will now attempt to show that while a 91 perfect hierarchy exists for a subset of ecological subdisciplines, not all such subdisciplines are members of a perfect hierarchy. This is despite the fact that one of the latter subdisciplines is often considered to deal with the highest level of ecology. The three disciplines of ecology that, when narrowly enough constructed, do form a perfect hierarchy, are individual ecology (the parts are individuals), population ecology (the parts are single populations, defined as those individuals in some place belonging to a single species) and community ecology (the parts are collections of populations occurring in some place). Individual ecology is itself decomposable into physiological, behavioral, and functional-morphological ecology; all such disciplines focus on the individual but have somewhat different objectives and theoretical structures. Population ecology deals with single species populations one-at-atime. Phenomena of interest include kinds of items in the diet, behavioral and physiological thermoregulation, territory size and mating strategies. The phenomena of interest in population ecology are aggregate properties of the individuals composing the population; examples are age structure, sex ratios, growth rates and reproductive schedules. Community ecology deals with a group of populations in some place. Here the aggregate properties of interest concern the various species populations: abundance distributions, species diversity, species-turnover rates, and soon. These three kinds of ecology satisfy all of conditions (a)-(c), at least ideally. That condition (a) is satisfied follows from the definition of the subdisciplines. That (c) is satisfied follows from the definitions of populations and communities. Condition (b) is satisfied if communities comprise mutually exclusive populations. Because communities are in practice rather arbitrarily and dissynchronously defined, this need not be the case, but one might imagine that a study by a consortium of researchers would designate communities in this fashion, and if the world's communities were ever catalogued, that they would consists of non-overlapping populations. 92 THOMAS W. SCHOENER A fourth subdiscipline of ecology, often considered the highest level, is ecosystem ecology. The parts are ecosystems; an ecosystem is denned as a community or communities plus the physical environment (Whittaker, 1975). Once the physical environment is brought into the picture as a part, condition (c), that each level is exhaustively composed of parts from lower levels, is clearly violated. One might try to argue that physiological ecology also has "parts," e.g., environmental input such as solar radiation, that are purely physical; if so, however, then individual ecology would violate condition (b) and the perfect hierarchy would be destroyed from below. For reasons expressed in the following paragraphs, I prefer not to think of physiological ecology this way, and I would argue that ecosystem ecology is skewed aside from the hierarchy from individuals to communities. For the sake of completeness, a final subdiscipline of ecology is often recognized— evolutionary ecology. It can be defined as that portion of the larger science of evolutionary biology which is relevant to ecology. (One might simply recognize evolutionary biology as the "science" in question, but I am trying to relate terms used here to those commonly found in the literature.) I see evolutionary ecology as arranged almost entirely laterally with respect to ecology's other subdisciplines, and certainly not in any perfect hierarchy. It is not so clear what the "parts" of evolutionary ecology are. If they are alleles and/or genotypes, and if evolutionary ecology were the lowest level, then condition (c) is violated. If its "parts" also include individuals and populations, then condition (a) is violated, and either or both of conditions (b) and (c) are also violated. Less formally, some ecologists are interested in evolutionary phenomena at various levels: the individual, the population, and the community {e.g., Lewontin, 1970; Wilson, 1980). All this may mean that evolutionary ecology is better considered a "perspective" (in Wimsatt's [19766, p. 254] sense; for more on identifying boundaries of sciences, see Dardenand Maull [1977]). As mentioned, the rationale for propos- ing a hierarchy is that typically reduction is attempted from higher-level sciences to lower-level sciences. However, the fact that one science stands higher than another in a perfect hierarchy is neither a necessary nor sufficient condition for reduction of the higher to the lower science. Levels are defined with respect to parts; reduction is defined with respect to theories. Hence reduction may or may not be possible, given a perfect hierarchy (Beckner, 1974). It is also false to argue that if sciences are not in a perfect hierarchy, one cannot be reduced to another. One might be misled by making the argument that parts in the higher-level science may not be exhaustively composed of parts in the lower-level science; therefore connectability is violated. But connectability refers to "terms," not "parts"; the former is a more inclusive category than the latter, so that even if there are "parts of parts" in a higher-level science not occurring as parts in the lowerlevel science, they may still occur as terms at the lower level, or at least be relatable to terms at the lower level. A related complication is that the theoretical structure of a particular ecological subdiscipline may include as "terms" those predominately used at higher levels, or even include the "parts" of higher levels. For example, in models of the costs and benefits of territorial defense, a major conceptual issue in individual ecology, the term "rate of intrusion" is necessary. In turn this term is strongly related to "number of individuals in a population," a term of major explanatory focus in population ecology. But the fact that there exists another subdiscipline of ecology devoted to explaining such properties as population number need not destroy the integrity of lower-level subdisciplines using those terms: In individual ecology, population number might simply be considered an input parameter in the same sense as radiant energy or some other physical quantity whose etiology is unnecessary for some kind of explanation in that subdiscipline. On the other hand, there might exist some "metatheory" spanning several disciplines such that, for example, understanding population phenomena may contribute to predic- COMMUNITY ECOLOGY tive power at the individual level (see also below). More generally, the subdisciplines that we showed stand in a perfect hierarchy on the basis of their parts may not have entirely discrete bodies of theory. Moreover, if in some sense theories can be said to be hierarchical, a perfect hierarchy denned with respect to parts may not imply the equivalent sort of hierarchy with respect to theories or descriptions (Wimsatt, 1974). More on the relationship between hierarchical phenomena and hierarchical theories is given below in the section on emergent properties. In short, our analysis of levels has left entirely open the question of the reducibility of ecology's subdisciplines. We now attack that issue directly. Formal reducibility of community ecology This section considers the possible reductive relationships between community ecology, population ecology and individual ecology. I will first attempt to show that the population-dynamical approach to modelling community-ecological phenomena makes a reduction of community to population ecology plausible. I will then attempt to show how much if not all of the theoretical model-structure of population ecology might be reduced to individual ecology. Community phenomena such as numbers of species and their abundance distributions can in principle be understood by analyzing a set of differential (or difference, or hybrid) equations, each having the abundance of a component species as the dependent variable. For each such equation, independent variables may include population abundances of other species on the same trophic level and/or on different trophic levels and physical quantities such as the supply of some nutrient. The equations represent changes in abundances through time, as these are affected by the independent variables and parameters through births, deaths, immigrations and emigrations. Such equations in fact compose a large part of the theoretical machinery of the subdiscipline population ecology. Certain phenomena of interest there, e.g., population growth, are directly rep- 93 resentable by such equations; others, such as age structure, are representable by a more extensive set of equations whose output can be combined to give changes in total number of individuals in a population. So commonplace is the use of such equations in community ecology that it is easy to miss that this usage in fact may automatically constitute a reduction of that subdiscipline to population ecology. To be convinced that this interpretation makes sense, it is helpful to imagine theoretical approaches in community ecology that do not involve population-dynamical equations. A number of prominent ones exist, including the early MacArthur (1960) broken-stick models for species abandances and the MacArthur-Wilson (1967) theory of island biogeography. The fact that the first has been declared obsolete by its founder (MacArthur, 1966) and the second by Williamson (1983) may indicate a general trend of declining popularity of such models. Although many, myself included, are far from ready to write off the second as yet, replacement of MacArthur-Wilson dynamics (where the dependent variable is number of species) with population-dynamical models is certainly conceivable. All this illustrates that the reduction of community to population ecology is far from complete, although it is plausible that it will eventually become entirely or nearly so. A second difficulty for the just-proposed course of reduction is that a theory having to do with evolution in communities (e.g., character displacement) may not be representable using models whose variables are of the kind listed above. Because the same problem arises for the reduction of population ecology, I discuss the two together below. A much stronger kind of reduction of community ecology to population ecology would occur were there to exist no experimental laws or valid theoretical laws that in any major way entail interactions between species populations. Something like this view has been favored by ecologists from Gleason (1926) to Simberloff (1983; see Simberloff, 1980, for the weakest of disclaimers). The latter writes, for 94 THOMAS W. SCHOENER number of existing systems, to make a statistically valid generalization. I will next try to demonstrate that the reduction of population to individual ecology is plausible and already has some prototypes among mechanistic approaches that incorporate population dynamics. Approaches in the other class are in present condition not suitable as they contain no terms for births and deaths. They would thus violate Nagel's condition of connectability unless suitable extensions were made (in Schaffner's [1974] sense), in which case they would converge to the populationdynamical approaches (see above). Moreover, I will argue that the consequent formal transitivity from community to individual ecology is sufficiently simple as to result in a useful explanatory reduction (sensu Wimsatt, 1976a) of community to individual ecology. The key condition to showing a reduction of a population-ecological theory to an individual-ecological one is as follows. Each parameter of the population-dynamical equations employed at the higher level must be able to be translated completely into individual-ecological (behavioral and physiological) parameters. A single community-ecological parameter may correspond to one or more individual-ecological parameters, and the latter can be arranged in any functional form. It is this identification, I shall argue, that ultimately can be A lot of the controversy in present-day interpreted as meeting Nagel's two critecommunity ecology can thus be viewed as ria. about the strong reducibility of community Let us assess this condition in detail. The to population ecology, i.e., whether or not population-dynamical equations employed species populations are additive or con- in the theory of population and community junctive. If Simberloff and colleagues can ecology are often "descriptive," in the sense show that species interactions are minor, that they are not derived but are chosen then community ecology will cease to exist as the mathematically most convenient as an interesting theoretical discipline. As expression that might in a very qualitative is well known among ecologists, many per- sense embody the appropriate ecological sons, myself included, strongly oppose the effect. Rarely are they chosen because they view that anything like this has been shown have been shown in an extensive number or even that recent research results are of cases to fit ecological data. Hence, they headed in that direction (e.g., Schoener, should not be regarded as "experimental 1982; Roughgarden, 1983; Quinn and laws," in the sense such terms have in physDunham, 1983; Schoener, 1983; Connell, ics. An example of such an equation (for 1983; Paine, 1984). The only reason the population ecology) is the logistic equation issue is not yet settled is that so little of single-species population growth. This research has been done, relative to the equation is written example, "we are asking if species' individual responses to the physical environment suffice to explain their distributions" (Simberloff, 1983). If it can be shown that neither vertical (e.g., predation) nor horizontal (e.g., competition) connections in the food web are very important, then the ecology of single-species populations is sufficient to explain the phenomena of focus in community ecology—species diversity, relative abundances of species, species turnover, and so on. (Notice that almost certainly predation and competition will be shown either both important or both unimportant, as they march in logical lock-step. That is, significant resource competition at one level implies significant predation at the level of the resources and vice versa [Hairston et al, I960].) In a very literal sense the community then becomes a whole which is entirely the sum of its parts, and the limits that one places on the set of species composing the community become totally arbitrary. This does not mean that community-level phenomena would necessarily disappear from ecological consideration. But it does mean that the theoretical explanation for such phenomena would at best involve large-number concepts such as the central limit theorem— e.g., the lognormal distribution of species abundances results from many independent effects acting multiplicatively on independent populations (May, 1975). COMMUNITY ECOLOGY 95 kind of derivation when carried out provides an explanation for an upper-level generalization. where N is population size, r is intrinsic The preceding and similar derivations rate of increase and K is carrying capacity. make explicit the common assumption of This equation produces an S-shaped plot single-species equations that all individuals of N vs. t, and the inflection point (point are identical. One cannot simply argue that where dN/dt is at a maximum) is exactly we are considering the average individual, at K/2. However, many real population- because mathematical expectations will growth curves are not S-shaped; of those generally not go through, e.g., E(f(N)) # that are, many have systematic deviations f(E(N)) (although they may approximately of the inflection above or below K/2 do so). However, one can construct a sim(Schoener, 1973; Pomerantz et al., 1980). ilar equation for each intraspecific class of Thus, despite the fact that certain authors individuals that is desirable to distinguish. have treated the logistic curve as a "law" This will increase the complexity of the (e.g., Pearl, 1925), it is not in fact even much model, perhaps dramatically, but the prinof a statistical law, to say nothing about its ciple remains the same. failure as an absolute law. Finally, note that N, the number (or denAlthough originally not derived in a sity) of individuals, is included in the dermechanistical way, the logistic equation can ivation. One might misleadingly argue that be so derived. The details are elsewhere this is a population characteristic only, so (Schoener, 1973) but the end result is writ- that the reduction is undermined. While ten N is a population characteristic, it is an essential concept of behavioral ecology as dN/dt = R[E(1 - AN*) well—to understand the time and energy - C - YN*]N (3) budget of an individual, we need to know where E = Te, \ = AT, and the symbols the density of other individuals. Terms are defined as follows: R = number of indi- found at the population level may also be viduals resulting from conversion of one found at the behavioral level and be vital unit net energy input; e = net energy har- there. vested by an individual feeding for unit The logistic equation is the single-species time; A = time spent by an individual in version of the Lotka-Volterra model, interaction with a single other individual described above in connection with the ML per unit time; T = proportion of total time protocol. A similar derivation (Schoener, spent in activity (feeding or interaction); 19746) results in the parameter of the C = cost of maintenance and replacement Lotka-Volterra model being written as a^ = per unit time per individual (C = M + D F / (7y + EiXij)/(7ii + EiXji). Notice that in prinR, where M is metabolic rate and DF is the ciple there is nothing non-individual-ecoindividual death rate); y = energy cost of logical about terms describing interspecific interaction with another individual per interactions; they are exactly the same type individual per unit time; N* = N — 1. of term as those for intraspecific interacWhen rearranged, eq. 3 is exactly the logis- tions, so far as units are concerned and so tic in terms of the variables. When the far as they would be measured in a behavapproximation is made that N* = N, the ioral study. macroparameters of eq. 2 can be written The preceding is certainly not the only as r = R(E - C) and K = (E - C ) / ( T + way to derive a single-species populationEX). Each is decomposed into a combina- growth curve or one incorporating intertion of parameters having behavioral or specific competition. Other ways to derive physiological meaning. (The one possible the logistic exist, each with a rather specific exception is DF, which could conceivably domain of applicability. Moreover, the sort be so decomposed [Schoener, 1973, 19746] of competition represented is entirely one but has not been in this particular deri- type of interference; resources are assumed vation.) As noted by Popper (1974), this "superabundant." Interestingly, when (2) 96 THOMAS W. SCHOENER resource-competition equations are derived directly, they do not take on logistic form but take on other, sometimes similar forms. For example, a simple single-species equation in which the population is limited by its resources is S-shaped but has its inflection between 0 and K/2 (as do many real examples; for Drosophila, see Pomerantz et al., 1980). This equation is written dN/dt = RN[IE/(y + N) - C] (4) where IE = bF 0 /T, y = l/(aT), and the symbols not in eq. 3 are defined as follows: b = the net caloric value of a unit of resource; Fo = the amount of resource just after the resource has renewed; T = the renewal time of the resource; and a = the consumption rate per unit resource of an individual consumer. Here there is no term corresponding to r; if K is taken to mean "equilibrium population size," rather than the specific parameter in eq. 2, then K = ( I E / Q - y. Multispecies versions of resource competition are more complex and can take on a variety of non-Lotka-Volterra forms (Schoener, 19746, 1976, 1978; Abrams, 1980). Encouragingly, these forms (see above) often fit the data better than do the Lotka-Volterra equations, even when number of free parameters is controlled for. Other examples similar to those just presented exist in the second group of papers reviewed above. In some cases specific equations are not used, but rather arguments about the convexity or slope of functions are used instead (e.g., part of Holt, 1983; Sih, 1984). Such arguments show how a variety of mechanistically reasonable equations conforming to a set of general mathematical properties will produce a given community-ecological prediction. While the preceding sort of mechanistic derivation has certainly not been done for all equations used in population ecology, it is easy to imagine that it could be done for at least that subset which works reasonably well. Put another way, it is plausible that for every equation whose parameters are not so decomposable, there exists an equation which is empirically indistinguishable from the non-decomposable one and whose parameters are decomposable into individual-ecological ones. The above procedure, in which population-dynamical equations are derived from mechanistic arguments about individual-ecological processes, simultaneously provides connectability and derivability. While the latter is not necessarily implied by the former, it can be if for every term A in the reduced science but not in the reducing one there is a term B in the reducing science such that A and B are related in a biconditional (Kemeny and Oppenheim, 1956, cited in Nagel, 1961). By "biconditional" is meant the relation "A if and only if B." Let us take as an example of A the macroparameter K, where K is given the broad definition of equilibrium population size. The two derivations given above produced two translations of K, one for interference and the other for consumptive competition. So while we have shown "K if B," where B is a particular set of microparameters arranged in a particular form, we have not shown "K if only B." In other words, there is a one-to-many mapping of terms in the reduced science to terms in the reducing science (e.g., Hull, 1976; Wimsatt, 1980a). Hence biconditionality would seem to fail. However, recall that we are interested in explaining higher level patterns in objects such as K. The two derivations of K are of populations controlled by entirely different factors, one the time and energy lost in encounter and the other resource depletion. It is highly likely that much more regular patterns will be found for K's from populations of only the first type, or from those of only the second type, than from a mixture of the two types. Thus our theoretical laws might be most satisfactory when they treat the two types of populations separately. If they do, then K becomes almost a non-concept—one needs to specify which type of K. Under such conditions, i.e., under a pluralistic interpretation of K, biconditionality may indeed be satisfied. Even if it is not, we still can show Nagel's two conditions, but I think that it is reasonable to expect that an advanced theory of community and population ecology will satisfy biconditionality much more than does the COMMUNITY ECOLOGY present one. Finally, I can think of no plausible many-to-one mappings between community or population ecology and individual ecology, at least given the statistical nature of ecological laws. Many-to-one mappings, were they to exist, would destroy the formal reduction (e.g., Hull, 1976). It is worth noting that the view just expressed, that megaparameters having a variety of derivations are likely to be fairly useless in ecological theory, is nearly antithetical to Levins's (1966) advocacy of sufficient parameters in ecology. He writes ". . . temporal variation, patchiness of the environment, productivity of the habitat, and mode of hunting could all have similar effects by way of their contributions to the uncertainty of the environment. Thus uncertainty emerges as a sufficient parameter." I am skeptical that this or other parameters with so varied an etiology will lead to much understanding in community ecology, particularly given the great phenomenological variation that seems to exist. Now let us examine the issue left dangling above, that a theory having to do with evolution in populations (or communities) involves evolutionary concepts not reducible to behavioral or physiological ecology. There are two ways out of this quandary. The first way is simply to define all evolutionary concepts out of community and population ecology and into evolutionary ecology. Indeed, a few ecologists are nervous with evolutionary ideas because of their resistance to experimental test and so would be quite happy with this banishment. However, assuming we retain the evolutionary aspect of community and population ecology, there is a second way to defend their ultimate reducibility. That is to show that community and population ecology can be reduced to individual ecology and evolutionary ecology, taken jointly. In other words, the evolutionary part of the theory is embodied in equations with evolutionary as well as populationaldynamical parameters and with evolutionary variables such as gene frequencies. I do not have any complete examples of such a reduction for a specific population- or community-ecological theory, but I see nothing impossible about it in principle, especially 97 if decompositions of the populationdynamical parameters have already been made. For example, elsewhere (Schoener, 1973) I have suggested how much decomposition of the population parameters r and K can be used to resolve some of the controversy concerning for what traits r- and K-selection, respectively, should be more dominant. One might also argue the reduction of evolutionary versions somewhat differently, as follows. Behavioral and physiological ecology also have evolutionary aspects. Hence "terms" already exist to describe evolutionary concepts, so that an expanded individual ecology that has evolutionary content will allow an evolutionary community or population ecology to be reduced solely to individual ecology. This then raises the question of what individual ecology might be reduced to—is physiological ecology reducible to physics and chemistry plus evolutionary ecology, for example? One might also wonder whether evolutionary ecology or evolutionary biology is reducible to lower sciences. I do not intend to deal with any of these questions here, but I note that Ayala (1968; see also Campbell, 1974) has argued for the irreducibility of evolutionary biology. Briefly, Ayala's argument is that teleological concepts, by which he means concepts concerning adaptations and how the latter are produced by natural selection by way of increasing fitness in particular environments, are entirely absent from physics and chemistry. This makes it inconceivable, according to Ayala, that Nagel's formal conditions could be satisfied. One nasty technical flaw often frustrating attempts to satisfy Nagel's conditions literally has been pointed out by a number of persons (summary in Wimsatt, 1980a, p. 216). This is the use of approximations. Where such approximations are used, one does not have perfect derivability in Nagel's sense. A number of examples of such approximations occur in the derivations of eqs. 3 and 4 above; a function of exponential form was assumed the same as a rectangular hyperbola, for example. However, not making the approximations would only have incurred a modest increase in com- 98 THOMAS W. SCHOENER plexity in the necessary equations. Probably this state of affairs would hold for all approximations used in the mechanistic approaches described above. That is, in principle we can derive an equation exactly corresponding to our mechanistic assumptions, but for ease of manipulation and, consequently, the better to understand our models, we use approximations. This issue does, however, bring up the question of feasibility, to which we return below. Technical problems aside, is it conceivable that all of the interesting theory of community and population ecology, including evolutionary versions, could be reduced in Nagel's or a more liberal sense to individual ecology? One place where a reduction must certainly fail, if it is to fail at all, is with the complex of concepts associated with group selection. In certain group-selection models, extinction of the entire population depends, sometimes in a threshold fashion, on population size. The common scenarios are of a population that overeats its food supply, attracts too many predators, or (most plausibly) kills its host. How can an ecology that deals entirely with individuals reduce such a theory? I think the ontological reduction (a la Nagel or with Schaffner's [1974] extensions) could go forward as follows. Before population size acts to exterminate all individuals in the population at once, the population is presumably behaving according to the sorts of models discussed above, so that such models tell us when critical population sizes are reached. Moreover, for the most plausible scenario of group selection, populations of parasites, the individual ecology of the host, especially its physiological ecology, is crucial for predicting actual values of critical parasite loads. Even for the other group-selection scenarios listed above (which to my knowledge have never been shown to occur in nature—as opposed to the laboratory, e.g., Wade [1977]), the critical population sizes could be predicted using a set of differential equations representing food supply and consumer populations or representing predators and prey (e.g., Gilpin, 19756). Such models, of course, could probably be reduced in the sense illustrated by our pro- totypes above. Hence, with a somewhat more complicated set of links, the logical empiricist reduction of Nagel is made plausible for ecological aspects of certain groupselection theory. Possibly the reduction would be too involved to be very explanatory. The preceding hypothetical scheme also illustrates how reduction can serve to unify subdisciplines in a very powerful way. As stated above, individual ecology uses terms from population ecology, but the former discipline need not explain such terms to have a valid and unique theoretical structure—the terms may simply be considered as inputs, to be measured by the scientist as soil types would be measured, but not to be understood. However, having an explanation for population size couched in individual-ecological concepts not only enriches population ecology but enriches individual ecology as well. Thus, those interested in feeding strategies can predict, using population models, the changing input feeding individuals have on populations of their food; those interested in escape strategies can make similar predictions for predator populations. If such changes are short-term enough, they should in turn affect individual strategies and how we predict them. The reduced versions of population's and community ecology will doubless fit more naturally into such an expanded theory. One may or may not then retain the separate designations of the subdisciplines—the theoretical structures of the fields would be greatly unified, even though the respective phenomena must of course remain distinct. In summary of this section, I have argued that a non-evolutionary community ecology is in principle reducible to a non-evolutionary individual ecology via a reduction through population ecology, and that an evolutionary community (and population) ecology is probably in principle reducible to either a non-evolutionary individual ecology plus evolutionary ecology or to an evolutionary individual ecology by itself. Furthermore, I have argued that for certain aspects of the upper-level theory, the reduction is practical and/or has already taken place. Notice that there is nothing COMMUNITY ECOLOGY but complexity barring the way from systems of equations with many variables being reduced in the same way as the logistic equation was reduced above. For example, we could have many species in a food web rather than a few, and we could be interested in modeling indirect effects (those passing through intermediate species) rather than direct ones—the reduction could in principle still go forward. Moreoever, the behavioral complexity focused upon by the non-populationdynamical mechanistic approach could in principle be incorporated into populationdynamical equations. Finally, when there is one equation per species, the sometimes unsatisfactory assumption that all individuals are equal could be taken care of by replacing it with a set of equations for each species, distinguishing (as is often done) age classes, or size classes, or sexes. The resulting complexity, while not being a formal impediment, could of course be a major practical impediment, so that the reduction would contribute little to understanding. We shall return to this possibility below. Emergent properties: A side issue A major objection to my claims in the previous section might be that I have ignored emergent properties, which ecologists are discovering all the time {e.g., Richmond et al., 1975; Salt, 1979). The existence of these emergent properties, it might be argued, invalidates any reductionist demonstration, no matter how apparently convincing. In a completely formal, positivistic sense, this argument is incorrect. As Nagel (1961) points out, reduction does not deal with properties; rather it deals with experimental and theoretical laws. One cannot "deduce" properties per se; therefore it is meaningless to talk about the irreducibility of properties. Emergent, when applied strictly to properties, is therefore not the equivalent of Nagel's irreducible. Hence, it may be better to speak of emergence with respect to relations between statements (theoretical constructs) rather than between properties. But we can still ask the question, for community or pop- 99 ulation ecology: can those concepts associated with so-called emergent traits not be explained by some population-dynamical model whose parameters are ultimately decomposable into individual-ecological parameters? It is hard for me to imagine they cannot. As Edson et al. (1981) point out (in reply to Salt, 1979), just because a relationship is not additive between components does not mean it is qualitatively different from additive ones (also see Hempel and Oppenheim, 1948). In particular, relationships between individuals or populations derived from individual-ecological principles will seldom be linear. To take the simplest of examples, if a certain amount of resource I is to be divided among N individuals, then each individual gets I/N resource, assuming no limitations on an individual's resource-consumption abilities. Where limitation does exist, each individual's share can be represented as I/(N + x) (Schoener, 1978). These are already highly nonlinear terms. To rephrase, the fact that the whole is not the sum of its parts by itself does not rule out reducibility, and if the whole were the sum of its parts, we would have an especially strong form of reductionism, as discussed above. Labelling properties "emergent" which show nonlinear "composition functions" (in Hempel and Oppenheim's [1948] sense) could not be taken to imply that theories associated with those properties are irreducible, so this use of the term may be illadvised, at least without clearly distinguishing which sense of the term is meant (e.g., Wimsatt, 1976&). Moreover, for population and community ecology, where nonlinearity is the rule, this distinction would not divide such functions into anything like two equally sized groups. An interesting subconcept, which attempts to isolate that portion of a broad concept of emergence that is unique, is Beckner's (1974) "event reduction." It is denned as follows. Let T h be a theory of a higher-level science and T, be a theory of a lower-level science. Then T h is subject to complete (restricted) event reduction to T, if and only if every event which exhibits the phenomenon described by T h is explicable in T,, under every (some) description 100 THOMAS W. SCHOENER of the event in the vocabulary of T h . An "event" is most generally a particular occurrence or happening. For community or population ecology, an "event" might be taken to mean the occurrence of a process, or part of a process, in some ecological community, e.g., the change in population size of a component species. Complete event reduction is stronger than mere reduction, a la Nagel. If Simberloff and colleagues are correct about species interactions being so weak in nature as to be ignorable, then complete event reduction of community to population ecology would almost certainly go through under the revised theory that would then exist. As pointed out, many ecologists do not believe this hypothesis about communities to be correct. Nonetheless, as I elaborate below, event reduction can be a useful concept for community ecology so far as research strategies are concerned. T H E MECHANISTIC APPROACH AS A RESEARCH STRATEGY Wimsatt (1980a) has written that "the in principle claim of the reductionist is seldom in dispute," and that in the fields he is familiar with, "the issue between scientists who are reductionists and holists is not over the in principle possibility of an analysis in lower-level terms but on the complexity and scope of the properties and analyses required." Whether this is true or false for community ecology (I doubt community ecologists have thought much about it until recently), Wimsatt is certainly correct that, given that reduction is in principle possible, its execution may not be worth the trouble in terms of insights gained or research facilitated. Toward evaluating this possibility, I now discuss the pros and cons of the mechanistic approach to community ecology as (to use Wimsatt's phrase) a "research strategy." Many advantages of the mechanistic approach have been mentioned above and discussed in other papers in this symposium. For myself, its chief advantage is that it allows a theoretical understanding of how variation in individual-ecological properties—those of behavioral and physiological ecology—affect population and commu- nity structure. As Wimsatt (1976a) points out, this would not be so vital were there few exceptions to laws at the macrolevel, or were exceptions homogeneous when translated into microlevel terms. In fact, variation at the community (and population) level is extensive, so much so that rather than exceptions to a few "laws," it appears that community ecology is a genuinely pluralistic field, with many different "laws," each restricted to a rather narrow domain (Schoener, 1985). There are at least three major consequences of the advantage just discussed. First, as illustrated in the theoretical papers of Schoener (1973, 1974, 1976, 1978), Abrams (1980, 1982), Holt (1983) and Sih (1984) discussed above, qualitative predictions about how behavioral and physiological properties affect community and population dynamics and equilibrium become possible. For example, does an energy-maximizing predator stabilize or destabilize a predator-prey relationship? What behavioral traits would result in a population with a leptokurtic utilization distribution? How does metabolic rate affect population growth rate and stability of species interactions? Second, from an array of possible submodels available for a community (or ecosystem) model, the mechanistic approach suggests which to select. The most appropriate model would not be an issue were all models with roughly similar qualitative properties to behave the same way. But it is becoming obvious that in some major cases, and perhaps in many, they do not. Two relevant examples from community ecology stand out. In the first, Gilpin and Justice (1972) showed that, depending upon whether the zero-isocline of a competition model were linear (Lotka-Volterra) or concave, two qualitatively opposite predictions would be made about the outcome of competition in an actual system, two species of Drosophila. In fact, the isoclines were in reality concave, and the Lotka-Volterra model gave the incorrect prediction. At a more general level, Turelli (1981) showed that which of three qualitatively similar population-growth functions were used in a stochastic model determined the degree COMMUNITY ECOLOGY and direction of the effect of environmental variation on community stability: one gave a positive effect, one a negative effect, and one no effect! Ecosystem ecologists are also becoming aware of the problem. After citing some examples, Watt (1975), in a spate of disillusionment with ecosystem modelling, wrote "What is the meaning of the phrase 'a general function which describes this curve is . . . ?' Does it mean that the function was plucked out of thin air as being reasonable, or that it was tested against various sorts of ecological data to ensure that it described reality reasonably well, or that it was the product of some type of deductive process which will be outlined at some later time so as to be completely intelligible? Particularly where the function is new in ecological writings, and the explanation for its origin is not given, the critic is basically trapped in a guessing game with the author" (p. 140). My suspicion, as also voiced above, is that the first of Watt's alternatives is almost always true, and unfortunately, it appears that this may be no longer good enough. The above examples make me less than optimistic, contra Levins (1966; see also Wimsatt, 19806), about the robustness of community-ecological models, even regarding small details, much less at the scale he is talking about. If choice of model or submodel makes a difference, how is one to choose? The answer may well lie with the mechanistic approach: select an appropriate mechanistically derived model, rather than one that is arbitrary or at best purely descriptive. And as a coda, do not hesitate to change models or submodels when the situation changes. The third consequence is perhaps the most ambitious in its claims, but some outstanding examples of its success exist. It is that the mechanistic approach allows quantitative predictions to be made about community structure from behavioral and physiological considerations which can be tested with independently gathered macrolevel data. Four studies illustrating this advantage were described above and 101 are briefly reiterated here. First, Belovsky (1984, 1986) fitted by non-linear regression population data describing competition between moose and hare. The "bestfit" population parameters were then translated into behavioral parameters, via a mechanistic model, and those estimates were compared with independently derived estimates of the behavioral parameters obtained from behavioral-ecological (feeding-strategy) considerations. The two were found to be very close, greatly increasing our confidence in the theory. Second, Tilman (Titman, 1976;Tilman, 1977, 19866) used Michaelis-Menten growth considerations to predict quantitatively the values of nutrient ratios that determine different kinds of competitive outcomes. These predictions were verified with experiments. Third, Abrams (1981a) checked his estimates of a competition "coefficient" obtained from a model of shell dynamics with observations of marked shells in the field. Again, the two were very close. Fourth, Spiller (1985) evaluated a mechanistic competition-coefficient formula with field observations, then performed field experiments to measure the coefficient directly. Again, agreement was very good. All four of these studies are extremely powerful, in that they allow two independent assessments of a community-ecological theory. When the two are in agreement, our confidence in the theory is greatly increased. One might wonder from the rosy picture I have just painted why ecologists have not all boarded the mechanistic bandwagon. I think the basic caution of the dissenters is that this approach may portend an extraordinary degree of complexity when manyspecies interactions are considered. The complexity could arise in two kinds of places in the theory. First, any particular model, if it is to incorporate enough behavioral or physiological variation, may have to be so complex as to be analytically opaque. Already, a tradeoff in this area is detectable within the mechanists themselves. Those who delete population dynamics from their approach can incorporate more behavioral variation than those who do not (see above). Second, even if individual models are man- 102 THOMAS W. SCHOENER ageable, too many models, each with a very narrow application, may render the entire theory so massive and arcane that community ecology will become an impossibly esoteric field, unteachable to undergraduates and run mainly by experts in information retrieval. Worse, a theory too composed of special cases may be untestable, at least without intergalactic travel, as the earth may not contain sufficient communities to provide adequate statistical power. Some ecologists are probably willing to give up a lot of precision and linkage to lower levels if these things can be avoided. Moreover, as Wimsatt (1980a) points out, advocacy of a reductionist approach coincides with emphasizing internal, rather than external, factors when simplification is necessary. Thus mechanistic people will stress behavioral and physiological detail at the expense of, say, food-web detail. Twospecies systems rather than many-species systems, and direct rather than indirect effects, will be emphasized. This is already to some extent happening (see contrasts in Diamond and Case [1985] for example). As pointed out above, it is not that in principle the mechanistic approach is unable to handle phenomena involving numerous population- or community-level variables, e.g., numerous species. It is just that in practice, this may be too overwhelming. The hope that computer technology can make any "in principle" actual is dashed by reading Boyd (1972) and Wimsatt (1980a). For example (Wimsatt, 1980a), there are approximately 10130 possible chess games of 100 moves, larger by about 41 orders of magnitude than the number of elementary particles in the universe and by about 8 orders of magnitude of the number of physical events between such particles since the "big bang." So there have not been enough actual states to represent the chess game even if the universe since its inception were a computer! Those who have ever contemplated a very microreductionist approach to community ecology, e.g., following the fate of each individual (rather than representative individuals) in a set of interactions potentially very much more complicated than chess should be sobered by these calculations. That which is in principle possible may in fact not be physically possible. The mechanistic people, of course, are not advocating such an approach, and their hope is that reduction (in the way I have described it) may actually sometimes lead to meaningful simplification, not greater complexity. Even for the same degree of complexity (as measured, say, by the number of free parameters in a model), the descriptive approach may be more suitable than the mechanistic one if description is an end in itself. That is, it is conceivable that the most descriptive model for a particular case is nonmechanistic, or more likely, that the single model describing a set of cases better than any other is nonmechanistic. Because, as stressed above, ecological phenomena in toto rarely fit any single model well, the latter is in my opinion not so likely; an example is found in my own work on habitat shift (Schoener, 1974&). This is also why the role of upper level generalizations in "winnowing out" inappropriate lower level representations (as suggested by Wimsatt, 1976&, footnote 11) is not likely to be conspicuous for population and community ecology even if it were looked for carefully. A related advantage for nonmechanistic models, especially linear ones, is their typically intimate association with statistical estimation. Again, however, estimation is possible with nonlinear models; it is just more cumbersome. Moreover, if the assumptions of the estimation {e.g., linearity) are far from true, reliability of the estimation is compromised, and a more complicated estimation procedure (or no procedure) may be preferable. Finally, of course, reduction has to stop somewhere along its downward path. While I have argued that it may often be practical to reduce community and population ecology to individual ecology, would it be sensible to go farther? That is, should we use physiological laws such as the metabolicrate-to-body-weight function in their simple descriptive form, or should we use a probably more complicated mechanistic version were one available? And if the answer is yes, should we continue through biochemistry, physical chemistry and phys- COMMUNITY ECOLOGY ics? If this reductio ad absurdum (or ad nauseum\) were possible in principle, it would be strangulating in practice. Scientists will place bounds on a train of reductions that are in principle possible when the sequence becomes too long to have explanatory power (Wimsatt, 1976ft). Despite occasional bursts of ambitious pronouncement, we are not going to know for a very long time how the balance of advantages and disadvantages will finally fall. But it is amusing, not very risky, and perhaps even a bit inspirational to speculate, which I now do. A MECHANISTIC ECOLOGIST'S UTOPIA What if the mechanistic program realized its wildest aspirations? What would ecology be like then? Here I imagine the characteristics of a mechanistic community-ecologist's Utopia. I distinguish six such characteristics. First, the macroparameters of community ecology will be de-emphasized. Less use will be found for concepts like "niche overlap," "niche breadth," and indeed even "niche." "Niche overlap," for example, might be represented by an array of more specific concepts, such as Abrams's (1980ft) competition ratio, Schoener's (1974a) competition coefficient, and so on. Second, theoretical models will have proliferated, and each will have a rather specific domain. A pluralistic theory will have replaced an attempted universal one. Pluralism will involve specificity at both the organismic and environmental levels, i.e., with respect to the biological traits of the type of organism being considered (e.g., generation time) and the environmental traits of the community's location (e.g., degree of spatial fragmentation). Elsewhere (Schoener, 1985a), I have suggested a first list of such traits. Third, arbitrary models whose sole virtue is mathematical convenience will no longer be acceptable. In order to be used, a model will have to be mechanistically justifiable. It may be that manipulation of such models will require a great deal of mathematical skill with approximations and so on, and perhaps a lot of computer time as well. 103 Fourth, in both observational and experimental approaches, a greater emphasis will be placed on discovering the mechanism of an interaction or process, not just its existence and strength. The ingenuity required to get at such mechanisms will probably be much greater than that needed to design the removal or introduction experiments that most of us do today. Fifth, individual-ecological terms, e.g., those from behavioral and physiological ecology, will commonly appear in designations of kinds of ecological communities. Thus we might have ectothermic communities, semelparous communities, or long-generationed communities. Sixth, population- and community-level hypotheses will be framed in much more precise and obviously testable terms than is presently the case. Perhaps Beckner's (1974) application strategy involving event reduction (see above) will be realized: the "revision of higher-level theory in a manner that facilitates event reduction; that is, the introduction of higher-level descriptions with an eye toward the lower-level explanation of events under those descriptions." The use of quantities and units from behavioral and physiological ecology may bring testability of population- and community-ecological models on a par with that currently possible for, say, feeding-strategy models (e.g., Krebs et ai, 1983). Notice that nothing in this scenario suggests replacement of community ecology by individual ecology as a science, despite the prospect of reduction. The phenomena of community ecology will still be of interest (unless the Florida State proposal is correct), although as stressed above, there will be a good deal more unity between the subdisciplines than presently exists. (In this regard, I am supporting Wimsatt's [1976ft, p. 222] view of "interlevel" reduction.) Of course, as already noted, actualization of the mechanistic program could well falter on complexity and unwieldiness. Exactly what will happen remains to be seen, but we may ask in closing about the effect this and other philosophical analyses might have on the development of community ecology. Will a philosophically selfaware science pursue a different path than 104 THOMAS W. SCHOENER one that is philosophically ignorant? Philosophers are sometimes surprisingly selfeffacing on this question (e.g., Beckner, 1974), and in fact it is probably unanswerable; we are participants in an experiment without a control. ACKNOWLEDGMENTS I thank P. Abrams, M. Price, J. Quinn, J. Roughgarden, A. Shapiro and D. Spiller for comments on a previous draft. I am especially indebted to J. Griesemer for pointing out much of the relevant philosophical literature to me and for very detailed criticism and discussion. Supported by N.S.F. grant DEB 81-18920. REFERENCES and its role in competitive interactions. Amer. Zool. 26:51-69. Boyd, R. 1972. Determinism, laws and predictability in principle. Philos. Sci. 39:431-450. Campbell, D. T. 1974. 'Downward causation'in hierarchically organized biological systems. In F. J. Ayala and T. Dobzhansky (eds.), Studies in the philosophy of biology: Reduction and related problems, pp. 179-186. University of California Press, Berkeley. Case, T. J. 1982. Coevolution in resource-limited competition communities. Theor. Pop. Biol. 21: 69-91. Case, T. J. and R. G. Casten. 1979. Global stability and multiple domains of attraction in ecological systems. Amer. Natur. 113:705-714. Colwell, R. K. 1984. What's new? Community ecology discovers biology. In P. W. Price, C. N. Slobodchikoff, and W. S. Gaud (eds.), A new ecology: Novel approaches to interactive systems, pp. 387-396. Wiley, New York. Connell.J. H. 1983. On the prevalence and relative importance of interspecific competition: Evidence from field experiments. Amer. Natur. 122: 661-696. Crowell, K. L. 1962. Reduced interspecific competition among the birds of Bermuda. Ecology 43: 75-88. Darden, L. and N. Maull. 1977. Interfield theories. Philos. Sci. 44:43-64. Diamond, J. M. and T. Case. 1985. Ecological communities. Harper and Row, New York. (In press) Edson, M. M., T. C. Foin, and C. M. Knapp. 1981. "Emergent properties" and ecological research. Amer. Natur. 118:593-596. Gilpin, M.E. 1975a. Limit cycles in competition communities. Amer. Natur. 109:51-60. Abrams, P. A. 1975. Limiting similarity and the form of the competition coefficient. Theor. Pop. Biol. 8:356-375. Abrams, P. A. 1980a. Are competition coefficients constant? Inductive versus deductive approaches. Amer. Natur. 116:730-735. Abrams, P. A. 1980A. Resource partitioning and interspecific competition in a tropical hermit crab community. Oecologia 46:365—379. Abrams, P. A. 1981a. Alternative methods of measuring competition applied to two Australian hermit crabs. Oecologia 51:233-239. Abrams, P. A. 1981ft.Competition in an Indo-Pacific hermit crab community. Oecologia 51:240-249. Abrams, P. A. 1982. Functional response of optimal Gilpin, M. E. 19856. Group selection in predation-prey foragers. Amer. Natur. 120:382-390. communities. Princeton Univ. Press, Princeton, Abrams, P. A. 1983. The theory of limiting similarNew Jersey. ity. Annu. Rev. Ecol. Syst. 14:359-376. Ayala, F.J. 1968. Biology as an autonomous science. Gilpin, M. E. and K. E. Justice. 1972. Reinterpretation of the invalidation of the principle of comAm. Sci. 56:207-221. petitive exclusion. Nature 36:273-274. Ayala, F.J. and T. Dobzhansky. 1974. Studies in the philosophy of biology: Reduction and related problems. Gleason, H. A. 1926. The individualistic concept of the plant association. Bull. Torrey Bot. Club 53: University of California Press, Berkeley. 1-20. Ayala, F. J., M. E. Gilpin, and J. G. Ehrenfeld. 1973. Competition between species: Theoretical models Hairston, N. G., F. E. Smith, and L. B. Slobodkin. 1960. Community structure, population control and experimental tests. Theor. Pop. Biol. 4:331and competition. Amer. Natur. 94:421—425. 356. Beckner, M. 1974. Reduction, hierarchies and Hempel, C. G. and P. Oppenheim. 1948. Studies in the logic of explanation. Philos. Sci. 15:135-175. organicism. In F. J. Ayala and T. Dobzhansky (eds.), Studies in the philosophy of biology: Reduction Holt, R. D. 1983. Optimal foraging and the form of the predator isocline. Amer. Natur. 122:521—541. and related problems, pp. 163-177. University of California Press, Berkeley. Hull, D. L. 1976. Informal aspects of theory reduction. In R. S. Cohen, C. A. Hooker, A. C. MichBelovsky, G. E. 1978. Diet optimization in a generalos, andj. W. Van Evra (eds.), pp. 653-670. PSA alist herbivore: The moose. Theor. Pop. Biol. 14: 1974, D. Reidel, Dordrecht, Holland. 105-134. Belovsky, G. E. 1984a. Moose and snowshoe hare Keast, A. 1970. Adaptive evolution and shifts in niche occupation in island birds. Biotropica 2:61-75. competition and a mechanistic explanation from Kemeny, J. G. and P. Oppenheim. 1956. On reducforaging theory. Oecologia 61:150-159. tion. Philosophical Studies 7:6-19. Belovsky, G. E. 19846. Snowshoe hare optimal foraging and its implications for population dynam- Krebs,J. R., D. W. Stephens, and W. J. Sutherland. ics. Theor. Pop. Biol. 25:235-264. 1983. Perspectives in optimal foraging. In A. H. Brush and G. A. Clark, Jr. (eds.), Perspectives in Belovksy, G. E. 1986. Generalist herbivore foraging COMMUNITY ECOLOGY ornithology: Essays presented for the centennial of the American Ornithologists' Union, pp. 165-216. Cam- 105 philosophy of biology: Reduction and related problems, pp. 259-284. University of California Press, Berkeley. Price, M. V. 1986. Structure of desert rodent communities: A critical review of questions and approaches. Amer. Zool. 26:39-49. Levins, R. 1968. Evolution in changing environments. Price, M. V. and N. M. Waser. 1984. On the relative Princeton Univ. Press, Princeton, New Jersey. abundances of species: Post-fire changes in a Lewontin, R. C. 1970. The units of selection. Annu. coastal sage scrub rodent community. Ecology Rev. Ecol. Syst. 1:1-18. 65:1161-1165. Lister, B. C. 1976. The nature of niche expansion in West Indian Anolis lizards I: Ecological con- Price, M. V. and N. M. Waser. 1985. Microhabitat use by heteromyid rodents: Effects of artificial sequences of reduced competition. Evolution 30: seed patches. Ecology. (In press) 659-676. MacArthur, R. H. 1960. On the relative abundance Price, P. W., C. N. Slobodchikoff, and W. S. Gaud. 1984. A new ecology: Novel approaches to interactive of species. Amer. Natur. 94:25-36. systems. Wiley, New York. MacArthur, R. H. 1966. A note on Mrs. Pielou's Pulliam, H. R. 1986. Niche expansion and contraccomments. Ecology 47:1074. tion in a variable environment. Amer. Zool. 26: MacArthur, R. H. and R. Levins. 1967. The limiting 71-79. similarity, convergence and divergence of coex- Quinn.J. F. and A. E. Dunham. 1983. On hypothesis isting species. Amer. Natur. 101:377-385. testing in ecology and evolution. Amer. Natur. MacArthur, R. H. and E. O. Wilson. 1967. The theory 122:602-617. of island biogeography. Princeton Univ. Press, Rasmussen.J. B. 1983. An experimental analysis of Princeton, New Jersey. competition and predation and their effects on May, R. M. 1972. Limit cycles in predator-prey comgrowth and coexistence of chironomid larvae in munities. Science 177:900-902. a small pond. Ph.D. Diss., University of Calgary, Alberta. May, R. M. 1975. Patterns of species abundance and diversity. In M. L. Cody andj. M. Diamond (eds.), Richmond, R. C , M. E. Gilpin, S. P. Salas, and F. J. Ecology and evolution of communities, pp. 81-120. Ayala. 1975. A search for emergent competitive Harvard University Press, Cambridge. phenomena: The dynamics of multispecies Drosophila systems. Ecology 56:709-714. McMurtrie, R. 1976. On the limit to niche overlap Roughgarden, J. 1972. Evolution of niche width. for nonuniform niches. Theor. Pop. Biol. 10:96107. Amer. Natur. 106:683-719. Roughgarden, J. 1974. Species packing and the comMedawar, P. 1974. A geometric model of reduction petition function with illustrations from coral reef and emergence. In F. J. Ayala and T. Dobzhansky fish. Theor. Pop. Biol. 5:163-186. (eds.), Studies in the philosophy of biology: Reduction and related problems, pp. 57-63. University of Cal- Roughgarden, J. 1976. Resource partitioning among ifornia Press, Berkeley. competing species—A coevolutionary approach. Theor. Pop. Biol. 9:388-424. Moermond, T. C. 1979. Habitat constraints on the behavior, morphology and community structure Roughgarden, J. 1983. Competition and theory in of Anolis lizards. Ecology 60:152—164. community ecology. Amer. Natur. 122:583-601. Moermond, T. C. 1986. A mechanistic approach to Salt, G. W. 1979. A comment on the use of the term the structure of animal communities: Anolis liz"emergent properties." Amer. Natur. 113:145ards and birds. Amer. Zool. 26:23-37. 151. Murdoch, W. W. 1969. Switching in general predSchaffer, W. M. 1981. Ecological abstraction: The ators: Experiments on predator specificity and consequences of reduced dimensionality in ecostability of prey populations. Ecol. Monogr. 39: logical models. Ecol. Monogr. 51:383-401. 335-354. Schaffner, K. F. 1974. The peripherality of reductionism in the development of molecular biology. Murdoch, W. W. and A. Oaten. 1975. Predation and J. His. Biol. 7:111-135. population stability. Adv. Ecol. Res. 9:1-131. Schluter, D. 1982. Seed and patch selection by GalaNagel, E. 1961. The structure ofscience: Problems in the pagos ground finches: Relation to foraging effilogic of scientific explanation. Harcourt, Brace and ciency and food supply. Ecology 63:1106—1120. World, New York. Paine, R. T. 1984. Ecological determinism in the Schluter, D. and P. R. Grant. 1984. Determinants of competition for space. Ecology 65:1339-1348. morphological patterns in communities of Darwin's finches. Amer. Natur. 123:175-196. Pearl, R. 1925. The biology ofpopulation growth. Knopf, New York. Schoener, T. W. 1969. Optimal size and specializaPomerantz, M. J., W. R. Thomas, and M. E. Gilpin. tion in constant and fluctuating environments: 1980. Asymmetries in population growth reguAn energy-time approach. Brookhaven Symp. lated by intraspecific competition: Empirical Biol. 22:103-114. studies and model tests. Oecologia 47:311-322. Schoener, T. W. 1971. Theory of feeding strategies. Popper, K. R. 1974. Scientific reduction and the Annu. Rev. Ecol. Syst. 2:369-404. essential incompleteness of all science. In F. J. Schoener, T. W. 1973. Population growth regulated Ayala and T. Dobzhansky (eds.), Studies in the by intraspecific competition for energy or time: bridge University Press, Massachusetts. Levins, R. 1966. The strategy of model building in population biology. Am. Sci. 54:421-431. 106 THOMAS W. SCHOENER Some simple representations. Theor. Pop. Biol. 4:56-84. Schoener, T. W. 1974a. Some methods for calculating competition coefficients from resource-utilization spectra. Amer. Natur. 108:332-340. Schoener, T. W. 19746. Competition and the form of habitat shift. Theor. Pop. Biol. 6:265-307. Schoener, T. W. 1975. Presence and absence of habitat shift in some widespread lizard species. Ecol. Monogr. 45:233-258. Schoener, T. W. 1976. Alternatives to Lotka-Volterra competition: Models of intermediate complexity. Theor. Pop. Biol. 10:309-333. Schoener, T. W. 1978. Effect of density restricted food encounter on some single-level competition models. Theor. Pop. Biol. 13:365-381. Schoener, T. W. 1982. The controversy over interspecific competition. Am. Sci. 70:586-595. Schoener, T. W. 1983. Field experiments on interspecific competition. Amer. Natur. 122:240-285. Schoener, T. W. 1985a. Kinds of ecological communities: Ecology becomes pluralistic. In J. M. Diamond and T. Case (eds.), Ecological communities. Harper and Row, New York. (In press) Schoener, T. W. 19856. Resource partitioning. In]. Kikkawa and D. Anderson (eds.), Community ecology—Pattern and process, Chapter 6. Blackwell Scientific Publ., Oxford. Sell, D. W., H. J. Carney, and G. L. Fahnenstiel. 1984. Inferring competition between natural phytoplankton populations: The Lake Michigan example. Ecology 65:325-328. Sih, A. 1984. Optimal behavior and density-dependent predation. Amer. Natur. 123:314-326. Simberloff, D. 1980. A succession of paradigms in ecology: Essentialism to materialism and probabilism. Synthese 43:3-39. Simberloff, D. 1983. Competition theory, hypothesis testing, and other community-ecological buzzwords. Amer. Natur. 122:626-635. Slatkin, M. W. 1980. Ecological character displacement. Ecology 61:163-177. Sober, E. 1984. Conceptual issues in evolutionary biology: An anthology. MIT Press, Cambridge, Massachusetts. Spiller, D. A. 1986. Consumptive competition coefficients: An experimental analysis with spiders. Amer. Nat. (In Press) Strong, D. R., D. Simberloff, L. G. Abele, and A. B. Thistle. 1984. Ecological communities: Conceptual issues and the evidence. Princeton Univ. Press, Princeton, New Jersey. Tilman, D. 1977. Resource competition between planktonic algae: An experimental and theoretical approach. Ecology 58:338-348. Tilman, D., S. S. Kilham, and P. Kilham. 1984. A reply to Sell, Carney, and Fahnenstiel. Ecology 65:328-332. Titman, D. 1976. Ecological competition between algae: Experimental confirmation of resourcebased competition theory. Science 192:463—465. Turelli.M. 1981. Niche overlap and invasion of competitors in random environments. I. Models without demographic stochasticity. Theor. Pop. Biol. 20:1-56. Van Valen, L. 1965. Morphological variation and width of ecological niche. Amer. Natur. 99:377390. Wade, M. J. 1977. An experimental study of group selection. Evolution 31:134-153. Watt, K. E. F. 1975. Critique and comparison of biome ecosystem modeling. In B. C. Patten (ed.), Systems analysis and simulation in ecology, Vol. 3, pp. 139-152. Academic Press, New York. Werner, E. E. 1984. The mechanisms of species interactions and community organization in fish. In D. R. Strong, Jr., D. Simberloff, L. G. Abele, and A. B. Thistle (eds.), Ecological communities: Conceptual issues and the evidence, pp. 360—382. Princeton Univ. Press, Princeton, New Jersey. Werner, E. E. and D. J. Hall. 1976. Niche shifts in sunfishes: Experimental evidence and significance. Science 191:404-406. Werner, E. E. and D.J. Hall. 1977. Competition and habitat shift in two sunfishes (Centrarchidae). Ecology 58:869-876. Werner, E. E. and D. J. Hall. 1979. Foraging efficiency and habitat switching in competing sunfishes. Ecology 60:256-264. Whittaker, R. H. 1975. Communities and ecosystems. 2nd ed. The Macmillan Company, London. Williamson, M. 1983. Variations in population density and extinction. Nature 303:201. Wilson D. S. 1980. The natural selection of populations and communities. Benjamin/Cummings, Menlo Park, California. Wimsatt, W. C. 1974. Complexity and organization. In K. F. Schaffner and R. S. Cohen (eds.), Boston Studies in the Philosophy of Science 20:67-86. Wimsatt, W. C. 1976a. Reductive explanation: A functional account. In R. S. Cohen, C. A. Hooker, A. C. Michalos, and J. W. Van Evra (eds.), pp. 671-710. PSA 1974. D. Reidel, Dordrecht, Holland. Wimsatt, W. C. 19766. Reductionism, levels of organization, and the mind-body problem. In G. G. Globus, G. Maxwell, and I. Savodnik (eds.), Consciousness and the brain: A scientific and philosophical inquiry, pp. 205-267. Plenum Press, New York. Wimsatt, W. C. 1980a. Reductionistic research strategies and their biases in the units of selection Tilman, D. 1982. Resource competition and community controversy. In T. Nickles (ed.), Scientific discovery, structure. Princeton Univ. Press, Princeton, New pp. 213-259. D. Reidel Publishing, Dordrecht, Jersey. Holland. Tilman, D. 1986a. Evolution and differentiation in terrestrial plant communities: The importance of Wimsatt, W. C. 19806. Randomness and perceivedthe soil resource: light gradient. In J. M. Diamond randomness in evolutionary biology. Synthese 43: and T. Case (eds.), Community Ecology. Harper and 287-329. Row, New York. Tilman, D. 19866. A consumer-resource approach to community structure. Amer. Zool. 26:5-22.