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AMER. ZOOL., 26:5-22 (1986) A Consumer-Resource Approach to Community Structure1 DAVID TILMAN Department of Ecology and Behavioral Biology, 318 Church St. S.E., University of Minnesota, Minneapolis, Minnesota 55455 SYNOPSIS. Because all species are consumers and all, eventually, are consumed by other species, consumer-resource interaction is one of the most fundamental processes of ecology. Simple models that include the direct mechanisms of consumer-resource interactions may thus be the fundamental building-block for models of community structure. These models are easily extended to include such complexity as the effects of physical limiting factors, spatial heterogeneity in resource supply, fluctuating resource supply, and multiple trophic levels. Each such modification places constraints on the traits of species that can persist. Consumer-resource models make predictions about many aspects of community structure, including species richness, species composition, species dominance, population dynamics, morphological or physiological traits of species, and patterns of phenotypic variation within species. Thus, each model affords numerous opportunities to test and modify or reject it. A review of a variety of communities suggests that much of the structure of each community can be explained by a relatively simple consumer-resource model, but that different elements of complexity may be important in different communities. many of the details of the biology of particular species in particular habitats are The biosphere contains over a million described species, and possibly another probably peculiar to those species. Howmillion species yet to be described. Any ever, the similar patterns observed among given community may contain hundreds of communities suggest that there may be a species, each interacting with at least sev- few major underlying factors or processes eral other species and an often variable that constrain many communities (Macabiotic environment. Amid this complex- Arthur, 1972; Lawton, 1984). Such patity, ecologists have found what seem to be terns in the species composition, species repeatable patterns in species diversity (e.g., dominance and diversity of communities, Pianka, 1966; MacArthur and Wilson, and in the morphology of dominant species 1967; Connell, 1978; Grime, 1979; Hus- in communities are often called, simply, ton, 1979; Tilman, 1982; Abramsky and community structure. There has been conRosenzweig, 1984; Shmida etal, 1984), in siderable debate as to how strong such patspecies dominance (Preston, 1948; Whit- terns in community structure are and taker, 1977; Sugihara, 1980), in species whether there are a few major constraincomposition on gradients (e.g., Pigott and ing factors or processes (e.g., Connor and Taylor, 1964; Zedler and Zedler, 1969; Simberloff, 1979; SimberlofF and Connor, MacArthur, 1972; Whittaker and Niering, 1979, 1981; Strong, 1980; and numerous 1975; Tilman, 1982, 1986), in life histories papers in Strong et al., 1984). I do not wish (Grime, 1979), and in the functional roles to enter this debate. Rather, I would like and morphology of unrelated species living to explore a theoretical, mechanistic in physically similar but geographically approach that may provide some insights separated habitats (Mooney, 1977; Cody in explaining those patterns that are found and Mooney, 1978; Orians and Paine, to be robust. 1983). Because of the complexity of natThere are two main types of constraints ural communities and the uniqueness of placed on organisms: those from their the evolutionary history of each species, physical environment and those from their biotic environment. The reproductive and mortality rates of a population are influenced by many aspects of the physical envi1 From the Symposium on Mechanistic Approaches to ronment, such as temperature, humidity the Study ofNatural Communities presented at the Annual Meeting of the American Society of Zoologists, 2 7 - and topography. Such physical factors can be thought of as limiting factors for each 30 December 1983, at Philadelphia, Pennsylvania. INTRODUCTION DAVID TILMAN species (Levin, 1970; Levins, 1979). Additionally, each population exists in a network of other species. Within this network, all species are consumers and all, eventually, are consumed. The items which a species consumes are called its resources. That the consumer-resource interaction is the central biotic interaction is illustrated by any diagram of a food web. In a food web, there are two distinct types of links: consumer-resource interactions and the various processes that supply the abiotic resources required by plants. Thus, each species is constrained by the availability of its resources, by the dependence of its growth rate on resource availability, by the rate at which it is consumed by other species, and by various physical limiting factors. The effects of physical limiting factors can often be incorporated by considering how they influence consumerresource interactions and resource supply. There is no a priori reason to believe that any one of these constraints is more or less important than another. However, for a given community, one or a few constraints may be of overriding importance in determining particular characteristics of that community. If this were so, we would be able to simplify our initial approach by ignoring all but these constraints. Thus, we might have reason to believe that the species richness and species composition of a desert plant community is most greatly influenced by water availability, and choose, initially, to ignore plant-herbivore interactions. Or, we may believe that the species composition of a foliage-feeding insect community is most influenced by predation, and ignore the interactions among herbivores and plants. As recent work on "indirect effects" has illustrated, all such simplifications are potentially dangerous (Levine, 1976; Holt, 1977; Lynch, 1978; Lawlor, 1979; Vandermeer, 1980; Tilman, 1983). What we need to do, for any given community, is find a minimum subset of explanatory factors. One way to find such a minimum subset, given the complexity of nature, would be to use a stepwise criterion for inclusion. Starting with a simple mechanisticallybased theory, it would be possible to build a more complete theory by adding only those factors that explained a significant additional portion of the patterns observed. If the initial theory were based on consumer-resource interactions, this would yield a minimum subset of the food web interactions, and would include the important direct and indirect interactions. In that spirit, I will outline a theoretical approach to community structure by starting with a highly idealized consumerresource interaction and adding other elements to it one at a time. The most basic element of the food web is the consumerresource interaction. I will start by considering a two-trophic level system (i.e., a resource level and a consumer level) that goes to equilibrium in a spatially and temporally uniform environment. Next I will discuss how this system is altered by adding spatially variable resource supply rates, or a physical factor, or another trophic level, or temporally varying resources. For each of these alternatives, I will suggest some communities that may be adequately described by it and will discuss the constraints placed on community structure by each form of the model. If a particular model successfully explains one aspect of community structure, such as patterns in species diversity, but does not explain another aspect, such as patterns in life histories, I would suspect that the model is incomplete or wrong. There are numerous elements in the patterns we observe in nature. A robust ecological theory should be able to explain many different types of patterns simultaneously. At this stage in our efforts, it may be more productive to try to test our theories not by seeing how much more of one particular type of pattern each theory can explain, but by applying each theory to a host of different types of patterns. Thus, once the ability of a theory to predict species diversity patterns has been tested, for instance, it may be best to test it next against its predictions as to which species should be dominant, or against its predictions about life history and morphological variations both within and among species. Although I focus this paper mostly on patterns in species diversity, actual tests of the applicability of the consumer- COMMUNITY STRUCTURE: CONSUMER-RESOURCE APPROACH resource approach, or any other approach, should test theory against all aspects of community structure. The viewpoint presented in this paper differs from what I perceive to be the frequent tendency for ecologists to believe that only one type of interaction will be important in a given situation. For instance, there have been many debates over whether it is competition or predation that is important in a given system. Although simplification is a necessary starting point for research, dichotomous logic should not be applied to what are, in reality, continuous processes. The presence of a predator, for instance, can modify the outcome of the interactions between two competitors, but it does not eliminate their competitive interaction. It is very possible for the structure of a community to be determined by the interplay of competition and predation. There are, though, some regions in which a single species comprises the vast majority of the biomass on a trophic level. As a first approximation, might these tend to meet the criteria given above for monocultures? Highly productive marine estuaries often have large expanses dominated by a single species of salt grass, such as Spartina alterniflora. In such monospecific stands, physical disturbances, which uproot sections of salt grass, are rare. For a Georgia salt marsh (Teal, 1962), the major species feeding on Spartina were a grasshopper and a plant hopper, which, in total, consumed about 7% of the annual production, a rather insignificant amount. Nitrogen may be the main limiting resource for the Spartina (Gallagher, 1975; Chalmers, 1979; Hopkinson and Schubauer, 1984). All other species, which are shorter than the dominant Spartina, are probably light limited because of the dense shade cast by Spartina. Thus, as a first approximation, the monoTwo TROPHIC LEVELS: SPATIAL AND specific portions of some salt marshes may TEMPORAL HOMOGENEITY be considered to be equilibrium stands limited by a single resource with an insignifiOne limiting resource ' For an equilibrium community with two cant third trophic level. In order to explain trophic levels and a single limiting resource the coexistence of other plant species with in a physically uniform habitat, theory pre- the dominant, or the observed zonation in dicts that the one species with the lowest salt marshes, it would be necessary to relax equilibrial requirement for the limiting at least one of these assumptions. resource, termed R*, should competitively Fresh water marshes are another highly displace all other species (Fig. 1; O'Brien, productive habitat in which all species, with 1974; Hsu et ai, 1977;Tilman, 1977, 1982; the possible exception of the dominant Armstrong and McGehee, 1980). The species, are likely to be limited by the same mechanism of this displacement is resource resource, light. In many marshes in which consumption. There will be increases in herbivory is of minor importance and the population density of the species with physical disturbances are rare, there are the lowest equilibrial requirement for the large expanses dominated by a single limiting resource, such as species A in Fig- species of cattail, Typha latifolia. Many other ure 1A and B, until it reduces the single areas in which there are almost monospelimiting resource down to RA*. At RA*, the cific stands of plants tend to be highly proreproductive rate of species B is less than ductive, such as the coastal stands of redits mortality rate. Thus, if a community has woods in California, the coastal douglas fir one limiting resource, two trophic levels stands of Washington, marine kelp forests {i.e., lacks a significant trophic level preying (Mann, 1973; Reed and Foster, 1984), and on the consumer species), a physically uni- sedge meadows (Bernard, 1974). Even in form habitat and goes to equilibrium, we the diverse tropics, some of the least diverse would expect there to be but a single con- forests occur on the most productive soils sumer species, i.e., to be a monoculture. (Huston, 1980). Even when there is only a I know of no natural communities which single limiting resource, monocultures are meet all these assumptions and thus should predicted by theory only if herbivores are have a single species on the consumer level. absent and the systems are undisturbed. DAVID TILMAN A. Resource Growth Curves B. Dynamics 100 1.2- C. Competition: Temperature Gradient \ 1 / 1/ \ a: \ \ A A / \/ B D. Competition: pH Gradient 100' ( I - Holcus) (2-Alopecurus) ( 3 " Arrhenatherum) V 50/ \ C Low / D OC \ E High Temperature 4.0 5.0 6.0 Soil pH 7.0 FIG. 1. A. The solid curves labeled A and B are resource dependent growth (reproduction) curves for species A and species B. The broken line labeled m is the mortality rate, that both species experience. R* is the environmental concentration of the resource at which reproduction equals death. RA* is the amount of the resource required for the survival of species A in this habitat. RB* is the resource level required for survival of species B. Figure from Tilman (1982). B. When the two species of part A compete for this single limiting resource, the species with the lower R*, species A, competitively displaces species B. The mechanism of displacement is resource consumption. The population density of species A can increase until the resource level is reduced to RA*. At RA*, there is insufficient resource for the survival of species B. The thick lines show the population densities of species A and B, and the thin line the environmental concentration of the resource predicted by numerical solution of a Monod model of competition (Tilman, 1982). Figure from Tilman (1982). C. The equilibrium resource requirement, R*, of 5 different species, labeled A to E, is shown to depend on temperature. Note that each species is shown to have the lowest R* for a particular range of temperatures. Theory predicts that species with the lowest R* within a given temperature range should competitively displace all other species from that range. The temperature ranges in which species A to E are predicted to be dominant are indicated with broken lines. D. Under experimental conditions in which all species should have been limited by light availability, the long-term Park Grass fertilization experiments at Rothamsted, England, have shown that the three dominant species are separated along an experimentally-imposed pH gradient. See Tilman (1982, p. 170) for more details. This suggests that the competitive ability of these species for light depends on pH, much as illustrated in part C of this figure. Figure from Tilman (1982). Reed and Foster (1984) found that marine kelp forests subject to frequent disturbances and herbivory by sea urchins had a diverse assemblage of annual algal species whereas nearby areas with low disturbance rates and low densities of herbivores were much less diverse. It would be interesting to know the extent to which light is the COMMUNITY STRUCTURE: CONSUMER-RESOURCE APPROACH major limiting resource in such productive habitats, in general, and if disturbance and herbivory are of lesser intensity in monospecific stands than in nearby stands that are more diverse. It may be that natural monocultures tend to have a single limiting resource, have low densities of herbivores and low disturbance rates, as the simple theory presented here suggests. This hypothesis can be tested only through experimental manipulations. Grassland communities that have been experimentally fertilized have dramatic decreases in species richness (Tilman, 1982). Those provided with all nutrients in excess, such as some regularly mowed plots from which herbivorous mammals were excluded in the Rothamsted Park Grass Experiments in England, have almost become monocultures after 100 years of fertilization (Tilman, 1982). In these communities, light likely became the only limiting resource. Theory and such observations suggest that, to the extent to which a trophic level is not a monoculture, it is necessary to consider a model more complex than one with a single limiting resource, two trophic levels, spatial and temporal homogeneity, and equilibrium. Two limiting resources If there were several limiting resources, but a two-trophic level community was at equilibrium in a physically-uniform habitat, there could be no more consumer species than there were limiting resources (Armstrong and McGehee, 1980; Tilman 1980, 1982). For many animal communities, such an approach may seem able to explain the coexistence of as many animal species as are observed. The resources consumed by herbivorous animals are plants. Several authors (e.g., Grubb, 1977) have argued that various parts of a plant species (such as roots, leaves, flowers, fruits, seeds, and stems) function as distinct resources. Thus, there would be no conceptual problem with saying that the simple assumptions above could allow several times more herbivore species than plant species, and as many predator species as herbivore species. For many communities, the observed diversity of herbivorous and predaceous animals may be less than the num- ber of their resources. Thus, these simple assumptions could, potentially, explain the diversity of these trophic levels. Indeed, it could be asked why there are not more animal species (Tilman, 1982). A problem occurs, though, for most plant communities. Experimental manipulations of plant resources have shown that there are from one to at most four or five limiting plant resources in a given habitat (Tilman, 1982). And yet, these habitats often contain hundreds of plant species. Clearly, to explain the structure of these plant communities, it will be necessary to invoke one or more additional factors, such as spatial heterogeneity, temporal variability or another trophic level. Two TROPHIC LEVELS: SPATIAL STRUCTURE Spatial heterogeneity in a physical factor More complex patterns can occur if there is a spatially-structured habitat. The spatial structure can be in either the intensity of physical limiting factors or in the supply rates of limiting resources, or both. At equilibrium, in a physically-structured habitat with one limiting resource and two trophic levels, it is possible for a potentially unlimited number of species to coexist if each species is a superior competitor for the limiting resource under a particular physical regime. For instance, if the physical variable is temperature, a species will be able to exist in a habitat if there is a microhabitat with a temperature range for which it has the lowest R* for the limiting resource of all the competitors. A hypothetical case is illustrated in Figure 1C. An experimental study of algal competition for a single limiting resource at various temperatures showed that this simple approach had reasonably good predictive power (Tilman et al., 1981). Similar diagrams could be drawn for the dependence of each species' R* on any other physical limiting factor. Consider, for instance, the patterns shown by three species of parasitic wasps introduced into commercial orange orchards in southern California to control an insect pest, the red scale, Aonidiella aurantii (DeBach and Sundby, 1963). These three species of wasps, Aphytis chrysomphali, 10 DAVID TILMAN A. lingnanensis, and A. melinus, all of which apparently compete for a common resource, the red scale, were introduced sequentially to southern California. Each introduction led to a period of rapid competitive displacement. All three wasps still exist in California, but each occupies a climatically different region. Although other factors are surely involved, the current distributional patterns of these species suggest that each may be a superior competitor for red scale for a particular range of physical conditions (perhaps temperature), much as illustrated in Figure 1C. Consider, also, the various plots which received complete mineral fertilizer in the Park Grass Experiments. Because of the great plant biomass produced in these plots by the high availability of all mineral nutrients, light is the most likely limiting resource. The soil pH of these plots varied depending on whether or not the plots were limed and whether they received nitrogen as ammonium or nitrate. Figure 1D shows that the three most abundant plants in these plots, Holcus lanatus, Alopecurus pratensis and Arrhenatherum avenaceum, were each dominant at a different pH. These differences would be explained if their light requirements {i.e., the R* for light of each species) depended on pH, with Holcus having the lowest R* for light at low pH, Alopecurus having the lowest R* at intermediate pH, and Arrhenatherum having the lowest R* for light at highest pH, much as illustrated in Figure 1C. Thus, if the resource requirements of consumer species depend on the level of one or more spatially-variable physical factors, many species can potentially coexist at equilibrium on one limiting resource. Similarly, seasonal or other regular temporal changes in physical factors could allow many such species to coexist stably. Spatial heterogeneity in resource supply If there is just one limiting resource, only one species will be able to exist at equilibrium in a community of immobile consumers with two trophic levels, no matter how spatially heterogeneous the supply rate of the resource might be (Tilman, 1982). This is predicted because, in each micro- habitat, the population density of the consumer will, at equilibrium, be great enough to reduce resource levels down to its R*. The one species with the lowest R* will be able to displace all competitors from these microhabitats. As soon as there are two or more limiting resources, the number of species that can coexist depends on the types of resources. Figure 2 shows the various ways that the reproductive rate of a species may depend on the joint availabilities of two resources (Tilman, 1980). The curves drawn are resource-dependent growth isoclines. All environmental availabilities of R, and R2 which fall on one of these isoclines lead to the same reproductive rate. This rate is the reproductive rate which exactly balances the mortality rate experienced by the species in that habitat. Thus, all availabilities of R, and R2 along each of these isoclines lead to no net change in the population density of the consumer. If resource availabilities were in the shaded region outside an isocline, the population size of the species would increase. If resource availabilities were in the unshaded region inside an isocline, the population size would decrease because reproductive rate would be less than mortality rate. Most of the resources consumed by plants are essential. Plants require 20 or so different mineral elements (N, P, K, Ca, Mg, etc.), water and light. A plant cannot decrease its need for one of these essential resources by having more of another. Thus, the long-term reproductive rate of a plant (sensu Hubbell and Werner, 1979) is determined by the one resource in lowest availability relative to need, and is independent of the availability of all other non-limiting resources. Essential resources give isoclines with right-angle corners (Fig. 2A). Some resources, such as the pollen collected by pollinators, are complete foods nutritionally, but the need for pollen as a food source can be decreased by such energy-rich but protein-poor foods as nectar. Such resources are called hemi-essential (Fig. 2B). Most of the foods eaten by animals, because they are parts of other living organisms, are nutritionally complete, and thus can be substituted for each other. They may be perfectly substitutable COMMUNITY STRUCTURE: CONSUMER-RESOURCE APPROACH 11 for each other, giving straight-line isoA. Essential B. Hemi-essential clines (Fig. 2C), or complementary, giving isoclines which bow inward (Fig. 2D), or antagonistic, giving outward-bowing isoclines (Fig. 2E), or switching, giving outward-facing right-angle-corner isoclines (Fig. 2F). Many herbivores are specialized on one or a few host plant species, and tend to switch from one resource to another, consuming the one resource that leads to 1 ° 1 the greatest reproductive rate. I call D. Complementary C. Substitutable resources that are consumed in a switching manner "switching resources." Indeed, optimal foraging theory (Rapport, 1971; Covich, 1972) predicts that for nutritionally substitutable resources, consumers should show switching behavior in two of the three general cases (Tilman, 1982). The isoclines of Figure 2 can be used to predict the outcome of competition for various types of limiting resources. Let us E. Antagonistic F. Switching first consider two plant species competing for two essential resources. If the isoclines cross, as shown in Figure 3A, the point at which they cross is the environmental concentration (or availability) of the two resources for which both species could exist in a habitat. At this point, species A of Figure 3A is limited by R2 and species B is limited by R,. The coexistence would be R« or S r S. stable if each species consumed relatively more of the resource that limited it at equi- FIG. 2. The solid curves show the environmental librium. Optimal foraging theory (Tilman, concentrations of resources 1 and 2 for which the 1982) predicts that a plant should consume reproductive rate of a population just balances its rate, for various types of resources. R, and two essential resources in the proportion mortality R, are environmental availabilities of resources 1 and in which the plant is equally limited by the 2. S, and S2 are supply points for the resources. If a resources. Such optimal foraging, assumed habitat has resource availabilities that fall in the shaded in Figure 3A and B, causes the two-species region outside this isocline, population size of the equilibrium points to be locally stable (Til- consumer species should increase. In the unshaded region inside the isocline, population size should man, 1980). These consumption rates decrease. The shapes of the isoclines shown define 6 define the types of habitats in which both different types of resources. species can coexist or one species competitively displaces the other (Fig. 3A). In Figure 3, R, and R2 are the environ- should be used. Every possible resource mental availabilities of resources 1 and 2. supply point can be associated with (mapped Si and S2 are the maximal amounts of all into) a particular equilibrium outcome of forms of resources 1 and 2 in the habitat, competition. Assuming that mortality rates and are used to define the rate of supply are constant from one habitat to the next, of each resource (Tilman, 1982). The point each habitat is characterized by its resource (Si, S2) is called the resource supply point. supply point. For Figure 3A, habitats with It is an idealization of resource supply that a low rate of supply of R, (i.e., a small value is useful in graphical theory. For actual for S,) and a high rate of supply of R2 (i.e., cases, realistic resource supply functions a large S2) will be dominated by species A, R r S 12 DAVID TILMAN A. I A c. B wins A wins A & B Coexist CM CO A & B coexist CM CO L- o CM CM CE i or u A wins or D. A & B Coexist A wins or S-| R1 or FIG. 3. A. The thin, solid lines with right-angle corners are resource-dependent growth isoclines for species A and B (see Fig. 2). The point at which these isoclines cross, indicated by a dot, is a two-species equilibrium point. The thick, solid lines coming out from this two-species equilibrium point have slopes equal to the ratio of RS:R, in the diets of species A and B. These lines indicate the resource supply points (S,, S2), for which these two species can stably coexist. Any habitats with resource supply points in the region of coexistence will have their environmental availabilities, R, and R,, reduced down to those of the two-species equilibrium point. B. When four species compete for two essential resources, and have resource isoclines as illustrated, there are habitats in which various pairs of these species can coexist. If there is point-to-point spatial heterogeneity in resource supply rates within a habitat, as illustrated by the circle, all four could coexist in this habitat. C. The solid lines show the resouce-dependent isoclines of species A and B, which are competing for two switching resources. The two species equilibrium point, shown with a dot, is stable. Species A and B will coexist in habitats with resource supply points (S,, Ss), in the region indicated. D. However, no more than two species can coexist when limited by two switching resources, no matter what the traits of the species and no matter how spatially heterogeneous the habitat may be, as illustrated above. As shown, species A and/or B will displace all other species, at equilibrium, from all habitats in which R, and R» are limiting. COMMUNITY STRUCTURE: CONSUMER-RESOURCE APPROACH with species B driven to extinction. This occurs because species A and B are both limited by R1; and species A can reduce Rt to a level below that required for the survival of species B. In habitats with high rates of supply of Rt but low rates of supply of R2, both species will be limited by R2, and species B will displace species A (Fig. 3A). Species A and B should stably coexist in habitats which have resource supply points (Si, S2), in the intermediate region shown (Fig. 3A). In this region, each species is limited by a different resource. For two species to stably coexist when competing for the same limiting resources, each species must be a superior competitor for one resource and an inferior competitor for the other resource, and each species must consume relatively more of the resource that limits it at equilibrium. These requirements can be used to explore the plausibility of coexistence in various cases. Consider, for instance, the observed coexistence of soil bacteria and vascular plants, both of which require and may be limited by inorganic nitrogen. The available evidence suggests that bacteria have much lower requirements (R*) for nitrogen than do any vascular plants (e.g., Goring and Clark, 1948; Paul, 1976; Anderson etai, 1981; Elliot etai, 1983). How could vascular plants coexist with bacteria? Bacteria also require reduced carbon (organic matter) as an essential resource. If bacteria are relatively more limited by organic matter and vascular plants by nitrogen or some other resource, their coexistence could be explained. Indeed, consistent with this view, the addition to soils of non-nitrogenous organic matter or organic matter with very high carbon:nitrogen ratios, such as straw, greatly increases bacterial biomass (Behera and Wagner, 1974; Elliot et al, 1983) and reduces vascular plant growth (Biederbeck, 1980; Persson, 1980; Parton etai., 1983), presumably because bacteria, no longer limited by organic matter, reduce available nitrogen to levels below that required by the vascular plants. A similar pattern may explain the coexistence of heterotrophic bacteria and algae in the plankton of lakes. Both require phosphorus, but 13 only bacteria require organic compounds for their growth. Bacteria have much lower requirements for phosphorus than algae (Currie and Kalff, 1984a, b), but are limited by organic matter (Rhee, 1972; Mayfield and Innis, 1978; Meffert and Overbeck, 1979; Cole, 1982; Currie and Kalff, 1984a, b). Diagrams such as Figure 3A and B, and the associated differential equations could be used to model these cases. If more than two species were to compete for two essential resources (Fig. 3B), their requirements could define habitats in which various pairs of species could coexist. If there were spatial heterogeneity in the supply rates of the limiting resources within a region, it would be possible for many more than two species to coexist on two limiting resources. For instance, the circle shown in Figure 3B could represent the range of point to point spatial variation in the supply rates of limiting resources in a habitat (Tilman, 1982). Such spatial variation in the resource supply points would allow all four species to coexist in this habitat. Indeed, there is no simple limit to the number of plant species that can potentially coexist on two essential resources in a spatially heterogeneous habitat (Tilman, 1982). In contrast, for animals competing for switching resources, the number of species that can coexist in a spatially heterogeneous habitat can be no greater than the number of switching resources (Tilman, 1982). Consider, first, two species competing for switching resources (Fig. 3C). The equilibrium point is locally stable, allowing these two animal species to coexist much as do the two plants of Figure 3A. However, no matter how isoclines may be drawn for cases with many species competing for two switching resources (Fig. 3D), there is only one stable two-species equilibrium point. This equilibrium point is shown with a dot in Figure 3D. The points at which the other isoclines cross are not stable equilibrium points because they are further from the origin than the stable point. Species A and B will be able to continue growing until they reduce resource levels down to their two-species equilibrium 14 DAVID TILMAN point, at which point there are insufficient resources for the survival of species C and D. Thus, in either a spatially homogeneous or spatially heterogeneous habitat, only two species can coexist on two switching resources (Fig. 3D). Similar arguments can be made for antagonistic resources. However, for all other types of resources, spatial heterogeneity can allow many more species to coexist than there are limiting resources. Thus, for plants, spatial heterogeneity in the supply rates of limiting resources may be a very important factor in determining the diversity of a community. For animals, which are motile consumers, spatial heterogeneity can cause them to switch from one resource to another. Switching, though, means that no more animals can coexist than there are limiting resources, no matter how spatially heterogeneous the habitat may be. If many animal species respond to their resources by switching, spatial heterogeneity may be less important in allowing many animals to coexist than it may be for plants (Tilman, 1982). Two TROPHIC LEVELS: TEMPORAL VARIABILITY Many processes do not go to equilibrium. Even for the simple case of a physically homogeneous habitat with one limiting resource and two trophic levels, the longterm pattern in dynamically-changing communities can differ markedly from that in otherwise comparable communities that go to equilibrium. Armstrong and McGehee(1976a, b, 1980)and Levins(1979)have demonstrated that several species can stably persist on a single limiting resource if resource levels fluctuate. A qualitative insight into the processes involved may be gained from Figure 4. (For more details, see Tilman, 1982, pp. 237-243.) If resource levels fluctuate, the growth rate of a species can depend both on the average availability of the resource and the variance in resource availability through time. Some species, such as species B in Figure 4A and B, can exploit variance in resource supply by having the gain in their reproductive rate when resource levels go above the mean be greater than the loss when levels fall below the mean. For species B, temporal variance in resource supply functions, in a sense, as another resource. For species A, which has a linear dependence of its growth rate on resource levels, fluctuations in resource levels around the mean do not influence its mean reproductive rate. This is because its decrease in growth when resource levels fall is exactly balanced by its increase when resource levels rise. Thus, species A responds only to average availability. For other species (not illustrated), fluctuating resources could act as a limiting factor (Tilman, 1982). As shown by Armstrong and McGehee (1980), these two species can coexist on one fluctuating resource because species A is relatively more limited by the average availability and species B is relatively more limited by the variance in resource availability (Fig. 4B). Armstrong and McGehee (1980) suggest that, in theory, an unlimited number of species could coexist on a few limiting but fluctuating resources as long as the species have the appropriate differences in their growth responses to average resource availabilities versus variance. There are many habitats in which there are continual fluctuations in the availabilities of the limiting resources. If these represent small fluctuations around the mean, it is likely that the dominant species will be those that are the best competitors for the limiting resources in the absence of fluctuations. If the fluctuations are large relative to the mean, it is possible for the species that exploit variance (or are least limited by variance) to be the dominants. However, whatever their magnitude, such fluctuations could explain the long-term persistence of many more species than there were limiting resources. It may be that the high diversity of many planktonic algal communities and terrestrial plant communities can be explained by such dynamic processes, with many species persisting in a habitat by exploiting resource fluctuations. An experimental study of the effects of periodic nutrient pulses on the diversity of algal communities grown in chemostats revealed that 5 to 7 species persisted in the periodically perturbed chemostats (Som- COMMUNITY STRUCTURE: CONSUMER-RESOURCE APPROACH A. Growth Curves 15 B. Resource Isoclines Species B 09 rr * o O R, Resource Average FIG. 4. A. The solid curves are resource-dependent growth (reproduction) curves for species A and B. The broken curve shows the mortality rate, m experienced by each species. Note that species A has a lower R* for this resource than does species B. B. Species A and B of part A above will respond differently to resource fluctuations. Because of its linear response to resource levels, the growth rate of species A will be determined by the average resource availability, and will be unaffected by fluctuations. In contrast, at a low average availability of the resource, the growth rate of species B will increase with fluctuations because of the initial exponential increase in its growth rate with resource level at low resource levels. Thus, species B requires less resource, on average, to survive in a fluctuating habitat than to survive in a constant habitat. This could allow the species to stably persist in a fluctuating habitat, as illustrated. The solid lines in this figure are resource-dependent growth isoclines, and the dotted lines show the potential region of coexistence. mer, 1984), but that only 1 to 3 species coexisted in the equilibrium chemostats (Sommer, 1983, 1984). The results of the equilibrium chemostat experiments are consistent with the predictions of the equilibrium theory of consumer-resource interaction illustrated in Figure 3B (Sommer, 1983), as are the results of numerous other studies of algal nutrient competition in equilibrium chemostats (Tilman et al., 1982). One of the most notable examples of such dynamic coexistence may be deserts, in which one of the main limiting resources, water, has extremely high unpredictability. Different plant species may be able to specialize on rainfall events of different magnitudes or frequencies, and thus there is the theoretical potential for many species to coexist on this one resource. There are other limiting resources in deserts, especially soil nitrogen (Power, 1980), that may help explain coexistence. In the deserts of the southwest United States, long-lived plants such as creosote and mesquite may be mainly exploiting seasonal average rainfall patterns whereas the numerous species of annual plants may be exploiting temporal variance in rainfall. In theory, at least, it is possible for each species to be a superior competitor at a particular point along the continuum from exploiting only the average rainfall to exploiting only the variance. THREE TROPHIC LEVELS Let us go back to the simplest two-trophic level model and modify it by adding a third trophic level. What kind of structure could an equilibrial, spatially homogeneous community have if it had three trophic levels and a single limiting resource? Consider a food web with a resource level, a consumer, and a top consumer (predator) level. An extension of the ideas developed by Levin et al. (1977) shows that there is no limit to the number of species that can potentially coexist in such a community if the consumer which is the superior competitor for the limiting resource in the absence of predation is the most suscepti- 16 DAVID TILMAN ble to predation, the consumer which is the next best resource competitor is the next most susceptible to predation, and so on (Tilman, 1982). This comes from two inequalities. If the number of resource types is R, the number of primary consumer species is C, and the number of top consumer (predator) species is T, theory predicts that the number of top consumer species must be less than or equal to the number of consumer species (their prey). The number of consumer species must be less than or equal to the sum of the number of their resources and the number of top consumer species (their predator) (Tilman, 1982). Thus, C< R+ T and T < C. One resource could support one consumer, which could support one top consumer. However, with one resource and one top consumer, two consumers could coexist. With two consumers, there could be two top consumers. Two top consumers and a resource, though, could allow three consumers to coexist. This process could go on indefinitely, as long as the top consumers and consumers had the appropriate traits (Tilman, 1982). The experimental studies of Paine (1966) on an intertidal invertebrate community showed that species richness was highly dependent on the presence of a top predator, the starfish Pisaster, which preyed preferentially on the species that were the best competitors for open space, a major limiting resource. The rocky intertidal community studied by Paine thus had three trophic levels: a limiting resource, space; sessile, filter-feeding invertebrates; and a predator on the sessile invertebrates. When Paine removed starfish from an area, the species richness of the second trophic level fell from about 15 to about 8. Lubchenco (1978) also studied a three-trophic level, intertidal system. For the macrophytic algae of tide pools, light and nutrients were probably major limiting resources. The algae were fed upon by an herbivorous snail, Littorina littorea. Lubchenco found that the species richness of the algal community was highest at intermediate snail densities. The snail was found to feed preferentially on the algae which were the best competitors in the absence of herbivory. Both of these studies show that the structure of the middle trophic level can be greatly influenced by the action of species on a third trophic level. Qualitatively, these studies seem to be similar to predictions made by a simple model of a three-trophic level system. When the effect of the third trophic level was minimal, as when Pisaster or Littorina was in low abundance, species diversity was low, as would be expected for a simple two-trophic level system consisting of one or a few limiting resources and some consumer species. Comparably, when Littorina was in very high density, the interactions between the macrophytic algae and their limiting resources may have been relatively unimportant, and the system might have approximated a two-trophic level system, with the original resource level no longer important. At intermediate densities of Littorina, all three trophic levels would have been important. Several recent discussions of food webs suggest that there is constancy in the structure of food webs, independent of the type of habitat or the equilibrium or non-equilibrium nature of the habitat (Cohen 1978; Briand and Cohen, 1984). This constancy, first expressed as there being a constant ratio of prey to predators in food webs, is now thought to result from there being a constant proportion of the species on the first, second and third trophic levels. For a three trophic level system, the inequalities above state that the number of consumer species must be less than or equal to the sum of the number of resources and predators. The data in Briand and Cohen (1984), though only expressed on a percent basis, are amazingly consistent with this prediction. Their survey of 62 food webs showed that the proportion of species in any given trophic level was independent of the total number of species in the food webs. They found that 19% of the species were on the first level, 52% were on the second level, and 29% were on the third level. The sum of 19% and 29% is 48%, 17 COMMUNITY STRUCTURE: CONSUMER-RESOURCE APPROACH very close to the observed 52% for the middle trophic level. If species were randomly distributed among the three trophic levels, 33% of the species would be expected to be on each level. If this were so, the ratio of the sum of the number of species on the first and third levels to the number of species on the second level would be 2.0. The ratio predicted by the inequalities above is 1.0. The actual ratio, 0.90, is much closer to that predicted by theory than to that expected by chance alone. This is consistent with the hypothesis that a significant portion of the species diversity of communities may be explained by the interplay of competition andpredation. However, as is the case for all such correlational data sets, there are numerous alternative explanations for these observations. DIRECT VERSUS INDIRECT EFFECTS Within the framework of the consumerresource approach, when only two trophic levels are considered, the interactions included are simple ones caused directly by resource consumption. Thus, two consumers, both of which were limited by the same resources, would functionally behave as competitors for the limiting resources. However, as soon as a third trophic level is added, it is possible for the total effect of one species on another to be qualitatively different than might be assumed from their trophic positions. For instance, the two species in the top consumer level of Figure 5A always function as competitors because they are both limited by the same resources. In contrast, the top consumers in Figure 5B may function as if they are competitors or mutualists depending on the strength of the various links (Levine, 1976; Lawlor, 1979; Vandermeer, 1980). This major shift in the functional relations between these top consumer species is caused by the several pathways whereby species may affect each other in systems with at least three trophic levels. Top consumer 1 will affect top consumer 2 (Fig. 5B) directly through consumption of consumers 1 and 2, and indirectly through the effects of changes in the densities of consumers 1 and 2 on their resource levels. If, for Figure 5B, top consumer 1 preferen- A. i i Resource Resource 2 Consumer I Consumer 2 Resource Resource 2 Consumer I Consumer 2 Top Consumer I | Top Consumer 21 B. C. Resource I | Resource 2 FIG. 5. Parts A, B and C show increasingly complex approximations to a food web. All of the links are either consumer-resource interactions or are resource supply. For part C, the top consumers may effect each other "indirectly" in two different ways: through their effects on the availabilities of resources 1 and 2 or through effects mediated via the competition of the consumer species for the resources. It may be that the process of resource re-supply is as important or more important than differential consumption in structuring this community. The appropriate subsection of the food web would directly include the direct and indirect interactions important in a given community. 18 DAVID TILMAN tially feeds on consumer 1 and top consumer 2 preferentially feeds on consumer 2, increases in the density of top consumer 1 would lead to decreases in the density of consumer 1, indirectly providing more resources for consumer 2, and thus increasing the growth rate of top consumer 2. The comparable process causes increases in the density of top consumer 2 to increase the growth rate of top consumer 1. Thus, the two top consumer species, which are directly competing for the consumer species, can function as if they are mutualists (Levine, 1976; Lawlor, 1979; Vandermeer, 1980). Experimental studies by Lynch (1978) support the ability of such indirect effects to modify the direct effect of one species on another. Lynch (1978) found that two species of herbivorous zooplankton functioned as indirect mutualists during the time of the season when their resources, algae, were severely nutrient limited, but functioned as competitors when the algae were not as strongly competing for nutrients. This major, qualitative change, caused by indirect effects, illustrates how a broader view of the food web may be needed to understand community structure. I want to stress, though, that the "indirect effects" of one species on another are indirect only in the sense that they are mediated through another factor. They are directly included in a food web, such as Figure 5C. By their act of consumption, top consumers decrease the density of their prey, and thus directly influence them. Top consumers also may directly influence the rate of supply of limiting resources. If the consumers are plants and the resources are nutrients, top consumers may supply nutrients through excretion of wastes which contain N, P, K, etc. If light is a limiting resource, a top consumer which ate one plant would increase the availability of light for other plants (Tilman, 1983). For Lubchenco's (1978) study, increased densities of the herbivorous snail Littorina littorea probably led to increased availability of light on rock surfaces. It also probably increased the point-to-point variance in light availability on rock surfaces. If light were a limiting resource in that study, it would be possible to interpret the effect of Littorina littorea as being caused by its influence on the rate of supply and spatial heterogeneity of a limiting resource, light. In this case, resource competition theory would predict a humped diversity curve (Tilman, 1982), as Lubchenco observed. Similarly, for invertebrates of the rocky intertidal (Paine, 1966), there is a humped relationship between species diversity and disturbance, whether the disturbance is caused by Pisaster predation or wave or log action. All such disturbances influence the rate of supply of the limiting resource, space, and thus are predicted to lead to a humped diversity curve (Tilman, 1982). Thus, top consumers can have three types of effects on their prey: a direct effect from their consumption of the prey, indirect effects mediated through other species that influence their prey, and indirect effects from the resupply of the resources required by the prey. The alternative interpretations of the work by Lubchenco (1978) and Paine (1966) presented in this paper indicate that further experimentation will be needed to determine the relative importance of direct and indirect pathways in particular systems. Both paths are easily included in a consumer-resource model with three trohic levels. OVERVIEW The most simplified, idealized food web has two trophic levels, a spatially homogeneous habitat, and temporal homogeneity. This idealized case can be considered to be the simplest functional element of the food web. In such a food web, theory predicts that the number of consumer species must be less than or equal to the number of limiting resources. When any of the simplifying assumptions of this idealized case are relaxed, theory predicts that there is no simple limit to the number of consumer species which could potentially coexist. Thus, if it is assumed that the habitat has spatial heterogeneity in a physical limiting factor, or variability in the supply rate of a limiting resource, or that interspecific interactions do not go to equilibrium, or that there are three trophic levels, it is possible for a potentially unlimited COMMUNITY STRUCTURE: CONSUMER-RESOURCE APPROACH number of species to coexist when competing for a few limiting resources. However, even given such complexity, it is possible for more than one species to coexist on several resources only if the species have the appropriate traits relative to each other. For many species to coexist on one limiting resource in a habitat with spatial variability in a physical limiting factor, each species must be a superior competitor for that resource for some particular level or range of the physical factor, and must be an inferior competitor outside that range. For species to coexist because of spatial heterogeneity in the supply rates of two limiting resources, the species must be inversely ranked in their requirements for one resource versus the other, and each species must consume the resources in the ratio in which it is limited by them. The tradeoffs required for species to coexist because of nonequilibrium interactions are less clear, but available results suggest that species have to be differentiated in their ability to compete for the average availability versus the variance in the resource. For species to coexist because of interactions among three or more trophic levels, species on intermediate trophic levels must be inversely ranked in terms of their competitive abilities for resources versus their susceptibility to predation. In addition, if any of these mechanisms is operative in a given community, the pattern of variation in the traits of individuals within a given species should also be consistent with the trends predicted above. For example, if there is genotypic variation in a plant species, and if this plant species is coexisting with other plants because it is specialized on a particular proportion of two limiting essential resources, each genotype should also be specialized on a particular proportion of the resources such that it can coexist with the other individuals in its own and other species. Each mechanism which could explain a high diversity community places different constraints on the traits of the coexisting species. One way to determine what level of complexity might be necessary to explain the structure of a given community would be to determine the traits of the coexisting 19 species. If the species were observed to have traits consistent with the constraints imposed by one of the food web structures but inconsistent with the others, the other structures could be rejected as being of lesser importance. If it seemed that the traits were partially consistent with several of the constraints, it could be that several were operative. In that case, it would be necessary to determine the predicted relationships between the multiple constraints which could allow the species to coexist, and determine if the species had the appropriate suite of characteristics. In this paper I have presented a greatly simplified view of some of the factors which may influence the structure of natural communities. There are many complicating factors which I have not mentioned. Among these are the complexities of multiple stable equilibria that may result from age or size structure in populations (Hassell and Commins, 1976), coexistence that may result from differential immigration and extinction rates in patchy habitats (Levin and Paine, 1974; Slatkin, 1974; Armstrong, 1976), and patterns caused by genetic variability within and among species. There is little empirical evidence currently available that would support the view that one or another of the models outlined in this paper is of general importance or is always unimportant in natural communities. To some extent, the complexity of theory required in ecology will reflect the complexity of the questions being asked. I would like to suggest, though, that all of the above models are extensions of the consumer-resource approach to ecology. This approach, by emphasizing the feeding relations among organisms, incorporates one of the most basic processes in the biology of populations. Each species is a consumer and each, eventually, is consumed. It may be that much of the structure of natural communities can be explained by considering greatly simplified subsections of the food web. In many complex processes, a few steps often become rate-limiting, and control of the majority of the observed dynamics. Perhaps by explicitly studying the mechanisms of consumer-resource 20 DAVID TILMAN interactions and using these to build and test models of food webs, we will be able to find a minimal subset of the food web that explains most of the patterns we observe. ACKNOWLEDGMENTS This material is based on work supported by the National Science Foundation under Grant No. BSR-8114302-A02. I thank two anonymous reviewers and Mary Price for their comments on this paper, and Sue McEachran for help preparing this manuscript. I also thank the John Simon Guggenheim Memorial Foundation for supporting me during part of the time I prepared this manuscript. REFERENCES Abramsky, Z. and M. L. Rosenzweig. 1984. Tilman's predicted productivity—diversity relationship shown by desert rodents. Nature 309:150-151. Anderson, R. V., D. C. Coleman, C. V. Cole, and E. T. Elliott. 1981. 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