Revista Chilena de Historia Natural REVIEW 73: 175-198, 2000

The coexistence of species

La coexistencia de especies

CALEB E. GORDON

Department of Ecology and Evolutionary Biology, University of Arizona, Tutson, AZ 85721 USA, e-mail: [email protected]

ABSTRACT

This paper is a critical literature review on the topic ofthe coexistence of similar species within ecological communities. A conceptual framework is provided for dividing coexistence studies and concepts into three distinct time scales. The first six sections deal primarily with ecological-scale, or mesoscale coexistence, defined as coexistence in the classic sense of the competitive exclusion principle and Lotka-Volterra models, wherein interacting populations have had enough time to reach equilibrium. The first four sections briefly review resource partitioning studies and competitive coexistence models, and discuss the relative contributions of, and interaction between empirical and theoretical approaches to the problem of ecological-scale coexistence. The next two sections discuss the importance of biological trade-offs and the role of competition in structuring ecological communities. Based on compelling empirical evidence on both sides of the competition debate, a view of competition's role in structuring communities is proposed wherein the effects of competition are important but incomplete. The next section briefly reviews coexistence as it has been incorporated into habitat selection models, which represents coexistence at a finer time scale generated by the behavioral decisions of individual organisms. Linkages between this type of coexistence and mesoscale coexistence are discussed. Finally, a larger scale of coexistence is explored in which the assumptions of fixed niches, habitats, and species pools in communities are relaxed. This section links global and evolutionary species diversity literature to mesoscale ecological coexistence, focusing on the effects of ecosystem productivity and province size. Factors that govern diversity at large scales may be used to calibrate expectations and make predictions about mesoscale coexistence within particular communities. The study of diversity dynamics at geologic time scales suggests some sort of competitive saturation process, yet community dynamics on the scale of glacial oscillations often appear unsaturated and non-equilibrial. This provides additional support for the idea that competition has an important, but only partial structuring effect on biological communities. Because coexistence is affected by competitive as well as non- competitive influences, both must be incorporated to develop accurate models, make useful predictions, and gain fuller understanding of the coexistence of species within ecological communities.

Key words: coexistence, competition, community structure, resource partitioning, niche.

RESUMEN

Este artículo es una sfntesis critica de la literatura sobre la coexistencia de especies similares en comunidades ecologicas. Se propone una estructura conceptual para dividir Ios estudios y conceptos sobre la coexistencia a tres escalas distintas de tiempo. Las primeras seis secciones se refieren principalmente a la coexistencia a una meso-escala, o escala ecologica, definida como coexistencia en el sentido clásico del principio de exclusion competiti va, y el modelo Lotka-Volterra, en el cuallas poblaciones han interactuado por un tiempo suficiente para llegar a un equilibrio. Las primeras cuatro secciones revisan brevemente Ios estudios de division de recursos y Ios model os de coexistencia en la literatura teorica, y discuten !as contribuciones relativas de, y la interaccion entre Ios enfoques empfricos y teoricos a! estudio de la coexistencia en una meso-escala. En !as proximas dos secciones, se considera la importancia de compromisos biologicos y la competencia en la estructuracion de comunidades ecologicas. Considerando la fuerte evidencia que presentan ambos ban dos del debate sobre la competencia, se propone una organizacion conceptual de la estructura comunitaria en la cuallos efectos de la competencia son importantes pero incompletos. La proxima seccion examina la coexistencia a una escala temporal mas fina tal como se ha incorporado en Ios modelos de seleccion de habitat. A estaescala, la dinamicade !as interacciones refleja el comportamiento de organism os individuales. Se discute la relacion entre la coexistencia a este nivel y la coexistencia a la meso-escala. Finalmente, se explora un ni vel de escala más amplio de coexistencia, en el cual !as suposiciones de nichos, habitats, y especies fijos son relajadas. Esta parte enlaza la literatura sob re la diversidad global y evolutiva de especies con la coexistencia ecologica a la meso-escala dentro de comunidades especfficas. El estudio de !as dinamicas de la diversidad a la escala geologica parece revelar

(Received March 2, 1999; accepted July 2, 1999; managed by F. M. Jaksic) 176 GORDON

algún proceso de saturaci6n competitiva. Sin embargo, !as dinamicas de comunidades en la escala de oscilaciones glaciales frecuentemente no parecen saturadas ni en equilibrio. Estas observaciones apoyan la idea que el efecto de la competencia sobre la estructura comunitaria es importante pero parcial. Y a que la coexistencia puede ser afectada por fuerzas competitivas a la par que es influenciada por factores no competitivos. Para desarrollar model os precisos, hacer predicciones utiles, y obtener un entendimiento más completo de la coexistencia de especies dentro de comunidades ecol6gicas es necesario tomar en cuento ambos tipos de factores.

Palabras clave: coexistencia, competencia, estructura comunitaria, division de recursos, nicho.

INTRODUCTION debate over the role of competition in structuring ecological communities is reviewed, focusing on The coexistence of similar species in ecological the implications for the coexistence of species in communities is one of the oldest, most studied, ecological communities. and most perplexing problems in ecology. Dating back to theoretical and experimental studies in the early part of this century, the coexistence Defining ecological coexistence problem has provided a conceptual basis for a vast and diverse body of research. This research The problem of ecological coexistence was crys- has produced a rich diversity of modeling tools tallized by the results of Gause ( 1934 ). His and a wide base of empirical data that have illu- laboratory experiments with paramecia showed minated many aspects of the structure and func- that when two competitor species were intro- tioning of ecological communities. Ecological duced together in a lab culture, one or the other coexistence continues to be a popular research species would always go extinct. This led to paradigm today, yet the very size and importance "Gause's principle" or, "the competitive exclu- of the body of coexistence research have contrib- sion principle" (Hardin 1960) which states that uted to its current state of disorganization. To- two species with identical niches cannot coexist. day, studies with the word "coexistence" in the This principle has served as the conceptual title may have almost nothing in common except basis for a legacy of investigations of ecological their conceptual origin. Several different areas of coexistence. I define ecological coexistence as research centered on coexistence are not feeding coexistence in the sense of Gause. This is the back to one another. Terms are being used in classical coexistence problem as it is most com- unclear and heterogeneous ways. Scales of space monly treated in ecological literature. At this and time are often not clearly defined. scale, we are integrating over many smaller-scale The goals of this review are twofold. The first interactions, behaviors, and decisions of indi- is to summarize what we have learned about eco- vidual paramecia, and over the entire test tube. logical coexistence to date. This section is a We are studying the system at the point where critical review of resource partitioning studies some sort of ecological equilibrium can poten- and a more comprehensive review of coexistence tially have been reached. One or the other species theoretical studies, which represent the two ma- may have been driven extinct through competi- jor approaches to the ecological coexistence prob- tion. The niches and habitats of species, as well lem. The strengths and limitations of these two as the species pools of communities or regions are approaches are discussed, as well as the relative fixed. roles of empiricism and theory in the study of ecological coexistence. The second goal of this review is to draw to- Resource partitioning studies gether ideas from several other areas of research that have made important contributions to our The empirical approach to the ecological coexist- understanding of ecological coexistence. Studies ence problem is embodied by resource partition- of habitat selection help us to understand coexist- ing studies. In the words of Schoener (1974), ence at a finer scale of space and time, giving us "The major purpose of resource partitioning stud- a more mechanistic basis for understanding coex- ies is to analyze the limits interspecific competi- istence at the ecological scale. Studies of global tion place on the number of species that can stably species diversity patterns have revealed how spe- coexist." The essence of this highly popular cies coexist at larger scales of space and time, research paradigm is to go into nature, find coex- illuminating evolutionary constraints that govern isting sets of ecologically-similar species and coexistence at the ecological scale. Finally, the measure niche differences among them. But how THE COEXISTENCE OF SPECIES 177

do you measure niches in nature? G. E. Hutchinson found that two patterns were predominant, each ( 1957) codified the concept of the niche by de- representing about 41% of published cases in scribing it as a hypervolume with "n" dimensions which appropriate data were collected. The first (or niche axes) corresponding to the number of is distinct preference organization (MacArthur & biotic and abiotic factors to which species may Levins 1967) in which each species' realized exhibit differential responses. It is impossible to niche corresponds with the most preferred part of identify all of the relevant niche axes in a given its fundamental niche. The second is shared community or assemblage. Even among those preference organization (Rosenzweig 1991) in variables that can be identified as important niche which all species prefer the same region of a axes in certain situations, there are many that are niche axis (an overall better, or more productive difficult or impossible to measure empirically. part). In the latter scenario, realized niches are Thus, the reality is that resource partitioning spread out along the axis according to a hierarchy studies do not measure overall niche differences in which the competitively-superior species oc- between species. Instead they measure the vari- cupy the best part of the axis, and the competi- ation along one, or several environmental or bio- tively-inferior species are relegated to worse parts logical axes that represent an unknown fraction of the axis. The weakest competitors must also be of "n". This places an important limitation on the the most tolerant of poor conditions in order to interpretation of resource partitioning studies in survive. The actual prevalence of shared-prefer- the context of ecological coexistence. Lack of ence organization may be higher than Wishieu's observed variation cannot be taken as a rejection 41% as this type of organization was twice as of Gause' s principle because it does not necessar- common as distinct preference organization ily mean that species' niches are identical. In among studies that used more discriminatory ex- fact, where niche differences cannot be found in perimental manipulations. Wishieu was also able resource partitioning studies, they are routinely to make additional generalizations about when assumed to be manifest on unmeasured niche and where to expect shared- vs. distinct-prefer- axes, " ... similarity of species along one dimen- ence community organization. Shared-prefer- sion should imply dissimilarity along another. .. " ence scenarios were more likely to occur along (Schoener 1974). gradual, or quantitative gradients (e.g., tempera- Nonetheless, resource partitioning studies are ture) as opposed to disjunct, or qualitative gradi- critically valuable as empirical observations, and ents (e.g., specific host species). Shared-prefer- have revealed much about patterns of ecological ences were also more prevalent among autotrophs coexistence in nature. Given that resource parti- than among heterotrophs, and among vertebrates tioning studies do not measure all niche axes but than among invertebrates. merely a subset, it is important to ascertain whether Despite important limitations, resource parti- there are biases within this subset. The variables tioning studies have the advantage of biological and study systems that ecologists have chosen for reality. Ecologists have documented ecological resource partitioning studies are not chosen at segregation of coexisting species along many dif- random. They are biased towards well-known ferent environmental and biological gradients. organisms and easily-measured environmental and By considering the results of many resource par- biological axes. At best, these biases are not titioning studies together, we have identified pat- correlated with features of community structure. terns in nature which point to some generalities If this is true, then the overall results from these about ecological coexistence mechanisms studies are generally representative of a larger (Schoener 1974, Wishieu 1998). biological phenomenon. At worst, ecologists have Two widespread practices within studies of re- selected cases that confirm preexisting opinions source partitioning indicate that these empirical or that otherwise represent a skewed subset of approaches may only have scratched the surface overall community patterns. We have few tools of the array of niche axes that are partitioned for separating these two scenarios and obtaining among species in nature. The first is the use of unbiased conclusions. body size as a niche axis (Wilson 1975, Basset One way to avoid subjective biases in resource 1995). This variable is not really a niche axis partitioning studies is to seek patterns of a differ- because it does not describe a relationship be- ent nature than those sought by the authors of tween an organism and its environment. It is individual data sets. Irene Wishieu (1998) used rather a black box with an array of different niche this approach to study the importance of different axes implicitly subsumed within it. Various au- mechanisms of community organization among thors have explained the ecological significance resource partitioning studies published between of body size as a function of birth and death rates 1983 and 1993 in the U.S. journal,Ecology. She (Zi v 1998), resource harvesting efficiencies 178 GORDON

(Reichman & Roberts 1994 ), metabolic require- the reach of emptnctsts. These questions in- ments (Wilson 1975), home range size (Basset clude: What are the limits to the ecological 1995), or other factors that vary with body size. similarity of coexisting species? How is ecologi- In essence, the variable of body size is used as a cal coexistence affected by such factors as differ- proxy for the myriad environmental and biologi- ent carrying capacities, different resource utiliza- cal variables that scale exponentially with body tion functions, different levels of variability or size (Peters 1983, Calder 1984). Because of the environmental patchiness? A variety of math- scaling effect, the ecologically-relevant variables, ematical approaches have made substantial con- themselves, correspond well with body size and tributions to our understanding of ecological co- may include any factor that scales in this way. existence. Examples of apparent resource partitioning by body size are prevalent in the literature, including well- known patterns of constant size ratios among ecolo- The Lotka-Volterra model and analogues gically-similar coexisting species (Hutchinson 1959, Horn & May 1977). This suggests that The largest category among mathematical ap- many of the niche axes that provide a basis for proaches to ecological coexistence includes stud- niche separation in nature are not commonly meas- ies that model the dynamics of systems of ordi- ured in resource partitioning studies. Many of nary differential equations. The vast majority of these would be impossible to measure directly. such studies have used the Lotka-Volterra model The other black box in resource partitioning (eq. 1). studies .is the use of taxonomically-circumscribed sets of species (e.g., Johnson 1986, Fletcher & Underwood 1987, Dickman 1988). In essence, this widespread practice represents the use of dN =r-N. shared ancestry as a proxy for ecological similar- df I ity (Azofsky 1996). Using taxonomically- circumscribed sets of species in resource parti- tioning studies makes the assumption that interspecific competition should be greater among This equation models the growth of competing closely-related species than among distantly re- species (change in population size, N for species lated species, even in the absence of any a priori i through j in time) as functions of the species' ecological explanation for this difference. This intrinsic rates of growth (r), carrying capacities assumption has often been confirmed when tested (K) and competitive effects on one another (a). (Thompson et al. 1991 but see Jaksic et al. 1993 In such studies, the criterion for coexistence of for a counter example). The actual mechanism species is that they increase when rare. Classical behind this pattern is the set of unknown physi- studies of coexistence theory are primarily con- ological, behavioral, and ecological differences cerned with describing the mathematical dynamics that provide niche segregation between of this system with various values, behaviors, and taxonomically-distant species. These differences alternative forms of the parameters, r, K, and α constitute niche axes that are difficult to identify Competitive coexistence has been shown to and/or measure but that account for ecological result from interspecific differences in any of coexistence nonetheless. these parameters (May 1974, Abrams 1975, 1983, Roughgarden & Feldman 1975, Armstrong & McGehee 1980). In general, coexistence is facili- Coexistence theoretical studies tated in these models when parameter values ex- hibit density-dependent behavior (Abrams 1975, The multi-dimensional, unmeasurable nature of Roughgarden & Feldman 1975, Armstrong & ecological niches is not the only problem con- McGehee 1980), or different patterns of variabil- fronting empirical studies of coexistence. It is ity (Abrams 1976, Chesson & Warner 1981, Turelli also difficult to measure other important attributes 1978, 1981, Levins 1979). such as the fitness functions of individuals along One limitation of Lotka-Volterra-based studies niche axes, or the fundamental vs. actual prefer- of ecological coexistence is that many have ences of individuals. One way to get around these analyzed only the behavior of the system at equi- problems is to analyze coexistence using ideal- librium. Some theoreticians have shown increased ized mathematical models. This has permitted possibilities for competitive coexistence in non- ecologists to ask sophisticated questions regard- equilibrial conditions (Armstrong & McGehee ing ecological coexistence that have been out of 1980, Caswell 1982). THE COEXISTENCE OF SPECIES 179

Another limitation is that most Lotka-Volterra existence problem, and within the field of ecol- modelers assume that all species have identi- ogy in general. The original conclusion of cally-shaped resource utilization curves. Several MacArthur & Levins ( 1967) was that the means theoreticians have shown that competitive coex- of the species' resource utilization curves had to istence is facilitated when interacting species have be separated by a minimum distance (d) of the differently -shaped curves (Roughgarden 197 4). standard deviation of the curves (w). This par- Another assumption in many Lotka-Volterra com- ticular result was highly sensitive to model struc- petitive coexistence studies is that niches differ ture such that, "The limiting similarity relation- only along a single niche axis. The incorporation ship (could) be affected by most aspects of the of multi-dimensional variation in niches also re- population biology of a group of interacting sults in increased opportunities for competitive species." (Abrams 1983). This rendered the d>w coexistence (MacArthur & Levins 1967, May result biologically irrelevant, yet we have learned 1974, Pianka 1974). much about the factors that influence the quali- Still other dynamical modeling studies of com- tative behavior of competitive coexistence dy- petitive coexistence have used analogues to the namics from MacArthur and Levins', and related Lotka-Volterra model and have shown additional models. The principal error of limiting similar- theoretical possibilities for competitive coexist- ity theory was merely that it attempted to push ence (Abrams 1975, Turelli 1978, Armstrong & the interpretation of a mathematical model be- McGehee 1980). yond a justifiable level of resolution. Limiting The Lotka-Volterra-based approach to ecolo- similarity theoreticians were not necessarily us- gical coexistence problems saw its greatest pe- ing flawed models but were essentially reading riod of popularity during the 1970's, at which their results out to too many significant digits time it was one of the favorite subjects of given the biological precision of the parameters MacArthur, May, Levins, and many other eco- and fitness functions in Lotka-Volterra models. logical theoreticians. This began with the influ- ential, "limiting similarity" paper of MacArthur & Levins (1967), who studied the equilibrial Lotka-Volterra model with metapopulation dy­ behavior of a Lotka-Volterra system with spe- namics cies showing distinct preference organization along a single niche axis. They achieved a result While limiting similarity studies and studies of consistent with Gause's principle, that ecologi- Lotka-Volterra-based models in general have de- cally-identical species could not coexist. They clined in recent decades, one area that has lived then went a step further to attempt to describe on, and even flourished since Abrams' review, is the limits to the ecological similarity of coexist- the study of Lotka-Volterra competition models ing competitors mathematically. This paper was with patchiness. The idea that colonization and a stimulus for a multitude of subsequent papers extinction dynamics of patches could promote the dealing with the theory of limiting similarity, coexistence of competitors was first concep- and with the conditions for competitive coexist- tualized in Hutchinson's notion of a fugitive spe- ence in general. Abrams reviewed the area of cies (Hutchinson 1951). A fugitive species al- limiting similarity theory in 1983 and concluded ways loses out in in-patch competition, but its that it had generally been unsuccessful. He proficiency at colonizing new patches prevents it noted that the limiting similarity relationship from being competitively excluded from the en- was highly sensitive to the structure of param- tire matrix of patches, so long as the subpopu- eters, resource utilization curves, and relation- lations (within single patches) of the competitive ships in the models (Abrams 1983). Rosenzweig dominant species have a non-trivial probability has described limiting similarity theory as, of going extinct. The colonization of new patches " ... quicksand that trapped the energies of com- allows the fugitive species to continually "flee" munity ecologists for more than ten years and from competition as long as the landscape con- nearly killed the sub-discipline" (Rosenzweig tains some unoccupied patches. This sort of 1995). The virtual extinction of studies pub- coexistence depends on a trade-off between com- lished in the tradition of limiting similarity theory petitive ability and dispersal ability (Tilman after Abrams' review is a testament to the fact 1994). that this area was generally deemed to be un- Mathematical representations of this idea be- fruitful by ecologists. gan with an extension of Levins' original meta- The fall of limiting similarity theory contains population model (Levins 1969) which included an important lesson that applies to the role of two species competition as in equations 2a and b mathematical approaches to the ecological eo- from Hastings ( 1980). 180 GORDON

shown that increased disturbance and fragmen- tation in metapopulations favor the fugitive spe- cies relative to the competitive dominants (Nee & May 1992, Dytham 1994, Tilman et al. 1994, Moilanen & Hanski 1995, Tilman et al. 1997, but see McCarthy et al. 1997). In general, these influences favor fugitives by increasing the im- In this model, p, is the proportion of patches portance of colonization relative to in-patch com- occupied by species, i, c is its rate of colonizing petition. Disturbance and/or fragmentation can new patches, and m is the rate at which local elevate local extinction probabilities, which pro- populations (in a single patch) go extinct. This duces more patch vacancies for fugitives. Frag- model incorporates a competitive hierarchy among mentation and habitat destruction raise inter-patch species. For the competitively-dominant species, distances, putting an additional premium on dis- growth depends only on its own rates of c and p, persal. The result is, " ... a community composed whereas the growth of the competitively-inferior of more rapidly dispersing, weedy species." (fugitive) species depends on the c's and p's of (Tilman et al. 1997). Moilanen and Hanski ( 1995) both itself, and of the dominant species, since the looked at particular spatial distributions of patches dominant can always exclude the inferior species and showed that for a given level of habitat de- from a given patch. struction, the competitive dominants do best if Versions of this model were used to develop the patches are aggregated rather than highly inter- idea of regional coexistence of species (Cohen spersed. This is because patch aggregation main- 1970, Levins & Culver 1971, Horn & MacArthur tains short interpatch dispersal distances, which 1972, Slatkin 1974, Hanski & Ranta 1983). Slatkin enable even the less-dispersive species to (1974) showed that with certain assumptions, the recolonize patches. equations used by Levins and Culver and Horn and MacArthur were, " ... formally the same as the Lotka-Volterra competition equations, and the Consumer-resource theory criteria for coexistence and exclusion (could) be written down directly." Slatkin also relaxed the In the Lotka-Volterra model, interspecific com- assumption of independent distributions of spe- petition is represented by the a parameter. But cies and extended the results of this model to non- what does α represent? What mechanisms are equilibrial solutions. really driving the competition? Some modelers A number of studies have developed the idea of were unsatisfied with this "black box" repre- regional coexistence further. Several authors sentation of competition. They described to the have focused on the evolution of different disper- Lotka-Volterra model as "phenomenological" and sal strategies adapted to particular spatio-tempo- sought a more "mechanistic" model to explicitly ral mosaics of patches (Levin et al. 1984, Cohen represent competition (Tilman 1980, 1987). & Levin 1991). Hanski (1981) analyzed the ef- Tilman ( 1980) invented such a class of models, fects of predation on the coexistence of competi- known as consumer-resource theory, which has tors in a metapopulation. Hanski and Zhang become the basis for a substantial body of recent ( 1993) included several costs of migration and work on competitive coexistence. Tilman noted showed that increased dispersal in such models that in classical Lotka-Volterra studies, coexis- was not always beneficial. Tilman ( 1994) showed tence was often explained based on implicit rela- that coexistence was possible for an unlimited tionships between consumers and resources, i.e., number of species in a metapopulation model as that the resources are what the competitors ex- long as the dispersal rate of each successive com- ploit, partition, etc. Tilman' s consumer-resource petitively-inferior species increased by an amount model explicitly includes the dynamics of both proportional to the abundance of the competi- the consumers and the resources. Consumer spe- tively superior species (a new limiting similarity cies compete not through a mysterious parameter, relationship). He also showed that increased but directly, through the consumption of common longevity of species had the same effect as in- resources. creased colonization rates in allowing a species Graphical representations have provided a use- to coexist with a competitive dominant. ful tool for interpreting the criteria for coexist- Recently, several studies have applied meta- ence of competing consumers in consumer-re- population Lotka-Volterra coexistence models to source models. Zero net growth isoclines situations with disturbance, habitat destruction, (ZNGI' s) can be plotted for each consumer spe- and fragmentation. These studies have generally cies in a two-dimensional state space defined by THE COEXISTENCE OF SPECIES 181 the density of two different resources (one on fully extended to spatial, or non-equilibrium prob- each axis). Points on the ZNGI represent re- lems, and for why Lotka-Volterra models con- source levels when the consumer species is at tinue to be the model of choice in metapopulation equilibrium (zero net growth). The consumption coexistence studies. vector for a consumer species represents the amount of each resource eaten by that consumer. Analyses have shown that in order for two con- Keystone predators and food-web theory sumers to coexist, two conditions must be met. First, their ZNGI' s must cross. Second, the slope In the midst of the limiting similarity theory era, of each species' ZNGI must be shallower than Levin (1970) published a paper in which he noted that of the other with respect to the resource that that competitive exclusion could result not only forms the larger component of that species' con- from resource-based competition, but from com- sumption vector. In other words, each species petitive dynamics with respect to any limiting must consume more of the resource that is more factor, including predation. He cited Paine' s limiting to its own growth. Any intersection ( 1966) famous demonstration of predator-medi- point between isoclines is an equilibrium point ated competitive coexistence as an example. He with both species coexisting, but the equilibrium included a diagram that showed how consumer is only stable if the second condition is met dynamics were linked to the dynamics of both (Tilman 1980, Vincent et al. 1996). resources and predators in an ecosystem. This The primary advantage of consumer-resource gave rise to food-web models, which have pro- theory in modeling ecological coexistence is its vided another important mathematical tool for explicit, mechanistic treatment of resource-based studying competitive coexistence dynamics. competition. This has made consumer-resource Food web models are essentially another out- theory especially useful for exploring community growth of Lotka-Volterra models that can get dynamics with different types of resources. For even more mechanistic than consumer-resource example, some have modeled the coexistence of theory. These models include separate equations consumers on essential (nonsubstitutable) vs. sub- representing the dynamics of a top predator, one stitutable resources (Tilman 1980, Abrams 88, or two consumer (=prey) species, and a resource. Vincent et al. 1996). Consumer-resource theory Coexistence criteria parallel those of consumer has also been extended to coexistence problems resource models. ZNGI' s are plotted for con- with varying productivity and consumer func- sumer species not in resource-resource phase tional responses (Abrams 88), spatially separate- space, but in resource-predator phase space. As vs. intermixed resources (Vincent et al. 1996), in consumer-resource theory, coexistence requires communities with guild structure (Morris & that the ZNGI' s cross. There is also a similar Knight 1996), and optimally-foraging consumers requirement regarding the relative impacts and (Vincent et al. 1996). slopes of the ZNGI' s (see discussion of con- Consumer-resource models have more para- sumer-resource theory). In essence, the predators meters and variables per species than basic, Lotka- must rely more heavily on the species that is the Volterra models of competition. In general, con- better resource exploiter (lower ZNGI intercept sumer-resource models added a level of complex- on resource axis) (Holt et al. 1994, McPeek 1996). ity by including explicit resource dynamics. Cer- This amounts to another trade-off criterion for tain advantages were thereby gained, but only at coexistence (see later section on trade-offs). the cost of decreased analytical tractability, sim- Food-web theory has provided new insights plicity, and flexibility. As a result, consumer- into ecological coexistence primarily by virtue of resource models have not been applied to as wide its explicit, mechanistic treatment of competi- a variety of problems as have Lotka-Volterra tion. This competition can be either resource- models. For example, no one has yet modeled the based, as in consumer-resource theory, or preda- coexistence of more than two species in a con- tor-based. Predator-mediated competition causes sumer-resource model. Authors who have sought competing prey species to divide niche space not to extend consumer-resource theory to multi-spe- along resource utilization dimensions, but along cies problems such as productivity-diversity rela- predator avoidance dimensions. This is an impor- tionships (Abrams 1988), and community compo- tant innovation of food-web models, and has pro- sition (Morris & Knight 1996), have done so vided the basis for a great deal of overlap between strictly by extrapolation from two-species coex- food-web models and predator-prey theory (see istence scenarios. The added complexity of con- references in Vance 1978, Holt et al. 1994, Liebold sumer-resource theory is also the likely explana- 1996). In particular, most food-web models have tion for why these models have not been success- focused on the keystone predator effect, i.e., they 182 GORDON assume that a single predator species can prey on used a diffusion system to represent spatial move- all species of consumer (Vance 1978, Holt et al. ments in a Lotka-Volterra-based competitive 1994, Liebold 1996). These models have some- model (e.g., Merino 1996). Several such models times left out explicit resource dynamics alto- have shown that competitive coexistence is fa- gether and replaced them with parameters that cilitated by variation in dispersal rates among govern consumer growth as in the Lotka-Volterra species (Shigesada & Roughgarden 1982, Schat model (Vance 1978, Holt et al. 1994). et al. 1996). In a model by Mimura et al. (1991 ), As a consequence of the complexity of food- diffusion movements in a two-island system pro- web models, the analytical and flexibility con- duced spatial segregation of competitors leading straints on these models are even more severe to coexistence in the absence of any interspecific than for consumer-resource models. The most differences. simple food-web models typically have around Others have incorporated more realistic move- l 0 parameters (8 in Lie bold 1996, 12 in Holt et al. ment patterns, especially convection and intra- 1994 and McPeek 1996). Coexistence studies specific avoidance (Namba 1989) or attraction. have been limited to equilibrial, two species, Intraspecific attraction produces aggregation ef- consumer species, and fixed-parameter cases. fects in PDE models, which can allow competitors McPeek ( 1996) incorporated spatial variability to coexist even in homogeneous environments by studying the requisites for species to be able to (Britton 1989, Holmes et a! 1994 ). This parallels coexist in multiple, spatially-separate habitat empirical studies that have suggested that types (habitat generalists). This is a simplified intraspecific aggregation promotes coexistence in and less-explicit treatment of spatial heterogene- Drosophila communities (Shorrocks & Sevenster ity than in other coexistence modeling approaches. 1995), insect communities associated with dung Liebold (1996) extended the results of a food web pads and carcasses (Hanski & Cam be fort 1991 ), model to spatially-heterogeneous cases and the and possibly other cases. The principal· limitation productivity-diversity relationship, but this was of PDE models is that they are analytically diffi- based on somewhat speculative extrapolation cult. As a result, models are less manipulable and rather than a rigorous treatment of these sce- the results are less generalizable than in ODE narios in his model. models. Another way that ecologists have incorporated spatial processes in studies of competitive coex- Spatially more sophisticated models istence is with cellular automaton models. These models are comprised of grids of cells that define All of the classes of ecological coexistence mod- space explicitly. Each cell represents a popula- els discussed up until this point are based on tion or patch that is described by a particular state systems of ordinary differential equations (ODE). at any given time unit. The cells in these models As such, they all share a number of constraints shift among different states discretely in time and limitations common to this type of modeling according to a set of uniform and constant rules approach. Such models are only analytically (Halley et al. 1994). The models are run through tractable with a small number of variables and simulations consisting of various numbers of time parameters. While simplicity in modeling has its steps, and then the resulting distribution of states advantages, there are some cases where addi- in the model is analyzed. Coexistence is assessed tional complexity is desirable. ODE models are based on species' continued persistence at the not spatially explicit. As a result, treatment of end of simulations. spatial effects and heterogeneity has been limited Competition has been incorporated into such (Eckshmitt & Breckling 1994, but see metapo- models in several ways. Some have included pulation section). Many of our ideas on commu- discrete versions (difference equations) of the nity structure and niche evolution involve spatial Lotka-Volterra system as an interaction rule in heterogeneity. A variety of alternative modeling the model (Dytham & Shorrocks 1992, Comins & approaches have provided some more spatially Hassell 1996). Others have simply specified that sophisticated in sights into the issue of ecological one species can always exclude another from a coexistence. cell (Halley et al. 1994 ). Ziv (1998) included Partial differential equations (PDE) allow explicit competition for common resources (as in modelers to incorporate spatial and temporal dy- consumer-resource theory) into his model. namics simultaneously. This has provided a way Many studies have explained competitive coex- to treat spatial effects more extensively than in istence in these models as a result of self-organ- ODE models of ecological coexistence (Holmes izing patterns of spatial aggregation that develop et al. 1994 ). Most PDE coexistence models have (Dytham & Shorrocks 1992, Halley et al. 1994, THE COEXISTENCE OF SPECIES 183

Comins & Hassell 1996). Dytham & Shorrocks Laan et al. 1995), or may not (e.g., Hansson ( 1992) showed that such aggregation could result 1995) be spatially-explicit. The primary dis- from an intraspecific attraction probability, but tinction of individual-based models is their high other models have produced such aggregations level of biological detail. They model states and and competitive coexistence even in the absence interactions among individuals, whereas the of intraspecific attraction, and in homogeneous smallest unit in a cellular automaton model is environments (Halley et al. 1994, Comins & usually a subpopulation. The fine resolution of Hassell 1996). individual-based models permits the incorpora- Dytham ( 1994) used a cellular automaton model tion of detailed life-history information. to reproduce and extend the results of Nee & Reichman & Roberts ( 1994 ), used such a model May's (1992) Lotka-Volterra metapopulation to study the coexistence of three rodent species model, which looked at the effects of habitat on seed patches of different densities based on destruction and fragmentation on competitive optimal foraging behaviors and allometrically- coexistence. Like Nee & May, he showed that scaling metabolic requirements of differently- habitat destruction and fragmentation favor dis- sized individuals. persive species relative to sedentary species (fu- One class of simulation models has paralleled gitives and competitive dominants, respectively, consumer-resource theory by modeling the coex- see earlier section). Dytham' s model further istence of multiple consumer species competing showed that the sedentary species were least de- for common resources that obey their own, ex- pressed in parts of the "world" that contained plicit dynamics. These have explored consumer aggregations of remaining intact habitat patches. coexistence with varying time scales of consum- This is consistent with the result of Moilanen & ers and resources (Loreau 1992), varying under- Hanski' s (1995) metapopulation model. Dytham ground nutrient mixing processes (Huston & also showed that in certain parts of the world, DeAngelis 1994 ), and source-sink resource dy- patches of intact, suitable habitat could become namics (Loreau & DeAngelis 1997). Van der isolated and remain uninhabited by any species. Laan et al. (1995) included a dazzling amount of Cellular automaton models do not have the life-history information into a model of herbiv- analytical difficulties of many other types of ore-mediated competition between two species of models, and are particularly useful for studying oak trees. Hansson (1995) used individual-based spatial processes. However, this method has its simulation models to study competitive niche own limitations and constraints. Some have noted shifts in communities of competing predator spe- that interaction rules are usually less realistic cies and their prey. He used 288 different models than in differential equation models (Halley et al. to represent all possible permutations of several 1994, but see Ziv 1998). An important constraint different numbers of predator and prey species, is that rules are uniform over the grid and con- competition intensities, and rates and regulation stant through time. This makes it difficult to of prey growth. incorporate density dependent effects, or varied Individual-based models are the empiricist's and nonlinear functional responses. Another dif- dream and the modeler' s nightmare. They are the ficulty with cellular automaton models is the in- former because they can incorporate lots of eco- herent complexity of being spatially explicit. logical detail, especially life-history information Results are often sensitive to the size and shape of and spatial effects that have been difficult to han- the grid of cells (Molofsky 1994). Complicated dle in other types of models. They are the latter spatial patterns are often interpreted qualitatively because the high complexity largely defeats the for their resemblance to natural patterns (Halley primary purpose of ecological modeling: to under- et al. 1994) rather than being analytically com- stand the processes and mechanisms that underlie pared with quantitative predictions. ecological patterns. With so many different vari- ables and relationships influencing the outcomes of individual-based simulations, it is hard to disen- Other modeling approaches tangle the effects of each one. Few tools exist for quantitatively analyzing the outputs of such mod- The most complex models of ecological coexis- els. Some individual-based models have included tence are individual-based simulation models. smaller amounts of detail and have been an effec- Such models are similar to cellular automaton tive tool for studying processes that are hard to models in that they define states and interaction include in other types of models (e.g., Reichman & rules, and then run simulations consisting of a Roberts 1994). More detailed models may be number of discrete time steps. One difference is useful tools for specific management applications that individual-based models may (e.g., van der but their generality is limited. 184 GORDON

Tanner et al. (1994) used a projection matrix showed that the G-function would have to have model to study ecological coexistence. The pa- humps (multiple peaks) in order to achieve rameters in the matrix were constructed empiri- multispecies coexistence. They suggested that cally from an extensive data set of transition such non-linearities in G-functions would repre- probabilities to and from each of ten species of sent complex interactions between strategy pa- coral in the Great Barrier Reef. They ran the rameters and other parameters. One example of model through discrete time steps that produced such an interaction would be a trade-off between successional dynamics. They observed patterns the strategy parameter and some other life history analogous to fugitive species coexistence, with parameter (see later section on trade-offs). short-lived, good colonists peaking in abundance In one sense, game theory has provided an early after disturbance and longer-lived, poor important innovation to coexistence theory by colonists exhibiting a more gradual rise, peaking extending mathematical models to larger time when the community appeared to reach an equi- scales. On the other hand, looking at the problem librium. However, matrix models assume that all at this scale has served as a humbling lesson transitions between species are first-order regarding the inadequacy of our ecological-scale Markovian processes. In other words, they as- models for dealing with larger-scale coexistence sume that the probability of a given species ap- problems. There is no current theoretical or em- pearing at a given point is strictly a function of pirical basis for constructing realistic G-func- the previous occupant. This makes such a model tions that would incorporate multiple humps to a powerful tool for studying successional dynam- allow for the coexistence of multiple species (strat- ics (see references in Tanner et al. 1994 ), where egies). Even if such a function could be con- transitions may obey this assumption, but makes structed it would not be adequate for modeling it difficult to apply to ecological coexistence niche evolution because such functions are not problems which may include zero-order replace- fixed in evolutionary time. The processe.s of ment (random) or higher order interactions such coevolution and environmental change should as density dependence, or priority effects (Tanner cause changes not only in the parameter values, et al. 1994). but in the very fitness optima that those parameter Another modeling approach that has recently values are approaching as well. been applied to ecological coexistence is game theory. Such models start with a fitness-generat- ing function (G-function) which defines the dy- Empiricism, mathematics and coexistence namics of population density as affected by vari- ous parameters. Examples could include any of One curious development within the field of eco- the ODE competitive coexistence models dis- logical coexistence research is the virtual lack of cussed earlier. Rather than assume that param- interchange between empirical and theoretical eter values are fixed, game theory treats these studies (Abrams 1983, but see Schoener 1974 ). parameters as "strategies" that are permitted to On the one hand, empiricists cannot seem to inter- evolve, and that approach values at which fitness est theoreticians in their results. Perhaps because is maximized (Vincent & Vincent 1996). I dis- logistical constraints prevent them from measur- cuss game-theoretical models of coexistence here ing variables such as total niche similarity, com- because they are theoretical models of coexist- petition, and resource overlap (Abrams 1983 ). ence, and because they incorporate an ecological- On the other hand, theoreticians cannot convince scale model such as a Lotka-Volterra or con- the empiricists that their results are biologically sumer-resource model within it. Game theoreti- relevant because of the simplifying assumptions cal models are a bit out of place in this section, that are necessary for their models (Simberloff however, because they have extended mathemati- 1983). Indeed, both sides have powerful advan- cal models to the problem of coexistence at a tages as well as strong limitations, and both have larger time scale. They model shifting life-his- taught us much about species coexistence. How- tory traits, behaviors, or niches in evolutionary ever, the chasm between these two conceptually time. linked areas is troubling. There is much to be Vincent & Vincent (1996) used a consumer- gained by identifying possible linkages between resource model as a G- function in such a model these two approaches. to study the coexistence of plants with different Ab rams' frustration with the sensitivity of com- root-shoot allocation strategies. Their result was petitive coexistence models to the structure of that when evolution proceeded to equilibrium, the competition coefficient led him to remark, there was only a single species that possessed the " .. .it would seem to be more useful to explain the optimum root-shoot allocation strategy. They differences in niche overlap in different commu- THE COEXISTENCE OF SPECIES 185

nities rather than to look for universal patterns." Biological trade-offs as coexistence mechanisms (Abrams 1975). Although made by a theoreti- cian, this statement appears to rationalize an In recent studies of ecological coexistence, trade- exclusively empirical approach to the coexist- offs ha.ve increasingly been cited as "coexistence ence problem, devoid of general theoretical ex- mechanisms" (Shmida & Ellner 1984, Brown planation. However, such an approach would 1989, Chesson 1991, Tilman 1994, Rosenzweig not allow us to understand the mechanisms and 1995, McPeek 1996). Rosenzweig (1995) de- processes that underlie empirical patterns. Eco- scribed the essence of trade-offs in the "trade-off logical theories are a necessary complement to principle" which states that, " ... phenotypes excel empirical studies of ecological coexistence, yet at most functions by losing the ability to perform resource partitioning studies have frequently other functions well." Earlier, regional coexist- ignored coexistence theoretical literature. Our ence was explained based on a trade-off between understanding of ecological coexistence would competitive ability and dispersal. This particular be enhanced if resource partitioning studies were trade-off is best represented by the notion of a more informed by coexistence theory. Such weed. Weedy, or pioneer species have sacrificed theory can profitably be used to develop hypoth- competitive ability in order to become more mo- eses and predictions for resource partitioning bile (Connell & Slatyer 1977, Shmida & Ellner studies, and to interpret the meaning of empiri- 1984 ). The reason for this trade-off is that physi- cal results. ological investments in dispersal (e.g., seed pro- Mathematical models must make simplifying duction) usually come at the cost of investment in assumptions to achieve any level of tractability structures for local exploitation (e.g., roots) and and generality, yet ecological dynamics are nota- vice versa (See Tilman 1994 for an example from bly complex relative to systems in other scientific prairie grasses). This trade-off ensures that the disciplines. The hope for mathematical approaches species who are the best at one thing (e.g., disper- to ecological coexistence rests on the tendency sal) will be the worst at the other (e.g., in-patch for ecological systems to sometimes exhibit low- exploitation). The result is that the trade-off dimensional dynamics. This result is produced functions as a niche axis or coexistence mecha- when one or a few ecological parameters exert nism that presents opportunities for resource par- such a strong influence on system dynamics at a titioning among competitors. particular scale, or in a particular region of phase The dispersal-exploitation relationship is only space, that the effects of the myriad variables and one example of how a biological trade-off can parameters that influence ecological dynamics at serve as a coexistence mechanism. Brown sug- other spatio-temporal scales or in other regions gested three other trade-offs that functioned as are swamped out. These other sources of varia- coexistence mechanisms in his desert rodent as- tion can then be ignored without sacrificing too semblages (Brown 1989). Each of these trade- much accuracy. Mathematical models of eco- offs promoted the coexistence of one or more logical coexistence have proliferated despite the rodent species by ensuring that there was a part of often complex and high-dimensional behavior of niche space in which each species was the most ecological communities. One possible explana- efficient forager. tion for this is, " ... the dubious but nonetheless Trade-offs are evident in mechanistic models popular cachet of legitimacy provided by math- of competitive coexistence. In such models, co- ematics to an idea ... " (Salt 1983) which may have existence requires that ZNGI' s cross, which is permitted serious consideration of many models equivalent to the species with the lower intercept with little relevance to actual ecological dynam- having the shallower slope. In the case of food- ics. For whatever reason, theoretical ecologists web models, this means that the species that is the have often treated the connection between their better resource exploiter is also more vulnerable models and the dynamics of actual communities to the predator. In essence, coexistence in these carelessly. Finding low-dimensional behavior in models requires that there be a trade-off between ecological systems is a difficult challenge and resource exploitation ability and predator avoid- must be taken seriously by theoreticians in order ance. The general importance of trade-offs as to design models that offer realistic theoretical coexistence mechanisms in communities has led explanations of ecological coexistence. This is to the view that trade-offs not only facilitate where empirical studies of coexistence have much coexistence, but are required for it (Brown 1989, to contribute. In essence, empirical pattern can Chesson 1991, Kotler et al. 1994, Tilman 1994, inform theory about which simplifying assump- Schluter 1995, McPeek 1996, Vincent et al. 1996). tions can be made without sacrificing too much Biological trade-offs function as coexistence biological accuracy. mechanisms in ecological communities because 186 GORDON

they cause niche space to be divided among mul- competitors could coexist even if all of the condi- tiple species. In the words of McPeek ( 1996), tions for Lotka-Volterra competitive exclusion "Trade-offs force species to differentiate among were met (i.e., homogeneous, unvarying environ- niche dimensions ... ". The result is that each ment, closed population). However, this claim species can ensure its coexistence in a community was largely dismissed when several different au- by mastering its own, singular trade. In the thors concluded that Ayala' s result was produced absence of trade-offs, communities would be by the overriding effect of intraspecific competi- dominated by single, jack-of-all-trade, super- tion relative to interspecific competition in the species (Rosenzweig 1995). experiment (Ay ala 1971, Borowsky 1971, Gilpin & Justice 1972). The second line of attack was a series of papers Competition, resource saturation and ecological that challenged the logical structure of the argu- coexistence ment for competitively structured communities (Connor & Simberloff 1979, Simberloff 1983). The research paradigms of coexistence theory Proponents of this idea suggested that competi- and resource partitioning both make the assump- tive structure in communities had been treated tion that communities are competitively struc- simultaneously as a prediction and as a foregone tured. Why should species segregate according to conclusion by many. They suggested that the trade-offs unless competition forces them to do hypothesis of competitive structuring of commu- so? In coexistence theory (often referred to as nities was in need of rigorous, hypothetico-de- "competitive coexistence" theory), this assump- ductive testing, particularly against the null hy- tion is the very fabric of the Lotka-Volterra model pothesis that communities are assembled at ran- and its analogues. Competition coefficients dom from among the species in a regional pool. largely govern interspecific dynamics, producing Various authors introduced statistical methodol- either coexistence or exclusion. Resource parti- ogy to this end, especially in a series of papers tioning studies measure ecological differences that tested whether congeners (presumed to be among species in coexisting assemblages. This ecologically-similar) coexisted in communities · does not assume competitive structure in itself. more or less frequently than would be expected However, when observed niche differences are by chance (Simberloff 1970, den Boer 1980, 1986, interpreted as mechanisms by which species have Azovsky 1996). These studies concluded that partitioned niche space, the notions of competi- congeners were more likely to coexist in natural tive exclusion and competitive structuring of communities than expected by chance (but see niches are implicitly invoked. A number of ecolo- scale-dependent result of Azovsky, 1996). On gists have attacked the assumption that niches are this basis, den Boer ( 1980) went as far as to competitively structured within communities, replace the competitive exclusion principle with suggesting alternative processes which may ex- "the coexistence principle", which stated that, plain the coexistence of species in ecological "Species that are ecologically closely related will communities. more often than not be found coexisting in the These alternative explanations commonly cite same habitats". the argument for individualistic-natured commu- The third attack on the idea of competitively nities (Strong 1983, den Boer 1986). They Claim structured communities was a number of papers that the distributions and abundances of species that reviewed extensive field evidence and con- are governed not by. pressure from adjacent spe- cluded that interspecific competition was rare in cies in niche space, but by the independent toler- natural communities (Connell1975, 1983, Wiens ances, preferences, and limits of each species 1977, Birch 1979, Strong 1983). These studies with respect to environmental gradients (Gleason concluded that factors other than interspecific 1926, Whittaker 1956). Ecologically-similar spe- competition, such as predation, parasites, envi- cies may, therefore, have increased chances of ronmental variability, and environmental het- coexisting because their shared ecological at- erogeneity, set more important limits to the tributes lead them to wind up in the same places growth of natural populations. These limits at the same times (den Boer 1980, 1986). depress natural populations below carrying ca- The attacks on the importance of interspecific pacity such that available resources are not ex- competition in communities came from three prin- hausted, and interspecific competition for these cipal directions. The first was a laboratory ex- resources is not significant. This conclusion periment with two species of Drosophila that directly parallels the results of coexistence purported to refute Gause's principle (Ay ala 1969, modeling studies (see earlier section) that have 1971 ). This experiment claimed to show that incorporated the effects of predation (e.g., THE COEXISTENCE OF SPECIES 187

Roughgarden & Feldman 1975), parasites (e.g., invalidate the assumption that niches should ex- Yan 1996), environmental variability (e.g., hibit competitive structuring. Abrams 1976, Turelli 1981, Chesson & Warner However, one might still suggest that environ- 1981 ), and/or environmental heterogeneity (e.g., mental variability or other factors create non- Levins & Culver 1971, Horn & MacArthur 1972, equilibrium conditions, which prevent compe- Tilman 1994 ). These, and other factors have all tition (or apparent competition) from having a been shown to promote coexistence essentially strong effect on community structure (Hutchinson by creating non-equilibrium conditions in which 1961, McNally 1995). Perhaps niches are still the consumers do not competitively exclude each distributed randomly or individualistically in com- other because they do not use up the resources munities. However, evidence of non-equilibrial completely (Abrams 1988, Huston & DeAngelis conditions in many extant ecological communi- 1994). ties does not automatically refute the idea the Has all of this literature succeeded in refuting competition is an important influence on the niche the idea that communities are competitively-struc- structure of communities. Competition could tured? The continuing popularity of the resource still be a major influence on niche structure even partitioning paradigm (see references in Wishieu if it only occurs during rare and brief intervals in 1998) and mathematical studies of competitive time (Wiens 1977). Consider the process of coexistence (see earlier sections) suggest that speciation. This is a phenomenon that has rarely, this idea is not dead. The notion that communi- if ever, been observed in extant communities, yet ties exhibit competitive structuring is still wide- no one would question its importance as a bio- spread in recent community ecological literature logical process governing diversity. (Rosenzweig 1995, Holt et al. 1994, Tilman et al. Disentangling the effects of competition from 1994). But what evidence is this based on? Are among the other factors that may shape the niche these ecologists blindly accepting the competi- structure of extant communities is a difficult chal- tion dogma and ignoring contrary evidence as lenge. Wins ton ( 1995) did just this in an analysis some have suggested (Simberloff 1983)? of morphological differences among sympatric There do exist examples in which interspecific freshwater minnows in the southeastern USA. He competition has been shown to be an important concluded that interspecific competition explained factor in extant, natural communities (Schoener observed patterns of community structure better 1974, 1983, Connell 1983, Denno et al. 1995). than random or phylogenetic hypotheses. How- Nonetheless, the empirical evidence that preda- ever, few studies of extant communities have tion is at least an equally important limiting fac- produced evidence germane to this issue. Similar tor is convincing. However, the prevalence of to speciation, the most compelling evidence for predation does not contradict the assumptions of the importance of competition in structuring com- competitively-structured communities. Holt munities comes from the fossil record (1977) first described how predation pressure Three well-documented pa1eontological patterns could produce niche segregation patterns identi- suggest that communities should exhibit compe- cal to those produced by competition. He de- titive structuring. The first is the rapid bursts in scribed this phenomenon as "apparent competi- species diversity that follow in the wake of mass tion". Other food web and keystone predator extinctions (Webb 1989, Kauffman & Fagerstrom modelers have since shown that even if predators 1993, Rosenzweig in press). Such bursts have limit consumers well below resource saturation, occurred after all of the major mass extinctions, ecologically identical species still can't coexist. and typically last 3-10 million years before diver- There is still "competitive" pressure to diverge, sity levels off. This is not a function of the and for coexisting species to subdivide niche idiosyncratic behavior of particular taxa, but is a space according to trade-offs. In the words of cumulative effect over whole communities. Why Vance (1978), " ... observed resource partitioning should such bursts be associated with mass between similar species implies nothing about extinctions? It must be something about the very the relative roles of competition for resources and absence of species, which promotes the proli- predation in structuring the community.". There- feration of many new forms. It suggests that fore, the prevalence of predation pressure does when many niches are empty, there is a sort of not mean that competitive pressures among coex- evolutionary vacuum, which causes niche space isting species are unimportant. Whether you call to be filled rapidly. it "competitively -structured", or "apparent- The second pattern is comprised of long-term competitively structured", the result is the same. diversity steady-states. This pattern has been Evidence that predation is an important limiting observed in many different communities and geo- factor in extant communities does not, therefore, logic periods when care has been taken to factor- 188 GORDON

out sampling effects (e.g., Rosenzweig & Taylor during one of these long-term steady states, how- 1980, Miller & Foote 1996, Rosenzweig in press). ever, competition is only partially responsible for Several paleontologists have recently described a structuring communities. This is suggested by phenomenon known as "coordinated stasis", in the modern day ecological data discussed earlier, which such periods of steady-state diversity are as 65 million years have passed since the last associated with little taxonomic turnover (Brett major mass-extinction. & Baird 1995). These steady states are the flip- What does this mean for coexistence studies? If side of the previous pattern. Once niche space is competition is only partially responsible for com- generally full, there must be some kind of com- munity structure, then competitive coexistence petitive suppression of new forms by the existing theory is only partially applicable as an explana- forms. At this stage, a new species can only tion for the coexistence of species in real biologi- survive by outcompeting, and replacing an exist- cal communities. Niche space has been parti- ing one. tioned among species according to trade-offs only The third pattern consists of taxonomic replace- partially. Species should be masters of their own ment series in geological time. The most well- trades to some extent, but their niches should be known example being therapsids, dinosaurs, and broader than is theoretically possible. Communi- eutherian mammals as the dominant large, terres- ties should have some vacancies. A productive trial quadrupeds in the Paleozoic, Mesozoic, and direction for future coexistence studies would be Cenozoic eras, respectively. This, and other ex- to frame the extent of niche partitioning within amples (marine invertebrates: Kauffman & the context of historical factors and non-equilib- Fagerstrom 1993) are essentially the taxonomic rium dynamics in particular systems, thereby as- signature of the two previous patterns. The forms sessing both the competitive, and the non-com- that dominate particular ecological niches in par- petitive components of coexistence. ticular time periods suppress the evolution of new Some investigators have developed useful and forms until they are wiped out. Then they are innovative ways of framing coexistence patterns rapidly replaced with ecological analogues, which within the context of competitive pressures in may originate from completely different taxa. particular communities. Pianka (1974) concep- These patterns imply that the function of change tualized the relationship between competition in diversity through time exhibits density-, or intensity and resource limitation in the form of species richness-dependence. In other words, the the demand/supply ratio. He noted that competi- number of species in a province exerts a negative tive pressure is high when this ratio is high, and feedback on the slope of the species accumulation that in such situations, niches should exhibit low curve. What processes other than competition interspecific overlap. He also noted that commu- can explain this negative feedback? The incorpo- nities with high levels of niche overlap may there- ration of new species must either be repressed by fore correspond to cases in which resources are preexisting ones (reduced speciation/invasion) or not saturated (low demand/supply ratios). This is must be balanced by losses of preexisting species consistent with Wiens' (1977) description of epi- (increased extinction). These processes repre- sodic competition, and with Pulliam' s (1985) sug- sent a sort of evolutionary competitive exclusion. gestion that grassland sparrows in Arizona expe- Thus, communities at or near diversity steady- rience strong interspecific competition and dis- states (which may be termed evolutionary crete microhabitat partitioning only during infre- equilibria) should exhibit competitively-struc- quent years of extreme food scarcity. tured niches. When the community is far from equilibrium (i.e., immediately following a mass extinction), the number of species is well below Coexistence at a finer scale: habitat selection the plateau that it may eventually reach, and dynamics diversity is rapidly rising. Species should not yet have been squeezed by interspecific competition. In studies of coexistence at the ecological scale, Niches should broad, species should be poor com- the niche characteristics of organisms are as- petitors, and communities should not be competi- sumed to be fixed. At the scale of the behavioral tively structured. Coexistence is easy. When the decisions of individual organisms, these charac- province approaches a plateau in species diver- teristics may be fluid (Rosenzweig 1987a). Imag- sity, competitive pressures are exerting their limit ine the niche in the former sense as a mean, and in on diversity. As a result, niches should be rela- the latter sense as including the variation about tively small (specialized), species should be good the mean. Coexistence at this finer scale occurs competitors, and the niches should exhibit com- before Gause's paramecia have had a chance to petitive structuring. Coexistence is harder. Even drive one another to extinction. THE COEXISTENCE OF SPECIES 189

Multi-species habitat selection models such as on the food availability in a given year. He isoleg theory, developed by Rosenzweig and as- suggested that the long-term coexistence of these sociates (1981, 1987a, Pimm et al. 1985), are species was dependent on a competitive balance essentially studies of coexistence at this finer produced by the year to year variation in food scale. Isoleg theory reflects the general phenom- production. enon that intraspecific competition causes spe- Other authors have conceptualized the between- cies to broaden their use of resources or habitats, scale transition of coexistence as a function of while interspecific competition causes them to realized vs. fundamental niche evolution. Wishieu restrict the number of resources or habitats they (1998) suggested that shared preference commu- use (Rosenzweig 1991, Mehrhoff & Turkington nity organization should evolve into distinct pref- 1995). In isoleg theory, interspecific competition erence organization over time. Her rationale was tends to cause species to segregate into different that in shared preference communities, density habitat types but allows for coexistence in some dependent dynamics are forcing some species cases. Patterns of species' occupancy of habitats into a portion of niche space that doesn't corre- depend on the densities of the interacting species, spond to their preference. Over evolutionary the competitive hierarchy among them, the pres- time, natural selection should favor mutations ence of detectable intra-type variation in patch that enhance species' efficiency at utilizing their quality, and on their fundamental habitat prefer- realized niches, such that eventually each spe- ences (Rosenzweig 1981, 1991, Brown & cies' fundamental niche coincides with its real- Rosenzweig 1986). ized niche. Species that initially shared prefer- Danielson ( 1991) took a very different approach ences for certain portions of niche space eventu- to multi-species habitat selection modeling by ally prefer their own distinct portion of niche assuming that species had distinct habitat prefer- space. This is essentially the idea of the "ghost of ences, and that individuals occupying a patch competition past" (Connell 1980). preempted all other individuals from that patch. Rosenzweig (l987b) suggested that the above His result was that one species can exert either a scenario requires environmental stability through positive or a negative effect on the other depend- evolutionary time. In variable environments, the ing on the densities of two species, the propor- evolution of species' fundamental niches cannot tions of different habitat patches in the landscape, keep up with the variation in their actual niches. and the amount of patch sampling by individuals. This would favor broad fundamental niches and Habitat selection modelers have sometimes the maintenance of shared-preference community framed their studies in the context of the competi- organization. Indeed, the prevalence of shared tive exclusion principle, describing observed re- preference scenarios in extant communities is sults as "coexistence mechanisms" (Brown 1989, testament to the fact that the transition from Morris 1996, Vincent et al. 1996). Coexistence at shared- to distinct-preference community organi- the scale of habitat selection processes is not, in zation does not always occur (Wishieu 1998). fact, identical to Gauseian coexistence, however. The relationship between habitat selection-medi- ated coexistence and ecological-scale coexist- Coexistence at the largest scale: species diver­ ence is an important frontier for community ecol- sity patterns ogy. Birch ( 1979) described one possible linkage Take Gause' s test tubes and let them go so far that between coexistence at these two different scales. the equilibrium reached by the initial competitors He noted that environmental and population fluc- is insignificant. How many species of paramecia tuations may cause species to be temporarily would ultimately be able to coexist within a par- pushed into marginal habitats by density-depend- ticular test tube given unlimited time for ent processes. The tolerance of competitively speciation? What factors would affect the number inferior species for suboptimal habitats is a way of species that would ultimately be reached? The for these species to persist despite temporary size of the tube? The amount of nutrient? Hetero- exclusions from their preferred habitats. In this geneous conditions within the tube? When we case, density dependent habitat selection dynam- relax the assumptions of fixed numbers of spe- ics act as a buffer to competitive exclusion, per- cies, niches, and habitats, we are extending the mitting the long-term coexistence of ecologically classical ecological coexistence problem to a new similar species. Wolff (1996) provided another level and asking new questions. What determines example, showing that the competitive relation- how many species can potentially coexist in par- ships between deer mice and white footed mice in ticular communities? To what extent is that po- the Appalachian Mountains flip-flop depending tential filled in actual communities? 190 GORDON

These questions are the fodder for studies of Given two communities with identical abundance global and evolutionary species diversity pat- distributions of species, the minimum viable popu- terns. The species diversity literature has rarely lation size limit will be reached for a species with been incorporated into studies of ecological a higher abundance rank in the less productive coexistence. Nonetheless, a brief review of sev- environment (Rosenzweig 1995). Each species eral species diversity concepts is warranted here needs a certain amount of the resource pie to since these larger scale patterns and processes survive, and so a smaller pie can support fewer provide an important context for interpreting co- species. existence at the ecological scale. The consequences of the productivity-diversity Schluter & Ricklefs (1993) divided the various relationship for ecological coexistence are pro- determinants of species diversity into local and found. The minimum portion of the resource regional factors. Local factors are so called be- "pie" required for a sustainable population can be cause they are attributes of a point locality. These represented as the area occupied by one species include habitat complexity (MacArthur & under a resource availability curve (Fig. 1 ). If the MacArthur 1961 ), disturbance frequency (Connell productivity of the ecosystem is increased, this 1978), and others (see references in Wright et al. raises the overall amount of resources, and spe- 1993). The most important of these is productiv- cies can obtain the same quantity of resource ity, defined as a rate of energy flow through the from a narrower portion of the niche axis (Fig. biological component of an ecosystem (see re- 1 b). This means that niches in highly productive views by Wright et al. 1993 and Rosenzweig & habitats may, in effect, be just as large as niches Abramsky 1993). in less-productive habitats even though they ap- The function of species diversity with increas- pear narrower or more specialized. We should ing productivity is either always increasing or therefore expect that coexisting species may ap- unimodal (Wright et al. 1993, Rosenzweig & pear to be more ecologically-similar in more pro- Abramsky 1993). The increasing phase of the ductive habitats than in less productive habitats diversity-productivity relationship has most of- even in the absence of all other differences. ten been explained based on the resources re- Regional determinants of species diversity are quired to sustain minimum viable populations. so called because they are attributes of the larger a b

Environmental gradient or niche axis Fig. I. Minimum niche breadth (the horizontal distance between the two vertical lines under each curve) as a function of ecosystem productivity (the amount of available resources) in a less (la) and more (lb) productive ecosystem. The amount of resources included in a niche is represented as the area in between the lines under the curve. While the niche in figure 1a is broader than the niche in figure 1b, the two contain identical resource levels and can therefore be considered to be equally sized. Narrower niches, and hence increased opportunities for the coexistence of similar species, are possible in the more produc- tive environment. Anchos mfnimos de nichos (la distancia horizontal entre !as dos lineas verticales bajo cada curva) en relaci6n a la productividad del ecosistema (la cantidad de recursos disponibles) en ecosistemas menos (la) y más (!b) productivos. La cantidad de recursos dentro de un nicho esta representada como el area dentro de !as dos lineas bajo la curva. Aunque el nicho en la figura I a es másamplio que el nicho en la figura 1b, Ios dos tienen la misma cantidad de recurs os, por lo que se puede considerar que Ios dos nichos tienen el mismo tamafio. Nichos másangostos son posibles en el ecosistema más productivo, entonces tiene alta potencial para la coexistencia de especies similares. THE COEXISTENCE OF SPECIES 191

spatial context of a particular locality (Schluter & lar organisms. Regions can be expected to be- Ricklefs 1993). The most important of these for have more or less like provinces for given taxa to explaining patterns of species diversity in natural the extent that within-region speciation is signifi- communities is province size. Rosenzweig ( 1995) cant. defined a biological province as, " ... a self-con- The province-size effect on species diversity tained region whose species originate entirely by has two important implications for ecological speciation within the region." Larger provinces coexistence. Firstly, since provinces are defined are more diverse than smaller provinces of equal by speciation from within, similar species that productivity (Rosenzweig 1995). This rela- coexist within a province should often share com- tionship between province-size and diversity is a mon ancestry. This provides an explanation for broadly general pattern, which has been noted by the frequent coexistence of congeners within eco- ecologists dating back at least to Hutchinson logical communities (den Boer 1980, 1986). ( 1959) and recently reviewed by Rosenzweig Contrary to den Boer' s interpretation of this pat- (1995). Rosenzweig admitted that technically, tern, it may be purely a result of within-province under his definition, the only truly discrete bio- radiation and is not contradictory to the notion of logical province (that we know of) is the earth. competitively -structured communities. However, the notion of a biological province as Secondly, the effect of province size on species an evolutionarily-isolated spatial unit is a highly diversity has implications for the competitive useful concept for understanding patterns of spe- structuring of communities and hence, the com- cies diversity. petitive coexistence of species within communi- In general, the effective size of a biological ties. Province size, and other regional diversity province is a function not only of geography, but determinants do not affect the size of the resource also of the spatial scale of movements of organ- pie within communities as do local determinants isms. A province is functionally bigger for sed- of species diversity. Rather, they appear to affect entary organisms than for highly mobile organ- how small a piece species can get away with and isms (Kotliar & Wiens 1990, Holt 1993, still persist through evolutionary time. Consider Rosenzweig 1995). Additionally, the notion of a two communities of equal local conditions (i.e., biological province is not just limited to discrete productivity, habitat structure); one a small is- land areas separated by water. Major habitat- land, the other, a vast continent. If species on the types within geographic areas can function as island subdivide niche space as finely as they do biological provinces since species may perceive on the continent, the chances are that many will them as islands of acceptable habitat in a sea of go extinct. The smaller size of island populations inhospitable surroundings (Terborgh 1973, would make them more vulnerable to the "extinc- Rosenzweig 1995). A classic example emerged tion vortex" of demographic stochasticity (Frankel from the data of Ralph (1985). He showed that & Soule 1981). The smaller areal extent occupied bird communities in Patagonia, Argentina were by the island populations would also make them least diverse in the most structurally-diverse habi- more vulnerable to being extinguished by singu- tat type (beech forests), contradicting the well- lar, localized catastrophic events. The only spe- known correlation between bird species diversity cies that persist in evolutionary time on the island and foliage height diversity (MacArthur & are those that maintain dense populations and MacArthur 1961, MacArthur 1964). Ecologists broad niches. Even though their piece of pie is have explained this result based on province size big enough so that it could normally be split up, effects. South American temperate beech for- they need to maintain an oversized niche to en- ests have low bird diversity despite their struc- sure survival through local environmental fluc- tural complexity because of a limited areal ex- tuations, and to maintain large population sizes. tent relative to other habitat types in the region, This pattern was described for island birds by such as shrub desert (Schluter & Ricklefs 1993, MacArthur et al. (1972) who referred to the in- Rosenzweig 1995). creased population sizes on islands as "density In summary, larger provinces have higher di- compensation" and to the habitat breadth of is- versities but provinces are not completely dis- land species as "ecological release". crete entities in nature. They roughly correspond This provides an explanation for the invasibility to isolated geographic areas or major habitat- of ecological communities on small provinces types within those areas. They can only be pre- such as oceanic islands. If species typically cisely defined, however, with respect to specific occupy wide niches relative to the productivity taxa because the effective size and the strength of level, this implies underused resources. There is the boundaries of a province varies according to less pressure for species to become efficient at the movements and habitat tolerances of particu- what they do. It really is paradise, that is, until a 192 GORDON scrappy continental species comes along who's (Valentine & Jablonski 1993). Though the used to fighting for its niche. geological imprints of glacial cycles are best It also leads to a prediction about community documented in the Pleistocene, Milankovitch structure and coexistence. Communities of large cycles are believed to have occurred throughout provinces should be more competitively- the Phanerozoic (Valentine & J ablonski 1993). structured, and should contain more opportunities Indeed, some paleontologists have noted drastic for ecologically-similar species to coexist than changes in community composition at the time communities of similar environments on small scale of glacial oscillations (southwest USA provinces. deserts: Van De vender & Spaulding 1979; eastern USA deciduous forests: Davis 1983; west coast USA marine invertebrates: Valentine & Jablonski How full are communities? 1993 ). This has led some to conclude that communities are generally non-equilibrial, Factors such as productivity and province size randomly assembled, and invasible, with non- affect how many species can coexist in particular competitively structured niches (Simberloff 1981, communities. In essence, they determine a sort of Johnson & Mayeux 1992, Valentine & Jablonski niche carrying capacity. But we may also ask 1993). Indeed, this evidence suggests that niche what proportion of the carrying capacity is actually space in communities is not, and most-likely has full. This question can be addressed by examining never been completely full. Therefore, the the dynamic factors that affect the accumulation evolutionary equilibria that we see in the fossil of species diversity in time. record do not represent the process of community The amount of time required for a community to coevolution taken to its maximum diversity fill its niche carrying capacity can be roughly endpoint. Even when we have seen diversity inferred from the paleontological patterns steady-states in the fossil record, such commu- discussed earlier (see competition section). nities could not have achieved the maximum Immediately following mass-extinctions, species possible niche partitioning, specialization and diversity rises sharply, leveling off after 3-10 diversification. The 3-10 million year process of million years, at which time levels of diversity community coevolution is trying to hit a target are roughly equal to those prior to the mass that is constantly moving on the scale of 10,000 extinction (Kauffman & Fagerstrom 1993, year oscillations. Rosenzweig in press). The process that leads to The interpretation of the evolutionary dynamics this replacement of diversity can be concep- of communities parallels the debate over the role tualized as a rough coevolution of all species in of competition in communities. Valentine and the community. Ultimately, a diversity steady J ablonski (1993) suggested that the observed state is reached, which corresponds to a sort of pattern of unsaturated communities was consistent evolutionary equilibrium. with neontological evidence for unsaturated Major mass extinction events have generally communities (e.g., Wiens 1974, Rotenberry & occurred less frequently than this, roughly once Wiens 1980, Strong 1983, Cornell & Lawton 1992, every 35 million years (Raup & Sepkoski 1984 ). Shorrocks & Sevenster 1995, MacNally 1995). If Therefore, there has typically been adequate time communities are not full, then species either must for communities to reach equilibrial diversities have oversized niches, or there are unoccupied in-between such episodes. Indeed, major portions of niche space. The consequence is that disturbances in diversity are interspersed with interspecific competition should be weak and long periods of relatively little change in diversity niches should not be competitively structured levels (Rosenzweig & Taylor 1980, Miller & Foote within communities, rendering them highly 1996, Rosenzweig in press). invasible (Simberloff 1981, Connell1983, Strong However, the determinants of niche carrying 1983). Communities are not highly coadapted capacities are shifting on a much faster time scale. webs but are ephemeral, unsaturated combinations Glacial cycles have occurred roughly every 10,000 of species (Connor & Simberloff 1979, Valentine years in the Pleistocene. These cycles are & Jablonski 1993, Holt 1993). associated with major shifts in climatic conditions On the other hand, Coope (1987) arrived at a worldwide. This can either be conceptualized as different conclusion from his data set on the drastic shifts in productivity within provinces, or species composition of Pleistocene beetle as latitudinal migrations of constant-productivjty assemblages in Great Britain. He observed some provinces, with consequential shifts in province changes in species composition through Plesito- size and shape. Such climate oscillations cene glacial oscillations but highlighted the rough correspond with astronomical Milankovitch cycles compositional constancy of particular species THE COEXISTENCE OF SPECIES 193 assemblages in the face of these geographic shifts. It should finally be noted that with a sufficiently Many species underwent drastic latitudinal shifts long-term perspective, there is no climax level of in tracking specific climatic zones and their species diversity. The overall trend of increasing corresponding beetle assemblages through these diversity of life through time testifies to this cycles. conclusion. Given enough time, certain lineages Again, the truth lies on neither extreme of the will invade new provinces (e.g., land), or develop spectrum but somewhere in between. Commu- important biological innovations (e.g., seeds) that nities are neither full and completely coevolved, radically change the ways in which organisms fill nor are they completely unsaturated. But can we up niche space. The biological trade-offs get any more specific about how full they are? themselves are plastic at this level and the ultimate One way to begin to address this question more potential for species' coexistence cannot be precisely is to look at the overlaps between fun- predicted. damental and realized niches in communities. Consider the evolution of the ghost of competition past (Connell 1980, Rosenzweig l987b, Wishieu CONCLUSION 1998). In this model, species with initially overlapping preferences or fundamental niches Despite the simplicity of the competitive exclusion are segregated in niche space by competition. If principle, the current state of knowledge about this segregation remains stable through time, how and when species may coexist reveals a species' fundamental niches should eventually highly complex and heterogeneous problem. approach their realized niches (see earlier Studies of coexistence published in the ecological discussion). Therefore, if the process of literature span an impressive range of mechanisms, community coevolution was ever allowed to techniques, scales, concepts, and patterns. One proceed until the niche carrying capacity were way to increase our understanding of species' completely full (an evolutionary climax), all coexistence will be to clearly define different species' fundamental niches would equal their types of coexistence problems, and then draw realized niches. All species would fully play to linkages between them. their strengths. Preferences that were initially A primary example is the linkage of patterns shared would all have become distinct. Therefore, and processes across scales. Coexistence has the prevalence of shared preferences vs. distinct been studied at time scales ranging from preferences may be viewed as an index of the behavioral interactions between individuals to fullness of particular communities. Wishieu niches evolving toward optima, and everywhere ( 1998) concluded that among resource partitioning in between. This paper provides a framework to studies in general, these two types of community divide coexistence into three distinct time scales. organization were equally common. Perhaps a Coexistence at the finest scale incorporates best first approximation therefore, would be that density-dependent habitat selection dynamics and communities are, on average, half full. behavioral interactions among individuals. In At the very least, Wishieu' s data suggest that studies of classical, Gauseian, or ecological-scale both scenarios are common in natural commu- coexistence, smaller-scale interactions are nities. This provides another independent line of integrated through time and community dynamics evidence for the partial competitive structuring of are studied at the point where populations have communities. Distinct -preference organization in had enough time to achieve equilibrium. At the extant communities is consistent with compe- highest scale, the niches, habitats, and species titively-structured niches, and with long-term pools of communities may themselves evolve, diversity steady states in the fossil record. Shared- and coexistence is affected by the factors that preference community organization in nature is control species diversity and coevolution. Various consistent with randomly, or non-competitively- authors have begun to make link.ages between structured niches, and with the haphazard and coexistence at these different scales (Birch 1979, ephemeral coexistence of species in finer-scale Connell 1980, Rosenzweig 1987b, Wolff 1996, studies of fossil communities. Species partition Vincent & Vincent 1996). These, and other multi- niche space competitively amongst themselves to scale approaches hold great potential for some degree, but they retain enough ecological enhancing our understanding of ecological flexibility and oversized fundamental niches to coexistence. roll with the 10,000 year punches. Communities Significant advances can also be made by are continually being pushed towards the climax developing better linkages between empirical and by community coevolution, and away from it by theoretical studies of ecological coexistence. shifting climate. Resource partitioning studies have provided 194 GORDON valuable empirical data on patterns of coexistence AY ALA FJ ( 1969) Experimental invalidation of the in nature. However, they have often ignored the principle of competitive exclusion. Nature 224: 1076- theoretical ecological literature on coexistence. 1079. Ideas that have emerged from coexistence theory AY ALA FJ ( 1971) Environmental fluctuations and population size. Nature 231: 112-114. can suggest important variables to be measured in AZOVSKY AI (1996) The effect of scale on congener purely observational studies, and can be used to coexistence: Can mollusks and polychaetes reconcile develop hypotheses in more experimental field beetles to ciliates? Oikos 77: 117-126. studies. For example, metapopulation coexistence BASSET A (1995) Body size-related coexistence: An models would suggest that dispersal abilities and approach through allometric constraints on home- competitive relationships should be measured in range use. Ecology 76: 1027-1035. coexisting sets of species. Increased measurement BIRCH LC ( 1979) The effects of species of animals which of competition among coexisting species would share common resources on one another's distribution and abundance. Fortschritte der Zoologie 25: 197- permit a better linkage to coexistence theory. 221. Experimental determination of realized vs. fun- BOROWSKY R ( 1971) Principle of competitive exclusion damental niches of coexisting species would help and Drosophila. Nature 230: 409-410. address the question of competitive niche BRETT CE & GC BAIRD (1995) Coordinated stasis and structuring in communities. evolutionary ecology of Silurian to middle Devonian Conversely, coexistence theorists should faunas in the Appalachian basin. In: Erwin DH & RL develop models that are more firmly rooted in Anstey (eds) New approaches to speciation in the empirical patterns of species coexistence. fossil record: 285-315. Columbia University Press, Competition-based models of ecological coexis- New York. BRITTON NF (1989) Aggregation and the competitive tence have been a useful first step, but to accurately exclusion principle. Journal of Theoretical Biology predict species coexistence in real communities, 136: 57-66. models should include both the competitive and BROWN JS ( 1989) Desert rodent community structure: A non-competitive components of coexistence. test of four mechanisms of coexistence. Ecological Explaining coexistence is an intrinsically Monographs 59: 1-20. difficult problem, yet the coexistence of species BROWN JS & ML ROSENZWEIG ( 1986) Habitat selection defines the very concept of an ecological in slowly regenerating environments. Journal of community, and is thus of central importance in Theoretical Biology 123: 151-171. CALDER W A Ill (1984) Size, function, and life history. ecology. Our understanding of the patterns and Harvard University Press, Cambridge, MA. xii + 431 processes of species' coexistence lies at the heart pp. of our ability to understand and predict the CASWELL H (1982) Life history theory and the dynamics of ecological communities. equilibrium status ofpopulations. American Naturalist 120: 317-339. CHESSON PL (1991) A need for niches? Trends in Ecology ACKNOWLEDGEMENTS and Evolution 6: 26-28. CHESS ON PL & RR WARNER (1981) Environmental variability promotes coexistence in lottery competitive Carlos Martinez del Rio and two anonymous systems. American Naturalist 117: 923-943. reviewers provided helpful comments on earlier COHEN D & SA LEVIN (1991) Dispersal in patchy versions of this manuscript. environments: the effects of temporal and spatial structure. Theoretical Population Biology 39: 63-99. CO HEN JE ( 1970) A Markov contingency table model for LITERATURE CITED replicated Lotka-Volterra systems near equilibrium. American Naturalist 104: 547-559. AB RAMS P (1975) Limiting similarity and the form of the COMINS HN & MP HASSELL (1996) Persistence of competition coefficient. Theoretical Population multispecies host-parasitoid interactions in spatially Biology 8: 356-375. distributed models with local dispersal. Journal of ABRAMS P (1976) Niche overlap and environmental Theoretical Biology 183: 19-28. variability. Mathematical Biosciences 28: 357-375. CONNELL JH (1975) Some mechanisms producing ABRAMS P (1983) The theory of limiting similarity. structure in natural communities: A model and Annual Review of Ecology and Systematics 14: 359- evidence from field experiments. In: Cody ML & JM 376. Diamond (eds) Ecology and Evolution of AB RAMS P ( 1988) Resource productivity-consumer Communities: 461-490. Harvard University Press, species diversity: simple models of competition in Cambridge. spatially heterogeneous environments. Ecology 69: CONNELL JH (1978) Diversity in tropical rainforests and 1418-1433. coral reefs. Science 199: 1302-1310. ARMSTRONG RA & R MCGEHEE (1980) Competitive CONNELL JH (1980) Diversity and the coevolution of exclusion. American Naturalist 115: 151-170. competitors, or the ghost of competition past. Oikos 35: 131-138. THE COEXISTENCE OF SPECIES 195

CONNELL JH (1983) On the prevalence and relative HALLEY JM, HN COMINS, JH LA WTON & MP importance of interspecific competition: evidence HAS SELL ( 1994) Competition, succession and pattern from field experiments. American Naturalist 122: in fungal communities: A cellular automaton model. 661-696. Oikos 70: 435-442. CONNELL JH & RO SLA TYER ( 1977) Mechanisms of HARD IN G ( 1960) The competitive exclusion principle. succession in natural communities and their role in Science 131: 1292-1297. community stability and organization. American HANSKI I (1981) Coexistence of competitors in patchy Naturalist 111: 1119-1144. environments with and without predation. Oikos 37: CONNOR EF & D SIMBERLOFF ( 1979) The assembly of 306-312. species communities: chance or competition? Ecology HANSKI I & Y CAMBEFORT (1991) Resource 60: 1132-1140. partitioning. In: Hanski I & Y Cambefort (eds) Dung COO PE GR ( 1987) The response of late Quaternary insect Beetle Ecology: 330-349. Princeton University Press, communities to sudden climatic changes. In: Gee Princeton. JHR & PS Giller (eds) Organization of Communities HANSKI I & E RANT A (1983) Coexistence in a patchy Past and Present: 421-438. Blackwell, England. environment: three species of Daphnia in rock pools. CORNELL HV & JH LA WTON (1992) Species Journal of Animal Ecology 61: 37-40. interactions, local and regional processes, and limits HANSKI I & DY ZHANG (1993) Migration, meta- to the richness of ecological communities: A population dynamics and fugitive coexistence. Journal theoretical perspective. Journal of Animal Ecology of Theoretical Biology 163: 491-504. 61: 1-12. HANSSON S (1995) Effects of exploitative food DANIELSON BJ ( 1991) Communities in a landscape: The competition on food niche dynamics - a simulation influence of habitat heterogeneity on the interactions analysis. Ecological Modelling 77: 167-187. between species. American Naturalist 138: 1105-1120. HASTINGS A (1980) Disturbance, coexistence, history, DA VIS MB ( 1983) Quaternary history of deciduous forests and competition for space. Theoretical Population of eastern North America and Europe. Annals of the Biology 18: 363-373. Missouri Botanical Garden 70: 550-563. HOLMES EE, MA LEWIS, JE BANKS & RR VEIT ( 1994) DEN BOER PJ (1980) Exclusion or coexistence and the Partial differential equations in ecology: spatial taxonomic or ecological relationship between species. interactions and population dynamics. Ecology 75: Netherlands Journal of Zoology 30: 278-306. 17-29. DEN BOER PJ (1986) The present status ofthe competitive HOL T RD (I 977) Predation, apparent competition, and exclusion principle. Trends in Ecology and Evolution the structure of prey communities. Theoretical 1: 25-28. Population Biology 12: 197-229. DENNO RF, MS MCCLURE & JR OTT (1995) HOL T RD (1993) Ecology at the mesoscale: the influence Interspecific interactions in phytophagous insects: of regional processes on local communities. In: Competition reexamined and resurrected. Annual Ricklefs RE & D Schluter (eds) Species Diversity in Review of Entomology 40: 297-331. Ecological Communities: 77-88. University of DICKMAN CR ( 1988) Body size, prey size, and community Chicago Press, Chicago. structure in insectivorous mammals. Ecology 69: 569- HOLT RD, J GROVER & D TILMAN (1994) Simple rules 580. for interspecific dominance in systems with DYTHAM C (1994) Habitat destruction and competitive exploitative and apparent competition. American coexistence: A cellular model. Journal of Animal Naturalist 144: 741-771. Ecology 63: 490-491. HORN HS & RH MacARTHUR ( 1972) Competition among DYTHAM C & B SHORROCKS ( 1992) Selection, patches, fugitive species in a harlequin landscape. Ecology and genetic variation: A cellular automaton modeling 53: 749-752. Drosophila populations. Evolutionary Ecology 6: 342- HORN HS & RM MAY (1977) Limits to the similarity 351. among coexisting competitors. Nature 270: 660-661. EKSCHMITT K & B BRECKLING (1994) Competition HUSTON MA & DL DEANGELIS (1994) Competition and coexistence: The contribution of modeling to the and coexistence: the effects of resource transport and formation of ecological concepts. Ecological supply rates. American Naturalist 144: 954-977. Modelling 75-76: 71-82. HUTCHINSON GE (1951) Copepodology for the FLETCHER WJ & AJ UNDER WOOD (1987) Interspecific ornithologist. Ecology 32: 571-577. competition among subtidal limpets: effect of HUTCHINSON GE ( 1957) Concluding remarks. Cold substratum heterogeneity. Ecology 68: 387-400. Spring Harbor Symposium on Quantitative Biology FRANKEL OH & ME SOULE (1981) Conservation and 22: 415-427. Evolution. Cambridge University Press, Cambridge, HUTCHINSON GE (1959) Homage to Santa Rosalia, or, United Kingdom. viii + 327 pp. Why are there so many kinds of animals? American GAUSE GF (1934) The Struggle for Existence. Williams Naturalist 93: 145-159. and Wilkins Press, Baltimore, Maryland. ix + 163 pp. HUTCHINSON GE (1961) The paradox of the plankton. GILPIN ME & KE JUSTICE ( 1972) Reinterpretation of American Naturalist 95: 137-145. the invalidation of the principle of competitive JAKSIC FM, P FEINSINGER & JE JIMENEZ (1993) A exclusion. Nature 236: 273-277. long-term study on the dynamics of guild structure GLEASON HA (1926) The individualistic concept of the among predatory vertebrates at a semi-arid neotropical plant association. Bulletin of the Torrey Botanical site. Oikos 67: 87-96. Club 53: 7-26. 196 GORDON

JOHNSON HB & HS MA YEUX ( 1992) A view on species McCARTHY MA, DB LINDENMAYER & M additions and deletions and the balance of nature. DRESCHLER ( 1997) Extinction debts and risks faced Journal of Range Management 45: 322-333. by abundant species. Conservation Biology 11: 221- JOHNSON RA (1986) Intraspecific resource partitioning 226. in the bumble bees Bombus ternarius and B. McPEEK MA (1996) Trade-offs, food web structure, and pennsylvanicus. Ecology 67: 133-138. the coexistence of habitat specialists and generalists. KAUFFMAN EG & JA FAGERSTROM (1993) The Phan- American Naturalist 148: Sl24-Sl38. erozoic evolution of reef diversity. In: Ricklefs RE & MEHRHOFF LA & R TURKINGTON ( 1995) Resource D Schluter (eds) Species Diversity in Ecological Com- use and co-existence: Experimental tests from a munities: 315-329. University of Chicago Press, Chi- sequence of different-aged pastures. Evolutionary cago. Ecology 9: 617-632. KOTLER BP, JS BROWN & WA MITCHELL (1994) The MERINOS ( 1996) Cyclic competition in the time periodic role of predation in shaping the behaviour, morphol- and diffusive case. Journal of Mathematical Biology ogy and community organisation of desert rodents. 34: 789-809. Australian Journal of Zoology 42: 449-466. MILLER AI & M FOOTE ( 1996) Calibrating the KOTLIAR NB & JA WIENS (1990) Multiple scales of Ordovician radiation of marine life: Implications for patchiness and patch structure: a hierarchical frame- Phanerozoic diversity trends. Paleobiology 22: 304- work for the study of heterogeneity. Oikos 59: 253- 309. 260. MIMURA M, SI El & Q FANG ( 1991) Effect of domain- LEVIN SA (1970) Community equilibria and stability, shape on coexistence problems in a competition-dif- and an extension of the competitive exclusion princi- fusion system. Journal of Mathematical Biology 29: ple. American Naturalist 104: 413-423. 219-237. LEVIN SA, D COHEN & A HASTINGS (1984) Dispersal MOILANEN A & I HANSKI (1995) Habitat destruction strategies in patchy environments. Theoretical Popu- and coexistence of competitors in a spatially realistic lation Biology 26: 165-191. metapopulation model. Journal of Animal Ecology LEVINS R (1969) Some demographic consequences of 64: 141-144. environmental heterogeneity for biological control. MOLOFSKY J (1994) Population dynamics and pattern Bulletin of the Entomological Society of America 15: formation in theoretical populations. Ecology 75: 30- 237-240. 39. LEVINS R ( 1979) Coexistence in a variable environment. MORRIS DW (1996) Coexistence of specialist and American Naturalist 114: 765-783. generalis! rodents via habitat selection. Ecology 77: LEVINS R & D CULVER (1971) Regional coexistence of 2352-2364. species and competition between rare species. Pro- MORRIS DW & TW KNIGHT ( 1996) Can consumer- ceedings of the National Academy of Sciences of the resource dynamics explain patterns of guild assem- United States of America 68: 1246-1248. bly? American Naturalist 147: 558-575. LIEBOLD MA (1996) A graphical model of keystone NAMBA T (1989) Competition for space in a heterogene- predators in food webs: Trophic regulation of abun- ous environment. Journal of Mathematical Biology dance, incidence, and diversity patterns in communi- 27: 1-16. ties. American Naturalist 147: 784-812. NEE S & RM MAY (1992) Dynamics of metapopulations: LOREAU M (1992) Time scale of resource dynamics and habitat destruction and competitive coexistence. Jour- coexistence through time partitioning. Theoretical nal of Animal Ecology 61: 37-40. Population Biology 41: 401-412. PAINE RT (1966) Food web complexity and species di- LOREAU M & DL DEANGELIS (1997) Source-sink dy- versity, American Naturalist 100: 65-75. namics and the coexistence of species on a single PETERS RH (1983) The ecological implications of body resource. Theoretical Population Biology 51: 79-93. size. Cambridge University Press, New York. xii + MacARTHUR RH (1964) Environmental factors affecting 329 pp. bird species diversity. American Naturalist 98: 387- PIANKA ER (1974) Niche overlap and diffuse competi- 397. tion. Proceedings of the National Academy of Sci- MacARTHUR RH, JM DIAMOND & JR KARR (1972) ences of the United States of America 71:2141-2145. Density compensation in island faunas. Ecology 53: PIMM SL, ML ROSENZWEIG & W A MITCHELL ( 1985) 330-342. Competition and food selection: Field tests of a MacARTHUR RH & R LEVINS (1967) The limiting simi- theory. Ecology 66: 798-807. larity, convergence, and divergence of coexisting PULLIAM HR ( 1985) Foraging efficiency, resource parti- species. American Naturalist 101: 377-385. tioning, and the coexistence of sparrow species. Ecol- MacARTHUR RH & JW MacARTHUR (1961) On bird ogy 66: 1829-1836. species diversity. Ecology 42: 594-598. RALPH CJ (1985) Habitat association patterns of forest MacNALL Y RC (1995) On large-scale dynamics and com- and steppe birds of northern Patagonia, Argentina. munity structure in forest birds: Lessons from some Condor 87: 471-483. eucalypt forests of southeastern Australia. Philosophi- RAUP DM & JJ SEPKOSKI (1984) Periodicity of cal Transactions of the Royal Society of London B extinctions in the geologic past. Proceedings of the 350: 369-379. National Academy of Sciences of the United States of MAY RM (1974) On the theory of niche overlap. Theoreti- America 81: 801-805. cal Population Biology 5: 297-332. THE COEXISTENCE OF SPECIES 197

REICHMAN OJ & E ROBERTS (1994) Computer simula- SHIGESADA N & J ROUGHGARDEN (1982) The role of tion analysis of foraging by Heteromyid rodents in rapid dispersal in the population dynamics of compe- relation to seed distributions: implications for coex- tition. Theoretical Population Biology 21: 353-372. istence. Australian Journal of Zoology 42: 467-477. SHMIDA A & S ELLNER ( 1984) The coexistence of plant ROSENZWEIG ML (1981) A theory of habitat selection. species with similar niches. Vegetatio 58: 29-55. Ecology 62: 327-335. SHORROCKS B & JG SEVENSTER (1995) Explaining ROSENZWEIG ML ( 1987a) Community organization from local species diversity. Proceedings of the Royal So- the point of view of habitat selectors. In: Gee JHR & ciety of London Series B 260: 305-309. PS Giller (eds) Organization of communities Past and SIMBERLOFF DS (1970) Taxonomic diversity of island Present: 469-490. Blackwell, England. biotas. Evolution 24: 23-47. ROSENZWEIG ML (1987b) Habitat selection as a source SIMBERLOFF DS (1981) Community effects of intro- of biological diversity. Evolutionary Ecology I: 315- duced species. In: Nitecki MH (ed) Biotic crises in 330. ecological and evolutionary time: 53-81. Academic ROSENZWEIG ML ( 1991) Habitat selection and popula- Press, New York. tion interactions: The search for mechanism. Ameri- SIMBERLOFF DS (1983) Competition theory, hypoth- can Naturalist S5-S28. esis-testing, and other community ecological ROSENZWEIG ML (1995) Species diversity in space and buzzwords. American Naturalist 122: 626-635. time. Cambridge University Press, New York. xx + SLATKIN M (1974) Competition and regional coexist- 436 pp. ence. Ecology 55: 128-134. ROSENZWEIG ML (in press) Preston's ergodic conjec- STRONG DR Jr. ( 1983) Natural variability and the mani- ture: the accumulation of species in space and time. fold mechanisms of ecological communities. Ameri- In: McKinney ML & JA Drake (eds) Biodiversity can Naturalist 122: 636-660. Dynamics: turnover of populations, taxa and commu- TANNER JE, TP HUGHES & JH CONNELL (1994) Spe- nities: 371-413. Columbia University Press, New cies coexistence, keystone species, and succession: York. A sensitivity analysis. Ecology 75: 2204-2219. ROSENZWEIG ML & ZN ABRAMSKY (1993) How are TERBORGH J (1973) On the notion of favorableness in diversity and productivity related? In: Ricklefs RE & plant ecology. American Naturalist 107: 481-501. D Schluter (eds) Species diversity in ecological com- THOMPSON DB, JH BROWN & WD SPENCER (1991) munities: 52-65. University of Chicago Press, Chi- Indirect facilitation of granivorous birds by desert cago. rodents: Experimental evidence from foraging pat- ROSENZWEIG ML & JA TA YLOR ( 1980) Speciation and terns. Ecology 72: 852-863. diversity in Ordovician invertebrates: filling niches TILMAN D (1980) Resources: A graphical-mechanistic quickly and carefully. Oikos 35: 236-243. approach to competition and predation. American ROTENBERR Y JT & JA WIENS ( 1980) Habitat structure, Naturalist 116: 362-393. patchiness, and avian communities in North Ameri- TILMAN D (1987) The importance of the mechanisms of can steppe vegetation: A multivariate analysis. Ecol- interspecific competition. American Naturalist 129: ogy 61: 1228-1250. 769-774. ROUGHGARDEN J (1974) Species competition and the TILMAN D (1994) Competition and biodiversity in spa- competition function with illustrations from coral tially-structured habitats. Ecology 75: 2-16. reef fish. Theoretical Population Biology 5: 163-186. TILMAN D, CL LEHMAN & C YIN (1997) Habitat de- ROUGHGARDEN J & M FELDMAN ( 1975) Species pack- struction, dispersal, and deterministic extinction in ing and predation pressure. Ecology 56: 489-492. competitive communities. American Naturalist 149: SALT GW (1983) Roles: their limits and responsibilities 407-435. in ecological and evolutionary research. American TILMAN D, RM MAY, CL LEHMAN & MA NOW ACK Naturalist 122: 697-705. (1994) Habitat destruction and the extinction debt. SCHAT CL, MN KUPERMAN & HS WIO (1996) An exact Nature 371:65-66. analytical solution of a three-component model for TURELLI M (1978) Does environmental variability limit competitive coexistence. Mathematical Biosciences niche overlap? Proceedings of the National Academy 131: 205-218. of Sciences of the United States of America 75: 5085- SCHLUTER D (1995) Adaptive radiation in sticklebacks: 5089. Trade-offs in feeding performance and growth. Ecol- TURELLI M (1981) Niche overlap and invasion of com- ogy 76: 82-90. petitors in random environments. I. Models without SCHLUTER D & RE RICKLEFS (1993) Convergence and demographic stochasticity. Theoretical Population the regional component of species diversity. In: Biology 20: 1-56. Ricklefs RE & D Schluter (eds) Species diversity in VALENTINE JW & D J ABLONSKI (1993) Fossil com- ecological communities: 230-240. University of Chi- munities: Compositional variation at many time cago Press, Chicago. scales. In: Ricklefs RE & D Schluter (eds) Species SCHOENER TW ( 197 4) Resource partitioning in ecologi- diversity in ecological communities: 341-349. Uni- cal communities. Science 185: 27-39. versity of Chicago Press, Chicago. SCHOENER TW ( 1983) Field experiments on interspecific V AN DER LAAN JD, L LHOTKA & P HOGEWEG (1995) competition. American Naturalist 122: 240-285. Sequential predation: A multi-model study. Journal of Theoretical Biology 174: 149-167. 198 GORDON

VAN DEVENDER TR & WG SPAULDING (1979) Devel- WILSON DS ( 1975) The adequacy of body size as a niche opment of vegetation and climate in the southwestern difference. American Naturalist 109: 769-784. United States. Science 204: 701-710. WINS TON MR ( 1995) eo-occurrence of morphologically V ANCE RR ( 1978) Predation and resource partitioning in similar species of stream fishes. American Naturalist one predator-two prey model communities. American 145: 527-545. Naturalist 112: 797-813. WISHIEU IC (1998) How organisms partition habitats: VINCENT TLS, D SCHEEL, JS BROWN & TL VINCENT different types of community organization can pro- ( 1996) Trade-offs and coexistence in consumer-re- duce identical patterns. Oikos 83: 246-258. source models: It all depends on what and where you WOLFF JO ( 1996) Coexistence of white-footed mice and eat. American Naturalist 148: 1038-1058. deer mice may be mediated by fluctuating environ- VINCENT TLS & TL VINCENT (1996) Using the ESS mental conditions. Oecologia 108: 529-533. maximum principle to explore root-shoot allocation, WRIGHT DH, DJ CURRIE & BA MAURER (1993) En- competition and coexistence. Journal of Theoretical ergy supply and patterns of species richness on local Biology 180: 111-120. and regional scales. In: Ricklefs RE & D Schluter WEBB SD (1989) The fourth dimension in North Ameri- (eds) Species diversity in ecological communities: can terrestrial communities. In: Morris D, Z 66-74. University of Chicago Press, Chicago. Abramsky, B Fox & MR Willig (eds) Patterns in the Y AN G ( 1996) Parasite-mediated competition: A model structure of mammalian communities: 181-203. Texas of directly transmitted macroparasites. American Tech. University Press, Lubbock. Naturalist 148: 1089-1112. WHITTAKER RH (1956) Vegetation of the Great Smoky ZIV Y ( 1998) The effect of habitat heterogeneity on spe- Mountains. Ecological Monographs 26: 1-80. cies diversity patterns: A community-level approach WIENS JA (1974) Climatic stability and the "ecological using an object-oriented landscape simulation model saturation" of bird communities in North American (SHALOM). Ecological Modelling Ill: 135-170. grasslands. Condor 76: 385-400. WIENS JA (1977) On competition and variable environ- ments. American Scientist 65: 590-597.