Ecology, 84(3), 2003, pp. 17-31 © 2003 by the Ecological Society of America COEXISTENCE: HOW TO IDENTIFY TROPHIC TRADE-OFFS JAMES S. CLARK, 1 ' 2 JACQUELINE MoHAN, 2 MICHAEL DiETZE, 2 AND INES IBANEZ 2 ^Department of Biology and Nicholas School of the Environment, Duke University, Durham, North Carolina 27708 USA ^University Program in Ecology, Duke University, Durham, North Carolina 27708 USA Abstract. Analyses of growth response to resource availability are the basis for inter- preting whether trophic trade-offs contribute to diversity. If different species respond most to resources that are limiting at different times, then those differences may trade off with other trophic or life-history traits that, together, help to maintain diversity. The statistical models used to infer trophic differences do not accommodate uncertainty in resources and variability in how individuals use resources. We provide hierarchical models for resource- growth responses that accommodate stochasticity in parameters and in data, despite the fact that causes are typically unknown. A complex joint posterior distribution taken over >10 2 parameters is readily integrated to provide a comprehensive accounting of uncertainty in the growth response, together with a small number of hyperparameters that summarize the population response. An application involving seedling growth response to light avail- ability shows that large trophic differences among species suggested by traditional models can be an artifact of the assumption that all individuals respond identically. The hierarchical analysis indicates broad trophic overlap, with the implication that slow dynamics play a more important role in preserving diversity than is widely believed. Key words: resource—consumel coexistence; competition; diversity; growth response; hierarchical Bayes; light; • r interactions; species interactions; tree seedlings. INTRODUCTION Theory, experiment, and observation suggest that trade-offs among species involving trophic interac- tions or life history are the logical and parsimonious explanation for the often rich diversity of plant com- munities (Tilman 1988, 1994, Pacala et al. 1996, Rees et al. 2001). Trophic trade-offs result from pat- terns of consumption. Examples include different minimal requirements for different resources (Til- man 1982), light response curves that shift the ad- vantage from early- to late-successional species as canopies close (Bazzaz 1979), and natural enemies that can promote diversity through preferential pre- dation on a superior competitor (Paine 1966, Pacala and Crawley 1992). Life-history trade-offs involve timing of reproductive effort, and life-history and trophic trade-offs often interact through allocation that can affect growth, seed size, fecundity, dispers- al, and survivorship (Loehle 1988, Tilman 1988, Clark 1991, Rees et al. 2001). The apparent agreement of evidence from disparate approaches is compelling. Theory emphasizes trade- offs, because models predict the extinction of species lacking parameter combinations that are sometimes fa- vored in competition or in potentially rare or transient environments (MacArthur 1972, May 1973, Tilman 1994). Field data can be found to support this view (reviews of Connell and Slatyer 1977, Rees etal. 2001). The alternative, that species are not importantly dif- ferent and densities therefore "drift" (Hubbell 2001), does not see much coverage in recent reviews of the subject. To some, the hypothesis is made more palat- able by the possibility that speciation might offset the inevitable extinction losses. Here we demonstrate that the motivation for trade- offs is less compelling and finds less support in data than is generally appreciated. The theoretical demand for trade-offs and the empirical support are influenced by assumptions that concern the structure of variability and the degree of uncertainty. Theoretical models as- sume that differences among species overwhelm var- iability among individuals, so much so that individual differences can be ignored. Individualdifferences need not be genetic, and they need not be associated with measurable environmental variation; any individual variation violates the assumptions of most ecological theory and almost all classical statistical models used to test it. 17