Ecology now has a well-developed theory of species coexistence. This theory provides a rigorous and practical definition of "coexistence" as the ability of species to increase when rare, and defines and partitions different classes of coexistence mechanism. However, a theory of species coexistence isn't the same thing as a theory of species diversity. Even leaving aside cases in which co-occurring species are not coexisting (e.g., because some are on their way to exclusion), the number of coexisting species and the strength of coexistence mechanisms are two different things. Here I ask how those two things are related. In particular, I use several simple models of different ecological scenarios to ask whether more species-rich communities will exhibit stronger coexistence mechanisms. Following Chesson (2008), "strength of coexistence" for a community can be defined in terms of a community-wide average of the strength of stabilizing mechanisms (coexistence mechanisms that strengthen intraspecific relative to interspecific density dependence, and so tend to cause species to increase when rare because rare species experience only interspecific density dependence). I also briefly consider other, more heuristic measures of "strength of coexistence".
Results/Conclusions
Intuitively, we might expect that more species-rich communities generally will exhibit stronger coexistence mechanisms, because the latter causes the former: strengthening coexistence mechanisms allows the coexistence of species that would otherwise be excluded. Drawing on new results from simple theoretical models as well as previously-published work, I show that this naive intuition is incorrect in general, for two reasons. First, causality goes both ways: the number of species in the community both affects and is affected by the strength of coexistence mechanisms. Second, whether or not more species-rich communities exhibit stronger coexistence mechanisms depends on the factors causing species richness and strength of coexistence mechanism to vary. For instance, I show that one can vary species richness and strength of coexistence mechanisms by varying the amplitude of environmental fluctuations, varying average environmental conditions, varying the properties of the species pool from which the community is assembled, etc. Each of these possibilities generates different relationships between realized species richness and realized strength of coexistence mechanisms. I conclude that there is in general little reason to expect the number of coexisting species to be related to the strength of coexistence mechanisms among those same species.