Does deterministic coexistence theory matter in a finite world? Insights from serpentine annual plants
Contemporary studies of species coexistence are underpinned by deterministic models that assume that competing species have continuous (i.e. non-integer) densities, live in infinitely large landscapes, and coexist over infinite time horizons. By contrast, in nature species are composed of discrete individuals subject to demographic stochasticity, and occur in habitats of finite size where extinctions occur in finite time. One consequence of these discrepancies is that metrics of species coexistence derived from deterministic theory may be unreliable predictors of the duration of species coexistence in nature. These coexistence metrics include invasion growth rates and niche and fitness differences, which are now commonly applied in theoretical and empirical studies of species coexistence. Here we test the efficacy of deterministic coexistence metrics on the duration of species coexistence in a finite world. We introduce new theoretical and computational methods to estimate coexistence times in stochastic counterparts of classic deterministic models of competition. Importantly, we parameterized this model using experimental field data for 90 pairwise combinations of 18 species of annual plants, allowing us to derive biologically-informed estimates of coexistence times for a natural system. Strikingly, we find that for species expected to deterministically coexist, habitat sizes containing only tens of individuals have predicted coexistence times of greater than 1, 000 years. We also find that invasion growth rates explain 60% of the variation in intrinsic coexistence times, reinforcing their general usefulness in studies of coexistence. However, only by integrating information on both invasion growth rates and species equilibrium population sizes could most (> 99%) of the variation in species coexistence times be explained. This integration is achieved with demographically uncoupled single species models solely determined by the invasion growth rates and equilibrium population sizes. Moreover, because of a complex relationship between niche overlap/fitness differences and equilibrium population sizes, increasing niche overlap and increasing fitness differences did not always result in decreasing coexistence times as deterministic theory would predict. Nevertheless, our results tend to support the informed use of deterministic theory for understanding the duration of species coexistence, while highlighting the need to incorporate information on species equilibrium population sizes in addition to invasion growth rates.