COS 62-2
A Lotka-Volterra theory of coexistence in nonstationary environments
Most models of interacting species assume a stationary environment (the environment may fluctuate, but with constant mean, variance, and other statistical moments). But this is at best an approximation to nature where all properties change continuously. Nonstationary environments provide serious challenges for both theoretical and empirical analysis because stable properties are more difficult to recognize. However, stable coexistence theory provides the key concepts of stabilizing and equalizing mechanisms that can be extended to the nonstationary case, allowing the study of stable coexistence in general nonstationary situations. Moreover, techniques from scale transition theory allow nonstationary fluctuations over time to be partitioned into contributions to stabilization of coexistence and contributions to average fitness inequality, which favor exclusion. Moreover, these techniques can be applied over finite timescales so that predictions can be specific to particular periods of time, an essential requirement in the nonstationary case where continual change may preclude any long-term prediction. We applied these techniques to understand stable coexistence in a multispecies Lotka-Volterra model of interacting species competing for shared resources in a nonstationary environment.
Results/Conclusions
We found that different aspects of environmental variation affected coexistence in different ways. Temporal variation in resource uptake rates promotes coexistence in both stationary and nonstationary environment if fluctuations occur on timescales as long or longer than the timescale for draw down of resources by consumption. In the nonstationary case, such variation can be partitioned into trends and fluctuations on different timescales, revealing contributions to stable coexistence and average fitness inequality over any given period of time. Fluctuations in resource uptake rates are generally neutral to coexistence in the stationary case, but in the nonstationary can favor exclusion through the accumulation of average fitness inequalities with time. However, the magnitude of the maintenance requirements affects the stability of coexistence from fluctuations in resource uptake rates, and so nonstationary variation in resource uptake rates can cause changes over time in the stability of species coexistence. Finally, we found in models with multiple resources that classical resource partitioning can limit the impact of nonstationary trends that build up fitness inequalities. These results collectively show how the ideas developed for the stationary case can be used to analyze the impact of nonstationary environments on the maintenance of species diversity.