Community robustness in discrete-time periodic environments

The influence of seasonal environmental variation on species coexistence is an ecologically important factor. Its two aspects are how seasonal variation contributes to coexistence mechanisms, and, given a seasonally varying coexistence pattern, how sensitive that coexistence is to nonstationary external influences (such as climate change). Here we develop a formula for calculating the robustness of discrete-time periodic dynamics. Robustness is defined as the sensitivity of the position of the cycle in phase space to varying model parameters. Though the results are different, the main biological conclusions are in line with those from a similar study concerning continuous-time cycles ( Barabas et al., 2012a ): species segregation in the timing of resource use or predator avoidance increases community robustness in a way that is analogous to the effects of resource partitioning. We also connect this formalism with the widely used and successful framework of Chesson (1994) , demonstrating that the merging of these two perspectives yields simplified expressions for robustness more amenable to analytical treatment. As an example, we apply our results to a two-cycle in a model of two competing annual plants with seedbanks, using our formulas to calculate the range of parameters that allow for the coexistence of the competitors. This helps us understand which components of the environmental variation the coexistence is sensitive to; in our case, the model is fairly robust against changing seed survival, moderately so against changing the variance in seed germination, and quite sensitive to changing the mean seed germination rates.