Stochasticity and extinction risk in a mutualist network

Background/Question/Methods

Extinctions can be described in population dynamic terms as a transition from a positive population size to zero. Consequently, the factors that influence population trajectories also affect extinction risk. Much of the existing theoretical work on extinction risk evaluates the influence of single factors, such as species interactions or environmental variability. But both are ubiquitous in ecological systems and affect community dynamics simultaneously. For this reason, extinction risk calculations that include only one of these factors are likely to be poor estimates.

To explore how species interactions and environmental variability combine to affect extinction risk, we analyze a mutualist model using both analytical and numerical approaches. In particular, we ask how including a stochastic term affects the probability of (a) an initial species loss and (b) extinction cascades.

For this study, we use a discrete-time plant-pollinator model with a single coexistence equilibrium. To derive extinction risk estimates analytically, we treat the linearized model as a first-order autoregressive process. We use the variance of population excursions away from the equilibrium to estimate the probability of any population jumping to zero in a given time step. In addition, we run numerical simulations on the full nonlinear model.

Results/Conclusions

In a one-plant one-pollinator community, extinction risk increased with increasing environmental variability. Decreasing pollinator reproductive rates elevated the extinction risk of plants and pollinators alike in the presence of environmental variability, even when reproduction was somewhat above the replacement rate. These lowered reproductive rates resulted not only in smaller equilibrium population size, but also greater variance in population sizes, with respect to the original environmental variance.

These results suggest that deterministic models of mutualist communities that are subject to environmental variability tend to underestimate extinction risk. Despite its underrepresentation in the theoretical literature, mutualism is a vital component of ecological and agricultural systems. In particular, the vast majority of flowering plants depend upon animal pollinators. In light of recent pollinator declines, understanding extinction risk in plant-pollinator communities is especially crucial. Models that include environmental variability alongside species interactions provide a clearer picture of extinction risk in mutualist communities than those that only consider interaction structure.