COS 91-8
Specialization, stability and stochasticity: Extinction risk in a plant-pollinator model
The vast majority of flowering plant species depend upon animal pollinators to reproduce. Consequently, extinctions within plant-pollinator networks are not isolated events but rather have the potential to elevate the risk of additional species losses both within and beyond plant-pollinator communities.
Mutualist models represent an underrepresented but growing part of the theoretical literature on extinction risk in a community context. Mutualist models that incorporate stochasticity are further underrepresented. In nature, however, pollination interactions are situated within stochastically varying environments. Consequently, we expect deterministic models to underestimate extinction risk.
To explore how species interactions and environmental variability combine to affect extinction risk, we analyze a discrete-time, population dynamic mutualist model. We assess the stability of the coexistence and extinction equilibria, and we use numerical methods to apply shocks and estimate the probability that species will be lost from the system.
In particular, we ask how the inclusion of environmental stochasticity affects the relative extinction risk of specialists and generalists of both species types.
Results/Conclusions
Because the structure of the interaction network necessarily influences extinction risk, we apply our model to simplified two-species, four-species (2-plant, 2-pollinator) networks as well as a 22-species pollination network derived from field data. The two-species version of the model has two equilibria (coexistence and extinction), which undergo bifurcations that destabilize coexistence and stabilize extinction with (a) increasing mortality and (b) decreasing offspring production per floral visit. Instances of the model with 4 and 22 species have additional partial-coexistence equilibria.
Our numerical results reveal the effect of specialization on extinction risk in these simplified and realistic pollination networks. We also show that applying stochastic shocks to the model elevates extinction risk for all species, relative to risk estimates under deterministic dynamics.
Mutualism is a vital component of ecological and agricultural systems. 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 or deterministic dynamics.