Environmental stochasticity increases extinction risk to a greater degree in pollination specialists than in generalists

Pollination sustains terrestrial food webs and agricultural systems and links the dynamics of interacting plant and pollinator species. Although environmental stochasticity is ubiquitous and can propagate through communities via species interactions in a way that increases extinction risk, it is unknown whether stochasticity affects species uniformly across pollination networks. In this paper, we introduce a stochastic dynamic model that makes novel use of the birth function and apply it to pollination networks of increasing size. We start with two- and four-species networks, in order to first illustrate the effects of stochasticity per se and then how those effects combine with specialization. We then describe the relationship between partner number and stochastic extinction risk in empirical networks with >20 species. In the 2-species network, increasing the variance of the stochastic term of the model increased the size of the region in parameter space where extinctions occur. In networks with 4 or more species, specialists were more vulnerable to extinction than generalists over a broad range of variances. Extinction risk in networks with >20 species declined nonlinearly with increasing mutualist partner number. Our results demonstrate the importance of including species interactions and stochasticity when using population-dynamic models to compare species' extinction risk. While models that omit either of these factors are likely to underestimate extinction risk, they disproportionately underestimate the vulnerability of specialists.