Extinctions and extirpations do not occur in isolation, but rather within communities of interacting species and dynamic environments. Single-species models demonstrate the influence of population dynamics and environmental variability on extinction risk, while the extinction cascade literature shows the importance of species interactions. In deterministic models, each primary extinction gives rise to only one sequence of subsequent losses. When stochasticity is present, however, numerous sequences are possible. Because the risk of each subsequent loss is influenced by the extent to which the remaining species reproduce and interact following previous extinctions, some sequences may be more likely to occur than others. Here, we explore how environmental stochasticity, population dynamics, and species interaction structure combine to affect the likelihood that potential sequences are realized, and how their importance changes along each sequence. We also investigate how the extinction risk of remaining species changes through time following each loss.
To do so, we use a population dynamic mutualist model with a stochastic shock applied at each time step. We apply this model to a two-plant, two-pollinator network, i.e. the simplest community that accommodates specialists and generalists. We then characterize patterns in realized extinction sequences over a range of shock variances.
Extinction sequences did not occur with uniform frequency. Of 65 combinatorically possible sequences, about half (32) were rendered deterministically impossible by the community interaction structure. Of the remaining sequences, all appeared in at least one replicate, but their frequency changed with shock variance. Longer sequences occurred more frequently at higher variance values. Additionally, we showed that extinction risk in species with extant mutualist partners differed between the initial stable community, the transient phase following a primary loss, and the subsequent re-equilibrated partial community.