Extinction debt in local habitats: quantifying the roles of random drift, immigration, and emigration

We developed a time-dependent stochastic neutral model for predicting diverse temporal trajectories of biodiversity change in response to ecological disturbance (i.e., habitat destruction) and dispersal dynamic (i.e., emigration and immigration). The model is general and predicts how transition behaviors of extinction may accumulate according to different combination of random drift, immigration rate, emigration rate, and the degree of habitat destruction. We show that emigration, the areal size of the destroyed habitat, and initial species abundance distribution can impact the total biodiversity loss in an intact local area. Among these, the species abundance distribution plays the most deterministic role, as it directly determines the initial species richness in the local target area. In contrast, immigration was found to slow down total biodiversity loss and can drive the emergence of species credits (i.e., a gain of species) over time. However, emigration process would increase the extinction risk of species and accelerate biodiversity loss. Finally but notably, we found that a shift in the emigration rate after a habitat destruction event may be a new mechanism to generate species credits.