Unifying Dynamic Models for Predicting Extinction Debts

Temporal trajectories of species richness and extinction debts under two different metapopulation parameter-changing scenarios. In (A,B), a gradual decreasing trajectory of biotic relaxation is presented, in which the colonization rate is assumed to be present stepwise changes while the extinction rate is kept without change. The functional form for the colonization rate is given as a stepwise function as , while the functional form for the extinction rate is a constant as . In (A), the solid black line indicates . The black dashed line was the unrealized tail end of the relaxation curve, while the green dashed line highlighted the shifting species richness expected at equilibrium . Finally, the gray arrow lengths indicate the size of extinction debts remaining to be paid before the next event happens (the next event here is the shift of colonization rate). In this scenario, only extinction debts emerge (red curve). In (C,D), a more complex fluctuating decreasing trajectory of biotic relaxation is presented. Here, both colonization and extinction parameters are assumed to fluctuate over the sampling time for the purpose of mimicking fluctuating climatic conditions. The functional form for the colonization rate is given as , while the functional form for the extinction rate is . In this scenario, both extinction debts and species credits can re-emerge in somewhat periodic ways (red and blue curve segments, respectively, in C). Like (A), the solid black line indicates , while the green dashed line is in (C).