Predicting the loss of phylogenetic diversity under non-stationary diversification models

We provide explicit formulae for the expected remaining PD in both models, conditional on N=n, conditional on K=k, or conditional on both events. When N=n is fixed, we show the convergence to an explicit deterministic limit of the ratio of new to initial PD, as n→∞, both under the field of bullets model, and when K=kn is fixed and depends on n in such a way that kn/n converges to p. We also prove the convergence of this ratio as T→∞ in the supercritical, time-homogeneous case, where N simultaneously goes to ∞, thereby strengthening previous results of Mooers et al. (2012).