  We characterize two universality classes of absorption-time distributions for
birth-death Markov chains. Based on generic features of the transition rates,
the asymptotic distribution is either Gaussian, Gumbel, or a convolution of
Gumbel distributions. Our rigorous calculations inform heuristics that enable
simple prediction of the absorption-time distribution. We show that several
birth-death models of evolutionary dynamics, epidemiology, and chemical
reactions fall into these classes, establishing new results for the
absorption-time distribution in each case.
