Lineages-through-time plots of neutral models for speciation

Drawing inferences about macroevolutionary processes from phylogenetic trees is a fundamental challenge in evolutionary biology. Understanding stochastic models for speciation is an essential step in solving this challenge. We consider a neutral class of stochastic models for speciation, the constant rate birth-death process. For trees with n extant species - which might be derived from bigger trees via random taxon sampling - we calculate the expected time of the kth speciation event (k=1,...,n-1). Further, for a tree with n extant species, we calculate the density and expectation for the number of lineages at any time between the origin of the process and the present. With the developed methods, expected lineages-through-time (LTT) plots can be drawn analytically. The effect of random taxon sampling on LTT plots is discussed.