Abstract
Trees describe evolutionary processes at different time scales. This chapter focuses on the two main probabilistic tree generating models, namely the birth-death process and the Kingman coalescent. It provides elements of combinatorics necessary to count these trees. The chapter determines the probabilities of the corresponding trees, ignoring the ages of the nodes. It also determines the probability densities of trees comprising ages at the nodes. While trees are used to model the support of biological evolution, they are also formal objects studied as such in computer science and mathematics. The Wright-Fisher model is central to population genetics, because it makes it possible to quantify the phenomenon of genetic drift. The effective population size is a central concept to population genetics because it makes it possible to quantify genetic drift. The process of lineage merging being Markovian, the derivation of the probability density of a tree generated according to the Kingman coalescent is almost immediate.