Sala Seminari (Dip. Matematica).
New developments concerning the relationships between species trees, representing the branching histories of populations of organisms, and gene trees, which represent the histories of individual genomic regions, have generated new combinatorial structures. These include “coalescent histories” and “ancestral configurations”, structures that for a given gene tree topology and species tree topology encode the different evolutionary configurations of the gene tree in the branches of the species trees. Many configurations might be possible for a given gene tree and species tree, and their number is a key quantity in the study of the likelihood of different evolutionary scenarios. Under the assumption of matching gene trees and species trees, I will present several enumerative results describing the behavior of the number of coalescent histories and ancestral configurations for increasing tree size. Techniques rely on generating functions and tools of analytic combinatorics.