Evolutionary models in population dynamics

Abstract

Agent-based evolutionary models describe processes that occur at the individual level, such as reproduction, migration, mutation and selection. Over many generations these processes can drive populations to divide into species, which in turn may become extinct or divide again. The information about these macroevolutionary effects can be condensed into dendrograms known as phylogenetic trees, which record the speciation and extinction events. Connecting the structuralproperties of these trees with the microevolutionary processes that produced them is a great challenge that would reconstruct the evolutionary history of groups of living species. In this project we intend to study the effects of mutations, selection and geographical distribution on the topological properties of phylogenetic trees, which will be characterized by indices that measure the symmetry of the branches (Sackin), the branch length distribution (gamma ) and also by the spectral analysis of the associated Laplacian matrix. Selection will be included in two ways: (i) using elements of game theory in the agent based genetic models and, (ii) including, in addition to recombinant nuclear DNA, the mitochondrial DNA transmitted by the maternal lineage. Both processes confer adaptive advantages to individuals affecting their reproduction and hence the resulting phylogenies. (AU)