The overall aim of this project is to better understand biological processes leading to speciation and diversification through a study of the dynamic and static behavior of various multilocus models. Existing approaches to the modeling of speciation are deficient in several ways. Usually a small number of loci or quantitative traits are considered, selection is assumed to be weak, population size is considered to be constant, and only a very limited number of selection regimes mostly reflecting the dominant paradigm of "rugged adaptive landscapes" have been studied. Recently a new metaphor of "holey adaptive landscapes" (Gavrilets 1997) has been put forward as a plausible alternative to the conventional view of rugged adaptive landscapes. This metaphor is the core of the research proposed here. This project will investigate: (i) dynamics of genetic and morphological diversification in (growing) populations and clades, (ii) evolutionary dynamics of metapopulations and hybrid zones, (iii) coevolutionary dynamics. The biological questions to be approached here are very diverse. However, there is a unifying theme underlying the methods to be used. This theme is that biological organisms can be viewed as very long sequences with thousands and millions elements (e.g. genes or DNA base pairs). Thus, from a mathematical point of view, biological evolution takes place in a space with an enormous number of dimensions. Consequently, a significant proportion of evolutionary changes are expected to happen along nearly neutral networks and on holey adaptive landscapes. Chance and contingency should play a major role in evolutionary dynamics. Here, a combination of analytical methods recently developed in theoretical evolutionary biology, mathematics, and physics and extensive numerical simulations will be used to take into account various factors operating in natural populations (selection, mutation, recombination, random drift, migration, extinction, colonization etc).