DYNAMICS WITH SELECTION

The subject of this thesis is population dynamics. We study its features in the absence or in the presence of a spatial structure, and this is reflected in the manuscript division into two parts. In the first one, we consider the competition as taking place among all individuals at the same time, and we show that a condition of detailed balance is satisfied in different evolutionary regimes (and not only, as known in literature, in the successional-mutations regime). We show that the adaptive dynamics of a population has many aspects in common with the out of equilibrium dynamics of glasses, the role of the temperature being played by the number of individuals in the population. We suggest numerous applications of such a correspondence. Next, we consider the evolution of interacting monomorphic populations. We show how the coupling causes a separation of the adaptive temporal scales, and that it is possible to establish a hierarchy in the degree of adaptation of the interacting populations. In the case of populations competing in space, the evolutionary dynamics is strongly modified by the locality of the interactions. The selection mechanisms are less effective in favouring the establishment of the fittest phenotype. We prove quantitatively that an increased rate of mutation involves an evolutionary disadvantage, since the presence of mutants slows the spatial growth of a population. We show how, if the mutation rate is variable, the selection favours not only a high reproduction rate, but also a low rate of mutation.