The geometry of evolution

Evolutionary processes explain the development of populations based upon the mechanisms mutation and selection. Due to mutations and other sources of variability populations consist of distinct phenotypes that differ in one or several trait variables. Long-term survival of a phenotype over several generations depends on its efficiency in resource allocation in competition with other phenotypes. Thus, competition of phenotypes acts as a mechanism of selection. I will present a unified geometric approach for studying competition in mathematical models of ecological interactions and infectious diseases and demonstrate how this theory can be used for gaining a better understanding of evolutionary processes in these systems.