Evolutionary branching under asymmetric competition

I investigate the evolution of a continuous trait, such as body size or arms level, which affects the outcome of competitive contests such that the contestant with the larger trait value has a higher probability of winning. I show that a polymorphism of distinctly different strategies can evolve in an initially monomorphic population even if mutations have only small phenotypic effect. In a simple Lotka-Volterra-type model of asymmetric competition, I derive the conditions under which two strategies can gradually evolve from a single ancestral strategy; the evolution of higher level polymorphisms is studied by numerical analysis and computer simulations of specific examples. High levels of polymorphism may build up during evolution. The coevolution of strategies in polymorphic populations, however, may also lead to extinction, which decreases the level of polymorphism. I discuss whether the evolution of several haploid strategies from a single initial strategy may correspond to the evolution of several sympatric species in a diploid outbreeding population.