A deterministic genetic model for sympatric speciation by sexual selection.

A deterministic haploid genetic model confirms and explores in more detail the results of our previous individual-based simulation model for sympatric speciation by sexual selection. With the deterministic model, we are able to elucidate parameter dependence by phase plane analysis. We clarify how and why sympatric speciation by sexual selection can happen in a number of ways: (1) Female preferences for or against particular types of males have different effects. Whereas the former affects how readily speciation is invoked, the latter changes the stability of speciation equilibrium. (2) When there is no cost on male ornamentations, speciation is triggered regardless of initial haplotype frequencies if sufficient female preference is provided. (3) There exists a threshold for female initial frequencies for speciation to be invoked, but male initial frequencies have little effect. (4) A small cost on female mate choice does not cancel speciation, but when large, it greatly reduces the possibility of speciation.