Abstract. 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.Key words. Cichlids, disruptive sexual selection, interbreeding, mate recognition system, separatrix, sexual selection, speciation.Received November 12, 1999. Accepted July 14, 2000.Sexual selection was first suggested by Darwin (1871) to explain exaggerated male secondary sexual characters and female preference for them. Fisher (1930) argued that the coadaptation between male secondary sexual characters and female preference occurs through a runaway process, and this argument was confirmed by theoretical models (O'Donald 1967;Lande 1981;Kirkpatrick 1982). Paterson (1985) coined the term, mate recognition system (MRS) for such a co-adapted mating system and reasoned that it assures species' identities by providing a concrete species recognition mechanism and preventing mating with other close species. Because the direction of runaway process, which is thought to be initiated by a random increase of female preference, is also random (Lande 1981), the resulting MRSs will differ among geographically isolated populations. Sexual selection has therefore been considered to be a strong force that causes allopatric speciation (Andersson 1994). A question that arises here is whether two different MRSs are established in one population sympatrically, if some initial variabilities of male secondary sexual characters and female preference are provided.This idea has been examined by computer simulation models (Wu 1985;Turner and Burrows 1995;Higashi et al. 1999). We and Turner and Burrows attained stable sympatric speciation. Turner and Burrows, starting from a population with an already established MRS, demonstrated the evolution of an alternative MRS while the first MRS remains in the population. Their analysis, however, is limited. They did not examine the dependence of their key parameter: the cost of the male secondary sexual character (Higashi et al. 1999). Simulations of our individual-based model started from evolutionary established (stationary) trait distributions, where the divergence of mating trait...