A Lotka–Volterra Model of Coexistence between a Sexual Population and Multiple Asexual Clones

Abstract

At carrying capacity, small advantages in competitive ability can compensate a sexual population for its two-fold disadvantage in growth capacity when facing invasion by asexual mutants. In this paper, we develop a generic analytical model to consider the ecology of a sexual population comprising equal numbers of males and females, competing for shared prey resources with multiple female-only clones. We assume that the clones arise from the sexual population and are distinguished from it only by having narrower resource niches and twice the growth capacity. For sexual populations, at density-dependent carrying capacity, intra-specific competition between clonal individuals prevents them from realizing their two-fold advantage in intrinsic growth. This prediction leads to three novel outcomes: (i) a sexual population can coexist with any number of clones, provided their combined competitive impact remains less than the impact of the clones on each other; (ii) a sexual species can immediately exclude asexual invaders if it is a fast growing and strong competitor of shared resources and also has refuge in an abundant alternative resource; (iii) the rate of accumulation of clones in a sexual population will be slowed by intra and inter-specific competition amongst the clones themselves, in addition to the competitive impact from the original sexual population.

Deleterious transposable elements and the extinction of asexuals

“…Moreover, all models for the advantage of sex must contend with various additional genetic and ecological costs, including those associated with the production and maintenance of males, the finding of mates, the maintenance of mechanisms for meiosis and syngamy, and the spread of sexually transmitted disease. (9,10,11) Whether the conditions required under any current model or combination of models have been sufficiently prevalent throughout Nature to account for the evolutionary success of sex and the relatively early extinction of sporadically arising asexuals therefore remains uncertain. There is reason then to ask, with Maynard Smith, (12) if something is missing from existing models.…”

Outcomes of reciprocal invasions between genetically diverse and genetically uniform populations of Daphnia obtusa (Kurz)

“…Yet, classical ecological theory predicts a much less than twofold cost of males in crowded environments. The ecological models of Case and Taper (1986), Gaggiotti (1994), Doncaster et al (2000Doncaster et al ( , 2003, Kerszberg (2000), Pound et al (2002Pound et al ( , 2004 all show how male presence can impose a considerably less than twofold cost on population growth for sexual populations at density-dependent carrying capacity. For example, the Lotka-Volterra model of Doncaster et al (2000) demonstrates that a sexual population requires only a small average per capita advantage in competition with an invading asexual mutant to halt the invasion process.…”

Evolutionary History of Contagious Asexuality in Daphnia Pulex

“…The role of selective asymmetries in mediating the spatial coexistence of asexual taxa and their close sexual relatives has been investigated in theoretical studies (Weeks 1993;Peck et al 1998;1999;Rispe et al 1998;Waxman and Peck 1999;Pound et al 2002) and documented in some cases (Browne 1980;Semlitsch 1993;Vrijenhoek and Pfeiler 1997; but see Lively et al 1998). Selective asymmetries are also believed to be responsible for maintaining the frequently observed marginal and northerly geographic distribution displayed by many asexual taxa, a phenomenon commonly referred to as geographical parthenogenesis (Glesener and Tilman 1978;Bell 1982;Lynch 1984;Peck et al 1998).…”