Equilibrium Properties of a Multi-locus, Haploid-Selection, Symmetric-Viability Model

Under haploid selection, a multi-locus, diallelic, two-niche Levene (1953) model is studied. Viability coefficients with symmetrically opposing directional selection in each niche are assumed, and with a further simplification that the most and least favored haplotype in each niche shares no alleles in common, and that the selection coefficients monotonically increase or decrease with the number of alleles shared. This model always admits a fully polymorphic symmetric equilibrium, which may or may not be stable.We show that a stable symmetric equilibrium can become unstable via either a supercritical or subcritical pitchfork bifurcation. In the supercritical bifurcation, the symmetric equilibrium bifurcates to a pair of stable fully polymorphic asymmetric equilibria; in the subcritical bifurcation, the symmetric equilibrium bifurcates to a pair of unstable fully polymorphic asymmetric equilibria, which then connect to either another pair of stable fully polymorphic asymmetric equilibria through saddle-node bifurcations, or to a pair of monomorphic equilibria through transcritical bifurcations. As many as three fully polymorphic stable equilibria can coexist, and jump bifurcations can occur between these equilibria when model parameters are varied.In our Levene model, increasing recombination can act to either increase or decrease the genetic diversity of a population. By generating more hybrid offspring from the mating of purebreds, recombination can act to increase genetic diversity provided the symmetric equilibrium remains stable. But by destabilizing the symmetric equilibrium, recombination can ultimately act to decrease genetic diversity. © 2011 Elsevier Inc

Similarity states of passive scalar transport in isotropic turbulence

By simple analytical and large-eddy simulations, the time evolution of the kinetic energy and scalar variance in decaying isotropic turbulence transporting passive scalars are determined. The evolution of a passive scalar field with and without a uniform mean gradient is considered. First, similarity states of the flow during the final period of decay are discussed. Exact analytical solutions may be obtained, and these depend only on the form of the energy and scalar-variance spectra at low wave numbers, and the molecular transport coefficients. The solutions for a passive scalar field with mean-scalar gradient are of special interest, and we find that the scalar variance may grow or decay asymptotically in the final period, depending on the initial velocity distribution. Second, similarity states of the flow at high Reynolds and Péclet numbers are considered. Here it is assumed that the solutions also depend on the low-wave-number spectral coefficients, but not on the molecular transport coefficients. This results in a nonlinear dependence of the kinetic energy and scalar variance on the spectral coefficients, in contrast to the final period results. The analytical results obtained may be exact when the similarity solutions depend only on spectral coefficients that are time invariant. The present analysis also leads directly to a similarity state for a passive scalar field with uniform mean scalar gradient. Last, large-eddy simulations of the flow field are performed to test the theoretical results. Asymptotic similarity states at large times in the simulations are obtained and found to be in good agreement with predictions of the analysis. Several dimensionless quantities are also determined, which compare favorably to earlier experimental results. An argument for the inertial subrange scaling of the scalar-flux spectrum is presented, which yields a spectrum proportional to the scalar gradient and decaying as k^-7/3. This result is partially supported by the small-scale statistics of the large-eddy simulations. © 1994 American Institute of Physics

On the problems of a closed marriage: celebrating Darwin 200

Darwin devoted much of his working life to the study of plant reproductive systems. He recognized that many of the intricacies of floral morphology had been shaped by natural selection in favour of outcrossing, and he clearly established the deleterious effects of self-fertilization on progeny. Although Darwin hypothesized the adaptive significance of self-fertilization under conditions of low mate availability, he held that a strategy of pure selfing would be strongly disadvantageous in the long term. Here, I briefly review these contributions to our understanding of plant reproduction. I then suggest that investigating two very different sexual systems, one in plants and the other in animals, would throw further light on the long-term implications of a commitment to reproduction exclusively by selfing

Selection against males in Caenorhabditis elegans under two mutational treatments

Within populations with mixed mating systems, selfing is expected to be favoured over outcrossing unless a countervailing process such as severe inbreeding depression is present. In this study, we consider the relationship between the expression of deleterious alleles and the maintenance of outcrossing in the nematode species, Caenorhabditis elegans. This species is characterized by an androdioecious breeding system composed of males at low frequency and self-fertilizing hermaphrodites that can only outcross via males. Here, we find that experimentally increasing the mutational load in four different isogenic wild isolates using 10 generations of Ethylmethane sulphonate (EMS) and UV irradiation mutagenesis significantly diminishes the cost of males. Males are maintained at higher frequencies in mutagenized versus non-mutagenized populations. Nevertheless, males still tend to be driven to low frequencies within isolates that are known to be prone to lose males. Further, we determine the viability effects of a single round of mutagen exposure and find that, for EMS, outcrossing overcomes the almost completely recessive and nearly lethal effects generated. We briefly interpret our results in light of current evolutionary theory of outcrossing rates

Mitotic recombination counteracts the benefits of genetic segregation

The ubiquity of sexual reproduction despite its cost has lead to an extensive body of research on the evolution and maintenance of sexual reproduction. Previous work has suggested that sexual reproduction can substantially speed up the rate of adaptation in diploid populations, because sexual populations are able to produce the fittest homozygous genotype by segregation and mating of heterozygous individuals. In contrast, asexual populations must wait for two rare mutational events, one producing a heterozygous carrier and the second converting a heterozygous to a homozygous carrier, before a beneficial mutation can become fixed. By avoiding this additional waiting time, it was shown that the benefits of segregation could overcome a twofold cost of sex. This previous result ignores mitotic recombination (MR), however. Here, we show that MR significantly hastens the spread of beneficial mutations in asexual populations. Indeed, given empirical data on MR, we find that adaptation in asexual populations proceeds as fast as that in sexual populations, especially when beneficial alleles are partially recessive. We conclude that asexual populations can gain most of the benefit of segregation through MR while avoiding the costs associated with sexual reproduction