Optimal sex ratios in structured populations

In this paper, we develop a general method to determine evolutionary equilibrium sex ratios and to check evolutionary stability, continuous stability and invadability in exact genetic models with or without dominance. This method is then applied to three kinds of models for structured populations: the first one concerns Hamilton's LMC model, except that only a fraction beta of female offspring mate with male offspring born in the same colonies, while a fraction 1-beta mate with male offspring chosen at random within the whole population; in the second model, it is assumed that partial dispersal of inseminated females occurs after mating; in the third model, partial dispersal of male and female offspring occurs before mating. In the first model, the effect of population regulation is studied while, in the other models, two kinds of dispersal are considered: proportional and uniform.     

Muller's ratchet and the pattern of variation at a neutral locus

The levels and patterns of variation at a neutral locus are analyzed in a haploid asexual population undergoing accumulation of deleterious mutations due to Muller's ratchet. We find that the movement of Muller's ratchet can be associated with a considerable reduction in genetic diversity below classical neutral expectation. The extent to which variability is reduced is a function of the deleterious mutation rate, the fitness effects of the mutations, and the population size. Approximate analytical expressions for the expected genetic diversity are compared with simulation results under two different models of deleterious mutations: a model where all deleterious mutations have equal effects and a model where there are two classes of deleterious mutations. We also find that Muller's ratchet can produce a considerable distortion in the neutral frequency spectrum toward an excess of rare variants.     

On the evolution of genetic incompatibility systems. IV. Modification of response to an existing antigen polymorphism under partial selfing

A 2-locus model of the evolution of self-incompatibility in a population practicing partial selfing is presented. An allele is introduced at a modifier locus which influences the strength of the rejection reaction expressed by the style in response to antigens recognized in pollen. Two causes of inbreeding depression are investigated. First, offspring viability depends solely on the source (self or non-self) of the fertilizing pollen. Second, offspring viability declines with the expression of recessive deleterious alleles, segregating at a third (disease) locus, which exhibit an imperfect association with antigen alleles. Evolutionary changes occurring at the disease locus are not considered in this study. The condition under which a modifier allele that intensifies the incompatibility reaction increases when rare depends upon the number of antigens, the frequency of recessive deleterious alleles at the disease locus, and the level of association between the antigen locus and the disease locus. It is the improvement of viability among offspring derived by outcrossing, rather than the prevention of self-fertilization, that may represent the primary evolutionary function of genetic incompatibility systems.     

Extinction of populations due to inbreeding depression with demographic disturbances

The process of population extinction due to inbreeding depression with constant demographic disturbances every generation is analysed using a population genetic and demographic model. The demographic disturbances introduced into the model represent loss of population size that is induced by any kind of human activities, e.g. through hunting and destruction of habitats. The genetic heterozygosity among recessive deleterious genes and the population size are assumed to be in equilibrium before the demographic disturbances start. The effects of deleterious mutations are represented by decreases in the growth rate and carrying capacity of a population. Numerical simulations indicate rapid extinction due to synergistic interaction between inbreeding depression and declining population size for realistic ranges of per-locus mutation rate, equilibrium population size, intrinsic rate of population growth, and strength of demographic disturbances. Large populations at equilibrium are more liable to extinction when disturbed due to inbreeding depression than small populations. This is a consequence of the fact that large populations maintain more recessive deleterious mutations than small populations. The rapid extinction predicted in the present study indicates the importance of the demographic history of a population in relation to extinction due to inbreeding depression.     

INBREEDING DEPRESSION VARIES WITH INVESTMENT IN SEX IN A FACULTATIVE PARTHENOGEN

The reproductive mode of facultative parthenogens allows recessive mutations that accumulate during the asexual phase to be unmasked following sexual reproduction. Longer periods of asexual reproduction should increase the accumulation of deleterious mutations within individuals, reduce population-level genetic diversity via competition and increase the probability of mating among close relatives. Having documented that the investment in sexual reproduction differs among populations and clones of Daphnia pulicaria , we ask if this variation is predictive of the level of inbreeding depression across populations. In four lake populations that vary in sex investment, we raised multiple families (mother, field-produced daughter, laboratory-produced daughter) on high food and estimated the fitness reduction in both sexually produced offspring relative to the maternal genotype. Inbred individuals had lower fitness than their field-produced siblings. The magnitude of fitness reduction in inbred offspring increased as population-level investment in sex decreased. However, there was less of a fitness reduction following sex in the field-produced daughters, suggesting that many field-collected mothers were involved in outcross mating.     

Inbreeding rate modifies the dynamics of genetic load in small populations

The negative fitness consequences of close inbreeding are widely recognized, but predicting the long-term effects of inbreeding and genetic drift due to limited population size is not straightforward. As the frequency and homozygosity of recessive deleterious alleles increase, selection can remove (purge) them from a population, reducing the genetic load. At the same time, small population size relaxes selection against mildly harmful mutations, which may lead to accumulation of genetic load. The efficiency of purging and the accumulation of mutations both depend on the rate of inbreeding (i.e., population size) and on the nature of mutations. We studied how increasing levels of inbreeding affect offspring production and extinction in experimental Drosophila littoralis populations replicated in two sizes, N = 10 and N = 40. Offspring production and extinction were measured over 25 generations concurrently with a large control population. In the N = 10 populations, offspring production decreased strongly at low levels of inbreeding, then recovered only to show a consistent subsequent decline, suggesting early expression and purging of recessive highly deleterious alleles and subsequent accumulation of mildly harmful mutations. In the N = 40 populations, offspring production declined only after inbreeding reached higher levels, suggesting that inbreeding and genetic drift pose a smaller threat to population fitness when inbreeding is slow. Our results suggest that highly deleterious alleles can be purged in small populations already at low levels of inbreeding, but that purging does not protect the small populations from eventual genetic deterioration and extinction.     

Inbreeding depression and the evolution of dispersal rates: a multilocus model

Inbreeding depression is one of the possible reasons organisms disperse. In this article, we present a two-locus model for the evolution of dispersal in the presence of inbreeding depression. The first locus codes for a modifier of the migration rate, while the second locus is a selected locus generating inbreeding depression. We express the change in frequency of the migration modifier as a function of allele frequencies and genetic associations and then use a quasi-equilibrium assumption to express genetic associations as functions of allele frequencies. Our model disentangles two effects of inbreeding depression: it gives an advantage to migrant individuals because their offspring are on average less homozygous, but it also decreases the degree of population structure, thus decreasing the strength of kin selection for dispersal. We then extend our model to include an infinite number of selected loci. When the cost of dispersal is not too high, the model predictions are confirmed by multilocus simulation results and show that inbreeding depression can have a substantial effect on the dispersal rate. For high costs of dispersal, we observe discrepancies between the model and the simulations, probably caused by associations among selected loci, which are neglected in the analysis.     

Microhabitat heterogeneity influences offspring sex allocation and spatial kin structure in possums

1. Sex allocation theory predicts that where dispersal is sex biased, the fitness consequences of producing male or female offspring are mediated by resource availability and maternal competitive ability. Females in poorer condition are expected to favour dispersing offspring to minimize resource competition with kin. Environmental heterogeneity may drive spatial variation in sex allocation through resource competition-related benefits to females and territory quality benefits to dispersing or philopatric offspring. 2. Here, we demonstrate that microhabitat heterogeneity can drive extremely fine-scale spatial heterogeneity in offspring sex allocation. Female bobucks (Trichosurus cunninghami) in temperate rainforest were more likely to produce male offspring than those in surrounding Eucalyptus forest. 3. A maternal physiological effect was identified, in that females of lower body mass were more likely to produce male offspring. This finding is consistent with resource competition predictions, in that smaller females are expected to have poorer competitive ability. 4. Genetic spatial autocorrelation analysis identified males as the more dispersing sex. Furthermore, overproduction of males by mothers in the rainforest habitat was geographically concordant with reduced philopatry, as inferred from spatial genetic analysis. This provides empirical validation of dispersal-related explanations of offspring sex allocation: that production of offspring of the dispersing sex minimizes the potential for resource competition with kin. 5. Spatial variation in dispersal via sex allocation responses to environmental heterogeneity can potentially contribute to spatial patterns in population dynamics.     

Genetic population structure of the white sifaka (Propithecus verreauxi verreauxi) at Beza Mahafaly Special Reserve,southwest Madagascar (1992-2001)

Gene flow within and between social groups is contingent on behaviourally mediated patterns of mating and dispersal. To understand how these patterns affect the genetic structure of primate populations, long-term data are required. In this study, we analyse 10 years of demographic and genetic data from a wild lemur population (Propithecus verreauxi verreauxi) at Beza Mahafaly Special Reserve, southwest Madagascar. Our goal is to specify how patterns of mating and dispersal determine kinship and genetic diversity among animals in the population. Specifically, we use microsatellite, parentage, and census data to obtain estimates of genetic subdivision (FST), within group homozygosity (FIS), and relatedness (r) within and among social groups in the population. We analyse different classes of individuals (i.e. adults, offspring, males, females) separately in order to discern which classes most strongly influence aspects of population structure. Microsatellite data reveal that, across years, offspring are consistently more heterozygous than expected within social groups (FIS mean = -0.068) while adults show both positive and negative deviations from expected genotypic frequencies within groups (FIS mean = 0.003). Offspring cohorts are more genetically subdivided than adults (FST mean = 0.108 vs. 0.052) and adult females are more genetically subdivided than adult males (FST mean = 0.098 vs. 0.046). As the proportion of females in social groups increases, the proportion of offspring sired by resident males decreases. Offspring are characterized by a heterozygote excess as resident males (vs. nonresident males) sire the majority of offspring within groups. We link these genetic data to patterns of female philopatry, male dispersal, exogamy, and offspring sex-ratio. Overall, these data reveal how mating and dispersal tactics influence the genetic population structure in this species.     

Sex biased natal dispersal in a closed, saturated population of Seychelles warblers Acrocephalus sechellensis

The distances that individuals disperse, from their natal site to the site of first breeding and between breeding sites, have important consequences for the dynamics and genetic structure of a population. Nearly all previous studies on dispersal have the problem that, because the study area encompassed only a part of the population, emigration may have been confounded with mortality. As a result long-distance dispersers may have been overlooked and dispersal data biased towards short distances. By studying a virtually closed population of Seychelles warblers Acrocephalus sechellensis we obtained almost unbiased results on several aspects of dispersal. As in the majority of other avian species, natal dispersal distance was female biased in the Seychelles warbler. Female offspring also forayed further from the natal territory in search of breeding vacancies than male offspring. The sex bias in natal dispersal distance did, however, depend on local breeding density. In males, dispersal distance decreased as the number of territories bordering the natal territory increased, while in females, dispersal distance did not vary with local density. Dispersal by breeders was rare and, unlike in most species, distances did not differ between the sexes. We argue that our results favour the idea that the sex bias in natal dispersal distance in the Seychelles warbler is due to inbreeding avoidance and not resource competition or intrasexual competition for mates.     

Mutation-selection balance, dominance and the maintenance of sex

A leading hypothesis for the evolutionary function of sex postulates that sex is an adaptation that purges deleterious mutations from the genome, thereby increasing the equilibrium mean fitness of a sexual population relative to its asexual competitor. This hypothesis requires two necessary conditions: first, the mutation rate per genome must be of order one, and, second, multiple mutations within a genome must act with positive epistasis, that is, two or more mutations of different genes must be more harmful together than if they acted independently. Here, by reconsidering the theory of mutation-selection balance at a single diploid gene locus, we demonstrate a significant advantage of sex due to nearly recessive mutations provided the mutation rate per genome is of order one. The assumption of positive epistasis is unnecessary, and multiple mutations may be assumed to act independently.     

Social selection in human populations: differential modification of the fitness by the sex of an affected parent

Social selection model of two alleles at a locus has been constructed where the fitness of offspring is modified differentially by the sex of an affected parent. It has been shown that the equilibrium frequency of deleterious alleles depends on the loss of fitness of an individual due to the trait (gamma), due to an affected mother (beta 1) and affected father (beta 2), and the probability that the heterozygote develops the trait (h). The equilibrium gene frequency is given approximately by alpha/hs for 0 less than h less than or equal to 1 and square root alpha/s for h = 0, where s = gamma + (beta 1 + beta 2) (1 - gamma)/2 for multiplicative models. The same result holds for the additive model if the value of gamma is small.     

A general approach to genetic equilibria with an uneven sex ratio.

It is shown that in a diploid population at a genetic equilibrium with an uneven sex ratio the distribution of all (inertial) autosomal genes is symmetric between the two sexes. If several allelic genes occur in the population then the sex ratios of the various genotypes uniquely determine the uneven population sex ratio. The equilibrium is unstable to invasion by new genes which are relatively more frequent among the less numerous sex. A new proof is given to the fact that if genotype sex ratios do not change then, following an invasion by a new allele, a new stable polymorphic equilibrium can only correspond to a sex ratio which is more even than the old one. Application of these general results to a model of offspring sex determination by parents' autosomal genes shows the equilibrium to be unstable to invasion by new genes which tend to increase the production of offspring of the minority sex, as proposed by Fisher. The relevance of the Shaw-Mohler formula in this context is shown to derive from its role in describing the dynamics of autosomal genes in general. In connection with a model for offspring sex determination by one parent, a new proof is given to the fact that, following an invasion by a new allele, a new stable polymorphic equilibrium can only correspond to a sex ratio which is more even than the old one.     

Sex-biased dispersal of adults mediates the evolution of altruism among juveniles

Population viscosity has been proposed as an important mechanism for the evolution of cooperation. The idea is that if individuals do not disperse far during the course of their lives, they will tend to interact with their genealogical relatives, which may give kin-selected benefits for cooperation. However, in the simplest model of population structure, the evolution of cooperation is unaffected by the rate of dispersal, owing to dispersal also mediating competition between social partners. This surprising result has generated much research interest in recent years. Here I show that dispersal does matter if there is a sex difference in dispersal rate, even when the expression of cooperation is not conditional upon the actor's dispersal status or sex. In particular, I show that cooperation among juveniles is relatively favoured when there is a small sex bias in adult dispersal in favour of the sex with the greatest variance in reproductive success, and is relatively disfavoured when this sex bias is large or in the opposite direction. This is because dispersal by individuals of each sex can have different consequences for the genetic structure of the population.     

Reproductive effort in viscous populations

Abstract.— Here I study a kin selection model of reproductive effort, the allocation of resources to fecundity versus survival, in a patch-structured population. Breeding females remain in the same patch for life. Offspring have costly, partial long-distance dispersal and compete for breeding sites, which become vacant upon the death of previous occupants. The main result is that the evolutionarily stable reproductive effort decreases as offspring dispersal rate increases. The result can be understood as follows: In a well-mixed population with global competition, neither adults nor juveniles compete with relatives, but in a patch-structured population with dispersal restricted to the juvenile phase, juveniles experience relatively less competition with relatives than adults, thus making juveniles relatively more valuable. Because this asymmetry between adults and juveniles decreases with the dispersal rate, so does the evolutionarily stable level of allocation to fecundity.     

Kin selection and natal dispersal in an age-structured population

We examine the effect of iteroparity on the evolution of dispersal for a species living in a stable but fragmented habitat. We use a kin selection model that incorporates the effects of demographic stochasticity on the local age structure and age-specific genetic identities. We consider two cases: when the juvenile dispersal rate is allowed to change with maternal age and when it is not. In the latter case, we find that the unconditional evolutionarily stable dispersal rate increases when the adult survival rate increases. Two antagonistic forces act upon the evolution of age-specific dispersal rates. First, when the local age structure varies between patches of habitat, the intensity of competition between adults and juveniles in the natal patch is, on average, lower for offspring born to older senescent mothers. This selects for decreasing dispersal with maternal age. Second, offspring born to older parents are on average more related to other juveniles in the same patch and they experience a higher intensity of kin competition, which selects for increasing dispersal with maternal age. We show that the evolutionary outcome results from a balance between these two opposing forces, which depends on the amount of variance in age structure among sub-populations.     

Genome-wide deleterious mutation favors dispersal and species integrity

Here I develop the idea that ubiquitous harmful genome-wide mutation with local differentiation favors dispersal, even though migration reduces average fitness. Historical contingency of the mutational process means that demes (sub-populations) differentiate from one another. Deleterious or lethal partially recessive mutations carried by migrants then do not encounter similar mutations in the recipient deme. Migrant offspring have higher fitness than offspring of residents, because migrant offspring are heterozygous rather than homozygous for harmful mutations. The advantage is inversely related to local inbreeding depression. Genome-wide deleterious mutation favors the evolution of dispersal, which in turn enhances the genetic integrity of the species.     

关于最大信息熵原理与群体遗传平衡一致性的探讨

汪小龙等建立了用最大信息熵原理推导一个基因座上群体遗传平衡的统一数学模型,并给出了模型的最大值解,此解正是Hardy-Weinberg平衡定律所给出的基因型频率。这说明当群体基因型信息熵最大时,群体基因型频率不再变化,达到平衡状态,从而证明了最大信息熵原理与Hardy-Weinberg平衡定律具有一致性,同时指出这一结论可以推广至有迁移、突变、选择、遗传漂变、近亲交配的群体以及多个基因座情形。概括地说就是：最大信息熵原理与群体遗传平衡具有一致性。但是,他们仅仅证明了最大信息熵原理与一个基因座上Hardy-Weinberg平衡定律具有一致性,本文在这个范围内将其推广至多个基因座,且每一个基因座均为复等位基因情形。至于最大信息熵原理是否与其它的群体遗传平衡具有一致性,他们的结论仅仅是猜想,并未严格推导。事实上,要想将这种一致性推广到迁移、突变、随机漂变和近亲交配等群体,则不见得正确。      

Relative effects of segregation and recombination on the evolution of sex in finite diploid populations

The mechanism of reproducing more viable offspring in response to selection is a major factor influencing the advantages of sex. In diploids, sexual reproduction combines genotype by recombination and segregation. Theoretical studies of sexual reproduction have investigated the advantage of recombination in haploids. However, the potential advantage of segregation in diploids is less studied. This study aimed to quantify the relative contribution of recombination and segregation to the evolution of sex in finite diploids by using multilocus simulations. The mean fitness of a sexually or asexually reproduced population was calculated to describe the long-term effects of sex. The evolutionary fate of a sex or recombination modifier was also monitored to investigate the short-term effects of sex. Two different scenarios of mutations were considered: (1) only deleterious mutations were present and (2) a combination of deleterious and beneficial mutations. Results showed that the combined effects of segregation and recombination strongly contributed to the evolution of sex in diploids. If deleterious mutations were only present, segregation efficiently slowed down the speed of Muller''s ratchet. As the recombination level was increased, the accumulation of deleterious mutations was totally inhibited and recombination substantially contributed to the evolution of sex. The presence of beneficial mutations evidently increased the fixation rate of a recombination modifier. We also observed that the twofold cost of sex was easily to overcome in diploids if a sex modifier caused a moderate frequency of sex.