"Runaway" social evolution: reinforcing selection for inbreeding and altruism.

Kin selection theory predicts that altruistic behaviors, those that decrease the fitness of the individual performing the behavior but increase the fitness of the recipient, can increase in frequency if the individuals interacting are closely related. Several studies have shown that inbreeding therefore generally increases the effectiveness of kin selection when fitnesses are linear, additive functions of the number of altruists in the family, although with extreme forms of altruism, inbreeding can actually retard the evolution of altruism. These models assume that a constant proportion of the population mates at random and a constant proportion practices some form of inbreeding. In order to investigate the effect of inbreeding on the evolution of altruistic behavior when the mating structure is allowed to evolve, we examined a two-locus model by computer simulation of a diploid case and illustrated the important qualitative features by mathematical analysis of a haploid case. One locus determines an individual's propensity to perform altruistic social behavior and the second locus determines the probability that an individual will mate within its sibship. We assumed positive selection for altruism and no direct selection at the inbreeding locus. We observed that the altruistic allele and the inbreeding allele become positively associated, even when the initial conditions of the model assume independence between these loci. This linkage disequilibrium becomes established, because the altruistic allele increases more rapidly in the inbreeding segment of the population. This association subsequently results in indirect selection on the inbreeding locus. However, the dynamics of this model go beyond a simple "hitch-hiking" effect, because high levels of altruism lead to increased inbreeding, and high degrees of inbreeding accelerate the rate of change of the altruistic allele in the entire population. Thus, the dynamics of this model are similar to those of "runaway" sexual selection, with gene frequency change at the two loci interactively causing rapid evolutionary change.     

Evolution of interactions in family-structured populations: mixed mating models

THE EFFECT OF INBREEDING ON SOCIALITY IS STUDIED THEORETICALLY FOR THE EVOLUTION OF INTERACTIONS BETWEEN SIBLINGS IN CERTAIN MIXED MATING SYSTEMS THAT GIVE RISE TO INBREEDING: sib with random mating and selfing with random mating. Two approaches are taken. First, specific models of altruism are studied for the various mating systems. In the case of the additive model, inbreeding facilitates the evolution of altruistic genes. Likewise, for the multiplicative model this is usually the case, as long as the costs of altruism are not too great. Second, the case of total altruism, in which the gene has zero individual fitness but increases the fitness of associates, is studied for a general fitness formulation. In this case, inbreeding often retards the ability of such genes to increase when rare, and the equilibrium frequency of those recessive genes that can increase is totally independent of the mating system and, consequently, of the amount of inbreeding. It appears from the results presented that inbreeding facilitates most forms of altruism, but retards extreme altruism. These results stem from the fact that inbreeding increases the within-family relatedness by increasing the between-family variance in allele frequency. In most cases this facilitates altruism. However, in the case of total altruism, only heterozygotes can pass on the altruistic allele, and inbreeding tends to decrease this heterozygote class. In either case, the important effect of inbreeding lies in altering the genotypic distribution of the interactions.     

Extinction and fixation times with dominance and inbreeding

The effect of partial inbreeding on extinction and fixation times of a selected allele with partial dominance is studied using a diffusion model. Asymptotic approximations are obtained for large populations and the accuracy of the approximations was found to increase with inbreeding level. They show that inbreeding reduces extinction and fixation times compared to random mating at least by a factor 1+F, where F is Wright’s fixation index. The reduction of extinction and fixation times due to inbreeding is stronger for strong selection and if alleles are either highly recessive or highly dominant. This bears implications for the effect of inbreeding on the signature of selective sweeps. These findings extend previous results obtained for random mating populations and help clarifying previous simulation and numerical results on the effect of inbreeding on the dynamics of selected alleles.     

Effects of Partial Inbreeding on Fixation Rates and Variation of Mutant Genes

Diffusion methods were used to investigate the fixation probability, average time until fixation and extinction, and cumulative heterozygosity and genetic variance for single mutant genes in finite populations with partial inbreeding. The critical parameters in the approximation are the coefficient of inbreeding due to nonrandom mating (F) and the effective population size (Ne), which also depends on F and the variance of family size. For large Ns, the fixation probability (u) is u = 2(Ne/N)s (F + h - Fh), where N is the population census, s is the coefficient of selection of the mutant homozygote and h is the coefficient of dominance. For Poisson family size (independent Poisson distributions of selfed and nonselfed offspring with partial selfing, and independent Poisson distributions of male and female numbers with partial sib mating), Ne = N/(1 + F), and the time until fixation is approximately equal to Ne/N times the time to fixation with random mating, but this relation does not hold, however, for other distributions of family size. The cumulative nonadditive variance until fixation or loss for dominant genes is reduced with increasing F while for recessive genes it is increased with intermediate values of F. The average time until extinction of deleterious mutations is reduced by increasing F. This reduction, when expressed as a proportion, is approximately independent of the initial gene frequency as well as the selective disadvantage if this is large.     

Kin selection and coefficients of relatedness in family-structured populations with inbreeding

We consider family specific fitnesses that depend on mixed strategies of two basic phenotypes or behaviours. Pairwise interactions are assumed, but they are restricted to occur between sibs. To study the change in frequency of a rare mutant allele, we consider two different forms of weak selection, one applied through small differences in genotypic values determining individual mixed strategies, the other through small differences in viabilities according to the behaviours chosen by interacting sibs. Under these two specific forms of weak selection, we deduce conditions for initial increase in frequency of a rare mutant allele for autosomal genes in the partial selfing model as well as autosomal and sex-linked genes in the partial sib-mating model with selection before mating or selection after mating. With small differences in mixed strategies, we show that conditions for protection of a mutant allele are tantamount to conditions for initial increase in frequency obtained in additive kin selection models. With particular reference to altruism versus selfishness, we provide explicit ranges of values for the selfing or sib-mating rate based on a fixed cost-benefit ratio and the dominance scheme that allow the spreading of a rare mutant allele into the population. This study confirms that more inbreeding does not necessarily promote the evolution of altruism. Under the hypothesis of small differences in viabilities, the situation is much more intricate unless an additive model is assumed. In general however, conditions for initial increase in frequency of a mutant allele can be obtained in terms of fitness effects that depend on the genotypes of interacting individuals or their mates and generalized conditional coefficients of relatedness according to the inbreeding condition of the interacting individuals.     

Change in frequency of a rare mutant allele: A general formula and applications to partial inbreeding models

 We deduce and prove a general formula to approximate the change in frequency of a mutant allele under weak selection, when this allele is introduced in small frequency into a population which was previously at a fixation state. We apply the formula to autosomal genes in partial selfing models and to autosomal as well as sex-linked genes in partial sib mating models. It is shown that the fate of a rare mutant allele depends not only on the selection parameters, the inbreeding coefficient and the reproductive values of the sexes in sex-differentiated populations, but also on coefficients of relatedness between mates. This is interpreted as a kin selection effect caused by inbreeding per se. Received: 3 December 2001 / Revised version: 10 April 2002 / Published online: 19 November 2002 Research supported in part by NSERC of Canada and FCAR of Québec. Mathematics Subject Classification (2000): Primary 60J80, Secondary 92D10, 92D25 Keywords or phrases: Adaptive topography – Partial selfing – Partial sib mating – Kin selection     

Selection for altruism through random drift in variable size populations

ABSTRACT: BACKGROUND: Altruistic behavior is defined as helping others at a cost to oneself and a lowered fitness. The lower fitness implies that altruists should be selected against, which is in contradiction with their widespread presence is nature. Present models of selection for altruism (kin or multilevel) show that altruistic behaviors can have 'hidden' advantages if the 'common good' produced by altruists is restricted to some related or unrelated groups. These models are mostly deterministic, or assume a frequency dependent fitness. RESULTS: Evolutionary dynamics is a competition between deterministic selection pressure and stochastic events due to random sampling from one generation to the next. We show here that an altruistic allele extending the carrying capacity of the habitat can win by increasing the random drift of "selfish" alleles. In other terms, the fixation probability of altruistic genes can be higher than those of a selfish ones, even though altruists have a smaller fitness. Moreover when populations are geographically structured, the altruists advantage can be highly amplified and the fixation probability of selfish genes can tend toward zero. The above results are obtained both by numerical and analytical calculations. Analytical results are obtained in the limit of large populations. CONCLUSIONS: The theory we present does not involve kin or multilevel selection, but is based on the existence of random drift in variable size populations. The model is a generalization of the original Fisher-Wright and Moran models where the carrying capacity depends on the number of altruists.     

Incest versus abstinence: reproductive trade‐offs between mate limitation and progeny fitness in a self‐incompatible invasive plant

Plant mating systems represent an evolutionary and ecological trade‐off between reproductive assurance through selfing and maximizing progeny fitness through outbreeding. However, many plants with sporophytic self‐incompatibility systems exhibit dominance interactions at the S‐locus that allow biparental inbreeding, thereby facilitating mating between individuals that share alleles at the S‐locus. We investigated this trade‐off by estimating mate availability and biparental inbreeding depression in wild radish from five different populations across Australia. We found dominance interactions among S‐alleles increased mate availability relative to estimates based on individuals that did not share S‐alleles. Twelve of the sixteen fitness variables were significantly reduced by inbreeding. For all the three life‐history phases evaluated, self‐fertilized offspring suffered a greater than 50% reduction in fitness, while full‐sib and half‐sib offspring suffered a less than 50% reduction in fitness. Theory indicates that fitness costs greater than 50% can result in an evolutionary trajectory toward a stable state of self‐incompatibility (SI). This study suggests that dominance interactions at the S‐locus provide a possible third stable state between SI and SC where biparental inbreeding increases mate availability with relatively minor fitness costs. This strategy allows weeds to establish in new environments while maintaining a functional SI system.     

Hitchhiking of Deleterious Alleles and the Cost of Adaptation in Partially Selfing Species

Self-fertilization is generally seen to be disadvantageous in the long term. It increases genetic drift, which subsequently reduces polymorphism and the efficiency of selection, which also challenges adaptation. However, high selfing rates can increase the fixation probability of recessive beneficial mutations, but existing theory has generally not accounted for the effect of linked sites. Here, we analyze a model for the fixation probability of deleterious mutants that hitchhike with selective sweeps in diploid, partially selfing populations. Approximate analytical solutions show that, conditional on the sweep not being lost by drift, higher inbreeding rates increase the fixation probability of the deleterious allele, due to the resulting reduction in polymorphism and effective recombination. When extending the analysis to consider a distribution of deleterious alleles, as well as the average fitness increase after a sweep, we find that beneficial alleles generally need to be more recessive than the previously assumed dominance threshold (h < 1/2) for selfing to be beneficial from one-locus theory. Our results highlight that recombination aiding the efficiency of selection on multiple loci amplifies the fitness benefits of outcrossing over selfing, compared to results obtained from one-locus theory. This effect additionally increases the parameter range under which obligate outcrossing is beneficial over partial selfing.     

Selection, subdivision and extinction and recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

Evolution of eusociality by kin selection: the effect of inbreeding between siblings

The effect of sib-sib inbreeding on the evolution of eusocial altruism in Hymenoptera by kin selection is examined by computer simulations. Inbreeding has minor effects on the ratio of relatedness to siblings: relatedness to offspring, but this ratio remains approximately one no matter what the degree of inbreeding. This implies that although inbreeding increases relatedness to siblings, relatedness to offspring increases to the same degree. Hence, inbreeding does not make the evolution of altruism more likely. If all the brothers of (non-mating) altruists outbreed, thereby increasing the frequency of altruism alleles in the outbred fraction of the population especially at low gene frequency, then altruism can be promoted by inbreeding. However, this is an indirect advantage, not attributable to inbreeding per se.     

On the Theory of Partially Inbreeding Finite Populations. II. Partial Sib Mating

It is assumed that a population has M males in every generation, each of which is permanently mated with c-1 females, and that a proportion beta of matings are between males and their full sisters or half-sisters. Recurrence equations are derived for the inbreeding coefficient of one random individual, coefficients of kinship of random pairs of mates and probabilities of allelic identity when the infinite alleles model holds. If Ft is the inbreeding coefficient at time t and M is large, (1-Ft)/(1-Ft-1)----1-1/(2Ne) as t increases. The effective population number Ne = aM/[1 + (2a-1)FIS], where FIS is the inbreeding coefficient at equilibrium when M is infinite and the constant a depends upon the conditional probabilities of matings between full sibs and the two possible types of half-sibs. When there are M permanent couples, an approximation to the probability that an allele A survives if it is originally present in one AA heterozygote is proportional to FISs1 + (1-FIS)s2, where s1 and s2 are the selective advantages of AA and AA in comparison with AA. The paper concludes with a comparison between the results when there is partial selfing, partial full sib mating (c = 2) and partial sib mating when c is large.     

Kin selection is implicated in partial sib-mating populations with constant viability differences before mating

The change in the frequency of a rare mutant allele under constant sex-differentiated viability selection in an infinite, partial full-sib mating population is studied. The diplo-diploid and haplo-diploid polygynous models are considered with a Poisson distribution for the number of offspring produced by every mated female. Reproduction is followed by weak selection among the offspring and then mating to form the next generation. It is shown that the rate of change with respect to the frequency of the mutant allele and the intensity of selection can be expressed in terms of costs or benefits of substituting the mutant type for the wild type, which correspond to average excesses in viability in females and males, multiplied by coefficients of relatedness to the individuals affected by such a substitution and reproductive values associated to the sexes of these individuals. This reveals hidden interactions between mated individuals and between males for mating, the former having positive effects on the reproductive success of related individuals and the latter having negative effects. Such interactions are the result of reproductive constraints when a fixed proportion of females must mate with a male sib and all females are fertilized as long as one mate is available. However, they affect the change in allele frequency because there is inbreeding or relatedness between mates and more generally relatedness between interacting individuals. Surprisingly, the effects of these interactions cancel out in a diploid population when the number of offspring is large enough so that the possibility for a female to have no male sib to mate with can be neglected and the viability differences are the same in both sexes.     

Selective sweeps in multilocus models of quantitative traits

We study the trajectory of an allele that affects a polygenic trait selected toward a phenotypic optimum. Furthermore, conditioning on this trajectory we analyze the effect of the selected mutation on linked neutral variation. We examine the well-characterized two-locus two-allele model but we also provide results for diallelic models with up to eight loci. First, when the optimum phenotype is that of the double heterozygote in a two-locus model, and there is no dominance or epistasis of effects on the trait, the trajectories of selected mutations rarely reach fixation; instead, a polymorphic equilibrium at both loci is approached. Whether a polymorphic equilibrium is reached (rather than fixation at both loci) depends on the intensity of selection and the relative distances to the optimum of the homozygotes at each locus. Furthermore, if both loci have similar effects on the trait, fixation of an allele at a given locus is less likely when it starts at low frequency and the other locus is polymorphic (with alleles at intermediate frequencies). Weaker selection increases the probability of fixation of the studied allele, as the polymorphic equilibrium is less stable in this case. When we do not require the double heterozygote to be at the optimum we find that the polymorphic equilibrium is more difficult to reach, and fixation becomes more likely. Second, increasing the number of loci decreases the probability of fixation, because adaptation to the optimum is possible by various combinations of alleles. Summaries of the genealogy (height, total length, and imbalance) and of sequence polymorphism (number of polymorphisms, frequency spectrum, and haplotype structure) next to a selected locus depend on the frequency that the selected mutation approaches at equilibrium. We conclude that multilocus response to selection may in some cases prevent selective sweeps from being completed, as described in previous studies, but that conditions causing this to happen strongly depend on the genetic architecture of the trait, and that fixation of selected mutations is likely in many instances.     

Some Effects of Selection When There Is Partial Full-Sib Mating

If there is selection only for viability between zygote formation and adulthood, the frequency of a particular allele changes between these two stages of life. With complete random mating this is all that happens, but if there is a positive probability that full sibs mate, there is an extra change between adulthood and the appearance of zygotes in the next generation. This occurs because there are then correlated frequencies of the alleles carried by the mates. An expression for the change in the frequency of an allele, which incorporates these two effects, is derived, and the result is found to be consistent with earlier work by the author on the probability of survival of a rare allele in a large population. The result is inconsistent with the usual expression for the change in frequency of an allele when there is partial inbreeding because that expression does not incorporate the second change in frequency within one generation.     

Pedigree and marker information requirements to monitor genetic variability

There are several measures available to describe the genetic variability of populations. The average inbreeding coefficient of a population based on pedigree information is a frequently chosen option. Due to the developments in molecular genetics it is also possible to calculate inbreeding coefficients based on genetic marker information. A simulation study was carried out involving ten sires and 50 dams. The animals were mated over a period of 20 discrete generations. The population size was kept constant. Different situations with regard to the level of polymorphism and initial allele frequencies and mating scheme (random mating, avoidance of full sib mating, avoidance of full sib and half sib mating) were considered. Pedigree inbreeding coefficients of the last generation using full pedigree or 10, 5 and 2 generations of the pedigree were calculated. Marker inbreeding coefficients based on different sets of microsatellite loci were also investigated. Under random mating, pedigree-inbreeding coefficients are clearly more closely related to true autozygosity (i.e., the actual proportion of loci with alleles identical by descent) than marker-inbreeding coefficients. If mating is not random, the demands on the quality and quantity of pedigree records increase. Greater attention must be paid to the correct parentage of the animals.     

Inbreeding reveals mode of past selection on male reproductive characters in Drosophila melanogaster

Directional dominance is a prerequisite of inbreeding depression. Directionality arises when selection drives alleles that increase fitness to fixation and eliminates dominant deleterious alleles, while deleterious recessives are hidden from it and maintained at low frequencies. Traits under directional selection (i.e., fitness traits) are expected to show directional dominance and therefore an increased susceptibility to inbreeding depression. In contrast, traits under stabilizing selection or weakly linked to fitness are predicted to exhibit little‐to‐no inbreeding depression. Here, we quantify the extent of inbreeding depression in a range of male reproductive characters and then infer the mode of past selection on them. The use of transgenic populations of Drosophila melanogaster with red or green fluorescent‐tagged sperm heads permitted in vivo discrimination of sperm from competing males and quantification of characteristics of ejaculate composition, performance, and fate. We found that male attractiveness (mating latency) and competitive fertilization success (P₂) both show some inbreeding depression, suggesting they may have been under directional selection, whereas sperm length showed no inbreeding depression suggesting a history of stabilizing selection. However, despite having measured several sperm quality and quantity traits, our data did not allow us to discern the mechanism underlying the lowered competitive fertilization success of inbred (f = 0.50) males.     

Effect of selection against deleterious mutations on the decline in heterozygosity at neutral loci in closely inbreeding populations.

Transition matrices for selfing and full-sib mating were derived to investigate the effect of selection against deleterious mutations on the process of inbreeding at a linked neutral locus. Selection was allowed to act within lines only (selection type I) or equally within and between lines (type II). For selfing lines under selection type I, inbreeding is always retarded, the retardation being determined by the recombination fraction between the neutral and selected loci and the inbreeding depression from the selected locus, irrespective of the selection coefficient (s) and dominance coefficient (h) of the mutant allele. For selfing under selection type II or full-sib mating under both selection types, inbreeding is delayed by weak selection (small s and sh), due to the associative overdominance created at the neutral locus, and accelerated by strong selection, due to the elevated differential contributions between alternative alleles at the neutral locus within individuals and between lines (for selection type II). For multiple fitness loci under selection, stochastic simulations were run for populations with selfing, full-sib mating, and random mating, using empirical estimates of mutation parameters and inbreeding load in Drosophila. The simulations results are in general compatible with empirical observations.     

Inbreeding depression in fecundity and inbred line extinction in the bulb mite,Rhizoglyphus robini

This study investigated the magnitude of inbreeding depression in fecundity, and whether the depression is purged during six generations of sib mating in the bulb mite, Rhizoglyphus robini. The progeny resulting from a single generation of brother-sister mating suffered significant inbreeding depression in fecundity. During the following six generations of continuous sib-mating, 58% lines were lost, 45% because of sterility and 13% because of preadult mortality. The lines were then outcrossed, and their inbreeding depression compared with that of the base population. The inbreeding depression for the outcrossed population was 0.15, and for the base population 0.19, but the difference was not significant. The lack of significant purging of inbreeding depression indicates that it was caused either by detrimental genes of small effect, or by the breaking down of overdominant relations between alleles. However, the large proportion of extinct lines points to the former mechanism as a predominant cause of inbreeding depression. Theory predicts that the probability of line extinction with inbreeding increases with its load of mutations. If phenotypic variation in fecundity was partly because of differences in numbers of mutations carried by individuals, the fecundity of the line founder could be expected to correlate with the probability that the line derived from it will survive long-term inbreeding. Indeed, fecundity of founder females was significantly associated with line survival, which suggests that line extinction rate may be used as a method to study individual mutational loads, for example, in studies of sexual selection.     

Altruism, sex, and inbreeding when the genotype-phenotype map is additive

Recently published theoretical results suggest that, in a sexual population, when genotypes code for phenotypes in a complex manner, it is possible for altruistic genotypes to spread through a metapopulation (i.e. through a collection of subpopulations). This spread tends to occur during periods when the environment deteriorates throughout the metapopulation. By contrast, under asexual reproduction, non-altruistic genotypes seem to be favoured, at least when subpopulations are substantial in size. The most relevant previous study makes use of Kauffman and Levin's "NK model" as a way to relate genotypes to fitness. Unfortunately, there are both conceptual and technical problems with the application of the NK model to populations that contain many different genotypes (e.g. polymorphic diploid populations with more than a few loci under selection). The present study presents a more tractable and biologically plausible model to study the causal relationship between sexual reproduction and altruism. In particular, phenotypes are determined by additive interactions among alleles at different loci in a diploid genome, with up to 200 loci under selection. In addition, subpopulations are substantially larger than those considered in the most relevant previous work. The results show that, so long as there are multiple "fitness peaks" in "phenotype space", the additive genotype-phenotype map leads to results that are similar to those from the NK model. Various parameters are manipulated in an effort to discover the determinants of altruistic and non-altruistic outcomes. The findings should facilitate further investigations, and they should help to establish the plausibility of the suggested relationship between sexual reproduction and altruism. The results also suggest that inbreeding can lead to a similar result as asexuality. That is, inbreeding seems to enhance the probability that altruistic phenotypes will be eliminated.