"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.     

Selfishness and altruism can coexist when help is subject to diminishing returns

Altruism and selfishness are 30-50% heritable in man in both Western and non-Western populations. This genetically based variation in altruism and selfishness requires explanation. In non-human animals, altruism is generally directed towards relatives, and satisfies the condition known as Hamilton's rule. This nepotistic altruism evolves under natural selection only if the ratio of the benefit of receiving help to the cost of giving it exceeds a value that depends on the relatedness of the individuals involved. Standard analyses assume that the benefit provided by each individual is the same but it is plausible in some cases that as more individuals contribute, help is subject to diminishing returns. We analyse this situation using a single-locus two-allele model of selection in a diploid population with the altruistic allele dominant to the selfish allele. The analysis requires calculation of the relationship between the fitnesses of the genotypes and the frequencies of the genes. The fitnesses vary not only with the genotype of the individual but also with the distribution of phenotypes amongst the sibs of the individual and this depends on the genotypes of his parents. These calculations are not possible by direct fitness or ESS methods but are possible using population genetics. Our analysis shows that diminishing returns change the operation of natural selection and the outcome can now be a stable equilibrium between altruistic and selfish alleles rather than the elimination of one allele or the other. We thus provide a plausible genetic model of kin selection that leads to the stable coexistence in the same population of both altruistic and selfish individuals. This may explain reported genetic variation in altruism in man.     

A novel fitness proxy in structured locally finite metapopulations with diploid genetics, with an application to dispersal evolution

Many studies of evolutionarily stable strategies (ESS) for technical reasons make the simplification that reproduction is clonal. A post-hoc justification is that in the simplest eco-evolutionary models more realistic genetic assumptions, such as haploid sexual or diploid sexual cases, yield results compatible with the clonal ones. For metapopulations the technical reasons were even more poignant thanks to the lack of accessible fitness proxies for the diploid case. However, metapopulations are also precisely the sort of ecological backdrop for which one expect discrepancies between the evolutionary outcomes derived from clonal reproduction and diploid genetics, because substantially many mutant homozygotes appear locally even though the mutant is rare globally. In this paper we devise a fitness proxy applicable to the haploid sexual and diploid sexual case, in the style of Metz and Gyllenberg [Metz, J.A.J., Gyllenberg, M., 2001. How should we define fitness in structured metapopulation models? Including an application to the calculation of ES dispersal strategies. Proc. R. Soc. Lond. B 268, 499-508], that can cope with local population fluctuations due to environmental and demographic stochasticity. With the use of this fitness proxy we find that in dispersal evolution the studied clonal model is equivalent with the haploid sexual model, and that there are indeed many differences between clonal and diploid ESS dispersal rates. In a homogenous landscape the discrepancy is but minor (less than 2%), but the situation is different in a heterogeneous landscape: Not only is the quantitative discrepancy between the two types of ESSs appreciable (around 10%-20%), but more importantly, at the same parameter values, evolutionarily stability properties may differ. It is possible, that the singular strategy is evolutionarily stable in the clonal case but not in the diploid case, and vice versa.     

The robustness of Hamilton's rule with inbreeding and dominance: kin selection and fixation probabilities under partial sib mating

Assessing the validity of Hamilton's rule when there is both inbreeding and dominance remains difficult. In this article, we provide a general method based on the direct fitness formalism to address this question. We then apply it to the question of the evolution of altruism among diploid full sibs and among haplodiploid sisters under inbreeding resulting from partial sib mating. In both cases, we find that the allele coding for altruism always increases in frequency if a condition of the form rb>c holds, where r depends on the rate of sib mating alpha but not on the frequency of the allele, its phenotypic effects, or the dominance of these effects. In both examples, we derive expressions for the probability of fixation of an allele coding for altruism; comparing these expressions with simulation results allows us to test various approximations often made in kin selection models (weak selection, large population size, large fecundity). Increasing alpha increases the probability of fixation of recessive altruistic alleles (h<1/2), while it can increase or decrease the probability of fixation of dominant altruistic alleles (h>1/2).     

Genotypic selection in Daphnia populations consisting of inbred sibships

The genetic basis of fitness reduction associated with inbreeding is still poorly understood. Here we use associations between allozyme genotypes and fitness to investigate the genetic basis of inbreeding depression in experimental outdoor populations of the water flea, Daphnia magna. In Daphnia, a phase of clonal reproduction follows hatching from sexually produced resting eggs, and changes in genotype frequencies during the clonal phase can be used to estimate fitness. Our experiment resembles natural colonization of ponds in that single clones colonize an empty pool, expand asexually and produce sexual offspring by selfing (sisters mate with their clonal brothers). These offspring diapause and form populations consisting of selfed sibships in the following spring. In 12 of 13 experimental populations, genotypes of selfed hatchlings after diapause conformed to Mendelian expectations. During the subsequent ca. 10 asexual generations, however, genotype frequencies changed significantly at 19 of 27 single loci studied within populations, mostly in favour of heterozygotes, with heterozygosity at multiple loci affecting the change in genotype frequency multiplicatively. Because variance in heterozygosity among siblings at a given marker reflects only heterozygosity in the chromosomal region around this marker, our results suggest that selection at fitness-associated loci in the chromosomal regions near the markers were responsible for these changes. The genotype frequency changes were more consistent with selection acting on linked loci than on the allozymes themselves. Taken together, the evidence for abundant selection in the chromosomal regions of the markers and the fact that changes in genotype frequencies became apparent only after several generations of clonal selection, point to a genetic load consisting of many alleles of small or intermediate effects, which is consistent with the strong genetic differentiation and repeated genetic bottlenecks in the metapopulation from which the animals for this study were obtained.     

Percolation on fitness landscapes: effects of correlation, phenotype, and incompatibilities

We study how correlations in the random fitness assignment may affect the structure of fitness landscapes, in three classes of fitness models. The first is a phenotype space in which individuals are characterized by a large number n of continuously varying traits. In a simple model of random fitness assignment, viable phenotypes are likely to form a giant connected cluster percolating throughout the phenotype space provided the viability probability is larger than 1/2(n). The second model explicitly describes genotype-to-phenotype and phenotype-to-fitness maps, allows for neutrality at both phenotype and fitness levels, and results in a fitness landscape with tunable correlation length. Here, phenotypic neutrality and correlation between fitnesses can reduce the percolation threshold, and correlations at the point of phase transition between local and global are most conducive to the formation of the giant cluster. In the third class of models, particular combinations of alleles or values of phenotypic characters are "incompatible" in the sense that the resulting genotypes or phenotypes have zero fitness. This setting can be viewed as a generalization of the canonical Bateson-Dobzhansky-Muller model of speciation and is related to K-SAT problems, prominent in computer science. We analyze the conditions for the existence of viable genotypes, their number, as well as the structure and the number of connected clusters of viable genotypes. We show that analysis based on expected values can easily lead to wrong conclusions, especially when fitness correlations are strong. We focus on pairwise incompatibilities between diallelic loci, but we also address multiple alleles, complex incompatibilities, and continuous phenotype spaces. In the case of diallelic loci, the number of clusters is stochastically bounded and each cluster contains a very large sub-cube. Finally, we demonstrate that the discrete NK model shares some signature properties of models with high correlations.     

The effects of deleterious mutations in cyclically parthenogenetic organisms

Cyclically parthenogenetic organisms experience benefits of both sexual and asexual reproductive modes in a constant environment. Sexual reproduction generates new genotypes and may facilitate the purging of deleterious mutations whereas asexuality has a two-fold advantage and enables maintenance of well-fitted genotypes. Asexual reproduction can have a drawback as increased linkage may lead to the accumulation of deleterious mutations. This study presents the results of Monte Carlo simulations of small and infinite diploid populations, with deleterious mutations occurring at multiple loci. The recombination rate and the length of the asexual period, interrupted by sexual reproduction, are allowed to vary. Here I show that the fitness of cyclical parthenogenetic population is dependent on the length of the asexual period. Increased length of the asexual period can lead both to increased segregational load following sexual reproduction and to a stronger effect of deleterious mutations on variation at a linked neutral marker, either by reducing or increasing the variation.     

The advantages of segregation and the evolution of sex

In diploids, sexual reproduction promotes both the segregation of alleles at the same locus and the recombination of alleles at different loci. This article is the first to investigate the possibility that sex might have evolved and been maintained to promote segregation, using a model that incorporates both a general selection regime and modifier alleles that alter an individual's allocation to sexual vs. asexual reproduction. The fate of different modifier alleles was found to depend strongly on the strength of selection at fitness loci and on the presence of inbreeding among individuals undergoing sexual reproduction. When selection is weak and mating occurs randomly among sexually produced gametes, reductions in the occurrence of sex are favored, but the genome-wide strength of selection is extremely small. In contrast, when selection is weak and some inbreeding occurs among gametes, increased allocation to sexual reproduction is expected as long as deleterious mutations are partially recessive and/or beneficial mutations are partially dominant. Under strong selection, the conditions under which increased allocation to sex evolves are reversed. Because deleterious mutations are typically considered to be partially recessive and weakly selected and because most populations exhibit some degree of inbreeding, this model predicts that higher frequencies of sex would evolve and be maintained as a consequence of the effects of segregation. Even with low levels of inbreeding, selection is stronger on a modifier that promotes segregation than on a modifier that promotes recombination, suggesting that the benefits of segregation are more likely than the benefits of recombination to have driven the evolution of sexual reproduction in diploids.     

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.     

Sex causes altruism. Altruism causes sex. Maybe

This study presents a mathematical model in which the fitness of an individual depends on the individual's genotype (individual effects) and on the genotypes of other members of the individual's local group (group effects). The findings suggest that, if phenotypes are a result of complex interactions between genes at different loci, then fitness-enhancing group effects may become common in sexual populations. The spread of fitness-enhancing group effects is facilitated when environmental conditions sometimes deteriorate temporarily. This is so even if the genotypes with the highest group effects also tend to have relatively low individual effects. In this sense, the process described here can lead to the evolution of altruism. By contrast, when populations are asexual it appears that group effects are much less important in determining the outcome of evolution. Thus, in nature, asexual populations may tend to be characterized by more antagonistic interactions than those that typically prevail when reproduction is sexual. This might help to explain why asexual lineages are prone to rapid extinction.     

Darwinian selection and “altruism”

Models are proposed for evolution at a single locus affecting altruistic behavior in which genotypic fitnesses are Darwinian and frequency (but not density) dependent. The fitnesses are composed, either in a multiplicative or an additive way, of factors which depend on the receipt and donation of altruistic behavior. The factors are determined from the matrices of conditional probabilities which describe the genotypes of relatives. Since selection occurs, these probabilities are in terms of genotype frequencies. The relationship between the risk to helper and benefit to recipient which allows altruism to evolve is shown to depend on the kinship coefficient between helper and helped, the particular fitness function proposed and the degree of dominance of the altruism. The commonly accepted criteria of W. D. Hamilton [J. Theor. Biol.7 (1964), 1–16, 17–52] apply only in the additive case. A second class of models of social cooperation independent of relationship and its evolutionary dynamics are discussed.     

The kin structure of sexual interactions

The origin of sexual reproduction involved the evolution of zygotes from separate genomes and, like other social processes, should therefore be amenable to analysis using kin selection theory. I consider how kin structure affects sexual interactions in three contexts—the evolution of sexual reproduction, sex allocation and sexual conflict. Kin structure helps explain the even-handed replication of paternal and maternal genes under outbreeding. Under inbreeding, it predicts altruistic failure to replicate by one half of the diploid genome. Kin structure predicts optimal sex ratios and potential conflicts over sex ratio within social groups and individuals. Sexual conflict predictably occurs as a function of (i) the probability that current sexual partners will reproduce together in future and (ii) between-partner relatedness. I conclude that systematically analysing the kin structure of sexual interactions helps illuminate their evolution.     

Epistasis in monkeyflowers

Epistasis contributes significantly to intrapopulation variation in floral morphology, development time, and male fitness components of Mimulus guttatus. This is demonstrated with a replicated line-cross experiment involving slightly over 7000 plants. The line-cross methodology is based on estimates for means. It thus has greater power than the variance partitioning approaches historically used to estimate epistasis within populations. The replication of the breeding design across many pairs of randomly extracted, inbred lines is necessary given the diversity of multilocus genotypes residing within an outbred deme. Male fitness is shown to exhibit synergistic epistasis, an accelerating decline in fitness with inbreeding. Synergism is a necessary, but not sufficient, condition for a mutational deterministic hypothesis for the evolutionary maintenance of sexual reproduction. Unlike male fitness measures, flower morphology and development time yield positive evidence of epistasis but not of synergism. The results for these traits suggest that epistatic effects are variable across genetic backgrounds or sets of interacting loci.     

Models of the evolution of altruism

There are two ways of calculating the spread of a gene for altruism. One, originally proposed by Hamilton, is to allow for the effects of the gene on the survival and reproduction of collateral relatives of the individual carrying it (i.e., “inclusive fitness”); this leads to the condition k > 1/r for the spread of the gene, where k is a benefit/cost ratio. The other is to count only the direct offspring of a carrier, but to allow for the altruistic acts performed toward the carrier by its relatives (“neighbour modulated fitness” or “personal fitness”). A recent personal fitness model (L. L. Cavalli Sforza and M. W. Feldman, 1978, Theor. Pop. Biol.14, 268–280) analyses parent-offspring and sib-sib altruism and concludes that k > 1/r is applicable only when fitness components are combined additively. The present paper analyses some simple models in which the phenotypic effects are carefully specified. It is concluded that it is sometimes, but not always, appropriate to combine fitness components additively. The relative roles of inclusive and personal fitness models are compared. The former have the virtue of being easier to think about in causal terms; and the latter of incorporating the evolution of altruism into the corpus of population genetics as an example of frequency-dependent selection.     

Population structure, mating system, and sex-determining allele diversity of the parasitoid wasp Habrobracon hebetor

Besides haplo-diploid sex determination, where females develop from fertilized diploid eggs and males from unfertilized haploid eggs, some Hymenoptera have a secondary system called complementary sex determination (CSD). This depends on genotypes of a 'sex locus' with numerous sex-determining alleles. Diploid heterozygotes develop as females, but diploid homozygotes become sterile or nonviable diploid males. Thus, when females share sex-determining alleles with their mates and produce low fitness diploid males, CSD creates a genetic load. The parasitoid wasp Habrobracon hebetor has CSD and displays mating behaviours that lessen CSD load, including mating at aggregations of males and inbreeding avoidance by females. To examine the influence of population structure and the mating system on CSD load, we conducted genetic analyses of an H. hebetor population in Wisconsin. Given the frequency of diploid males, we estimated that the population harboured 10-16 sex-determining alleles. Overall, marker allele frequencies did not differ between subpopulations, but frequencies changed dramatically between years. This reduced estimates of effective size of subpopulations to only N3 approximately 20-50, which probably reflected annual fluctuations of abundance of H. hebetor. We also determined that the mating system is effectively monogamous. Models relating sex-determining allele diversity and the mating system to female productivity showed that inbreeding avoidance always decreased CSD loads, but multiple mating only reduced loads in populations with fewer than five sex-determining alleles. Populations with N3 less than 100 should have fewer sex-determining alleles than we found, but high diversity could be maintained by a combination of frequency-dependent selection and gene flow between populations.     

Density dependent selection in parthenogenetic and self-mating populations

The consequences of density dependent selection on genetically heterogeneous, diploid populations reproducing by self-mating or various parthenogenetic mechanisms is investigated. A logistic fitness function that depends upon both the genotype of an individual and the density of the population is used. Such a fitness function simultaneously determines the population size and the genotype frequencies. The equilibrium solutions to a one locus and two locus model are given as well as some generalizations to n loci and nonlogistic fitness functions. Conditions are found that maintain several different genotypes simultaneously in the equilibrium population. The interaction of such selection with the genetic mechanisms which determine mode of reproduction in parthenogenetic populations is also discussed.     

Multilocus heterozygosity and inbreeding depression in an insular house sparrow metapopulation

Inbreeding causes reduction of genetic variability that may have severe fitness consequences. In spite of its potentially huge impact on viability and evolutionary processes especially in small populations, quantitative demonstrations of genetic and demographic effects of inbreeding in natural populations are few. Here, we examine the relationship between individual inbreeding coefficients (F) and individual standardized multilocus heterozygosity (H) in an insular metapopulation of house sparrows (Passer domesticus) in northern Norway in order to evaluate whether H is a good predictor for F. We then relate variation in fitness (i.e. the probability of surviving from fledging to recruitment) to F and H, which enables us to examine whether inbreeding depression is associated with a reduction in genetic variability. The average level of inbreeding in the house sparrow metapopulation was high, and there was large inter-individual variation in F. As expected, standardized multilocus heterozygosity decreased with the level of inbreeding. The probability of recruitment was significantly negatively related to F, and, accordingly, increased with H. However, H explained no significant additional variation in recruitment rate than was explained by F. This suggests that H is a good predictor for F in this metapopulation, and that an increase in F is likely to be associated with a general increase in the level of homozygosity on loci across the genome, which has severe fitness consequences.     

The population genetics of clonal and partially clonal diploids

The consequences of variable rates of clonal reproduction on the population genetics of neutral markers are explored in diploid organisms within a subdivided population (island model). We use both analytical and stochastic simulation approaches. High rates of clonal reproduction will positively affect heterozygosity. As a consequence, nearly twice as many alleles per locus can be maintained and population differentiation estimated as F(ST) value is strongly decreased in purely clonal populations as compared to purely sexual ones. With increasing clonal reproduction, effective population size first slowly increases and then points toward extreme values when the reproductive system tends toward strict clonality. This reflects the fact that polymorphism is protected within individuals due to fixed heterozygosity. Contrarily, genotypic diversity smoothly decreases with increasing rates of clonal reproduction. Asexual populations thus maintain higher genetic diversity at each single locus but a lower number of different genotypes. Mixed clonal/sexual reproduction is nearly indistinguishable from strict sexual reproduction as long as the proportion of clonal reproduction is not strongly predominant for all quantities investigated, except for genotypic diversities (both at individual loci and over multiple loci).     

Segregation and the evolution of sex under overdominant selection

The segregation of alleles disrupts genetic associations at overdominant loci, causing a sexual population to experience a lower mean fitness compared to an asexual population. To investigate whether circumstances promoting increased sex exist within a population with heterozygote advantage, a model is constructed that monitors the frequency of alleles at a modifier locus that changes the relative allocation to sexual and asexual reproduction. The frequency of these modifier alleles changes over time as a correlated response to the dynamics at a fitness locus under overdominant selection. Increased sex can be favored in partially sexual populations that inbreed to some extent. This surprising finding results from the fact that inbred populations have an excess of homozygous individuals, for whom sex is always favorable. The conditions promoting increased levels of sex depend on the selection pressure against the homozygotes, the extent of sex and inbreeding in the population, and the dominance of the invading modifier allele.