Inbreeding and evolution by kin selection

Because alleles associated with altruistic behaviors can increase in frequency when altruists increase the fitness of closely related individuals, it has been assumed that inbreeding presents the most favorable conditions for the evolution of altruism. Using a family-structured model of kin selection, we varied the proportion of the population mating with sibs and the proportion mating randomly to investigate the hypothesis that inbreeding facilitates the evolution of altruistic behaviors.We partitioned total gene frequency change of the altruistic allele into two components: (1) the change in gene frequency owing to selection within families, or individual selection; this component of selection is always negative and selects against altruistic social behaviors; and (2) the change in gene frequency owing to fitness differences between families, or group selection; this component of selection favors the evolution of altruistic social behaviors. Because inbreeding increases the component of group selection at the expense of individual selection by increasing the between-group variation, it facilitates the spread of the altruistic allele. Computer simulations show that even small amounts of inbreeding (within-sibship mating) significantly increase the rate of gene frequency change.     

"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.     

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).     

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.     

The evolution of recombination in permanent translocation heterozygotes

The evolution of a selectively neutral locus that controls the degree to which alleles at a single selected locus are linked with a particular set of chromosomes in a permanent translocation heterozygote is studied. With complete selfing and fitness overdominance a new allele at the modifying locus will increase in frequency if it increases the linkage of all alleles at the selected locus to a particular set of chromosomes. With random mating a new allele at the modifying locus will increase when rare if it increases the linkage of alleles at the selected locus to a particular set of chromosomes. In addition, a parameter analogous to the coefficient of linkage disequilibrium in usual two-locus models with random mating must be nonzero if a new allele at the modifying locus is to increase in frequency at a geometric rate when rare. With mixed selfing and random mating a new allele at the modifying locus will apparently increase when rare only if it increases the linkage of alleles at the selected locus to a particular set of chromosomes.     

Kin selection in human populations: theory reconsidered

Past considerations of kin selection have assumed a dyadic fitness exchange relationship between altruist and recipient. This approach does not account for all alleles affected by altruistic behavior. This can be corrected by focusing on matings rather than on individuals. I present a model that tries to account for fitness changes resulting from altruistic acts, not only for the altruist and recipient but also for their spouses, in an evolving population. Results from this model indicate that Hamilton's rule fails to predict when the altruism allele will increase in frequency and, more important, suggest that kin selection can, at most, account for low levels of a gene for altruism but only if fairly extreme conditions are met.     

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.     

Sib mating designs for mapping quantitative trait loci

The power to separate the variance of a quantitative trait locus (QTL) from the polygenic variance is determined by the variability of genes identical by descent (IBD) at the QTL. This variability may increase with inbreeding. Selfing, the most extreme form of inbreeding, increases the variability of the IBD value shared by siblings, and thus has a higher efficiency for QTL mapping than random mating. In self-incompatible organisms, sib mating is the closest form of inbreeding. Similar to selfing, sib mating may also increase the power of QTL detection relative to random mating. In this study, we develop an IBD-based method under sib mating designs for QTL mapping. The efficiency of sib mating is then compared with random mating. Monte Carlo simulations show that sib mating designs notably increase the power for QTL detection. When power is intermediate, the power to detect a QTL using full-sib mating is, on average, 7% higher than under random mating. In addition, the IBD-based method proposed in this paper can be used to combine data from multiple families. As a result, the estimated QTL parameters can be applied to a wide statistical inference space relating to the entire reference population. This revised version was published online in July 2006 with corrections to the Cover Date.     

Conditions for the evolution of altruism under darwinian selection

A model of population structure is discussed which under certain circumstances allows for evolution of altruistic traits, beyond the classical restrictions imposed by kin selection theory and related concepts such as reciprocal altruism. Essentially, the model sees a large population as socially subdivided into small groups without any barriers, however, to free random mating. An altruistic trait is defined as lowering, locally, the fitness of a carrier below that of noncarriers within the same group; but the local fitness of an individual randomly chosen in a group increases with the number of altruists. It is shown that altruism can evolve even if the groups are randomly formed. The conditions for such evolution are contrasted with those prevailing when the groups are formed either with some phenotypic assortment between the members or on the basis of kinship. It is shown that any possibility of evolution tends to rapidly disappear as groups become large, unless there is complete positive assortment or individuals in the groups are kin. The example of alarm calls is also considered, and the two extremes of random and sib-groups are contrasted, using a model by Maynard Smith. It is shown that alarm calls can evolve in small groups of unrelated individuals under conditions qualitatively similar but quantitatively more rigorous than those prevailing for sib-groups.     

Mating system and ploidy influence levels of inbreeding depression in Clarkia (Onagraceae)

Inbreeding depression is the reduction in offspring fitness associated with inbreeding and is thought to be one of the primary forces selecting against the evolution of self-fertilization. Studies suggest that most inbreeding depression is caused by the expression of recessive deleterious alleles in homozygotes whose frequency increases as a result of self-fertilization or mating among relatives. This process leads to the selective elimination of deleterious alleles such that highly selfing species may show remarkably little inbreeding depression. Genome duplication (polyploidy) has also been hypothesized to influence levels of inbreeding depression, with polyploids expected to exhibit less inbreeding depression than diploids. We studied levels of inbreeding depression in allotetraploid and diploid species of Clarkia (Onagraceae) that vary in mating system (each cytotype was represented by an outcrossing and a selfing species). The outcrossing species exhibited more inbreeding depression than the selfing species for most fitness components and for two different measures of cumulative fitness. In contrast, though inbreeding depression was generally lower for the polyploid species than for the diploid species, the difference was statistically significant only for flower number and one of the two measures of cumulative fitness. Further, we detected no significant interaction between mating system and ploidy in determining inbreeding depression. In sum, our results suggest that a taxon's current mating system is more important than ploidy in influencing levels of inbreeding depression in natural populations of these annual plants.     

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.     

Nuclear–mitochondrial epistasis: a gene's eye view of genomic conflict

We use population genetic models to investigate the cooperative and conflicting synergistic fitness effects between genes from the nucleus and the mitochondrion. By varying fitness parameters, we examine the scope for conflict relative to cooperation among genomes and the utility of the “gene's eye view” analytical approach, which is based on the marginal average fitness of specific alleles. Because sexual conflict can maintain polymorphism of mitochondrial haplotypes, we can explore two types of evolutionary conflict (genomic and sexual) with one epistatic model. We find that the nuclear genetic architecture (autosomal, X‐linked, or Z‐linked) and the mating system change the regions of parameter space corresponding to the evolution by sexual and genomic conflict. For all models, regardless of conflict or cooperation, we find that population mean fitness increases monotonically as evolution proceeds. Moreover, we find that the process of gene frequency change with positive, synergistic fitnesses is self‐accelerating, as the success of an allele in one genome or in one sex increases the frequency of the interacting allele upon which its success depends. This results in runaway evolutionary dynamics caused by the positive intergenomic associations generated by selection. An inbreeding mating system tends to further accelerate these runaway dynamics because it maintains favorable host–symbiont or male–female gene combinations. In contrast, where conflict predominates, the success of an allele in one genome or in one sex diminishes the frequency of the corresponding allele in the other, resulting in considerably slower evolutionary dynamics. The rate of change of mean fitness is also much faster with positive, synergistic fitnesses and much slower where conflict is predominant. Consequently, selection rapidly fixes cooperative gene combinations, while leaving behind a slowing evolving residue of conflicting gene combinations at mutation–selection balance. We discuss how an emphasis on marginal fitness averages may obscure the interdependence of allelic fitness across genomes, making the evolutionary trajectories appear independent of one another when they are not.     

Maternal effect genes and the evolution of sociality in haplo-diploid organisms

Maternal care and female-biased sex ratios are considered by many to be essential prerequisites for the evolution of eusocial behaviors among the hymenoptera. Using population genetic models, I investigate the evolution of genes that have positive maternal effects but negative, direct effects on offspring fitness. I find that, under many conditions, such genes evolve more easily in haplo-diploids than in diplo-diploids. In fact, the conditions are less restrictive than those of kin selection theory, which postulate genes with negative direct effects but positive sib-social effects. For example, the conditions permitting the evolution of maternal effect genes are not affected if females mate multiply, whereas multiple mating reduces the efficacy of kin selection by reducing genetic relatedness within colonies. Inbreeding also differentially facilitates evolution of maternal effect genes in haplo-diploids relative to diplo-diploids, although it does not differentially affect the evolution of sib-altruism genes. Furthermore, when the direct, deleterious pleiotropic effect is restricted to sons, a maternal effect gene can evolve when the beneficial maternal effect is less than half (with inbreeding, much less) of the deleterious effect on sons. For kin selection, however, the sib-social benefits must always exceed the direct costs because genetic relatedness is always less than or equal to 1.0. The results suggest that haplo-diploidy facilitates (1) the evolution of maternal care, and (2) the evolution of maternal effect genes with antagonistic pleiotropic effects on sons. The latter effect may help explain the tendency toward female-biased sex ratios in haplo-diploids, especially those with inbreeding. I conclude that haplo-diploidy not only facilitates the evolution of sister-sister altruism by kin selection but also facilitates the evolution of maternal care and female-biased sex ratios, two prerequisites for eusociality.     

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.     

Inferring purging from pedigree data

The harmful effects of inbreeding can be reduced if deleterious recessive alleles were removed (purged) by selection against homozygotes in earlier generations. If only a few generations are involved, purging is due almost entirely to recessive alleles that reduce fitness to near zero. In this case the amount of purging and allele frequency change can be inferred approximately from pedigree data alone and are independent of the allele frequency. We examined pedigrees of 59,778 U.S. Jersey cows. Most of the pedigrees were for six generations, but a few went back slightly farther. Assuming recessive homozygotes have fitness 0, the reduction of total genetic load due to purging is estimated at 17%, but most of this is not expressed, being concealed by dominant alleles. Considering those alleles that are currently expressed due to inbreeding, the estimated amount of purging is such as to reduce the expressed load (inbreeding depression) in the current generation by 12.6%. That the reduction is not greater is due mainly to (1) generally low inbreeding levels because breeders in the past have tended to avoid consanguineous matings, and (2) there is essentially no information more than six generations back. The methods used here should be applicable to other populations for which there is pedigree information.     

PROBLEMS WITH TESTING INBREEDING AVOIDANCE: THE CASE OF THE COLLARED FLYCATCHER

Four year's data on collared flycatchers, Ficedula albicollis, breeding in a nestbox plot on the island of Gotland, Sweden, was used to investigate whether individuals avoid mating with close kin (i.e., parents or sibs). Only one case of close inbreeding (0.5% of all pairs) was observed during the years of study. The observed frequency of close inbreeding was compared to expected frequencies based on two different null models. Assuming no inbreeding avoidance behaviors (e.g., dispersal or kin recognition), but taking into account the fact that mortality, and different arrival and pairing times of individuals reduce the probability of mating with close kin, the expected frequency of close inbreeding is 10% and 15% for female and male recruits (i.e., born in the study plot), respectively. However, assuming mating to be random within the study plot reduced the expected frequency of close inbreeding to 1% or less for both males and females. Consequently, conclusions drawn concerning inbreeding avoidance depend on the null model used. Contrasting estimated costs of tolerating close inbreeding with those of avoiding it (by dispersal to other plots), however, suggests that the costs of avoiding close inbreeding are substantially greater than those of tolerating it. Therefore, although inbreeding avoidance cannot be rejected as a cause of dispersal of this species, it is not the primary cause, and particularly not for sex-biased dispersal. The general problems of investigating inbreeding avoidance are discussed. It is argued that all previous null models based on random mating in finite populations produce expected frequencies of close inbreeding that in fact include inbreeding avoidance, since they implicitly assume random dispersal within a finite population. Thus, comparisons between observed and expected frequencies of close inbreeding based on random mating are inadequate. The most promising method of investigating inbreeding avoidance is to experimentally study individual movements and mating preferences in the presence and absence of close kin.     

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.     

Genetic management of captive populations: the advantages of circular mating

We performed computer simulations to evaluate the effectiveness of circular mating as a genetic management option for captive populations. As a benchmark, we used the method proposed by Fernández and Caballero according to which parental contributions are set to produce minimum coancestry among the offspring and matings are performed so as to minimize mean pairwise coancestry (referred to as the Gc/mc method). In contrast to other methods, fitness does not vary with population size in the case of circular mating, and can be higher than under random mating. Whether circular mating is an effective method in conserving captive populations depends on the trade-off between different considerations. On the one hand, circular mating shows the highest allelic diversity and the lowest mean pairwise coancestry for all population sizes. It also shows a relatively higher efficiency of purging deleterious alleles. More importantly, circular mating can significantly increase the success probability of populations released to the wild relative to the Gc/mc method. On the other hand, circular mating has the drawback of showing high inbreeding rates and low fitness in early generations, which can result to an increase in the extinction probability of the captive populations. However, this increase is slight unless population size and litter size are both very low. Overall, if the slight increase in extinction probability can be tolerated then circular mating fulfils the primary goals of a captive breeding program, i.e., it maintains high levels of genetic diversity and increases the success probability of reintroduced populations.     

Divergent allele advantage at MHC-DRB through direct and maternal genotypic effects and its consequences for allele pool composition and mating

It is still debated whether main individual fitness differences in natural populations can be attributed to genome-wide effects or to particular loci of outstanding functional importance such as the major histocompatibility complex (MHC). In a long-term monitoring project on Galápagos sea lions (Zalophus wollebaeki), we collected comprehensive fitness and mating data for a total of 506 individuals. Controlling for genome-wide inbreeding, we find strong associations between the MHC locus and nearly all fitness traits. The effect was mainly attributable to MHC sequence divergence and could be decomposed into contributions of own and maternal genotypes. In consequence, the population seems to have evolved a pool of highly divergent alleles conveying near-optimal MHC divergence even by random mating. Our results demonstrate that a single locus can significantly contribute to fitness in the wild and provide conclusive evidence for the ‘divergent allele advantage’ hypothesis, a special form of balancing selection with interesting evolutionary implications.