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.     

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.     

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.     

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).     

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.     

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.     

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.     

Inbreeding depression in small populations of self-incompatible plants.

Self-incompatibility (SI) is a widespread mechanism that prevents inbreeding in flowering plants. In many species, SI is controlled by a single locus (the S locus) where numerous alleles are maintained by negative frequency-dependent selection. Inbreeding depression, the decline in fitness of selfed individuals compared to outcrossed ones, is an essential factor in the evolution of SI systems. Conversely, breeding systems influence levels of inbreeding depression. Little is known about the joint effect of SI and drift on inbreeding depression. Here we studied, using a two-locus model, the effect of SI (frequency-dependent selection) on a locus subject to recurrent deleterious mutations causing inbreeding depression. Simulations were performed to assess the effect of population size and linkage between the two loci on the level of inbreeding depression and genetic load. We show that the sheltering of deleterious alleles linked to the S locus strengthens inbreeding depression in small populations. We discuss the implications of our results for the evolution of SI systems.     

The stationary distribution of allele frequencies when selection acts at unlinked loci

We consider population genetics models where selection acts at a set of unlinked loci. It is known that if the fitness of an individual is multiplicative across loci, then these loci are independent. We consider general selection models, but assume parent-independent mutation at each locus. For such a model, the joint stationary distribution of allele frequencies is proportional to the stationary distribution under neutrality multiplied by a known function of the mean fitness of the population. We further show how knowledge of this stationary distribution enables direct simulation of the genealogy of a sample at a single-locus. For a specific selection model appropriate for complex disease genes, we use simulation to determine what features of the genealogy differ between our general selection model and a multiplicative model.     

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.     

Evolutionary genetics of maternal effects

Maternal genetic effects (MGEs), where genes expressed by mothers affect the phenotype of their offspring, are important sources of phenotypic diversity in a myriad of organisms. We use a single‐locus model to examine how MGEs contribute patterns of heritable and nonheritable variation and influence evolutionary dynamics in randomly mating and inbreeding populations. We elucidate the influence of MGEs by examining the offspring genotype‐phenotype relationship, which determines how MGEs affect evolutionary dynamics in response to selection on offspring phenotypes. This approach reveals important results that are not apparent from classic quantitative genetic treatments of MGEs. We show that additive and dominance MGEs make different contributions to evolutionary dynamics and patterns of variation, which are differentially affected by inbreeding. Dominance MGEs make the offspring genotype‐phenotype relationship frequency dependent, resulting in the appearance of negative frequency‐dependent selection, while additive MGEs contribute a component of parent‐of‐origin dependent variation. Inbreeding amplifies the contribution of MGEs to the additive genetic variance and, therefore enhances their evolutionary response. Considering evolutionary dynamics of allele frequency change on an adaptive landscape, we show that this landscape differs from the mean fitness surface, and therefore, under some condition, fitness peaks can exist but not be “available” to the evolving population.     

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.     

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 hitchhiker's guide to altruism: gene-culture coevolution,and the internalization of norms

An internal norm is a pattern of behavior enforced in part by internal sanctions, such as shame, guilt and loss of self-esteem, as opposed to purely external sanctions, such as material rewards and punishment. The ability to internalize norms is widespread among humans, although in some so-called "sociopaths", this capacity is diminished or lacking. Suppose there is one genetic locus that controls the capacity to internalize norms. This model shows that if an internal norm is fitness enhancing, then for plausible patterns of socialization, the allele for internalization of norms is evolutionarily stable. This framework can be used to model Herbert Simon's (1990) explanation of altruism, showing that altruistic norms can "hitchhike" on the general tendency of internal norms to be personally fitness-enhancing. A multi-level selection, gene-culture coevolution argument then explains why individually fitness-reducing internal norms are likely to be prosocial as opposed to socially harmful.     

Functional pleiotropy and mating system evolution in plants: frequency-independent mating

Mutations that alter the morphology of floral displays (e.g., flower size) or plant development can change multiple functions simultaneously, such as pollen export and selfing rate. Given the effect of these various traits on fitness, pleiotropy may alter the evolution of both mating systems and floral displays, two characters with high diversity among angiosperms. The influence of viability selection on mating system evolution has not been studied theoretically. We model plant mating system evolution when a single locus simultaneously affects the selfing rate, pollen export, and viability. We assume frequency-independent mating, so our model characterizes prior selfing. Pleiotropy between increased viability and selfing rate reduces opportunities for the evolution of pure outcrossing, can favor complete selfing despite high inbreeding depression, and notably, can cause the evolution of mixed mating despite very high inbreeding depression. These results highlight the importance of pleiotropy for mating system evolution and suggest that selection by nonpollinating agents may help explain mixed mating, particularly in species with very high inbreeding depression.     

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.     

THE OPPORTUNITY FOR BALANCING SELECTION IN EXPERIMENTAL POPULATIONS OF CAENORHABDITIS ELEGANS

The role of balancing selection in maintaining diversity during the evolution of sexual populations to novel environments is poorly understood. To address this issue, we studied the impact of two mating systems, androdioecy and dioecy, on genotype distributions during the experimental evolution of Caenorhabditis elegans. We analyzed the temporal trajectories of 334 single nucleotide polymorphisms, covering 1/3 of the genome, and found extensive allele frequency changes and little loss of heterozygosities after 100 generations. As modeled with numerical simulations, SNP differentiation was consistent with genetic drift and average fitness effects of 2%, assuming that selection acted independently at each locus. Remarkably, inbreeding by self‐fertilization was of little consequence to SNP differentiation. Modeling selection on deleterious recessive alleles suggests that the initial evolutionary dynamics can be explained by associative overdominance, but not the later stages because much lower heterozygosities would be maintained during experimental evolution. By contrast, models with selection on true overdominant loci can explain the heterozygote excess observed at all periods, particularly when negative epistasis or independent fitness effects were considered. Overall, these findings indicate that selection at single loci, including purging of recessive alleles, underlies most of the genetic differentiation accomplished during the experiment. Nonetheless, they also imply that maintenance of genetic diversity may in large part be due to balancing selection at multiple loci.     

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.     

EVOLUTION BY FISHERIAN SEXUAL SELECTION IN DIPLOIDS

Most models of Fisherian sexual selection assume haploidy. However, analytical models that focus on dynamics near fixation boundaries and simulations show that the resulting behavior depends on ploidy. Here we model sexual selection in a diploid to characterize behaviour away from fixation boundaries. The model assumes two di-allelic loci, a male-limited trait locus subject to viability selection, and a preference locus that determines a female's tendency to mate with males based on their genotype at the trait locus. Using a quasi-linkage equilibrium (QLE) approach, we find a general equation for the curves of quasi-neutral equilibria, and the conditions under which they are attracting or repelling. Unlike in the haploid model, the system can move away from the internal curve of equilibria in the diploid model. We show that this is the case when the combined forces of natural and sexual selection induce underdominance at the trait locus.