Unifying the theories of inclusive fitness and reciprocal altruism

Inclusive fitness and reciprocal altruism are widely thought to be distinct explanations for how altruism evolves. Here we show that they rely on the same underlying mechanism. We demonstrate this commonality by applying Hamilton's rule, normally associated with inclusive fitness, to two simple models of reciprocal altruism: one, an iterated prisoner's dilemma model with conditional behavior; the other, a mutualistic symbiosis model where two interacting species differ in conditional behaviors, fitness benefits, and costs. We employ Queller's generalization of Hamilton's rule because the traditional version of this rule does not apply when genotype and phenotype frequencies differ or when fitness effects are nonadditive, both of which are true in classic models of reciprocal altruism. Queller's equation is more general in that it applies to all situations covered by earlier versions of Hamilton's rule but also handles nonadditivity, conditional behavior, and lack of genetic similarity between altruists and recipients. Our results suggest changes to standard interpretations of Hamilton's rule that focus on kinship and indirect fitness. Despite being more than 20 years old, Queller's generalization of Hamilton's rule is not sufficiently appreciated, especially its implications for the unification of the theories of inclusive fitness and reciprocal altruism.     

A quantitative test of Hamilton's rule for the evolution of altruism

The evolution of altruism is a fundamental and enduring puzzle in biology. In a seminal paper Hamilton showed that altruism can be selected for when rb - c > 0, where c is the fitness cost to the altruist, b is the fitness benefit to the beneficiary, and r is their genetic relatedness. While many studies have provided qualitative support for Hamilton's rule, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. Here we use a simulated system of foraging robots to experimentally manipulate the costs and benefits of helping and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different c/b ratios, we show that Hamilton's rule always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects as well as mutations with strong effects on behavior and fitness (effects not directly taken into account in Hamilton's original 1964 rule). In addition to providing the first quantitative test of Hamilton's rule in a system with a complex mapping between genotype and phenotype, these experiments demonstrate the wide applicability of kin selection theory.     

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).     

Genetic relatedness in viscous populations

Summary Hamilton's inclusive fitness rule shows that the evolution of altruism is facilitated by high genetic relatedness of altruists to their beneficiaries. But the evolution of altruism is inhibited when the beneficiaries are also close competitors of the altruist, as will often be true in structured or viscous populations. However, Hamilton's rule still gives the correct condition for the evolution of altruism if relatedness is measured with respect to the local competitive neighbourhood.     

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.     

Effects of information and group structure on evolution of altruism: analysis of two-score model by covariance and contextual analyses

An altruistic individual has to gamble on cooperation to a stranger because it does not know whether the stranger is trustworthy before direct interaction. Nowak and Sigmund (Nature 393 (1998a) 573; J. Theor. Biol. 194 (1998b) 561) presented a new theoretical framework of indirect reciprocal altruism by image scoring game where all individuals are informed about a partner's behavior from its image score without direct interaction. Interestingly, in a simplified version of the image scoring game, the evolutionarily stability condition for altruism became a similar form of Hamilton's rule, i.e. inequality that the probability of getting correct information is more than the ratio of cost to benefit. Since the Hamilton's rule was derived by evolutionarily stable analysis, the evolutionary meaning of the probability of getting correct information has not been clearly examined in terms of kin and group selection. In this study, we applied covariance analysis to the two-score model for deriving the Hamilton's rule. We confirmed that the probability of getting correct information was proportional to the bias of altruistic interactions caused by using information about a partner's image score. The Hamilton's rule was dependent on the number of game bouts even though the information reduced the risk of cooperation to selfish one at the first encounter. In addition, we incorporated group structure to the two-score model to examine whether the probability of getting correct information affect selection for altruism by group selection. We calculated a Hamilton's rule of group selection by contextual analysis. Group selection is very effective when either the probability of getting correct information or that of future interaction, or both are low. The two Hamilton's rules derived by covariance and contextual analyses demonstrated the effects of information and group structure on the evolution of altruism. We inferred that information about a partner's behavior and group structure can produce flexible pathways for the evolution of altruism.     

Altruism via kin-selection strategies that rely on arbitrary tags with which they coevolve

Hamilton's rule explains when natural selection will favor altruism between conspecifics, given their degree of relatedness. In practice, indicators of relatedness (such as scent) coevolve with strategies based on these indicators, a fact not included in previous theories of kin recognition. Using a combination of simulation modeling and mathematical extension of Hamilton's rule, we demonstrate how altruism can emerge and be sustained in a coevolutionary setting where relatedness depends on an individual's social environment and varies from one locus to another. The results support a very general expectation of widespread, and not necessarily weak, conditional altruism in nature.     

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.     

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.     

HLA and genomewide allele sharing in dizygotic twins

Gametic selection during fertilization or the effects of specific genotypes on the viability of embryos may cause a skewed transmission of chromosomes to surviving offspring. A recent analysis of transmission distortion in humans reported significant excess sharing among full siblings. Dizygotic (DZ) twin pairs are a special case of the simultaneous survival of two genotypes, and there have been reports of DZ pairs with excess allele sharing around the HLA locus, a candidate locus for embryo survival. We performed an allele-sharing study of 1,592 DZ twin pairs from two independent Australian cohorts, of which 1,561 pairs were informative for linkage on chromosome 6. We also analyzed allele sharing in 336 DZ twin pairs from The Netherlands. We found no evidence of excess allele sharing, either at the HLA locus or in the rest of the genome. In contrast, we found evidence of a small but significant (P=.003 for the Australian sample) genomewide deficit in the proportion of two alleles shared identical by descent among DZ twin pairs. We reconciled conflicting evidence in the literature for excess genomewide allele sharing by performing a simulation study that shows how undetected genotyping errors can lead to an apparent deficit or excess of allele sharing among sibling pairs, dependent on whether parental genotypes are known. Our results imply that gene-mapping studies based on affected sibling pairs that include DZ pairs will not suffer from false-positive results due to loci involved in embryo survival.     

Altruism,tit for tat and ‘outlaw’ genes

Summary In a prior study we combined game theory and inclusive fitness models to examine whether the guarded altruism that can evolve among non-relatives (tit for tat, TFT) might also evolve among close relatives, supplanting unconditional altruism. In most cases, TFT replaced unconditional altruism in family-structured models. Even when TFT is selected at a single locus, however, by withholding altruism from non-reciprocating relatives it may qualify as an outlaw from the standpoint of modifier genes at other loci. Here we examine this possibility with a series of haploid, two-locus models in which a modifier gene transforms TFT into unconditional altruism. The modifier allele spreads to fixation whenever Hamilton's Rule is satisfied, resulting in an unconditional altruist replacing the TFT strategy. As such, TFT may be regarded as an outlaw vulnerable to suppression by alleles at other loci.     

Male-biased mutation rates and the overestimation of extrapair paternity: problem, solution, and illustration using thick-billed murres (Uria lomvia, Alcidae)

The widespread utility of hypervariable loci in genetic studies derives from the high mutation rate, and thus the high polymorphism, of these loci. Recent evidence suggests that mutation rates can be extremely high and may be male biased (occurring in the male germ-line). These two factors combined may result in erroneous overestimates of extrapair paternity, since legitimate offspring with novel alleles will have more mismatches with respect to the biological father than the biological mother. As mutations are male driven, increasing the number of hypervariable loci screened may simply increase the number of mismatches between fathers and their legitimate offspring. Here we describe a simple statistic, the probability of resemblance (PR), to distinguish between mismatches due to parental misassignment versus mutation in either sex or null alleles. We apply this method to parentage data on thick-billed murres (Uria lomvia), and demonstrate that, without considering either mutations or male-biased mutation rates, cases of extrapair paternity (7% in this study) would be grossly overestimated (14.5%-22%). The probability of resemblance can be utilized in parentage studies of any sexually reproducing species when allele or haplotype frequency data are available for putative parents and offspring. We suggest calculating this probability to correctly categorize legitimate offspring when mutations and null alleles may cause mismatches.     

The influence of mating system on the intensity of parent-offspring conflict in primates

An evolutionary conflict of interest exists between parents and their offspring over the partitioning of parental investment (PI) among siblings. When the direct fitness benefits to offspring of increased PI, outweigh the inclusive fitness costs from lost future sibling fitness, selection should favour the evolution of offspring selfishness over altruism. In theory, this conflict is heightened when females are not strictly monogamous, as current offspring should be less altruistic towards future half-siblings than they would be towards full-siblings. Using data collected on foetal growth rate (representing prenatal PI) in primates, I test the prediction from theory that the resolution of the parent-offspring conflict will be closer to the offspring's evolutionary optima in polyandrous species than in more monandrous species. Using phylogenetic comparative analysis, and controlling for allometry, I show that offspring are able to obtain more PI when the probability of future full-siblings decreases, and that this is most pronounced in taxa where there is the opportunity for direct foetal access to the maternal bloodstream. These results support the hypothesis that the resolution of prenatal PI conflict is influenced by both a species' mating system and by its placental structure.     

VARIATION IN OFFSPRING SIZE WITH BIRTH ORDER IN PLACENTAL FISH: A ROLE FOR ASYMMETRIC SIBLING COMPETITION?

Asymmetric sibling competition arises when siblings with different competitive abilities share a limited resource. Such competition occurs in species with postnatal parental care and may also occur when mothers provision embryos between fertilization and birth (matrotrophy). We hypothesized that the combination of matrotrophy and the simultaneous provisioning of embryos in different stages of development (superfetation) leads to asymmetric competition between sibling embryos. Moreover, we expect the intensity of this competition to increase with the level of superfetation as high levels of superfetation result in greater temporal overlap between broods. This hypothesis predicts that offspring from early broods, which predominantly compete with less‐developed siblings, will be larger at birth than offspring from later broods, which experience competition from more and less‐developed siblings. Data on offspring size at birth from two populations of the highly matrotrophic fish, Heterandria formosa, and similar studies of poeciliid fish spanning a range of life histories are consistent with our hypothesis. Together these results suggest that sibling competition is a direct consequence of the evolution of matrotrophy and superfetation in poeciliid fish.     

The evolution of altruism: game theory in multilevel selection and inclusive fitness

Although the prisoner's dilemma (PD) has been used extensively to study reciprocal altruism, here we show that the n-player prisoner's dilemma (NPD) is also central to two other prominent theories of the evolution of altruism: inclusive fitness and multilevel selection. An NPD model captures the essential factors for the evolution of altruism directly in its parameters and integrates important aspects of these two theories such as Hamilton's rule, Simpson's paradox, and the Price covariance equation. The model also suggests a simple interpretation of the Price selection decomposition and an alternative decomposition that is symmetrical and complementary to it. In some situations this alternative shows the temporal changes in within- and between-group selection more clearly than the Price equation. In addition, we provide a new perspective on strong vs. weak altruism by identifying their different underlying game structures (based on absolute fitness) and showing how their evolutionary dynamics are nevertheless similar under selection (based on relative fitness). In contrast to conventional wisdom, the model shows that both strong and weak altruism can evolve in periodically formed random groups of non-conditional strategies if groups are multigenerational. An integrative approach based on the NPD helps unify different perspectives on the evolution of altruism.     

Not my brother's keeper: A thought experiment for Hamilton's rule

The now popular ‘selfish gene’ view defines evolutionary fitness at the gene level - in terms of the number of gene copies residing in future generations (or propelled from previous generations). Yet, most current biology textbooks still apply the concept of fitness to the individual, where it is defined more traditionally as the number of descendants residing in future generations. The existing literature remains ambiguous regarding whether one of these concepts is more meaningful than the other, or whether they both represent legitimate, functional definitions of fitness. In support of the latter view, I present a composite perspective that recognizes the gene as evolutionarily ‘selfish’, but also the individual as a ‘selfish vehicle’ for resident genes. Hamilton's rule explains, based on genetic relatedness, why natural selection has favoured behaviours that compel individuals (as ‘donors’ of help) to act for the good of copies of their genes residing in close kin (‘recipients’). I propose however, that natural selection should particularly favour helping behaviours directed at those recipient kin who have the highest relative probability of being the vehicle for a remarkably adaptive newly mutant gene, weighted by the proportion of genes shared with the donor. According to this ‘adaptive-genetic-novelty-rescue’ (AGNR) hypothesis, these favoured vehicles for shared gene copies are more likely to involve direct descendants (e.g. offspring) than other close kin from one's collateral lineage (e.g. siblings), even when the donor (e.g. a father) shares fewer genes with an offspring (e.g. a son) than with a sibling (e.g. a brother).     

Negative association between parental care and sibling cooperation in earwigs: a new perspective on the early evolution of family life?

The evolution of family life requires net fitness benefits for offspring, which are commonly assumed to mainly derive from parental care. However, an additional source of benefits for offspring is often overlooked: cooperative interactions among juvenile siblings. In this study, we examined how sibling cooperation and parental care could jointly contribute to the early evolution of family life. Specifically, we tested whether the level of food transferred among siblings (sibling cooperation) in the European earwig Forficula auricularia (1) depends on the level of maternal food provisioning (parental care) and (2) is translated into offspring survival, as well as female investment into future reproduction. We show that higher levels of sibling food transfer were associated with lower levels of maternal food provisioning, possibly reflecting a compensatory relationship between sibling cooperation and maternal care. Furthermore, the level of sibling food transfer did not influence offspring survival, but was associated with negative effects on the production of the second and terminal clutch by the tending mothers. These findings indicate that sibling cooperation could mitigate the detrimental effects on offspring survival that result from being tended by low‐quality mothers. More generally, they are in line with the hypothesis that sibling cooperation is an ancestral behaviour that can be retained to compensate for insufficient levels of parental investment.     

Fitness cost due to herbicide resistance may trigger genetic background evolution

This article investigates the possible existence of mechanisms counterbalancing the negative pleiotropic effects on development and reproduction that are conferred by alleles responsible for herbicide resistance in the weed Alopecurus myosuroides. We considered three herbicide-resistant, mutant acetyl-coenzyme A carboxylase (ACCase) alleles, Leu1781, Asn2041, and Gly2078, found in eight resistant populations. Of these, Gly2078 is the only allele with a known fitness cost. We compared plants homozygous for wild-type ACCase alleles that were siblings of plants carrying a given mutant resistant ACCase allele with plants from three populations where resistance did not evolve. In each of two series of experiments, we measured germination dynamics, seedling vigor, plant height, vegetative biomass, and seed production. The wild-type siblings of plants carrying Gly2078 performed better in the field, on average, than wild-type plants that were sibling of plants carrying other mutant ACCase alleles, and particularly those carrying Leu1781. We propose that rapid evolution of the genetic background of plants from the populations where the Gly2078 allele originally arose could partially counterbalance Gly2078 fitness cost, enhancing the spread of the resistant genotypes.     

Marker-assisted introgression using non-unique marker alleles I: selection on the presence of linked marker alleles

This paper investigates marker-assisted introgression of a major gene into an outbred line, where identification of the introgressed gene is incomplete because marker alleles are not unique to the base populations (the same marker allele can occur in both donor and recipient population). Those markers are used to identify the introgressed allele as well as the background genotype. The effect of using those markers, as if they were completely informative on the retention of the introgressed allele, was examined over five generations of backcrossing by using a single marker or a marker bracket for different starting frequencies of the marker alleles. Results were calculated by using both a deterministic approach, where selection is only for the desired allele, and by a stochastic approach, where selection is also on background genotype. When marker allele frequencies in donor and recipient population diverged from 1 and 0 (using a diallelic marker), the ability to retain the desired allele rapidly declined. Marker brackets performed notably better than single markers. If selection on background marker genotype was applied, the desired allele could be lost even more quickly than expected at random because the chance that the allele, which is common in the donor line, is present on the locus identifying the introgressed allele and is surrounded by alleles common in the recipient line on the background marker loci, will descend from the donor line (double recombination has taken place), is a lot smaller than the chance that this allele will stem from the recipient line (in which the allele occurs in low frequency). Marker brackets again performed better. Preselection against marker homozygotes (producing uninformative gametes) gave a slightly better retention of the introgressed allele.     

Spatial patterns and travelling waves in population genetics.

We consider a reaction-diffusion equation to model a multi-allelic, single locus problem. The population can migrate in a homogeneous region and the diffusion rates depend upon the genotype. It is shown that if there is an equilibrium point with all alleles present and if this polymorphism is stable for the classical reaction system then it is also stable for the reaction-diffusion equation. Also a simplified model is used to investigate which allele will spread in the two-allele case. Alleles which are associated with large fitness and small dispersion do best.