The concepts of relatedness - Hamilton's rule and kin selection

Here is a quotation from this wikipedia page

The relatedness parameter (r) in Hamilton's rule was introduced in 1922 by Sewall Wright as a coefficient of relationship that gives the probability that at a random locus, the alleles there will be identical by descent.[14] Subsequent authors, including Hamilton, sometimes reformulate this with a regression, which, unlike probabilities, can be negative.

Here is my question:

• What are all the different definitions of relatedness in biology?
  • how do we calculate them?
  • what do they mean?

Is that really trying to imply that there are significantly different definitions? It seems to me the intent was just to put it in terms of an equation with more useful numbers. This terrifying paper from 1964 gives some of the follow-up works, in particular works from Cockerham in 1954 and a number of papers by Kempthorne, in particular this from 1955 and this from 1963. There is also Malecot's method of coancestry from 1948. (WorldCat.org link) The idea was mainly to look relatedness outside of the specific limitations present in Wright's work. Some of the math in those are more accessible than others…

Kin Selection - Hamilton's Rule

r = the genetic relatedness of the recipient to the actor, often defined as the probability that a gene picked randomly from each at the same locus is identical by descent. B = the additional reproductive benefit gained by the recipient of the altruistic act, C = the reproductive cost to the individual of performing the act.

This inequality is known as Hamilton's rule after W. D. Hamilton who published, in 1964, the first formal quantitative treatment of kin selection to deal with the evolution of apparently altruistic acts.

Originally, the definition for relatedness (r) in Hamilton's rule was explicitly given as Sewall Wright's coefficient of relationship: the probability that at a random locus, the alleles there will be identical by descent (Hamilton 1963, American Naturalist, p. 355). Subsequent authors, including Hamilton, sometimes reformulate this with a regression, which, unlike probabilities, can be negative. Regression analysis producing statistically significant negative relationships indicates that two individuals can be less genetically alike than two random ones on average (Hamilton 1970, Nature & Grafen 1985 Oxford Surveys in Evolutionary Biology). This has been invoked to explain the evolution of spiteful behaviours. Spiteful behavior defines an act (or acts) that results in harm, or loss of fitness, to both the actor and the recipient.

In the 1930s J.B.S. Haldane had full grasp of the basic quantities and considerations that play a role in kin selection. He famously said that, "I would lay down my life for two brothers or eight cousins". Kin altruism is the term for altruistic behaviour whose evolution is supposed to have been driven by kin selection.

Haldane's remark alluded to the fact that if an individual loses its life to save two siblings, four nephews, or eight cousins, it is a "fair deal" in evolutionary terms, as siblings are on average 50% identical by descent, nephews 25%, and cousins 12.5% (in a diploid population that is randomly mating and previously outbred). But Haldane also joked that he would truly die only to save more than a single identical twin of his or more than two full siblings.

In 2011, experimentalists found empirically that Hamilton's rule describes very accurately the conditions under which altruism emerged in simulated populations of foraging robots. The accuracy of this first quantitative corroboration of Hamilton's rule is all the more impressive given that Hamilton's model made several simplifications that did not apply to the foraging robots.

Read more about this topic: Kin Selection

Famous quotes containing the words hamilton and/or rule :

&ldquo In politics, as in religion, it is equally absurd to aim at making proselytes by fire and sword. Heresies in either can rarely be cured by persecution. &rdquo
&mdashAlexander Hamilton (1757�)

&ldquo The first rule of venture capitalism should be Shoot the Inventor. &rdquo
&mdashRichard, Sir Storey (b. 1937)

Hamilton's rule and the causes of social evolution

Hamilton's rule is a central theorem of inclusive fitness (kin selection) theory and predicts that social behaviour evolves under specific combinations of relatedness, benefit and cost. This review provides evidence for Hamilton's rule by presenting novel syntheses of results from two kinds of study in diverse taxa, including cooperatively breeding birds and mammals and eusocial insects. These are, first, studies that empirically parametrize Hamilton's rule in natural populations and, second, comparative phylogenetic analyses of the genetic, life-history and ecological correlates of sociality. Studies parametrizing Hamilton's rule are not rare and demonstrate quantitatively that (i) altruism (net loss of direct fitness) occurs even when sociality is facultative, (ii) in most cases, altruism is under positive selection via indirect fitness benefits that exceed direct fitness costs and (iii) social behaviour commonly generates indirect benefits by enhancing the productivity or survivorship of kin. Comparative phylogenetic analyses show that cooperative breeding and eusociality are promoted by (i) high relatedness and monogamy and, potentially, by (ii) life-history factors facilitating family structure and high benefits of helping and (iii) ecological factors generating low costs of social behaviour. Overall, the focal studies strongly confirm the predictions of Hamilton's rule regarding conditions for social evolution and their causes.

1. Introduction

Hamilton's inclusive fitness theory [1,2], now 50 years old, has had a revolutionary effect on our understanding of evolution following the Modern Synthesis of the mid-twentieth century. Many works, both specialist [3–6] and more general [7–11], have explained the basis and predictions of the theory, also known as kin selection theory. Conceptually, its fundamental contribution has been to identify genes as self-promoting strategists whose evolutionary interests are conditional on the relatedness class in which they reside [1,12–14]. Put more exactly, genes are selected to act as if they are maximizing their inclusive fitness [13–15]. This insight has substantially extended population genetics, the genetical theory of natural selection and the Modern Synthesis because it shows that natural selection on any gene depends on the gene's effects, or lack of effects, on the direct fitness (offspring number) of bearers of copies of itself. Conspecific individuals are not sealed off from one another in terms of fitness, and traditional ‘individual selection’ is, ultimately, gene selection [12,13]. All higher levels of organization, such as genomes, multicellular organisms and societies, arise through major transitions in evolution that are conditional on cooperating genes finding a coincidence of inclusive fitness interests in bringing them about [9,13,16–19].

A simple but powerful formalization of inclusive fitness theory is provided by Hamilton's rule [20,21]. This states that a gene for any social action will undergo selection when the sum of indirect fitness (rb) and direct fitness (c) exceeds zero, where r is the relatedness of the social actor and recipient and c and b are the changes brought about by the social action in the offspring numbers of, respectively, the actor and the recipient. From Hamilton's rule follow the well-known conditions for the four possible types of social action as defined by the signs of c and b, namely cooperation or mutual benefit (+, +), altruism (−, +), selfishness (+, −) and spite (−, −) [6,7,9]. Specifically, in its most celebrated application, Hamilton's rule states that altruism (net loss of direct fitness) is selected if rb–c > 0. By identifying this condition, inclusive fitness theory solved the problem of altruism [7,12]. Because of its grounding in fundamental theory, its incorporation of the four types of social action and its universal taxonomic scope, the theory provides the best current basis for a unified understanding of social evolution [5,15]. For example, it enables conflict within family groups and intragenomic conflict to be understood in the same terms [9,22]. When applied to the major transitions [9,16,17], it provides an explanation of the biological hierarchy itself.

The evidence for inclusive fitness theory is extensive, diverse and growing [8,10,11,23,24]. Nonetheless, explicit empirical tests of Hamilton's rule in natural populations are relatively few. Hamilton's rule predicts that each social action arises only under certain combinations of values of r, b and c [7,9]. Factors bringing about the required values of r, b and c within natural populations create conditions for social evolution. Variation in these values may then cause social evolution in the sense of making the difference (given appropriate genetic variation) between whether or not social behaviour undergoes selection. For example, Hamilton's rule finds that positive relatedness is a necessary condition for the evolution of altruism and that altruism evolves more readily when b is high and c is low. So, for a given relatedness structure, identifying factors affecting the relative values of b and c gives insight into the causes of altruism [21,25]. In this review, I consider results from two approaches to using Hamilton's rule and its predictions to investigate the causes of social evolution. First, I review studies that have empirically tested Hamilton's rule by estimating its parameters using genetic and demographic data from natural populations. Second, I review comparative phylogenetic analyses that have identified predicted genetic, life-history or ecological correlates of social evolution.

A consideration of studies that have tested Hamilton's rule with empirical data is worthwhile because, although several prominent studies have reported such tests, it is well known that, while measuring relatedness using molecular markers is fairly straightforward, estimating b and c in natural populations is far from easy [21]. The impression has therefore arisen that empirical tests of Hamilton's rule are vanishingly scarce and that inclusive fitness theory's successful explanation of altruism relies simply on observing positive relatedness within social groups [26,27]. As will be shown, neither of these points is correct. However, to the best of my knowledge, no previous review has aimed to collate empirical tests of Hamilton's rule and systematically analyse the insights that they provide as regards the causes of social evolution. Crespi [28] highlighted the potential power of comparative phylogenetic analyses of the correlates of sociality to identify causes of social evolution operating over evolutionary time. But many relevant studies have appeared only recently as molecular phylogenies and advances in statistical methodology have become available and, again, a synthesis of the findings of such analyses has not been carried out. Overall, I seek to consider how tests of Hamilton's rule and comparative phylogenetic analyses of the correlates of sociality advance our knowledge of the causes of social evolution at ecological and evolutionary scales.

2. Empirical tests of Hamilton's rule in natural populations

A survey of the literature for studies estimating the parameters of Hamilton's rule using genetic and demographic data from natural populations reveals 12 studies that either have had this explicit aim or provide data permitting these parameters to be estimated (table 1 and figure 1 electronic supplementary material, table S1). The survey is not exhaustive and excludes some related studies. For example, in focusing on estimates of r, b and c, it excludes studies that test inclusive fitness theory by using empirical data to estimate inclusive fitness in other ways [42–46] or to test models of reproductive skew [47,48], which are derived from Hamilton's rule. In focusing on single species or populations, it excludes studies that test Hamilton's rule using correlations across species between social traits and relatedness, benefits or costs [49–52]. Finally, in focusing on common behaviours in natural populations, it excludes studies of rare behaviours [53] and recent applications of Hamilton's rule to social behaviour in humans [54] and robots [55]. Excluding these studies is conservative, in that most of them support the predictions of inclusive fitness theory. The lack of many more studies estimating the parameters of Hamilton's rule in natural populations shows that, indeed, benefits and costs of social actions are difficult to measure in field settings (many of the focal studies involved painstaking fieldwork over multiple years). Nonetheless, such studies are evidently not as scarce as has sometimes been suggested and, though biased towards altruistic brood-rearing behaviour, cover a broad range of other behaviours, including egg dumping, cannibalism and cooperative lekking (table 1 and figure 1 electronic supplementary material, table S1).

Table 1. Studies parametrizing and testing Hamilton's rule with genetic and demographic data from natural populations. See electronic supplementary material, table S1 for an expanded version of the table (giving estimates of the relatedness, benefit and cost terms of Hamilton's rule in each study).

Figure 1. Hamilton's rule has been tested in a wide range contexts and organisms, including egg dumping, joining behaviour, cannibalism and cooperative lekking in, respectively (a–d): (a) Egg-plant lace bug, Gargaphia solani (image credit: copyright 2013 www.Croar.net) (b) Polistine wasp, Polistes dominulus (image credit: Andrew Bourke) (c) Tiger salamander larva, Ambystoma tigrinum (image credit: Kerry Matz) and (d) Wild turkey, Meleagris galloparvo (image credit: Tim Simos/National Wild Turkey Federation).

(a) Assumptions of empirical tests of Hamilton's rule

The studies included in the present survey (table 1 and electronic supplementary material, table S1) make a number of assumptions. First, in reaching their specific conclusions, they assume that the fitness accounting is complete, and that there are not alternative behavioural choices that occur at appreciable frequencies whose benefits and costs could not be estimated. An example of such an alternative is the behaviour within the eusocial Hymenoptera in which a subset of females enter diapause early instead of helping or nesting in the current year [46]. Fitness returns from such behaviours may, indeed, be hard to measure (in this case, because they accrue in the following year), and to this extent the relevant analyses would be incomplete. But this would be true when attempting to apply empirical data from these systems in any sort of model. Second, more generally, applying Hamilton's rule uses the ‘phenotypic gambit’ [21], in which it is assumed that the exact genetic basis of the focal social behaviour (which is unknown in every case) is not such as to overturn the expectations based on Hamilton's rule. The phenotypic gambit is not an assumption of the field of social evolution alone but of behavioural ecology as a whole [21], and its justification comes from behavioural ecology's outstanding success as a research programme [11]. Third, applying Hamilton's rule to data generally makes the assumptions that the social action has additive effects on fitness and that selection for the social action is weak [21,55]. When costs and benefits are estimated as offspring numbers averaged over the lifetimes of the actors and recipients, and when traits are close to equilibrium, these assumptions may be justified [3,21]. However, there are cases in which non-additivity affects the selective outcome [56,57]. Nonetheless, overall, the empirical application of Hamilton's rule is justified because it often appears robust to violations of these assumptions [55] and because it yields a valuable generality at the expense of an exactness that, in natural systems, is almost impossible to achieve [21,58]. Furthermore, applying Hamilton's rule to empirical data is particularly useful because, given it is explicitly based on fitness differences (in the b and c terms), Hamilton's rule compels investigators to analyse the central problem of why individuals exhibit one set of behaviours and not another [20,21].

(b) Conclusions from empirical tests of Hamilton's rule: forms of social behaviour and fulfilment of Hamilton's rule

Because of the interest in addressing the problem of altruism, empirical tests of Hamilton's rule have concentrated on cases where social behaviour aids recipients at what appears, a priori, to be a direct fitness cost to the actor. Of the 12 focal studies (table 1 and electronic supplementary material, table S1), 10 found that actors did indeed incur a direct fitness cost (negative c) and hence exhibited altruism even though social behaviour was facultative (electronic supplementary material, table S1). In two remaining cases (egg dumping in lace bugs and kin-discriminating cannibalism in larval salamanders nos. 1 and 10 in table 1 and electronic supplementary material, table S1), there was a direct fitness return of zero (c = 0). Of the 10 studies in which there was demonstrated altruism, five found that Hamilton's rule was quantitatively fulfilled, i.e. actor–recipient relatedness (r) and benefit to recipients (b) were both positive and high enough for the total indirect fitness benefit to outweigh the direct fitness cost (−c), such that rb −c > 0. These cases involved guarding in an allodapine bee, joining behaviour in polistine wasps, cooperative lekking in wild turkeys and helper behaviour in white-fronted bee-eaters (nos. 2, 8, 9, 11 and 12). In three cases, involving guarding in an allodapine bee and joining behaviour in polistine wasps (nos. 3, 5 and 7), Hamilton's rule was quantitatively fulfilled in some contexts (some years, some group sizes) and not others. In one case, again involving joining behaviour in a polistine wasp (no. 6), social behaviour was selectively neutral (rb − c = 0). In the single remaining case, involving worker behaviour in a halictid bee (no. 4), Hamilton's rule was not fulfilled (rb − c < 0). Overall, therefore, among 10 cases of demonstrated altruism, Hamilton's rule was quantitatively fulfilled in five cases and fulfilled in some contexts in a further three cases. Moreover, egg dumping in lace bugs and kin-discriminating cannibalism in larval salamanders (nos. 1 and 10) were each found to yield a positive indirect fitness benefit despite the lack of direct benefit (electronic supplementary material, table S1), again explaining the occurrence of these behaviours by Hamilton's rule.

(c) Conclusions from empirical tests of Hamilton's rule: relatedness

The focal studies show that there is considerable diversity in the mechanisms that generate positive actor–recipient relatedness in social systems. Standard mechanisms generating such relatedness are population viscosity (philopatry) and kin discrimination [7,9]. Population viscosity can arise through subsociality (group formation via parent–offspring association) or, provided aggregating individuals are relatives, through semisociality (group formation via aggregation of members of the same or mixed generations) [9]. The focal studies include cases of subsociality (e.g. allodapine bee, halictid bee nos. 3 and 4 in table 1 and electronic supplementary material, table S1), cases of semisociality of relatives (e.g. polistine wasps nos. 5–9) and cases that probably involve a mixture of subsociality and semisociality (lace bug, allodapine bees, wild turkey, white-fronted bee-eater nos. 1, 2, 3, 11 and 12). The focal studies also include one clear case of kin discrimination at the individual level. The study of cannibalistic larval salamanders (no. 10) suggested that kin discrimination has evolved because it allows larvae to benefit from cannibalism while avoiding harm to coexisting relatives [39]. This supports a general finding that kin discrimination evolves not as an automatic corollary of kin selection but specifically in social contexts in which it generates benefits [52,59].

(d) Conclusions from empirical tests of Hamilton's rule: benefit and cost

There are several conclusions to be drawn from the focal studies (table 1 and electronic supplementary material, table S1) as regards benefits and costs and their role in the causation of social evolution:

(1) In cases involving cooperative breeding or eusociality, social behaviour is favoured despite its direct cost because it yields some combination, in relatives, of increased individual or nest survivorship or increased nest productivity (allodapine bees, polistine wasps, white-fronted bee-eater nos. 2, 3, 5, 6, 7, 8, 9 and 12 in table 1 and electronic supplementary material, table S1). In some cases, this effect can be pinned to specific advantages of larger social groups, such as the guard in an allodapine bee (no. 3) providing protection against usurpation that increases nest survivorship and providing benefits of division of labour that increase nest productivity [31,32]. Similarly, egg dumping by lace bugs and cooperative lekking in wild turkeys (nos. 1 and 11) yield indirect fitness benefits because they increase the survivorship of the brood of related recipients and the reproductive output of related, dominant males, respectively. Hence, the long-standing idea that advantages of larger group sizes relative to solitary living help generate the indirect fitness benefits that tilt the balance in favour of sociality receives detailed support from these studies.

(2) In one eusocial insect case (halictid bee no. 4), Hamilton's rule failed the test, because workers did not receive a sufficiently large indirect fitness benefit to offset their direct fitness cost. In this case, it was suggested that queens manipulated workers into helping [33]. However, several lines of evidence suggest that queen manipulation is not a general cause of the origin of eusociality in halictid bees or eusocial Hymenoptera as a whole [10,46,60].

(3) Social behaviour that, in net terms, is altruistic, can nonetheless involve a mixture of indirect and direct fitness gains. For example, in an allodapine bee and at least two of the polistine wasps (nos. 2, 5 and 7), social females gained some direct fitness either through nest inheritance or through laying eggs in the joint nest. However, the size of the direct fitness benefit in these females was, as data in the original studies showed [30,34,36], insufficient to outweigh the direct fitness return from solitary nesting, such that social behaviour remained altruistic (negative c electronic supplementary material, table S1). In other systems, including other populations of polistine wasps, direct benefits can be sufficiently large that joining behaviour becomes cooperative (mutually beneficial) but not altruistic [45,61]. In general, each b and c term is a difference of two components (recipient's direct fitness in the presence and absence of the social action, actor's direct fitness in the presence and absence of the social action). Hence, factors affecting any one of these four components can affect the form of the social behaviour, the balance of indirect and direct returns to actors and the conditions required for social behaviour to undergo selection.

(4) Cases in which Hamilton's rule was fulfilled in some contexts but not others (nos. 3, 5 and 7) point to possible ecological and demographic causes mediated by changes to b and c. One is annual variation in the external environment altering the relative values of the components of b and c such that sociality is disfavoured. For example, in an allodapine bee (no. 3), a year in which nest usurpations were rare appears to have increased the direct fitness return from solitary nesting (reflected in the increased c term in 1987 in the electronic supplementary material, table S1), making guarding unprofitable [31,32]. In a polistine wasp (no. 5), a drought year appears to have reduced the relative productivity of joint nests (reflected in the low b term in 1977 in the electronic supplementary material, table S1), making joining behaviour unprofitable [34]. These results suggest that environmental variability creates temporally fluctuating selection for sociality, so accounting for the coexistence of social and solitary behaviours within populations. Another possible cause of variation affecting whether Hamilton's rule is fulfilled is suggested by two studies of polistine wasps (nos. 5 and 7), which showed that joining behaviour was positively selected at low but not at high group sizes [34,36]. In these cases, variations in the relative frequencies of groups of different size could have accounted for the variable fulfilment of Hamilton's rule.

3. Investigating the causes of social evolution using comparative phylogenetic analyses

Almost 20 comparative phylogenetic analyses, mostly conducted within the past 10 years, have allowed investigators to identify genetic, life-history and ecological correlates of the origin of sociality and so pinpoint likely causes of social evolution on an evolutionary timescale in a broad variety of social systems and taxa (table 2 and electronic supplementary material, table S2). These studies vary widely in their scale and methodology and in their ability to distinguish between the antecedents (potential causes) of sociality and its consequences most, however, use some form of statistical comparative analysis (electronic supplementary material, table S2), lending rigour to their findings. Collectively, they provide valuable insights into the transitions that occur in social evolution and their potential causes.

Table 2. Comparative phylogenetic analyses of the genetic, life-history and ecological correlates of the origin of various forms of sociality. Correlates that arise as products of sociality once it has originated are not included. Conclusions are paraphrased from those of the original authors. See electronic supplementary material, table S2 for an expanded version of the table (listing identified correlates in detail).

(a) Genetic correlates

Hamilton's rule makes the general prediction that, other things equal, high relatedness is more conducive to forms of sociality involving altruism (cooperative breeding and eusociality) than low relatedness. In Boomsma's monogamy hypothesis [18,84,85], it makes the specific prediction that lifetime monogamy (leading to r_RO = r_O, i.e. actor's relatedness to recipient's offspring = actor's relatedness to own offspring) promotes obligate sociality. Both these predictions are borne out by the data. Multiple studies show that transitions to multicellularity (case no. 1 in table 2 and electronic supplementary material, table S2), cooperative breeding (birds and mammals nos. 8, 9 and 11) or eusociality (shrimp, thrips and Hymenoptera nos. 12, 15 and 18) occur preferentially under high-relatedness conditions. Boomsma's monogamy hypothesis is supported by the phylogenetic analysis of the evolution of obligate eusociality in the Hymenoptera (no. 18) and is consistent with monogamy being strongly associated with cooperative breeding in birds and mammals (nos. 8 and 9). It is also supported by the phylogenetic analysis of the evolution of obligate multicellularity (no. 1), which was found to be associated with subsociality, in that subsocial development of multicellular organisms creates conditions in which r_RO = r_O [62]. As a corollary, all these studies confirm that, contrary to previous claims [26,86] but consistently with inclusive fitness theory, high relatedness is primary not secondary in the evolution of cooperative breeding and eusociality [8–10].

In some cases (social spiders, eusocial thrips nos. 2 and 15), the occurrence of inbreeding contributes to the high relatedness associated with the origin of sociality, even though models show that inbreeding does not always affect relatednessin ways conducive to social evolution [87]. In social spiders, phylogenetic analysis showed that inbred, social lineages originate frequently but also go extinct frequently [63], demonstrating that sociality is not always successful on an evolutionary timescale. Eusocial aphids have intrinsic high relatedness in that colonies are founded subsocially by a single clonally reproducing female. Contrary to expectation based on Hamilton's rule, clonal mixing was found to be present in, and ancestral to, eusocial and non-eusocial Pemphigus aphids (no. 14). Nonetheless, within-group relatedness remains high within galls of eusocial aphids [9,75], and the association of aphid eusociality with galling suggests that population structure imposed by galling is a contributory factor in the group's social evolution [75].

(b) Life-history correlates

Queller & Strassmann [88] divided eusocial species into ‘fortress defenders’ (species that live within a defended food source) and ‘life insurers’ (species with external foragers whose reproductive investments are safeguarded by nest-mates). These concepts, which stress the long-standing idea that nesting acts as a key life-history facilitator of social evolution [9], receive support from the focal studies. Hence, the appearance of nesting is basal to the appearance of eusociality within vespid wasps [80] and, in termites, the switch to external foraging is associated with the origin of sterile workers [78,79] (case nos. 16 and 17 in table 2 and electronic supplementary material, table S2). Arnold & Owens [67,68] introduced the concept of life-history predisposition followed by ecological facilitation, according to which life-history traits predispose lineages to sociality but ecological factors determine whether it evolves or not. This concept also receives support in that several studies identify life-history traits preceding the origin of sociality, including extended maternal care (social spiders no. 2), increased adult longevity (birds no. 6), litter-bearing (mammals no. 10) and control over egg sex and interactions with larvae (eusocial Hymenoptera no. 17). However, the finding in birds that adult longevity is positively associated with the transition to cooperative breeding has been disputed on methodological grounds ([89] electronic supplementary material, table S2). In mammals, cooperative breeding was not found to be associated with adult longevity (no. 10). Several of the identified traits facilitate social evolution according to Hamilton's rule, because nesting, subsociality and (if present) extended longevity promote close, predictable family structure (high, consistent r) and litter-bearing facilitates the generation of large benefits by helping behaviour (high b).

(c) Ecological correlates

The focal studies indirectly identify predation risk as an ecological factor promoting sociality in primates and eusocial aphids (nos. 3 and 13 in table 2 and electronic supplementary material, table S2). This is consistent with the expectation from Hamilton's rule that low direct fitness returns from breeding alone (leading to low c) promote social behaviour. In birds, results of the focal studies are mixed as regards the influence of environmental variation [65–69]. Although methodological differences may explain some discrepancies (electronic supplementary material, table S2), available evidence suggests that non-passerine and passerine birds differ in their response to environmental variation. Specifically, cooperative breeding is positively associated with climatically stable environments in hornbills and non-passerine birds as a group (nos. 4 and 7) and with warm, climatically variable environments in African starlings and passerine birds as a group (nos. 5 and 7). Why non-passerines and passerines differ in this respect is not resolved, but differences between the groups in body size, territoriality and diet may be partly responsible [65,69]. From Hamilton's rule, one might predict harsh variable environments to promote cooperative breeding in passerine birds through decreasing direct fitness returns from breeding alone [66]. In non-passerine birds, one might predict stable environments to promote cooperative breeding indirectly if, because of traits of non-passerine birds, they increased adult survival and longevity and so decreased the number of territory vacancies. The resulting habitat saturation would again decrease direct fitness returns from breeding alone [65]. These interpretations predict that non-passerine and passerine birds differ in how their intrinsic traits interact with environmental factors with respect to the evolution of cooperative breeding, and hence require further studies for support or refutation. Finally, warm, dry, environmentally variable conditions were associated with sociality in African mole-rats (no. 19), once more suggesting, consistent with Hamilton's rule, that low direct fitness returns from solitary breeding promote cooperative behaviour.

4. Discussion

Overall, the studies considered in this review strongly confirm the predictions of Hamilton's rule regarding the conditions and likely causes that underpin social evolution at ecological and evolutionary timescales. Studies parametrizing Hamilton's rule with data from natural populations are not rare and demonstrate quantitatively that (i) altruism occurs even when sociality is facultative, (ii) in most cases, altruism is under positive selection via indirect fitness benefits that exceed direct fitness costs and (iii) social behaviour commonly generates indirect benefits by enhancing the productivity or survivorship of kin. The studies also provide evidence for environmental variability altering the direction of selection on social behaviour by changing the relative values of benefits and costs. Comparative phylogenetic analyses of the correlates of sociality show that cooperative breeding and eusociality are promoted by (i) high relatedness and monogamy and suggest that they are also promoted by (ii) life-history factors facilitating family structure and high benefits of helping and (iii) ecological factors generating low costs of social behaviour. Variations on these patterns, exceptions and unresolved discrepancies exist, especially as regards identifying, in comparative phylogenetic analyses, correlates of sociality that accurately reflect benefits and costs. Equally, Hamilton's rule is upheld in novel contexts such as egg dumping, cannibalism and cooperative lekking. Collectively, the focal studies provide strong, additional formal evidence for the predictions of inclusive fitness theory.

These findings also suggest promising avenues for future progress. First, in highlighting the general applicability of inclusive fitness theory, they suggest that extensions to additional taxa and contexts will be similarly fruitful. For example, although group formation in multicellularity follows predictions of the theory (table 2), studies estimating the empirical parameters of Hamilton's rule as it applies to the origin of multicellularity within single populations of cells remain to be performed, though several candidate systems exist [9,90]. Second, they suggest that Hamilton's rule for social actions other than altruism, such as spite, could be profitably tested by empirical parametrization [91]. Future empirical parametrizations might also benefit from incorporating more sophisticated methods of fitness accounting [92], or from quantifying effects of other social phenomena that can affect inclusive fitness returns such as sex ratio variation [60], reproductive skew [47] and kin competition [51]. Third, the predictive power of empirical parametrizations of Hamilton's rule could be improved in other ways. For example, in facultatively eusocial Hymenoptera, it remains to be shown (which would be challenging, but not impossible) that social behaviour increases in frequency under conditions in which Hamilton's rule is fulfilled and decreases in frequency under conditions in which it is not fulfilled.

Fourth, causation ultimately requires experimental demonstration, and the focal studies provide strong indicators of likely causes of social evolution that could inform experiments. Indeed, several studies, for example, in insects [48,93] and microbes [94,95], have already successfully tested inclusive fitness theory by experimentally varying the parameters of Hamilton's rule. Finally, phylogenomic and transcriptomic studies are now beginning to uncover some of the specific genes likely to be important in the origin and maintenance of sociality [96,97]. A combination of strong basic theory, applications to new contexts, additional comparative analyses, carefully targeted experimental manipulations and knowledge of genetic underpinnings will prove extremely potent in accelerating the future growth of our understanding of social evolution.

Introduction

Ideas are embedded in their history and language. Hamilton's ( 1970 ) theories of inclusive fitness and kin selection are good examples. As understanding deepened, the original ideas transformed into broader concepts of selection and evolutionary process. With that generalization, the initial language that remains associated with the topic has become distorted. The confused language and haphazard use of incorrect historical context have led to significant misunderstanding and meaningless argument.

Current understanding transcends the initial interpretation of ‘kin selection,’ which attaches to some notion of similarity by descent from a recent common ancestor. The other candidate phrases, such as ‘inclusive fitness’ or ‘group selection,’ also have problems. We are left with a topic that derives from those antecedent notions and clearly has useful application to those biological puzzles. At the same time, the modern understanding of altruism connects to the analysis of selection on multiple characters, to interactions between different species and to the broadest generalizations of the theory of natural selection.

A good scholarly history of kin selection and its descendants has yet to be written. Here, I give a rough historical outline in the form of a nonmathematical narrative (see Box 2). I describe the history from my personal perspective. Because I worked actively on the subject over several decades, I perceive the history by the ways in which my own understanding changed over time. Box 3 highlights other perspectives and key citations.

Box 1. Topics in the theory of natural selection

This article is part of a series on natural selection. Although the theory of natural selection is simple, it remains endlessly contentious and difficult to apply. My goal is to make more accessible the concepts that are so important, yet either mostly unknown or widely misunderstood. I write in a nontechnical style, showing the key equations and results rather than providing full derivations or discussions of mathematical problems. Boxes list technical issues and brief summaries of the literature.

Box 2. Scope

Quoting from Fawcett & Higginson ( 2012 ): Most research in biology is empirical, yet empirical studies rely fundamentally on theoretical work for generating testable predictions and interpreting observations. Despite this interdependence, many empirical studies build largely on other empirical studies with little direct reference to relevant theory, suggesting a failure of communication that may hinder scientific progress. … The density of equations in an article has a significant negative impact on citation rates, with papers receiving 28% fewer citations overall for each additional equation per page in the main text. Long, equation-dense papers tend to be more frequently cited by other theoretical papers, but this increase is outweighed by a sharp drop in citations from nontheoretical papers.

This article contains no equations beyond a few summary expressions. I do not write for other theoreticians. I do not attempt to be comprehensive. Rather, I try to evoke some lines of thought that I believe will be helpful to scientists who want to know about the theory.

A rough idea about the theory aids empirical study. It also helps to cope with the onslaught of theoretical articles. Those theoretical articles often claim to shift the proper framing of fundamental issues. The literature never seems to come to a consensus.

Here, I attempt to translate a few of the key points into nonmathematical summaries. Such translation necessarily loses essential components of understanding. Yet it seems worthwhile to express the main issues in way that can be understood by a wider audience. Refer to my earlier work for mathematical aspects of the theory and for citations to the technical literature (Frank, 1997a , b , 1998 , 2012a , b , c , 2013).

Box 3. Literature

For each topic related to kin selection theory, I list a small sample of key articles and reviews. This limited space does not allow comprehensive coverage or commentary on the particular articles, but should provide an entry into the extensive literature and the range of opinions.

Several reviews follow Hamilton's perspective (Alexander, 1974 Dawkins, 1979 Michod, 1982 Grafen, 1985 Lehmann & Keller, 2006 Wenseleers, 2006 Dugatkin, 2007 Bourke, 2011 Gardner et al., 2011 ). An associated literature emphasizes the problem of sociality and sterile castes in insects, with additional commentary on general aspects of the theory (Wilson, 1971 West-Eberhard, 1975 Trivers & Hare, 1976 Andersson, 1984 Brockmann, 1984 Alexander et al., 1991 Bourke & Franks, 1995 Queller & Strassmann, 1998 Foster et al., 2006 ).

Kin selection theory has been applied to a wide range of biological problems. Here, I can list only a few general overviews. Those overviews give a sense of the scope but do not include many significant applications (Trivers, 1985 Maynard Smith & Szathmáry, 1995 Crespi, 2001 Michod & Roze, 2001 West et al., 2007 Burt & Trivers, 2008 West, 2009 Davies et al., 2012 ).

The strongest criticisms arose from population genetics. The main issues concern how the specifics of genetics can vary from case to case and alter the outcome of selection, and how the full analysis of dynamics may provide an essential, deeper perspective on evolutionary process (Uyenoyama et al., 1981 Uyenoyama & Feldman, 1982 Karlin & Matessi, 1983 Kerr et al., 2004 Nowak et al., 2010 ).

Kin selection theory has a long association with debates about units and levels of selection. I give a very short listing, because that topic is beyond my scope (Lewontin, 1970 Dawkins, 1982 Keller, 1999 Okasha, 2006 ). The related topic concerning group selection does fall within my scope (Wade, 1978 Uyenoyama & Feldman, 1980 Wilson, 1983 Grafen, 1984 Nunney, 1985 Wade, 1985 Heisler & Damuth, 1987 Queller, 1992a Dugatkin & Reeve, 1994 Soltis et al., 1995 Sober & Wilson, 1998 Henrich, 2004 Traulsen & Nowak, 2006 West et al., 2008 Leigh, 2010 ).

The merging of kin selection theory with quantitative genetics and multivariate analyses of selection follows various lines of development (Cheverud, 1984 Queller, 1992b Wolf et al., 1998 , 1999 Bijma & Wade, 2008 McGlothlin et al., 2010 Wolf & Moore, 2010 ). Advanced aspects of the theory and new directions of theoretical development continue to appear (Rousset, 2004 Grafen, 2006 Taylor et al., 2006 Gardner et al., 2007 Fletcher & Doebeli, 2009 ).

Results

We modify the Nowak et al. [13] haploid model, which is simpler than their haplodiploid one but sufficient to demonstrate the important points. Our goal is not to exactly model eusociality in any particular organism but to examine the logic and truth of three general claims in Nowak et al. [13], claims that pertain to both the haploid and haplodiploid models. The basic model includes solitary and eusocial genotypes expressed in offspring, where solitaries always leave to reproduce, while eusocials stay and help their mother with probability q and leave to reproduce with probability 1 – q. Mothers and offspring are genetically identical. Differential equations describe changes in the numbers of solitary individuals and eusocial colonies based on colony-size–specific queen birthrates (b_i) and death rates (d_i), as well as worker death rates (α) and density dependence (η) (see Methods, Equation 1). If larger colony size (more workers) sufficiently increases the queen’s birthrate and/or decreases her death rate, the eusocial type can be favored over solitary reproduction under some probabilities of staying q. Using these equations, we recovered results indistinguishable from those of Nowak et al. [13] (e.g., their Figure 4). We then explored the effects of various assumptions by changing them one by one.

First, the models of Nowak et al. [13] assumed eusocial offspring stay with their mother so that there was always genetic relatedness among participants. In the haploid model, this meant that helpers were genetically identical (r = 1) to their mother and to the siblings they raised. To vary genetic relatedness in the haploid model, we allowed some offspring mixing between mothers before implementing their genetic helping rules. Each offspring has a probability r of being with her own mother before deciding whether to help her or leave to reproduce and a probability 1 – r of being with a random mother. This could result from offspring movement between nests, from mothers laying a fraction of their eggs in other nests, or from nest usurpation [30,31]. r is equivalent to relatedness to the new mother (after movement) because it represents identity to that mother above chance levels a fraction r is identical to the head of their colony and her offspring (r = 1), while the remainder are randomly associated with colonies (r = 0). After this temporary mixing, offspring execute the original Nowak et al. strategies: offspring with the solitary genotype always leave to reproduce alone, and offspring with the eusocial genotype stay and help their colony with probability q. Differential equations implementing this model are given in the Methods (Equation 2).

The filled circles in Fig. 1 show when selection on offspring favors eusociality under varying relatedness r, worker-assisted queen birthrate b, and probability of staying q (other parameters continue to match the standard Nowak et al. Figure 4 parameter values). Lowering relatedness clearly makes it more difficult for eusociality to evolve with lower r, a higher b is required to favor eusociality. In the extreme, when offspring are randomly associated with colonies so that relatedness is zero, even b = 500 (a 1,000-fold increase in the queen’s birthrate due to helpers) is insufficient to favor eusociality. As expected from inclusive fitness theory, relatedness is causal in the sense that some relatedness is necessary for eusociality and increasing relatedness increases the range of conditions allowing eusociality to evolve.

The worker-assisted birthrate b and the probability of staying q are allowed to vary, while other parameters are as in Figure 4 of Nowak et al. [13] (m = 3, b₀ = 0.5, d₀ = 0.1, d = 0.01, α = 0.1, η = 0.01). Filled circles show values of relatedness r and worker-assisted queen birthrate b that select for eusociality (for at least one value of q) if the decision is made by offspring (Equation 2). Reducing relatedness makes eusociality harder to evolve (requires higher b). When the decision is made by genes acting in mothers (Equation 3), eusociality evolves under much broader conditions (open and filled circles), and lowering relatedness make eusociality easier to evolve. The open circles represent the zone of potential conflict, in which mothers but not offspring favor eusociality. The data used to make this figure can be found in S1 Dataset.

Second, to address the issue of whether worker offspring are independent agents or simply robots carrying out the queen’s interests, we need to compare models of control by different agents. This means comparing models in which the decision to stay and help is made by genes in offspring bodies to models in which it is made by genes in the resident queens’ bodies. Though Nowak et al. [13] seem to argue for queen control, their models are for offspring control because they generally assume that genes expressed in worker bodies determine the decision to stay or leave.

However, inclusive fitness theory predicts that when queen control is possible, it will generally be more favorable for evolving eusociality [7] unless relatedness is one, in which case no conflict is expected. To model queen control under varying relatedness in the haploid model, we allowed offspring to mix exactly as in the offspring control model above but then allowed the resident queen’s genotype to determine if her mixed offspring pool helps or not. If the mother has the solitary genotype, all of her mixed pool disperses to become reproductives if the mother has the eusocial genotype, she causes a fraction q of her offspring pool to stay and help her, independent of offspring genotype. Differential equations governing this system are given in the Methods (Equation 3). As predicted by inclusive fitness theory, eusociality evolves much more easily under queen control (Fig. 1, all circles). The only exception, as expected under inclusive fitness theory, is when there is no mixing between nests so r = 1 and the two decision rules are selected identically. In fact, assuming that queens can control the trait, we see the expected opposite relationship with relatedness the less related the queen is to the offspring in her colony, the more the queen is selected to cause them to be workers.

The final claim that we examine is that eusociality is hard to evolve [13]. This depends on what is meant by “hard,” but we can usefully ask whether eusociality is as difficult to evolve as is implied in the Nowak et al. [13] paper. Their claim seems based on particular and odd choices for fitness functions and worker decision rules. The fitness function that they generally explored was a threshold function in which workers add no fitness gains to the queen below a colony of size m and add a fixed gain (increasing queen b or decreasing d) in colonies at or above size m, regardless of how many workers are added. This means that workers in colonies below that threshold contribute nothing until enough further workers join and that workers above the threshold also add nothing extra unless other workers die, returning the colony to the threshold. If most workers are contributing nothing, then it is not surprising that eusociality would be hard to evolve. In the example most explored, the threshold colony size m was set at 3 (their Figure 4), such that two workers were needed to raise the queen’s birthrate from b₀ = 0.5 to b = 4 and to lower her death rate from d₀ = 0.1 to d = 0.01 (they also let α = 0.1 and η = 0.01) [13]. This 8-fold increase in the queen’s birthrate allowed eusociality to evolve for some values of q, but lower values of b did not allow eusociality to evolve. Not surprisingly, requiring more workers before the queen increased fitness (higher m thresholds) made eusociality even more difficult to evolve.

As noted above, the assumption that workers must stay with probability q, regardless of the state of the colony, means they may be maladaptively staying in colonies that are too large to gain further benefits. It should be easy for workers to avoid this problem. For example, they might instead implement the rule to stay when the colony is below some threshold size w and leave when it is at or above that size. We implemented differential equations to model this change of assumption (see Methods, Equation 4) in the original Nowak et al. model with worker control and r = 1 (i.e., independently of the other changes explored above). Eusociality does evolve more readily. For example, for the same parameter values as in Figure 4 of Nowak et al., eusociality can now be favored under a somewhat lower benefits threshold (b = 3), that is, when helped queens get a 6-fold advantage.

In addition, the threshold fitness function assumed by Nowak et al. [13] prevents the earliest workers from contributing anything. However, it is easy to envision advantages that would come from having only a single worker [25,32]. To view this effect in isolation, we return to the Nowak et al. [13] decision rule (stay with probability q) and to their parameter values given above but allow a single worker to add half the contribution to the queen that two workers add (for both birthrate and death rate) (m = 3, b₀ = 0.5, d₀ = 0.1, d = 0.01, α = 0.1, η = 0.01). This simple change (implemented in Equation 1) makes it much easier to evolve eusociality, with b = 1.5 or only a 3-fold increase required (Fig. 2) versus 8-fold with the threshold model. This analysis does not resolve what actual fitness functions and decision rules apply in nature, but we note that evolution tends to take the easiest paths available and eschew the difficult ones.

The threshold model is that assumed in Figure 4 of Nowak et al. [13] (m = 3, b₀ = 0.5, d₀ = 0.1, d = 0.01, α = 0.1, η = 0.01), with no benefits of working below colony size 3 (two workers). The step model is identical except one worker benefits the queen half as much as two workers do. The data used to make this figure can be found in S1 Dataset.

This result appears very close to what is expected under inclusive fitness when r = 1: if two workers increase queen birthrate from 0.5 to 1.5, each raises it by 0.5, exactly the amount that the worker gives up by helping. However, the comparison is not accurate for two reasons. First, this comparison of birthrates neglects the workers’ effect on queen death rate in the model. Second, having gone back to the stay-with probability q decision rule, some workers waste their efforts by joining large colonies. In order to compare more closely with inclusive fitness, we altered both of these: the queen death rate is now unchanged by workers, and the stepwise birthrate function is implemented together with the stay-below-colony-size-w decision rule. For w = 3, eusociality is not favored at b = 1.5 (where inclusive fitness predicts it to be neutral [workers giving up 0.5 and adding 0.5 to the queen]) but is favored to evolve at b = 1.6. It is still possible to argue that eusociality is hard to evolve, depending upon one’s standard for what is hard, but it is considerably easier to evolve than implied by the initial Nowak et al. model and, not surprisingly hard relative to inclusive fitness predictions.

5. Incommensurability Exhibited and Transformed

Anthropologists and sociobiologists disagreed over the primacy and autonomy of cultural or biological explanation. Sahlins understands Wilson to argue that “any Durkheimian notion of the independent existence and persistence of the social fact is a lapse into mysticism. Social organization is rather, and nothing more than, the behavioral outcome of the interaction of organisms having biologically fixed inclinations” (Sahlins 1976b, p. 5). By contrast, Sahlins sees the biological character of human beings as entirely “infrastructural,” in the words of Gintis (2010), such that cultural explanation of behavior should proceed without reliance upon the lower level of biological explanation, just as biological explanation should proceed without reliance upon physics. Where Wilson depends upon questionable reductionist assumptions about the relationship between the sciences, Sahlins’ antireductionist understanding of emergent levels denied the significance of interaction between levels.

The belief that certain technical issues have been settled once and for all within scientific research programs leads to jaundiced views of new kinds of arguments that seem to insiders to violate these taboos. The revival of group selection arguments by David Sloan Wilson and Elliott Sober—as also later by E. O. Wilson himself—were interpreted by sociobiologists as a return to the flawed arguments of group selection that inclusive fitness was believed to have routed in the 1960s. This is the case even though they can be viewed as a reinterpretation of the applicability of George Price’s equation, from which Hamilton’s equations can be derived, to the relative balance of individual and group selection, suggesting conditions where group selection may indeed overcome the strength of individual selection (Hamilton 1975 Sober and Wilson 1998, pp. 71–7 for the application to cultural evolution see El Mouden et al. 2014).

Defenders of inclusive fitness theory now deny that group selectionist arguments are mathematically distinct from inclusive fitness theory, as Hamilton’s coefficient of relatedness in his equation for inclusive fitness is understood to include group dispersal processes affecting genetic relatedness within the power of its mathematical expression. For defenders of inclusive fitness orthodoxy, kinship selection, including the calculation of relatedness by the well-known fractions 1/2 and 1/8 for siblings and cousins, were simplifications for well-mixed populations. So-called group selection arguments, as also cultural evolution theory sometimes associated with it, flowed from basic misunderstandings of the power of inclusive fitness theory (West, El Mouden, and Gardner 2011). Critics of inclusive fitness theory returned the favor, arguing that newer approaches had smuggled in tacit group selection in extending Hamilton’s concept of relatedness beyond its original applicability, as well as failing to be accurately subject to empirical testing (Wilson 1998 Nowak, Tarnita, and Wilson 2010 Nowak 2011 Nowak and Allen 2015 see also Sober and Wilson 1998, pp. 31–50, on the “averaging fallacy”).

On the other hand, the new approaches to cultural evolutionary theory of Cavalli-Sforza and Feldman (1981) and Boyd and Richerson (1985) were interpreted by cultural anthropologists as a return to the stage theories of cultural evolution that the Boasian tradition had displaced from primacy in anthropology. The accompanying tendency to develop an interactive approach in terms of “dual inheritance theory” or “gene-culture coevolution” transgressed Sahlins’ strictures against violating the autonomy of hierarchically distinct sciences. Rather than debating whether real biological kinship or constructed, “fictive” kinship shaped behavior, cultural evolutionists saw the biology of kin selection as the “hook” that allowed cultural constructions of kinship to have their effect in organizing cooperation beyond kinship groups. Likewise, the emphasis on the inherent cultural agency of humans, combining themes from Boasian cultural relativism with structuralist emphasis on the arbitrariness of signification, implied that Darwinian explanations, even if cultural rather than genetic, would provide explanations that inappropriately went “behind the backs” of human cultural actors (Webster 1989).

As for the political valence of cultural evolution, one could argue that the failure of the political ferment of the 1960s and 1970s to radically change the world had tempered the voluntarism or radicalism of cultural anthropologists and Marxist evolutionary biologists, while the growth of identity politics in the academy ensured wide opposition to biological reductionism. Or, one might follow Etter, who suggested that the environmentalism of Sahlins and the SSG was “a manifestation of a remarkable and untenable vision of human omnipotence, perhaps linked to particular conditions of economic expansion,” which has now given way to austerity and political reaction (Etter 1978, p. 168). One might also consider the significance of increased levels of interdisciplinary cooperation and co-authorship in science itself for making plausible the thesis that human cooperation is a cultural project that transcends kinship.

Science can be seen to be undergoing a transition akin to the transition from band and tribal groups to modern complex societies and states, as wider social networks and bureaucracy transform small-group, “core set” researchers at a field’s frontier (compare Shapin 1994 and Porter 1996). The theory of cultural evolution is itself one example of this trend, where theoretical schemas get reconfigured and transported across distinct, traditional disciplines, but with the consequence that scientific reputations are no longer adjudicated by “band-level” personal judgments of small core sets on the cutting edge of a well-defined disciplines.

The relationship between biological and fictive kinship can be seen as similar to other ways that genetic and cultural evolution interrelate. Kinship relations are not just cultural “ideas” but relationships that are activated by particular activities and patterns of interaction. Particular forms of cooperation in humans, especially the extended social networks going beyond face-to-face bands, depend much more on bonds created by shared rituals and affinal ties (in-laws) than blood ties (Flannery and Marcus 2012, p. 164). This does not mean that kin-based altruism does not exist, but instead that the genetic system for kin selection is jury-rigged by cultural evolution in adapting to different local contexts.

Consider similar examples where human traits had previously been allocated to distinct spheres as hard-wired biology or cultural software. It is now common to recognize that literacy is a cultural adaptation that rewires the brain in ways that bring real biological differences, evident in brain scans that vary across different languages. The point, however, also extends to spoken language, as languages are studied as culturally-evolved systems that vary dramatically over time and bring about biological effects on the brain independent of genetic evolution (Bolger, Perfetti, and Schneider 2005 Dor 2015 Henrich 2016, ch. 13). In this sense, grammatical forms emerge in the same ways that technical toolkits do, through cultural adaptation to changing environments rather than emerging full-blown as a genetic trait. Instead of focusing on a hard-wired human nature that evolved in evolutionary psychology’s environment of evolutionary adaptedness (EEA), setting constraints on what kind of societies can emerge, the focus is on a genetically evolved capacity for culture that facilitates a different level of rapid and cumulative evolutionary selection.

Neighbor-modulated and inclusive fitness

Inclusive fitness is not the only way to formulate kin selection theory. As Hamilton ( 1964) himself noted, an alternative is to use neighbor-modulated fitness, which is, in some ways, a more intuitive notion. To see the difference between them, consider two viewpoints on what happens when altruism evolves by virtue of relatedness between social partners (figure 1a, 1b). One viewpoint is that relatedness is a source of correlated interaction: When the value of r is high, bearers of the genes for altruism are differentially likely to interact with other bearers and, therefore, to receive the benefits of other agents’ altruism. The upshot is that, a high r value means that bearers of the genes for altruism may have greater reproductive success, on average, than nonbearers. The other is to view relatedness as a source of indirect reproduction: When the value of r is high, recipients provide actors with an indirect means of securing genetic representation in the next generation. Therefore, the genes for altruism may spread, if the indirect representation that an altruist secures through helping its relatives exceeds the representation that it loses through sacrificing a portion of its own reproduction success.

Relatedness leads to correlated interaction. Two altruists (black) confer a fitness benefit (b) on each other at a cost (c) to themselves. As a result, they are fitter overall than two nearby nonaltruists (white). Genetic relatedness can give rise to such patterns of correlated interaction in a population, making altruists fitter (on average) than nonaltruists.

Relatedness leads to correlated interaction. Two altruists (black) confer a fitness benefit (b) on each other at a cost (c) to themselves. As a result, they are fitter overall than two nearby nonaltruists (white). Genetic relatedness can give rise to such patterns of correlated interaction in a population, making altruists fitter (on average) than nonaltruists.

Relatedness leads to indirect reproduction. An altruist (black) confers a fitness benefit (b) on a related recipient (white) at a cost (c) to itself. The recipient does not express the altruistic phenotype. However, it possesses conditionally expressed genes for altruism, which it transmits to some of its offspring (indicated by the dotted lines, which show the genetic similarity between the actor and the recipient's offspring). The recipient thereby provides the actor with a means of indirect reproduction—that is, an indirect route to genetic representation in the next generation.

Relatedness leads to indirect reproduction. An altruist (black) confers a fitness benefit (b) on a related recipient (white) at a cost (c) to itself. The recipient does not express the altruistic phenotype. However, it possesses conditionally expressed genes for altruism, which it transmits to some of its offspring (indicated by the dotted lines, which show the genetic similarity between the actor and the recipient's offspring). The recipient thereby provides the actor with a means of indirect reproduction—that is, an indirect route to genetic representation in the next generation.

The first perspective is captured in the neighbor-modulated fitness framework (figure 2), which looks at the correlations between an individual's genotype and its social neighborhood and helps predict when these correlations will make the bearers of the genes for altruism fitter, on average, than nonbearers (Hamilton 1964, Taylor PD and Frank 1996, Frank 1998, 2013). The second perspective is captured in the inclusive fitness framework (figure 3), which adds up all the fitness effects causally attributable to a social actor, weighting each component by the relatedness between the actor and the recipient, in order to calculate the net effect of a social behavior on the actor's overall genetic representation in the next generation (Hamilton 1964, Frank 1998, 2013, Grafen 2006).

Neighbor-modulated fitness. In a neighbor-modulated fitness analysis, we ascribe to A those fitness components that correspond to its personal reproductive success. Some of these components are influenced by the behavior of B, C, and D (as is shown by the arrows). A's total neighbor-modulated fitness is a simple sum of these components (3b), plus a component corresponding to A's own influence on its reproductive success (–c), plus a baseline component independent of the character of interest.

Neighbor-modulated fitness. In a neighbor-modulated fitness analysis, we ascribe to A those fitness components that correspond to its personal reproductive success. Some of these components are influenced by the behavior of B, C, and D (as is shown by the arrows). A's total neighbor-modulated fitness is a simple sum of these components (3b), plus a component corresponding to A's own influence on its reproductive success (–c), plus a baseline component independent of the character of interest.

Inclusive fitness. In an inclusive fitness analysis, fitness effects are assigned to the actors whose behavior was causally responsible for them. A therefore retains the effect –c for which it responsible but loses the 3b units of personal fitness it received by virtue of its interactions with B, C, and D. In compensation, it gains 3b units taken from the reproductive output of B, C, and D. To calculate A's inclusive fitness, these new slices are weighted by the actor's relatedness to the recipient.

Inclusive fitness. In an inclusive fitness analysis, fitness effects are assigned to the actors whose behavior was causally responsible for them. A therefore retains the effect –c for which it responsible but loses the 3b units of personal fitness it received by virtue of its interactions with B, C, and D. In compensation, it gains 3b units taken from the reproductive output of B, C, and D. To calculate A's inclusive fitness, these new slices are weighted by the actor's relatedness to the recipient.

Although correlated interaction and indirect reproduction may sound like different mechanisms, the inclusive and neighbor-modulated fitness frameworks are usually considered equivalent, because they generally yield identical results about when a social behavior will evolve (Taylor PD et al. 2007). Therefore, the choice is one of modeling convenience, not empirical fact. Hamilton ( 1964) and Maynard Smith ( 1983) both regarded inclusive fitness as easier to apply in practice, but, in recent years, this situation has largely reversed: Kin selection theorists have increasingly come to favor the neighbor-modulated fitness framework, citing its greater simplicity and ease of application (Taylor PD and Frank 1996, Gardner et al. 2007, Taylor PD et al. 2007).

In one respect, the neighbor-modulated approach is more general. To perform an inclusive fitness analysis, we need to be able to attribute each social phenotype to a single controlling genotype (Frank 1998). By contrast, a neighbor-modulated fitness analysis simply ignores the pathway from actor genotypes to social phenotypes, leaving us with one fewer causal path to worry about. A corollary is that the neighbor-modulated framework can apply in cases in which there is no principled way to ascribe a social character to a single controlling genotype. As Frank ( 1998, 2013) noted, cases in which phenotypes are controlled by actors of a species different from that of the recipient—such as host–parasite interactions—arguably fall into this category (but cf. Taylor PD et al. 2007).

The role and rule of relatedness in altruism

Andrew F. G. Bourke is at the School of Biological Sciences, University of East Anglia, Norwich NR4 7TJ, UK.

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Scientists aim to work on important, open problems: their papers and grant proposals tell us so, and, of course, such a focus is entirely proper. But if a field forever declares a problem to be open, it can give the impression that progress is never made. The study of social evolution runs this risk, because many researchers repeatedly assert that how altruism evolved remains an unsolved puzzle. In fact, in the early 1960s, the evolutionary biologist W. D. Hamilton came up with a solution to this ‘problem of altruism’ with his inclusive fitness theory 1 , 2 , which shows that it is possible for altruism to evolve if socially interacting individuals are related. Writing in Proceedings of the National Academy of Sciences, Kay et al. 3 conclude that multiple attempts to find alternatives to Hamilton’s solution have simply rediscovered it.

Biological altruism is defined as any social behaviour between individuals in which an action by an altruistic individual decreases its lifetime direct ‘fitness’ (that is, reduces the number of offspring it has) but increases the lifetime direct fitness of the recipient. By contrast, another type of social behaviour, termed reciprocal altruism, does not qualify as altruism in this sense. Reciprocal altruism occurs when social benefits are exchanged between interacting individuals 4 , and such cooperation evolves only when both partners experience a net gain in lifetime direct fitness 5 .

A prime example of biological altruism is the case of eusocial insects (those that have a worker caste), such as bees (Fig. 1), and in some of these species the workers have lost their ability to reproduce entirely. Such cases encapsulate the problem of altruism. By what means can natural selection, a process based on out-reproducing competitors, lead to self-sacrificial sterility?

Figure 1 | Altruistic insects. Buff-tailed bumblebees (Bombus terrestris) are prime examples of biological altruism. The worker bees reduce their own reproduction to boost that of another individual, the queen (the large bee in the middle of the lower half of the image). Kay et al. 3 assessed papers proposing that altruism can evolve without relatedness, and conclude that the models presented are actually consistent with the long-standing idea 1 that interacting individuals must be related for altruism to evolve. Credit: Andrew Bourke

According to Hamilton 1 , 2 , the answer lies in interacting individuals being positively related, meaning that they are genetically more alike than any individuals associating together randomly within a population. If altruism is directed towards relatives (kin), then, according to inclusive fitness theory, it can evolve by the process of kin selection. Considering this scenario mathematically, Hamilton demonstrated that an individual’s aid to a sister, for example to produce b extra offspring at a cost to the individual of c offspring, can be favoured by selection if the individual’s indirect fitness gain (r × b) through its sister’s extra offspring exceeds its direct fitness loss (c). In this formula, r stands for relatedness and equals the chance of a given gene being shared by the interacting social partners relative to the probability that two randomly selected individuals share the gene.

This condition, known as Hamilton’s rule, is met in examples of altruism observed in nature 6 . Moreover, all cases of eusociality found since Hamilton’s work involve family groups, and there are no known cases of altruism between non-relatives except for unicolonial ants (ants living in populations of merged colonies of a given species) 7 , 8 . However, unicolonial ants descend from species that lived in separate colonies of relatives, and so their altruism originally evolved in those ancestral societies 7 , 8 .

An individual that altruistically aids a non-relative (r = 0) loses direct fitness (c), but generates no compensating gain in indirect fitness (if r = 0, then r × b = 0, whatever the value of b). Hence, Hamilton’s rule shows that altruism directed towards unrelated recipients cannot evolve.

Since Hamilton’s work, the theoretical understanding of kin selection and inclusive fitness theory (which encompasses the social behaviours of selfishness and spite, as well as altruism and cooperation) has been enriched in key ways 2 , 9 . However, inclusive fitness theory has also attracted controversy 2 , 7 , 9 , 10 , one aspect of which concerns a large set of models that were used to claim that altruism can evolve without requiring relatedness. To assess the validity of this conclusion, Kay and colleagues systematically analysed the assumptions underlying these models.

The authors began with a list of 195 leading papers on the evolution of altruism and cooperation (generated from the top results of Google Scholar searches). Of these, 89 studies modelled the evolution of altruism 46 of them attributed altruism to kin selection, whereas 43 did not. Within the set of 43, 17 papers explicitly denied a role for relatedness.

Kay et al. report that, on the basis of their analysis of the life cycles presented, the life cycle of the individuals in each of these 17 models did, in fact, generate positive relatedness, either positive genetic relatedness or its cultural equivalent (arising through individuals imitating one another’s behaviour). Typically, this occurred because the life cycle involved low dispersal of offspring from their birthplace, and interactions happened mainly between neighbours. In such ‘viscous’ populations, as Hamilton recognized 1 , social behaviours will be directed towards relatives, just as would be the case for humans if successive generations of one family filled up each street and people interacted mainly with those living next door.

The authors also assessed the 26 modelling studies that did not invoke kin selection but, rather than explicitly denying a role for relatedness, attributed altruism to other processes. The explanation usually given in these cases was a mechanism described as spatial selection, a term derived from models that again involve altruists or cooperators clustering because of localized interactions under a regime of low dispersal. Kay et al. took a closer look at ten influential studies of this kind and conclude not only that spatial proximity served as the driver of positive relatedness, but also that the models converged on overtly kin-selection-based models because, in successive papers, the assumptions made grew closer to those made in kin-selection-based models.

Evolutionary trees can’t reveal speciation and extinction rates

Kay and colleagues did not attempt the essentially impossible task of reconstructing all the models examined to rerun them using variations of the assumptions or frameworks. The authors’ critique is therefore based on inference and not on new modelling. However, they highlight several previous studies in which deep dives into a subset of the alternative models have demonstrated in detail their compatibility with inclusive fitness theory. Kay et al. therefore conclude that all models purporting to show altruism evolving in the absence of relatedness rather provide a ‘backhanded’ validation that endorses Hamilton’s explanation of altruism. By extension, these models unwittingly provide support for inclusive fitness theory as a whole — beyond just supporting the theory’s insights on the evolution of altruism.

The authors speculate candidly about why modelling studies repeatedly ‘rediscover’ existing results and present them as novel. In drawing lessons from Kay and colleagues’ valuable work, it is therefore instructive to step back and examine the implications for the entire field.

First, partly because of nature’s complexity, evolutionary biology is particularly vulnerable to misplaced claims of novelty 11 . Making such claims on the basis of modelling studies could be avoided if researchers always sought to link their work to existing theory, stated their assumptions explicitly, and avoided over-abstraction to explain the real-life behaviours or traits of organisms, thereby generating testable biological predictions. In this regard, modelling viscous populations remains worthwhile because, as Kay et al. point out, many real-life organisms, notably plants, live in fixed locations and so represent such populations.

Second, some issues remain to be fully resolved in inclusive fitness theory, not least how best to define inclusive fitness 12 . More generally, there are many active research topics in the study of social evolution, such as understanding how social cheating is held in check. Therefore, although previous findings need to be acknowledged, continued exploration of the theory is valuable. Lastly, the theory has nonetheless achieved notable successes, one of which is solving the problem of altruism 3 , 7 , 9 . A legitimate desire to tackle important, open problems should not prevent the field from recognizing this.

Behavioral Ecology behavior and ecology from an evolutionary perspective

It is obvious to any naturalist that animals often appear to behave co-operatively (e.g. lions hunting prey). How, then, can we account for the evolution of co-operative behavior in terms of advantage to the individual? Moreover, how could &ldquoaltruistic&rdquo behavior evolve that seemingly benefited another individual at the expense of the performer (e.g. birds and mammals that give alarm calls to warn their conspecifics or the sterile castes of insects like worker bees)?

Altruism is defined as acting in a way that increases another individual&rsquos lifetime number of offspring at a cost to one&rsquos own survival and reproduction.

Kin Selection

William Hamilton first published his theory of kin selection in 1963 and 1964. The best way to understand the importance of kinship is to take a gene's eye view of evolution and natural selection. For while natural selection acts on individuals (i.e. it is individuals that die or reproduce), it is the genes that are being preserved. The gene is the unit of selection, not individuals. If you look at Natural Selection from this perspective, it opens up the possibility that there could be selection for genes that ensure their own replication even at the expense of the individual.

Thus, through Hamilton's theory of kin selection, the concept of the selfish gene was born. What Hamilton did was to formalize the concept in a way that could be quantified and measured. And like many revolutionary concepts in science, its elegance lay in its simplicity.

Hamilton's formula predicted that selection will favour altruism (i.e. genes for altruistic behaviour will increase in frequency) when:

where
Benefit to the recipient = k
Cost to the actor

and
r = Wright's coefficient of genetic relatedness

Kin Selection in Evolutionary Psychology

Evolutionary psychologists have attempted to explain prosocial behavior through kin selection by stating that “behaviors that help a genetic relative are favored by natural selection.” Human beings have developed a tendency over time to frame and interpret their actions as an avenue to the survival of their genetic material, making kin selection not a completely altruistic form of prosocial behavior and is perhaps better described as a component of social exchange theory. This theory does not necessarily imply that people “compute” genetic benefit when helping others, but there is an indication that those who behave in such a way are more likely to pass on their genes to future generations. [5]

Appendix A

(a) Assortment as regression or correlation

Let g₁ denote the gene in a focal individual and g₂ the gene in its group member (g = 1 for a C individual and g = 0 for a D individual), and let p denote the frequency of the cooperative gene in the entire population. Then the correlation between genes in group members equals Corr(g₁,g₂) = Cov(g₁,g₂)/(σ_g1 σ_g2) = Cov(g₁,g₂)/σ 2 _g, where σ 2 _g = p(1 − p) is the variance of allele frequency among individuals in the entire population. By definition, Cov(g₁,g₂) = E(g₁g₂)–E(g₁)E(g₂), where E denotes expectation. The E(g₁g₂) is obtained as the weighted average over C and D focal individuals, where allele frequency in the focal individual is given by g₁ = 1 for a C individual and g₁ = 0 for a D individual, and allele frequency in the group member is given by g₂ = e_C/(N𠄱) for a C focal individual, and g₂ = e_D/(N–1) for a D focal individual. This gives E(g₁g₂) = p · 1 · e_C/(N𠄱) + (1–p) · 0 · e_D/(N–1) = pe_C/(N𠄱). Furthermore, E(g₁) = E(g₂) = p. However, E(g₂) can also be written as the weighted mean allele frequency in partners of C and D focal individuals, E(g₂) = pe_C/(N𠄱) + (1–p)e_D/(N𠄱). Combining results yields Cov(g₁,g₂) = p(1–p)[(e_C–e_D)/(N𠄱)], so that Corr(g₁,g₂) = (e_C–e_D)/(N𠄱). Because σ_g1 = σ_g2, this is also the regression coefficient of the allele in the partner on the allele in the focal individual (and vice versa). Moreover, (e_C–e_D)/(N𠄱) also equals the correlation between the gene in the focal individual and the benefit experienced by the focal individual, because replacing the gene in the partner by benefit provided by the partner, that is, replacing g₂ = 0 or 1 with g₂ = 0 or b, yields the same result. When interactions are between species, the covariance term remains the same, and the variance of allele frequency among focal individuals equals Var(g₁) = p(1–p), so that (e_C–e_D)/(N𠄱) = Cov(g₁,g₂)/Var(g₁), which is the regression coefficient of the phenotypic type of the partner (i.e. 1 denoting a cooperator or 0 denoting a defector) on the gene in the focal individual.

(b) Variance of mean allele frequency among groups

Mean allele frequency of a group equals . The variance thereof equals . Substituting Cov(g_i, g_j) = rσ_g 2 yields . Hence, is zero when r = 𢄡/(N − 1), and increases with increasing r.

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