Information

Hamilton's inclusive fitness approach


The underlying intuition of Hamilton's model of inclusive fitness is that we should study social behaviors from the point of view of actors -- rather than the recipients. To build his model, Hamilton expresses the genotype of the actor $j$ in terms of the genotype of the recipient of the behavior, $i$. The genotype of $j$ is decomposed in two parts,"genes which are copies by direct replication of genes in $i$; the other part consists of non-replica genes"(Hamilton 1970, p. 1219). Hamilton (1970) further defines $q_{i}$ as the gene frequency of the replica part, $b_{ij}$ represents the replica fraction, and $q$ is the average gene frequency in the population. From these definitions Hamilton (1970) jumps to the equality: egin{equation} E (q_{j}) = frac{1}{1-b_{i}}left{ (b_{ij} - b_{i})q_{i} + (1-b_{ij})q ight} end{equation} where egin{align*} b_{i} = frac{1}{n}sum_{j}b_{ij} end{align*}

How did Hamilton derive the above equation?


Here is what I think Hamilton is doing. My impression is that the above equation expresses $E(q_j | q_i)$ as a linear regression on $q_i$. In other words, I think the above equation is equivalent to:

$E(q_j | q_i) = E(q_j) + eta (q_i - E(q_i))$

$E(q_j | q_i) = q + eta (q_i - q)$

In fact, this equation is equivalent to Hamilton's equation if the regression coefficient is:

$eta = (b_{ij} - b_i) / (1 - b_i)$

However, I haven't been able to derive this regression coefficient. Given that $eta = Cov (q_j, q_i)/Var (q_i)$, I suspect that the way to go is to rewrite $q_j$ and $q_i$ in terms of $b_{ij}$ and $b_i$ and calculate the regression coefficient.


Reference:

Hamilton 1970 "Selfish and Spiteful Behaviour in an Evolutionary Model" http://www.nature.com/nature/journal/v228/n5277/abs/2281218a0.html



It is not a regression (not at this stage of the paper, a regression will be done latter)

The only complicated thing to understand is $b_i$, which is the 'base relatedness', ie how $i$ is related to a random individual (to be compared to how related it is to individuals with whom it interacts).

To simplify let's first consider the situation where $b_i = 0$:

$E(qj) = b_{i,j} q_i + (1-b_{i,j}) q$ is just the translation of 'the gene frequency of the replica part is q_i' and 'the gene frequency of the non replica part is $q$'; because $b_{i,j}$ is the fraction of the replica part, ie the chances that our locus of interest belongs to the replica part of individual $i$ in individual $j$.

Now let's re-introduce $b_i$. The idea is to compare relatedness of the two individuals $i$ and $j$ to the average relatedness of $i$ with a randomly picked individual in the population (this random relatedness is exactly $bi$). This is important because $q$ already accounts for this 'random relatedness'.

So instead of giving probability $b_{i,j}$ to $q_i$, we give it probability $b_{i,j}-b_i$, which is the chance that the allele of interest is present because of the replica fraction being higher than random. And because now the quantity varies between 0 and $1-b_i$ we normalize it by $1-b_i$

The underlying intuition of Hamilton's model of inclusive fitness is that we should study social behaviors from the point of view of actors -- rather than the recipients

Not exactly, it is saying that we should study social behaviors from the point of view of the alleles causing it, that may be shared between the actors and the recipients. But this paper is not the paper that introduces inclusive fitness, quite the opposite it is the paper that tries to reconciliate kin selection with Price equation.


From the limited information, I can provide the following but I am not sure if this is what you are looking for. Also, I still don't see the statement where the author concludes we get the Linear regression model $E(q_i) = Aq_i + C$ which is odd notation since it says the expected value is a linear regression. In fact, if it is a linear regression, it should say $q_j = Aq_i + C$. $$ A = frac{ ext{cov}(q_i,q_j)}{ ext{var}(q_i)}quad ext{and}quad C = E[q_j] - frac{ ext{cov}(q_i,q_j)}{ ext{var}(q_i)}E[q_i]. $$ Now, we can write the variance and covariance as egin{align} ext{var}(q_i) &= E[q_i^2]-E^2[q_i] ext{cov}(q_i,q_j) &= E[q_iq_j]-E[q_i]E[q_j] end{align} where the expected value of a discrete random variable $X$ is calculated as $$ E[X] = sum_{i=1}^Nx_ip_X[x_i] $$ where $p_X[x_i]$ is probability of $x_i$ and $N$ can be countable infinite.


The mean of conditional PDFs comes up in optimal prediction where the minimum mean square error is $E_{Ymid X}[Ymid x]$. This optimal prediction covers linear and nonlinear. For the standard Gaussian PDF, the optimal prediction will be linear since $E_{Ymid X}[Ymid x]= ho x$ where $ ho$ is the correlation coefficient. I am going to short hand $E_{Ymid X}[Ymid x]$ to $E[Ymid x]$ $$ E[Ymid x] = mu_Y + frac{ hosigma_Y}{sigma_X}(x-mu_X) $$ where $mu_i$ $i=X,Y$ is the mean and $sigma_i$ is the standard deviation. If $X$ and $Y$ are not Gaussian, then the model can be nonlinear. Are there examples of non Gaussian be linear probably.


The validity and value of inclusive fitness theory

Social evolution is a central topic in evolutionary biology, with the evolution of eusociality (societies with altruistic, non-reproductive helpers) representing a long-standing evolutionary conundrum. Recent critiques have questioned the validity of the leading theory for explaining social evolution and eusociality, namely inclusive fitness (kin selection) theory. I review recent and past literature to argue that these critiques do not succeed. Inclusive fitness theory has added fundamental insights to natural selection theory. These are the realization that selection on a gene for social behaviour depends on its effects on co-bearers, the explanation of social behaviours as unalike as altruism and selfishness using the same underlying parameters, and the explanation of within-group conflict in terms of non-coinciding inclusive fitness optima. A proposed alternative theory for eusocial evolution assumes mistakenly that workers' interests are subordinate to the queen's, contains no new elements and fails to make novel predictions. The haplodiploidy hypothesis has yet to be rigorously tested and positive relatedness within diploid eusocial societies supports inclusive fitness theory. The theory has made unique, falsifiable predictions that have been confirmed, and its evidence base is extensive and robust. Hence, inclusive fitness theory deserves to keep its position as the leading theory for social evolution.

1. Introduction

Why should cooperation exist in a world of Darwinian competition? Answering this question is one of the great tasks of evolutionary biology. In particular, evolutionary biologists have sought to explain the puzzling existence of eusocial societies. In these, typified by the colonies of eusocial Hymenoptera (ants, bees and wasps) or of termites, some members (workers) are partially or completely sterile and labour altruistically on behalf of their reproductive nest-mates (queens). The problem has been to explain how natural selection, a process based on reproductive success, can bring about societies founded on altruism.

The leading theory in the study of social evolution and eusociality is Hamilton's [1] inclusive fitness theory, also known as kin selection theory. The formal version of inclusive fitness theory is summarized by Hamilton's rule (box 1). Informally, the theory shows that, other things equal, individuals should behave towards others as if they valued their reproduction in proportion to how related they are. Hence the theory shows that altruism can evolve between relatives, because a gene for altruism, by directing aid at individuals likely to bear the same gene, adds extra copies of itself to the population despite the reduced offspring production of its bearer (box 1). Hamilton's rule can be easily modified to apply to non-cooperative forms of social behaviour (box 1). Accordingly, inclusive fitness theory has proved extraordinarily rich, having been used to explain social phenomena in everything from microbes to people (e.g. [6,7]). Moreover, the theory transformed the study of behavioural ecology and evolutionary biology by leading to the gene's-eye or ‘selfish gene’ interpretation of natural selection [8]. Inclusive fitness theory therefore stands as one of the central pillars of modern evolutionary biology. However, like any theory with fundamental claims, it has attracted criticism. Early misunderstandings of the theory were addressed by a number of authors (e.g. [2,9,10]). Nonetheless, subsequently there have been renewed criticisms of the theory. These can conveniently be divided into three sets.

First, studies have presented models of social evolution that, it is argued, represent novel alternatives to inclusive fitness theory (e.g. [11–15]). However, other analyses have challenged the novelty of these models by showing that their results can be derived from inclusive fitness theory itself [3,4,16–20]. Second, a group of authors has criticized both the conceptual robustness of inclusive fitness theory and its empirical applications, especially in the eusocial insects [21–30]. In turn, several responses have argued that these critiques are without foundation and that inclusive fitness theory remains empirically illuminating [5,31–37]. Third, Nowak et al. [38] recently produced a comprehensive critique of inclusive fitness theory that questioned its mathematical basis as well as its explanatory value across all taxa. If the analysis of these authors is correct, then inclusive fitness theory has been a decades-long distraction in the field that is theoretically unsound, unnecessarily focused on genetic relatedness and poorly supported by the empirical evidence. If it is not correct, then the theory has been on the right lines all along and it is the critiques that are shaky. The critique by Nowak et al. [38] has met with both support [39–41] and rebuttal [42–50]. In a response, Nowak et al. [51] maintained their view that ‘Inclusive fitness theory is neither useful nor necessary to explain the evolution of eusociality or other phenomena’.

Box 1. Hamilton's rule.

In this review, I present a defence of inclusive fitness theory. Given the many existing responses to the first two sets of critiques, and the prominence and breadth of the article by Nowak et al. [38], I concentrate on meeting new points in that article. Nowak et al. [38] specifically criticized the mathematical basis and assumptions of inclusive fitness theory. These criticisms have already been met by existing responses, which have shown that inclusive fitness theory has a solid mathematical basis, that its assumptions are not restrictive, that limitations of the theory are shared by other approaches and that the alternative mathematical approaches proposed by Nowak et al. [38] do not substantially extend social evolutionary theory relative to existing theory (summarized in [48–50]). I therefore seek to address the new points of Nowak et al. [38] that have not yet received a full examination.

Note that some confusion in the debate over inclusive fitness theory has arisen because Nowak et al. [38] appear sometimes to use ‘inclusive fitness theory’ to mean the specific approach of modelling social evolution by calculating Hamilton's inclusive fitness itself [1], an approach which has long been recognized as being subject to technical limitations [52–54]. The solution in the field has been to model social evolution by applying Hamilton's rule [52,53] or by employing the so-called ‘direct fitness approach’ in which direct fitness incorporates social effects received by the actor [48,49,54–56]. These are still inclusive fitness approaches because they rely on Hamilton's core insight that selection of genes for social behaviour depends on social effects on genetic co-bearers (see below). Nowak et al. [38] criticized inclusive fitness theory in its general sense as well, for example, by querying the centrality of genetic relatedness in social evolution, by criticizing empirical studies claiming to support the theory and by arguing that the theory's explanation of the origin of eusociality is inadequate. In this review, I use inclusive fitness theory in its general sense, that is, to mean the entire body of theory stemming from the Hamiltonian approach to social evolution. My conclusion is that inclusive fitness theory is robust to recent criticisms and so retains its validity and value.

2. Theoretical aspects of inclusive fitness theory

(a) Fundamental insights of inclusive fitness theory

Nowak et al. [38] argued that inclusive fitness theory provides no additional insights on top of those provided by modelling social evolution using population-genetic, game-theoretic approaches (their ‘standard natural selection theory’). On the contrary, inclusive fitness theory has added three fundamental biological insights that, prior to inclusive fitness theory's development, natural selection theory had failed to recognize. The first is the insight that selection on a gene for a social behaviour depends on the behaviour's effects on the fitness of genetic co-bearers [1,2]. To expand, inclusive fitness theory finds that selection on a gene for social behaviour is determined by the gene's effects not only on the direct fitness of the bearer but also on the direct fitness of other individuals bearing the same gene (co-bearers, usually relatives) affected by the behaviour (box 1). This is the insight that allowed Hamilton [1] to solve the problem of altruism (see below) and that led to the gene's-eye view of adaptive evolution [8]. Effectively, any model of social evolution that relies on this point draws on the insight provided by inclusive fitness theory.

The second insight is that very different social behaviours can be explained by adjusting the signs and magnitudes of the same basic parameters [1,4]. This insight arises via inclusive fitness theory's explanation of the four basic social behaviours (cooperation, altruism, selfishness and spite) as occurring conditional on the signs of the effects of the social behaviour on the direct fitnesses of the social actor and recipient, and on actor–recipient relatedness (box 1). For example, changing these parameters takes us from the prediction that (other things equal) increasing relatedness within social groups promotes altruistic behaviour to the prediction that selfishness is curtailed by relatedness but can occur at any level of cost to non-relatives [1,5,57]. Hence, inclusive fitness theory has elucidated at a profound level the common basis to the different forms of social behaviour.

The third insight of inclusive fitness theory is the demonstration that conflict between members of a society is potentially present if they are unequally related to group offspring, since differential relatedness leads to unequal inclusive fitness optima [1,58]. From this has sprung an understanding of an immense range of kin-selected conflicts, including conflicts within families and eusocial societies (e.g. [59–61]) and intragenomic conflicts that follow the same underlying logic [5,62]. The corollary of this insight is that societies are stable to the extent that the inclusive fitness optima of their members coincide. This in turn provides the rationale for the entire ‘major transitions’ view of evolution, whereby the origin of novel types of group in the history of life (e.g. genomes within cells, multicellular organisms and eusocial societies) can be explained as the result of their previously independent constituent units achieving a coincidence of inclusive fitness optima through grouping [5,63]. From this standpoint, a multicellular organism is a eusocial society of cells in which the members of the society happen to be physically stuck together the more fundamental glue, however, is the clonal relatedness that (barring mutations) gives each somatic cell within the organism a common interest in promoting the production of gametes [5,64].

In sum, inclusive fitness theory is rich in insights, which is why it has guided research on social evolution so fruitfully since its inception. Moreover, the theory's insights are highly unifying, because, as further detailed below (see §3b), they allow a broad range of social behaviours, across many social contexts and taxa, to be understood in the same terms. By contrast, the critiques of inclusive fitness theory offer no insights of corresponding magnitude or range. Nowak et al. [38] proposed that researchers should construct bespoke population-genetic models for each particular social context under study. Such models may indeed prove informative in the context to which they are applied. However, because the exact genetic basis of different social behaviours is likely to vary (and is generally unknown), the sole use of such models would come at a cost to the ability of researchers to discern common selective processes acting across many social contexts, which inclusive fitness theory provides. Even the main model (‘mutation-selection analysis’ in part A of supplementary information) of social evolution of Nowak et al. [38] appears to be of limited generality [49], since it assumed asexual reproduction (most eusocial species reproduce sexually) and offered no general predictions. Finally, Nowak et al. [38] argued that their perspective assumes a ‘gene-centred approach’ that ‘makes inclusive fitness theory unnecessary’. This is puzzling, because entirely lacking from their perspective is the idea, which underpins each of inclusive fitness theory's insights, of the gene as a self-promoting strategist whose evolutionary interests are conditional on the kin class in which it resides (e.g. [8,62]).

(b) The problem of altruism

The problem of altruism is the problem of how reproductive self-sacrifice arises in nature. Simply put, how does natural selection lead to something like a sterile worker ant? As earlier discussed, inclusive fitness theory solved the problem by finding that a gene for altruism can spread if bearers aid relatives and Hamilton's rule is satisfied (box 1).

In their model of the evolution of eusociality, Nowak et al. [38] deduced that the problem of altruism is illusory. They wrote that ‘There is no paradoxical altruism that needs to be explained’ because they assumed that potential workers (daughters of a colony-founding female or queen) are ‘not independent agents’ but rather can be seen ‘as “robots” that are built by the queen’ or the ‘extrasomatic projection of [the queen's] personal genome’. If this claim were correct, then only the queen's interests would need to be addressed and one could conclude that worker altruism is more apparent than real. But it is incorrect, for two reasons. One is that, as has repeatedly been argued in response to previous ‘parental manipulation’ theories of the origin of eusociality [65], the inclusive fitness interests of workers and the mother queen do not coincide, because the two parties are differentially related to group offspring (e.g. [60,66,67]). The second is that worker behaviours such as eating of the queen's eggs [68], egg-laying in response to perceived declines in queen fecundity [69], sex-ratio manipulation by destruction of the queen's offspring [70] and lethal aggression towards the queen [71] all demonstrate that workers can act in their own interests and against those of the queen. In the light of this proven lack of worker passivity, workers' reproductive self-sacrifice is paradoxical at first sight and this is the genuine problem of altruism that inclusive fitness theory has solved.

(c) Alternative theory of eusocial evolution

Nowak et al. [38] presented an ‘alternative theory of eusocial evolution’ (as alluded to in §2b), backed up by a ‘mathematical model for the origin of eusociality’. However, these do not represent true alternative theories, either alone or in combination, because they do not make any points or predictions that have not been made within inclusive fitness theory.

Take first the alternative theory of eusocial evolution [38]. This suggested that there have been five critical steps in the evolution of insect eusociality: (i) individuals group around some common resource, typified by a defensible nest close to sources of food (ii) various pre-adaptations such as progressive provisioning (parental feeding of developing larvae) then ‘spring-load’ the group for becoming eusocial should this be favoured by selection (iii) ‘eusocial alleles’ arise that provide the genetic basis for eusocial evolution, a process that could involve nothing more complex than a single mutation that silences offspring dispersal if environmental factors favour the origin of eusociality, selection acts on these genes and eusociality originates (iv) emergent traits of the colony, arising from the interactions of its members, become subject to selection, with the roles of queens and workers being flexible expressions of the same genotypes and (v) between-colony selection, as one component of a system of multi-level selection, drives elaborations of the life cycle and caste structure of the eusocial society.

These steps constitute a reasonable scenario for the origin and elaboration of insect eusociality, but neither the sequence of steps nor the individual elements differ substantially from those that have been proposed to occur within the inclusive fitness framework (e.g. [67,72–74]). As regards the sequence of steps, almost all models of eusocial evolution assume a population of solitary individuals as a starting point, with non-dispersal then being favoured for some set of ecological reasons, and with other processes, including between-colony competition, then bringing about an increase in social complexity in established eusocial lineages (e.g. [73,75]). As regards the individual elements, in inclusive fitness theory, both the nest and the mode of provisioning have long been recognized as furnishing important pre-adaptations for social life. The nest facilitates the maintenance of relatedness and increases the benefits to would-be altruists of not dispersing (e.g. [65,76,77]). Progressive provisioning provides an opportunity for complex social interactions between parent and offspring [72,78]. In addition, a mutation at a single locus leading to non-dispersal of offspring is a standard assumption in models of the origin of eusociality within inclusive fitness theory [66]. Conditional expression of helping is exactly what inclusive fitness theory leads one to expect [67,77]. Benefits of division of labour stemming from the presence of multiple group members have previously been recognized as integral to the success of incipient eusocial societies (e.g. [79]). Finally, the between-colony selection that acts upon group-beneficial, emergent traits can be viewed with equal validity either as a component of multi-level selection, as Nowak et al. [38] suggested, or as selection on the benefit term (b) in Hamilton's rule [67].

Take now the supporting mathematical model for the origin of eusociality proposed (in part C of the supplementary information) by Nowak et al. [38]. This is a model for the origin of eusociality by non-dispersal of young, first assuming asexual reproduction and then assuming sexual reproduction in a haplodiploid population (i.e. one in which males are haploid and are produced from unfertilized eggs, as in the Hymenoptera). The model concludes that eusociality is favoured if the presence of workers boosts the queen's fecundity and survivorship. This is not a new prediction [42,43,49]. It is true that the model specifies that a greater than sevenfold increase in the queen's birth rate is required for the origin of eusociality. But this quantitative finding arises from the numerical values assumed for the model's parameters in various runs. It is not shown to be a necessary feature of eusocial evolution. The main prediction is not new because Hamilton's rule also finds that eusociality in mother–daughter associations originates when workers rear offspring of the queen additional to those she would have had alone (b > c) [80]. This can occur only through workers increasing the queen's fecundity or survivorship. Indeed, quantitative estimates of the terms in Hamilton's rule in facultatively eusocial bees and wasps have already documented the fulfilment of Hamilton's rule in precisely this way (e.g. [5,79,81]).

The alternative theory of eusocial evolution of Nowak et al. [38] also exhibits two important weaknesses. To begin with, by allowing groups to form in multiple ways in step (i) (e.g. subsocially through parent–offspring associations but also by any other means, including ‘randomly by mutual local attraction’), their scenario ignores two critical points that are inconsistent with it but consistent with inclusive fitness theory [42,43,46]. First, the evidence is that, in almost all eusocial lineages, eusociality has originated in social groups that were ancestrally subsocial and therefore characterized by high within-group relatedness [35,73]. Second, the evidence is that the origin of obligate or complex eusociality, defined as involving adult workers irreversibly committed to a worker phenotype, is associated with ancestral lifetime parental monogamy and hence, again, with predictably high within-group relatedness [35,80,82].

The other weakness is that one of the model's conclusions is poorly supported. Nowak et al. [38,51] argued that their finding that a large increase in the queen's birth rate is required for the origin of eusociality helps explain why it is hard for eusociality to evolve. Setting aside the point (above) that the quantitative conclusions of the model in Nowak et al. [38] stem from its numerical assumptions, I suggest that in fact the origin of eusociality is not a particularly rare event. Summing the number of eusocial origins across taxa conventionally defined as eusocial returns at least 24 independent origins of eusociality [5,83], or over double that number if one includes cooperatively breeding vertebrates [5]. The number of origins of complex eusociality from simple eusociality is smaller [5]. But the argument of Nowak et al. [38] that eusociality is rare and hence that the conditions required for it to originate are particularly stringent is weakly founded. The conditions required for the origin of eusociality are at least six times less stringent than those required for the origin of powered flight, which is a highly successful trait and yet has arisen independently only four times [84].

In sum, Nowak et al. [38] make a case for considering the effect of the population-dynamic context in which eusocial evolution occurs. But their alternative theory and its associated model add no fundamentally new elements on top of those identified within the inclusive fitness framework and, relative to this framework, exhibit substantial shortcomings.

3. Empirical aspects of inclusive fitness theory

(a) Status of the haplodiploidy hypothesis

The haplodiploidy hypothesis is the idea that the relatedness asymmetries caused by haplodiploid sex determination facilitate the origin of eusociality in haplodiploid species [1,85]. Nowak et al. [38] argued that the hypothesis has failed because eusociality has increasingly been found to occur in diploid species, which shows that ‘The association between haplodiploidy and eusociality fell below statistical significance’. They concluded that this serves to weaken inclusive fitness theory. However, the haplodiploidy hypothesis has not failed in the sense that it has been tested and falsified (the source of the ‘statistical significance’ to which Nowak et al. [38] allude is therefore unclear). Instead, a rigorous test has not been conducted. Such a test would require a phylogenetically corrected comparative analysis of the association of eusociality and systems of sex determination, which in turn would require a robust and detailed (e.g. family-level) phylogeny encompassing the entire pool of diploid and haplodiploid clades in which eusociality has and has not originated. No such phylogeny exists, and empirical analyses of the haplodiploidy hypothesis have therefore used approximate methods (e.g. [34]). Furthermore, even if such a phylogeny were constructed, the problem would remain that, with the exception of the haplodiploid eusocial thrips, all haplodiploid eusocial lineages lie within the aculeate Hymenoptera, which would mean that other aculeate features might confound effects of haplodiploidy [9,67]. Hence, the haplodiploidy hypothesis remains in limbo—hard to test, untested, arguably unhelpful, but not falsified.

More fundamentally, as has long been recognized [9,85] and repeatedly stressed (e.g. [67,77]), the haplodiploidy hypothesis is not an essential component of inclusive fitness theory, since Hamilton's rule for altruism can hold without the relatedness asymmetries caused by haplodiploidy being present. Highlighting the status of the haplodiploidy hypothesis to criticize inclusive fitness theory therefore misses the target. It also overlooks the fact that all diploid eusocial societies identified since the haplodiploidy hypothesis was proposed have turned out to be either clonal or family groups and so, as predicted by inclusive fitness theory (box 1), to exhibit positive relatedness. This is true of ambrosia beetle, social aphids, polyembryonic wasps, social shrimps and mole-rats [5]. It is even true of a newly discovered eusocial flatworm [86]. In short, the diploid eusocial societies, far from weakening inclusive fitness theory, serve to strengthen it.

(b) Evidence for inclusive fitness theory

In their critique of inclusive fitness theory, Nowak et al. [38] described the contribution of the theory to the empirical understanding of social evolution as ‘meagre’, suggested that research within the inclusive fitness framework has become an ‘abstract enterprise’, and characterized the evidence for the theory as weak. None of these points is the case: a wealth of studies, of a large variety of specific social phenomena in many taxa, have been directly stimulated by the theory and confirm the theory's predictions (table 1). Nowak et al. [38] also stipulated that to test the theory ‘one has to perform an inclusive fitness type calculation for the scenario that is being considered and then measure each quantity that appears in the inclusive fitness formula’. In fact, researchers have successfully tested the theory without measuring all factors [5]. For example, predicted effects of relatedness on social traits have been successfully tested either comparatively, with the assumption that unmeasured factors do not covary with the trait of interest, or experimentally, so that unmeasured factors are randomized across treatments through the experimental design [5]. Transitions from solitary to social living have also been tested in a phylogenetic context, with the finding that, as predicted, high within-group relatedness is associated with the origin of eusociality and cooperative breeding [35,87,101]. None of these approaches is unique to inclusive fitness theory they are standard methods of testing theory in evolutionary biology as a whole.

Table 1. Social phenomena that provide evidence for inclusive fitness theory.

Contrary to Nowak et al. [38], many of inclusive fitness theory's successful predictions are unique to the theory. For example, the theory uniquely predicted patterns of sex investment ratios and the distribution of male parentage between queens and workers in eusocial Hymenoptera [60,77,91,92,96]. It also uniquely predicted the finding in cooperatively breeding birds that helpers provide aid with higher frequency or to a greater extent when they are more closely related to the group aided [102–104]. More broadly, the theory uniquely predicts the absence of altruism (involving lifetime costs to direct fitness) between non-relatives, and indeed no such cases have been found except in systems clearly derived from ancestral societies of relatives [105].

Finally, inclusive fitness theory is unique in the range of social phenomena that it has successfully elucidated, including phenomena as superficially dissimilar as the origin of multicellularity and the origin of eusociality, or intragenomic conflicts and conflicts within eusocial societies (table 1). Overall, no other theory comes close to matching inclusive fitness theory's record of successful explanation and prediction across such a range of phenomena within the field of social evolution [42,44,46]. The challenge to any approach purporting to replace inclusive fitness theory is to explain the same phenomena without using the insights or concepts of the theory.

4. Conclusion

Recent critiques of inclusive fitness theory have proved ineffective on multiple fronts. They do not demonstrate fatal or unrecognized difficulties with inclusive fitness theory. They do not provide a distinct replacement theory or offer a similarly unifying approach. They do not explain previously unexplained data or show that explanations from inclusive fitness theory are invalid. And they do not make new and unique predictions [5]. The latest and most comprehensive critique of inclusive fitness theory [38], though broad-ranging in the scope of its criticism, suffers from the same faults. Certainly, relatedness does not explain all variation in social traits [106]. In addition, the long-standing message from inclusive fitness theory is that particular combinations of non-genetic (e.g. ecological) and genetic factors are required for the origin of eusociality (e.g. [5,76,77,85]). Nonetheless, relatedness retains a unique status in the analysis of eusocial evolution because no amount of ecological benefit can bring about altruism if relatedness is zero [1,5]. Additional theoretical explorations of the connections between, and limitations of, inclusive fitness theory and other modelling approaches should prove informative [49]. It is here, and in further empirical investigations of social phenomena, that the common ground between the critics and supporters of inclusive fitness theory is likely to be found [5]. But known limitations of the theory should not be allowed to obscure its penetrating insights, its elucidation of the role of relatedness in social evolution or its many empirical successes. Inclusive fitness theory retains its validity and value and hence deserves to keep its position as the leading theory for social evolution.


GENETIC SIMILARITY IN HOMO SAPIENS

The existence of evolved mechanisms for assessing genetic relatedness is less well known and more controversial in humans. When Hamilton (1971) applied his theory to H. sapiens, he showed that genetic relatedness, r, equated to Wright's (1951),FST measure of within-group variance (typically r ∼ 2FST). Citing an experimental study of a semi-isolated group of mice in which even random mating produced an FST of 0.18, or r = 0.31, Hamilton concluded that the within-group mice should treat ‘the average individual encountered as a relative closer than a grandchild (or half sib) but more distant than an offspring (or full sib), referring to an outbred population’ (p. 77). He extrapolated the finding to human population groups and deduced that co-operation between ‘non-kin’ would facilitate the growth of male coalitions and make warfare ‘a natural development from the evolutionary trends taking place in the hominid stock’ (p. 79). Subsequently, Hamilton (1975) made it explicit that altruism could result from any degree of genetic relatedness. He wrote, ‘Because of the way it was first explained’, the approach using inclusive fitness has often been identified with ‘kin selection’ … as a way of establishing altruistic behaviour by natural selection. But … kinship should be considered just one way of getting positive regression of genotype in the recipient, and that it is this positive regression that is vitally necessary for altruism. Thus the inclusive-fitness concept is more general than ‘kin-selection’ (pp. 140–141).

Applying Hamilton's theory to human dyads, small groups, and even larger ones, Rushton, Russell & Wells (1984 Rushton, 1989a) dubbed their application ‘genetic similarity theory’. They proposed that people maximize their inclusive fitness by marrying others similar to themselves, making friends with and helping the most similar of their neighbours, and engaging in ethnic nepotism. As the English language makes plain, ‘likeness goes with liking’. Although kin-selection theory sensu stricto does not explain positive assortative mating because individuals seldom mate with ‘kin’, the literature shows that spouses and close friends are highly similar, most on sociodemographic variables such as age, ethnicity, and educational level (r = 0.60), next most on opinions and attitudes (r = 0.50), then on cognitive ability (r = 0.40), and least, but still significantly, on personality (r = 0.20) and physical traits (r = 0.20). But, as Thiessen & Gregg (1980) asked, is the assortment due to genetic mediation, to shared upbringing, or to other environmental effects? Does it vary positively or inversely with the heritability of its components?

OPTIMAL OUTBREEDING AND BLOOD GROUP STUDIES

One study found women prefer the bodily scents of men with genes somewhat similar to their own, and not those of men with nearly identical genes or with genes totally dissimilar to their own ( Jacob et al., 2002). Each woman's choice was based on the human leukocyte antigen (HLA) (i.e. the basis for personal odors and olfactory preferences) inherited from her father, but not her mother. In a study of 1000 sexually-interacting couples of north European appearance (judged by photographs), those who produced a child together were 52% similar with respect to ten blood groups [ABO, Rhesus (Rh), MNSs, Kell, Duffy (Fy), Kidd (Jk), and HLA], whereas those who did not produce a child were only 43% similar ( Rushton, 1988). On the same blood loci and from the same population, pairs of close male friends were significantly more similar to each other than were randomly matched pairs from the same sample ( Rushton, 1989b). Such blood group differences are sufficient to identify more than 95% of true relatedness in paternity disputes. A significant positive association between kinship and fertility was found by Helgason et al. (2008) in a study of all known couples of the Icelandic population born between 1800 and 1965, with the greatest reproductive success being found in couples related at the level of third and fourth cousins.

TWIN AND ADOPTION STUDIES

Twin and adoption studies demonstrate a moderate to strong genetic contribution to people's tendency to socially assort and match phenotypes. Heritabilities can be calculated from the comparison of monozygotic (MZ) twin pairs, who share 100% of their genes, and dizygotic (DZ) twin pairs, who share 50% of their genes. For example, Rowe & Osgood (1984) analysed several hundred adolescent MZ and DZ twins and found those genetically inclined to delinquency were also genetically inclined to seek out similar others as friends. The association between friendship and delinquency was 60% heritable. Iervolino et al. (2002) examined several hundred pairs of siblings from adoptive-, step-, and twin-families and found that MZ twins had more similar friends than DZ twins who had more similar friends than step- and adoptive-siblings (i.e. who share only environments). Averaged across measures, the genes accounted for 40% of the variance.

Rushton & Bons (2005) studied several hundred MZ and DZ twin pairs along with their spouses and best friends on questionnaires measuring personality traits and social attitudes. They found: (1) friends and spouses were approximately as similar as siblings (r = 0.25), a level of similarity not previously recognized and (2) MZ twins chose more similar friends and spouses to their co-twin than did DZ twins. The heritability of the preference for similarity in social assortment ranged from 17% to 35% for spouse–spouse, friend–friend, and spouse–friend comparisons and, when corrected for attenuation due to measurement unreliability, 34% for all relationships. Guo (2006) found that with measures made of cognitive ability and personality, friends of MZ twins were significantly more similar to each other (r = 0.47) than were the friends of DZ twins (r = 0.26) or other full siblings, who in turn were more similar to each other than were random pairs from the same sample (r = 0.03). These results indicated a heritability of approximately 50%. In a study of 1800 twins, Kendler et al. (2007) found genetic influence on choice of peer-group increased with age, rising from 30% at 8–11 years to 50% at 15–25 years.

PHENOTYPE MATCHING STUDIES

Hamilton (1971: p. 77) noted that more heritable components within multifarious traits better reflect the underlying genotype. In line with Hamilton's prediction, research finds that social assortment is more pronounced on the more heritable components measured within sets of homogeneous anthropometric, cognitive, and social characteristics. For example, Russell, Wells & Rushton (1985), in a study of married couples, found that, across 36 physical traits, spousal similarity was greater on attributes with higher heritability such as wrist circumference (71% heritable) than on attributes with lower heritability such as neck circumference (48% heritable). On 54 indices of personality and leisure time pursuits, Rushton & Russell (1985) found that spousal similarity was greater on items with higher heritability such as ‘enjoying reading’ (41% heritable) than on items with lower heritability such as ‘having many hobbies’ (20% heritable). On 26 cognitive ability tests, Rushton & Nicholson (1988) found that spousal resemblance was greater on the more heritable subtests from the Wechsler Adult Intelligence Scale and the Hawaii Family Study of Cognition. When spouses assort on more heritable items, they report greater marital satisfaction ( Russell & Wells, 1991).

In a study of close friends, Rushton (1989b) found similarity was greater on the more heritable items across a wide range of anthropometric and social attitude measures, such as agreement with ‘military drill’ (40% heritable) and ‘church authority’ (25% heritable). In an experimental study of liking in acquaintances, Tesser (1993) manipulated people's beliefs about how similar they were to others on attitudes pre-selected as being either high or low in heritability. He found that people liked others more when their similarity had been chosen (by him) on the more heritable items. In a twin study by Rushton & Bons (2005), the phenotype matching for both spouses and close friends was again on the more heritable items.

BEREAVEMENT STUDIES

A study of 263 child bereavements found that: (1) spouses agreed 74% of the time on which side of the family a child ‘took after’ the most, their own or that of their spouse, and (2) the grief intensity reported by mothers, fathers, and grandparents was greater for children who resembled their side of the family than for children resembling the other side of the family ( Littlefield & Rushton, 1986). A study of bereavement in twins found that MZ twins, compared to DZ twins: (1) work harder for their co-twin (2) show more physical proximity to their co-twin (3) express more affection to their co-twin and (4) show greater loss when their co-twin dies ( Segal, 2000).

STUDIES OF FACE PREFERENCES

Several studies have found that people rate faces as more attractive when they resemble their own. Platek et al. (2002) morphed people's faces with those of toddlers and asked questions such as ‘Which one of these children would you like to spend time with?’ and ‘Which child would you adopt?’ People responded more positively toward children's faces that had been morphed with their own. During debriefing, the participants expressed surprise that any morphing had occurred. DeBruine (2002) found people trusted a stranger's face more when it had been morphed with their own than when it was left unchanged. Familiarity was ruled out by using morphs of celebrities only self-resemblance mattered.

Bereczkei, Gyuris & Weisfeld (2004) found similarity in the faces of spouses and opposite-sex adoptive parents, a result they attributed to sexual imprinting. DeBruine (2005) found that, although self-similarity of opposite-sex faces increased ratings of trustworthiness, it had no effect on ratings of attractiveness for a long-term partner and a negative effect on attractiveness for a short-term partner. When DeBruine et al. (2008) reviewed the literature, she concluded it remained unclear whether self-similarity was important in promoting mate choice, although it undoubtedly influenced trust and positive attributions. Functional magnetic resonance imaging studies are beginning to demonstrate the neural correlates associated with viewing kin and facial self-resemblance ( Platek, Krill & Kemp, 2008). The results suggest that the detection of resemblance is occurring below the level of conscious awareness ( Platek & Thomson, 2007).

ETHNIC NEPOTISM

The pull of genetic similarity does not stop at family and friends. Malat & Hamilton (2006) found that people prefer same-race health providers and perceive them as more trustworthy. Putnam (2004) found that the more ethnically diverse a community, the less likely its inhabitants are to trust others, from next-door neighbours to local governments.

Inclusive fitness theory has been used to explain why members of ethnic groups move into the same neighbourhoods, join together in clubs and societies, and are prone to develop ethnocentric attitudes toward those who differ in dress, dialect, and other appearance. For example, van den Berghe (1981) found that even relatively open and assimilative groups ‘police’ their boundaries against invasion by strangers using cultural ‘badges’ to mark group membership, such as scarification, linguistic accent, and clothing style. Irwin (1987) calculated coefficients of consanguinity within and between Eskimo tribes in the Hudson's Bay region of Canada and found prosocial behaviour such as wife exchange and anti-social behaviour such as the genocidal killing during warfare followed lines of genetic distance, albeit mediated by ethnic badging such as dialect and appearance.

Harpending (1979, 2006) analysed kinship within human populations. Via the equation r ∼ 2 FST, he found that compared to the total world genetic variance, random members of any one population are related r ∼ 0.25. He wrote, ‘Since FST among human populations on a world scale is reliably 10 to 15 percent, kinship between two individuals of the same population is equivalent to kinship between grandparents and grandchildren or between half siblings’ (2006, p. 327). Subsequently, Salter (2006) calculated genetic relatedness between populations using Cavalli-Sforza, Menozzi & Piazza's (1994: 75) compendium of genetic distances and showed that, if the world population were wholly English, then kinship between any two random English people would be (obviously) zero. However, if the world consisted of only English people and Danes, then two random English people (or Danes) with an FST of 0.0021 would have a kinship of 0.004 and be like 1/32 of a cousin. Two English people become the equivalent of 3/8 cousin by comparison with people from the Near East 1/2 cousins by comparison with people from India half-siblings by comparison with people from China and like full-siblings compared with people from sub-Saharan Africa (where the FST is 0.23). Because people have many more co-ethnics than relatives, the aggregate of genes shared with co-ethnics dwarfs those shared with extended families. Rather than being a poor relation of family nepotism, ethnic nepotism is virtually a proxy for it.


Homogeneous population

where is population-wide average fitness. Some simplifying assumptions are needed for this, notably that meiosis is ‘fair’, that on average there is no change in allele frequency in transmission from parent to offspring.

At this point it is worth mentioning Queller's (1992) paper which shows that if fitness W is regressed directly on genotypic value (of an individual and neighbours), we get a simple general form of inclusive or direct fitness without the many assumptions needed to make phenotypic arguments work. This elegant result is mainly of theoretical interest, as we typically get hold of the partial regressions by using phenotype as an intermediate variable. ( Queller's, 1992 discussion of the role of phenotype was to some extent foreshadowed by Cheverud, 1984 .)

Direct fitness

with everything evaluated at . Here P is the phenotypic value of the focal individual and Rk is the relatedness of the kth actor (or the type k actor depending on the setup) to the focal recipient. Provided cov(G,P) > 0 (which can always be arranged), Wdir will have the same sign as the change in average allele frequency.

Inclusive fitness

where Rk is the relatedness of the focal actor to the kth recipient (or to the type k recipient depending on the setup).

Notice that although Rk appears to be differently defined in eqns (4) and (5) the difference between formulae is purely technical and derives from the re-indexing. If we take these effects to be the fitness derivatives from eqn (2): dwk = ∂W/∂Pk, then eqns (4) and (5) are equivalent. However, the formulae are thought of in different ways. The terms of the direct fitness effect (eqn 4) are effects of the behaviour of others on the fitness of the focal individual the terms of the inclusive fitness effect (5) are the effects of the behaviour of the focal individual on the fitness of others.

An example of cooperation between patchmates

where R0 = 1 is the relatedness of the actor to itself, R1 is the relatedness between offspring native to the same patch and R2 is the relatedness of the actor to the competitively displaced individuals.

Notice that our original description of the model used an inclusive fitness format – specifying the effects of the behaviour. This is typically the most natural way to present a model, and it also guides our intuition and our reasoning. This accounts in large part for the popularity of the inclusive fitness paradigm.

and we see that this is the same as the inclusive fitness effect.

However, note that the terms of eqns (7) and (9), are interpreted in a different way. The terms of the inclusive fitness (eqn 7) are the fitness effects on all individuals (weighted by relatedness) of a single interaction. The terms of the direct fitness (eqn 9) are the fitness effects on a single individual of all interactions (again weighted by relatedness). This leads to a different analysis of the two last terms, the competitive effects. In eqn (7) the dispersal effect (1 − d) 2 , is counted as a component of the relatedness term (although there are other ways to do the analysis) whereas in eqn (9) this is counted as a component of the fitness effect (see also Gardner & West, 2006 ).


A class-structured population

Reproductive value

With this normalization, cj can be interpreted as the probability that the ancestor (today) of an allele selected at random in a distant future generation resides in class j. To interpret vj = cj/uj we begin by choosing a random class j individual today and ask for the probability that the ancestor (today) of an allele selected at random in a distant future generation belongs to that particular individual. Then the vj are proportional to these probabilities.

With this definition, eqn (11) shows that in the neutral population average class j fitness is vj. We point out that different treatments of direct fitness normalize fitness in different ways, for example average class j neutral fitness is set equal to vj (as here) in Taylor (1990) but set equal to 1 in Taylor & Frank (1996) . These different normalizations will lead to different multiplicative constants in the equations and this can cause confusion. We are convinced that the most natural definition of fitness in this general context is eqn (12) and hence average class j fitness is normalized at vj. However, for completeness we will provide the version of our final direct fitness formula for fitness normalized to 1 (see eqn 18, below).

We suppose that the actors belong to a single class. That seems a reasonable assumption, as actors belonging to different classes are apt to be doing different things or at least to find themselves in different circumstances, and can often be treated separately ( Pen & Taylor, 2005 Wild & Taylor, 2005 ). However, the recipients will generally live in several classes and our formulation will group them by class.

Price's formula

An interesting observation is that in a neutral population, will not change no matter how the mutant allele is distributed among the classes ( Taylor, 1990 , eqn 9 cites an observation of Uyenoyama for this).

where Gj and Wj are the genotype and fitness of a random class j individual (fitness normalized so that neutral fitness is vj) and uj is the class frequency. If you are wondering what happened to the denominator of average fitness (found in eqn 1) it is essentially found in the uj multiplier. Use the fact that average class j fitness is vj together with eqn (10) that ∑jujvj = 1.

Direct fitness

Inclusive fitness

A class-structured example

Now suppose the mutant allele causes a juvenile to behave cooperatively by giving benefit b to a neighbouring adult at cost c (e.g. a helping behaviour). The problem is to find conditions on b and c for this behaviour to be adaptive and to increase in frequency. Again we take phenotypic value P to represent the probability of cooperating, with as the resident value.

Inclusive fitness

Direct fitness

Interactions between species

In a homogeneous population all individuals can play the role of both actor and recipient. In a class-structured population there will typically be individuals who are recipients but not actors. In this case, inclusive fitness, which is actor centred, and direct fitness, which is recipient centred, provide equivalent modelling approaches. Are there examples of individuals who are actors but not recipients? If so, a direct fitness approach should work well, but inclusive fitness is problematic. The reason is simple – inclusive fitness works with one focal actor and it requires this actor to behave in a deviant manner. But this deviation needs to come from an altered genotype (as the whole point is to track allele frequency change) and if the actor is not a recipient it would not have a genotype. Direct fitness solves this problem by having at least two types of actor, one of which has a genotype and can also play the role of recipient. This observation seems to have been first made in Queller (1992) .

Here, we discuss a simple example of an interaction between species, similar to an example of Frank (1997) , which illustrates the issue. Suppose a parasite inhabits a host and the host carries a locus, which determines the level of ‘cooperative’ behaviour towards the parasite. Cooperation exacts a fitness cost for the host but elicits a response from the parasite (e.g. reduced virulence), which enhances the fitness of the host. There are different ways through which this response might work, perhaps a plastic reaction, perhaps, if the parasite has a relatively short generation time, a genetic change. We are interested in tracking the cooperative behaviour of the host.

Let W be the host fitness, let G and P be the host genotype and phenotype, and let P1 be the parasite phenotype. Our assumptions above are that P1 depends on P (i.e. the response of the parasite to the host) and W depends on both P and P1.


Abrams, P. A., Matsuda, H. and Harada, Y. 1993. Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol. Ecol.7: 465–487.

Bulmer, M. G. 1986. Sex ratio theory in geographically structured populations, Heredity56: 69–73.

Charlesworth, B. 1980a. Models of kin selection. In: Evolution of Social Behaviour: Hypotheses and Empirical Tests, (ed. H. Markl), Verlag Chemie, Weinheim.

Charlesworth, B. 1980b. Evolution in age-structured populations. Cambridge Studies in Mathematical Biology, Cambridge Univ. Press

Charnov, E. L. 1977. An elementary treatment of the genetical theory of kin selection, J. Theor. Biol.66: 541–550

Christiansen, F. B. 1991. On conditions for evolutionary stability for a continuously varying character, Amer. Nat.138: 37–50

Crow J. F. and Kimura M. 1970. An Introduction to Population Genetics Theory, New York: Harper and Row

Eshel, I. 1983. Evolutionary and continuous stability, J. Theor. Biol.103, 99–111

Eshel, I, and Motro, U. 1981. Kin selection and strong evolutionary stability of mutual help, Theor. Pop. Biol.19, 420–433

Forsyth, A. 1981. Sex ratio and parental investment in an ant population. Evolution36: 1252–1253

Frank, S. A. 1986. Hierarchical selection theory and sex ratios. I. General solutions for structured populations, Theor. Pop. Biol.29: 312–342

Grafen, A. 1984. Natural, kin and group selection, in Behavioural Ecology, An Evolutionary Approach (J. R. Krebs and N. B. Davies, eds) 62–84. Sinauer

Grafen, A. 1985a. A geometric view of relatedness, Oxford Surveys in Evolutionary Biology2: 28–89

Grafen, A. 1985b. Hamilton's rule OK, Nature318: 310–311

Hamilton, W. D. 1964. The genetical evolution of social behaviour, I and II, J. Theor. Biol.7: 1–52

Hamilton, W. D. 1970. Selfish and spiteful behaviour in an evolutionary model, Nature (Lond.)228: 1218–1220

Hamilton, W. D. 1972. Altruism and related phenomena, mainly in social insects, Ann. Rev. Ecol. Syst.3: 192–232

Hamilton, W. D. 1975. Innate social aptitudes of man: an approach from evolutionary biology. In: Biosocial Anthropology (R. Fox, ed.) pp 133–155. New York: John Wiley and sons

Iwasa, Y. 1981. Role of sex ratio in the evolution of eusociality in haplodiploid social insects, J. theor. Biol.93: 125–142

Jacquard, A. 1974. The Genetic Structure of Populations (trans. D. and B. Charlesworth) Biomathematics Series 5, Springer, New York

Leslie, P. H. 1948. Some further remarks on the use of matrices in population mathematics, Biometrika35: 213–245

Maynard Smith, J. 1974. The theory of games and the evolution of animal conflicts, J. theor. Biol.47: 209–221

Maynard Smith, J. and Price, G. R., 1973. The logic of animal conflict. Nature246: 15–18

Metz, J. A. J., R. M. Nisbet and Geritz, S. A. H. 1992. How should we define ‘fitness’ for general ecological scenarios? TREE7:198–202

Michod, R. E. and Hamilton, W. D. 1980. Coefficients, of relatedness in sociobiology, Nature288: 694–697

Pamilo, P. and Crozier, R. H. 1982. Measuring genetic relatedness in natural populations: methodology. Theor. Pop. Biol.21: 171–193

Price, G. R. 1970. Selection and covariance, Nature227: 520–521

Queller, D. C. 1985. Kinship, reciprocity and synergism in the evolution of social behaviour, Nature318: 366–367

Seger, J. 1981. Kinship and covariance, J. theor. Biol.91: 191–213

Taylor, P. D. 1981. Sex ratio compensation in ant populations. Evolution35: 1250–1251

Taylor, P. D. 1988a. An inclusive fitness model for dispersal of offspring, J. theor. Biol.130: 363–378

Taylor, P. D. 1988b. Inclusive fitness models with two sexes. Theor. Pop. Biol.34: 145–168

Taylor, P. D. 1989. Evolutionary stability in one-parameter models under weak selection, Theor. Pop. Biol.36: 125–143

Taylor, P. D. 1990. Allele frequency change in a class-structured population, American Naturalist135: 95–106

Taylor, P. D. and Getz, W. M. 1994. An inclusive fitness model for the evolutionary advantage of sib-mating. Evol. Ecol. 8: 61–69

Taylor, P. D. and Frank, S. A. 1996. How to make a kin selection model. J. theor. Biol. (in press)

van Tienderen, P. H. and De Jong, D. 1986. Sex ratio under the haystack model: polymorphism may occur. J. theor. Biol.122: 69–81


RB > C

Let me sum up: The &ldquor&rdquo means the &ldquocoefficient of relatedness,&rdquo or the degree to which two individuals are related to each other. You and a clone of yourself would have an &ldquor&rdquo of 1, since your genes would be fully identical. But your coefficient of relatedness with a non-twin sibling is roughly .5, because about half of any genes in your genome are from the same parent. The coefficient of relatedness drops off fast your &ldquor&rdquo with a first cousin is only .125, for example.

The &ldquoB&rdquo refers to benefit &ndash specifically, the benefit to the relative who&rsquos receiving an altruistic boon. For example, let&rsquos say that you rush into a fiery house to save your sibling, and this boosts your sibling&rsquos chances of having children from zero &ndash dead people don&rsquot have children &ndash to, say, 60%. This means that the &ldquoB&rdquo value would be pretty high!

In contrast, the &ldquoC&rdquo refers to the &ldquocost&rdquo to the organism who gives the help. Let&rsquos say that you get burned while saving your sibling. This reduces your probable lifetime fitness, because it&rsquos harder to get a mate and good jobs with a scarred face. The &ldquoC&rdquo in Hamilton&rsquos Rule quantifies this damage to your lifetime fitness.

Hamilton postulated that the only time organisms could evolve costly, sacrificial behavior would be when the partners are closely related enough, and the increase in beneficiaries&rsquo fitness is great enough, to override the costs of the sacrifice to the benefactors. For example, Hamilton&rsquos Rule predicts that ants will be closely related enough to their queen that their giving up reproduction will actually pay off genetically in the long term &ndash since the little ant eggs they&rsquore raising carry enough of their own genes to make up for their sacrifice.

Hamilton&rsquos Rule and inclusive fitness theory were the uncontested champions in the struggle to explain costly altruism in biology for nearly a half-century. But in the past decade, a number of scientists have been challenging inclusive fitness, often &ndash but not always &ndash on mathematical grounds. This is where the PNAS paper comes in.

To (over)simplify things, Ben, Nowak, and Wilson argue that inclusive fitness theory depends too heavily on linear regression models to explain how genetic relatedness affects evolution. Regression analysis is a statistical technique that identifies the different factors influencing an observed outcome. For example, let&rsquos say that students from the west side of your town are 30% more likely to attend college than kids from the east side. A regression analysis finds that several different factors combine to predict this difference: for example, the west side is wealthier than the east side there are more native English speakers on the west side and college recruiters visit west side high schools more often than east side schools. Together, these factors add up to explain the higher college attendance rate on the west side.

Similarly, evolutionary biologists have long been in the habit of using linear regression models to separate organisms&rsquo genetic fitness into components. For example, 50% of an organism&rsquos total genetic fitness might be due to the offspring it raises itself, and 25% due to the offspring its siblings help it raise, and 12% to the offspring its cousins help it raise. The authors of the PNAS paper argue, roughly, that this is an unhelpful way of modeling genetic fitness. To quote Ben&rsquos blog post on the paper:

At this point you may be asking &ldquoWait, does it really make sense to divide offspring into those produced on one&rsquos own versus those produced by help from others?&rdquo This is exactly the problem! Aside from the obvious point that no one reproduces without help in sexual species, nature is full of synergistic and nonlinear interactions, so that making clean divisions like this is impossible in most situations. Thus the idea of inclusive fitness theory only works in simplified toy models of reality.

So, Ben and the other authors claim, the inclusive fitness model is just not close enough to reality to be useful. The second major problem with the mathematics behind inclusive fitness theory, they argue, is that such mathematics can &ndash and does! &ndash lead researchers to make false attributions of causality when only correlations are evident. The paper offers some elucidating hypothetical examples, including the &ldquohanger-on:&rdquo an organism that has a gene which drives it to find high-fitness individuals and hang out with them. The hanger-on doesn&rsquot get any extra fitness benefit from palling around with its high-fitness peers, but an observer looking at the long-term population data would always find that individuals with the &ldquohanger-on&rdquo gene were found closely associated with individuals who had lots of offspring. An inclusive fitness analysis would conclude that the &ldquohanger-on&rdquo gene was actually a helping gene &ndash one that inspired individuals to sacrifice their own well-being in order to help nearby partners raise their own offspring. Of course, this would be exactly the wrong explanation: the hanger-on doesn&rsquot cause the high-fitness partner to have offspring. The high-fitness parter causes the hanger-on to glom on.

These and related arguments lead the authors of the PNAS paper to conclude that the right way to investigate the evolution of altruism is using old-fashioned Darwinian techniques based on natural selection models. Inclusive fitness, the authors argue, requires too many assumptions to work, doesn&rsquot make good predictions or offer explanations, and is too general to be applied to any real circumstances.

Now, what does all of this have to do with religion? Surprisingly, a lot. The main opponents of inclusive fitness theory have tended to be proponents of various sorts of group selection &ndash a broad term that generally refers to the ability of Darwinian processes to operate not only at the level of the gene, but also at the collective. For example, let&rsquos say two tribes occupy the same valley, but one of them has a preponderance of genes that encourage costly cooperation within the group. Over generations, the tribe whose members cooperate better with one another slowly take over and push out the other tribe. The costly-cooperation gene hurts the individuals who carry it within their own groups (since they&rsquore always sacrificing their own well-being to help their fellows), but helps the group as a whole (since the group functions better if it has lots of members who are willing to sacrifice for one another). The result? Over time, the costly-cooperation gene comes to dominate the valley, even though it imposes fitness costs on the individuals who have it.

Several writers, including Martin Nowak and David Sloan Wilson, have suggested that group selection might be a better explanation for the evolution of morality than inclusive fitness. This might seem plausible to an educated outsider, but there&rsquos a problem: many of these writers also use group selection to argue for the evolutionary utility of religion. In his 2002 book Darwin&rsquos Cathedral, for example, D.S. Wilson argued that religion overwhelmingly helps groups survive, and that religious practices and beliefs &ndash as well as the costly altruism they encourage &ndash have evolved by group selection.

On the other side of the equation, the proponents of inclusive fitness theory have tended to be among the most vociferous critics of religion writing today. Steven Pinker, Richard Dawkins, Jerry Coyne, and Daniel Dennett are all on record as being strongly pro-inclusive fitness and very much opposed to group selection theories. There are both personal and professional commitments on the line here to pick an example, Hamilton&rsquos memorial service in 2000 was organized by Richard Dawkins.

Now, I&rsquom not claiming that Richard Dawkins&rsquos personal friendship with and admiration for W.D. Hamilton means that Dawkins&rsquos support for inclusive fitness is automatically suspect. I happen to personally side with the religious adaptationists &ndash those who argue that religious phenomena are dedicated adaptations &ndash but I&rsquom not convinced that group selection is the way to get there. And there is evidence that inclusive fitness theory works very well in some situations for example, in explaining why red squirrels adopt some orphaned babies but not others (hint: they don&rsquot adopt babies whose &ldquor&rdquo coefficient doesn&rsquot meet the predictions of Hamilton&rsquos Rule).

The authors of the PNAS paper, including my buddy Ben, wouldn&rsquot contest the squirrel finding they freely admit that sometimes inclusive fitness theory works. Instead, they argue that it&rsquos simply not a universally generalizable rule. They have some very good points, and I think they&rsquore probably right. But what I&rsquom most interested in is how the debates around group selection illustrate how scientific and ideological commitments entwine and influence one another, no matter what the textbooks say. It is not coincidence that the ranks of the anti-group selectionists are a who&rsquos who of the New Atheists. It&rsquos also not coincidence that the group selection advocates tend to argue for religion&rsquos adaptive value.

And finally, it&rsquos not a failure of science that researchers&rsquo ideological and theoretical commitments are sometimes aligned people have to get their convictions from somewhere. If Daniel Dennett, say, believes that group selection is bunk because he&rsquos afraid that group selection will prove that religion is adaptive rather than a worthless &ndash or harmful! &ndash byproduct, I think that&rsquos great. Research and debate will eventually prove whether he&rsquos right or wrong, regardless of where his commitments come from. This is one of science&rsquos most admirable, and valuable, traits: hypotheses and predictions can come from anywhere, and testing and observation will eventually separate the wheat from the chaff. Ben&rsquos paper in PNAS is just one more fine example of how this winnowing process works.


Author information

Affiliations

Vanderbilt University, Nashville, 37235, Tennessee, USA

Laboratory of Applied Entomology, Faculty of Agriculture, Shizuoka University, Sizuoka 422-8529, Japan

School of Life Sciences, PO Box 874501, Arizona State University, Tempe, 85287-4501, Arizona, USA

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Samuel Alizon & Yannis Michalakis

Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, UK

Joao A. C. Alpedrinha, Jay M. Biernaskie, Sam Brown, Angus Buckling, Max N. Burton-Chellew, Claire El Mouden, Kevin Foster, Andy Gardner, Alan Grafen, Paul H. Harvey, Natalie Jiricny, Alex Kacelnik, Lorenzo Santorelli & Stuart A. West

Department of Zoology, University of Gothenburg, SE 405 30 Gothenburg, Sweden

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Jean-Baptiste Andre, Minus van Baalen & Thibaud Monnin

Department of Infectious Disease Epidemiology, MRC Centre for Outbreak Analysis and Modelling, Faculty of Medicine, Imperial College, St Mary’s Campus, Norfolk Place, London W2 1PG, UK

Department of Psychology, Neuroscience and Behaviour, McMaster University, 1280 Main St West, Hamilton, Ontario L8S 4K1, Canada

IST Austria, Am Campus 1, Klosterneuburg 3400, Austria

Evolutionary Genetics, Centre for Ecological and Evolutionary Studies, University of Groningen, PO Box 14, NL-9750 AA Haren, The Netherlands

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Department of Biology, University of Maryland, College Park, 20742-4415, Maryland, USA

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Redouan Bshary & Laurent Lehmann

Department of Ecology and Evolutionary Biology, University of California, 321 Steinhaus Hall, Irvine, 92697-2525, California, USA

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Michael A. Cant, Sasha R. X. Dall, Allen J. Moore & Andrew J. Young

Department of Ecology and Evolution, Biophore, University of Lausanne, 1015 Lausanne, Switzerland

Department of Biology, 167 Castetter Hall, MSC03 2020, 1 University of New Mexico, Albuquerque, 87131-000, New Mexico, USA

Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK

Tim Clutton-Brock, William A. Foster & Rufus A. Johnstone

Evolution, Ecology and Genetics, Research School of Biology, Australian National University, Canberra, ACT 0200, Australia

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Department of Biology and Biochemistry, University of Houston, Houston, 77204-5001, Texas, USA

Blaine J. Cole & Diane C. Wiernasz

Institutes of Evolution, Immunology and Infection Research, School of Biological Sciences, Ashworth Laboratories, University of Edinburgh, Edinburgh EH9 3JT, UK

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Department of Psychology, University of California, Santa Barbara, Santa Barbara, 93106-9660, California, USA

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USDA-ARS Bee Research Laboratory, BARC-E Bldg 476, Beltsville, 20705, Maryland, USA

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Department Biologie II Behavioral Ecology (Verhaltensökologie), Ludwig-Maximilians-Universität, München Großhaderner Str. 2 D - 82152 Planegg/Martinsried, Germany

Department of Entomology, University of Kentucky, Lexington, 40546-0091, Kentucky, USA

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CEFE - UMR 5175, 1919 route de Mende, F-34293 Montpellier Cedex 5, France

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Michael G. Gardner & Michael P. Schwarz

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Center for Pollinator Research, Huck Institutes of the Life Sciences, Pennsylvania State University, Chemical Ecology Lab 4A, University Park, 16802, Pennsylvania, USA

Muséum National d’Histoire Naturelle, CP39, 12 rue Buffon, 75005 Paris, France

Biology Department, University of Toronto, 3359 Mississauga Road, Mississauga, Ontario L5L 1C6, Canada

Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK

Biologie I, Universität Regensburg, D-93040 Regensburg, Germany

Department of Biosciences, PL 65 (Viikinkaari 1), FI-00014 University of Helsinki, Finland

Heikki Helantera & Liselotte Sundström

Department of Biology, University of Vermont, Burlington, 05405, Vermont, USA

School of Human Evolution and Social Change, Arizona State University, Tempe, 85287-2402, Arizona, USA

Department of Animal Ecology, Institute of Ecological Science, Faculty of Earth and Life Sciences, Vrije Universiteit, De Boelelaan 1085, NL-1081 HV Amsterdam, The Netherlands

Animal Ecology Group, Centre for Evolutionary and Ecological Studies, University of Groningen, PO Box 14, 9750 AA Haren, The Netherlands

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Environmental Microbiology, Swiss Federal Institute of Aquatic Research and Technology, Überlandstrasse 133, CH-8600 Dübendorf, Switzerland

Department of Biology, Centre for Social Evolution, University of Copenhagen, Universitetsparken 15, DK-2100 Copenhagen, Denmark

Timothy A. Linksvayer & Jes S. Pedersen

School of Biological Sciences, Royal Holloway, University of London, Egham TW20 0EX, UK

Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, 95064, California, USA

Department of Computer Science, University of Sheffield, Sheffield S1 4DP, UK

Department of Anthropology and Center for Population Biology, UC Davis, Davis, 95616, California, USA

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Department of Zoology, 730 Van Vleet Oval, University of Oklahoma, Norman, 73019, Oklahoma, USA

Department of Biology, Queen’s University, Kingston, Ontario K7L 3N6, Canada

Integrative Biology, University of Texas at Austin, 1 University Station C0930, Austin, 78712, Texas, USA

Psychologie — Université de Strasbourg, Ethologie des Primates — DEPE (IPHC CNRS UMR 7178), 23 rue Becquerel — Strasbourg 67087, Cedex, France

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David C. Queller & Jeff Smith

Department of Biochemistry, University of Zurich, Building Y27, Office J-46, Winterthurstrasse 190, CH-8057 Zurich, Switzerland

Swiss Institute of Bioinformatics, Quartier Sorge Bâtiment Génopode, CH- 1015 Lausanne, Switzerland

Research Department of Genetics, Evolution and Environment, Faculty of Life Sciences, University College London, 4 Stephenson Way, London NW1 2HE, UK

Centre for Behaviour and Evolution, Institute of Neuroscience, Faculty of Medical Sciences, Newcastle University, Henry Wellcome Building, Framlington Place, Newcastle upon Tyne NE2 4HH, UK

School of Marine and Tropical Biology, James Cook University, Queensland 4811, Australia

Station Biologique de Roscoff, CNRS-UPMC UMR 7144, 29680 Roscoff, France

Institut des Sciences de l’Evolution, University of Montpellier 2, Montpellier 34095, France

Department of Biology, University of North Carolina at Greensboro, 312 Eberhart Building, Greensboro, 27403, North Carolina, USA

Department of Biology, 3314 Spieth Hall, University of California — Riverside, Riverside, 92521, California, USA

ETH Zurich, Institute of Integrative Biology (IBZ), Universitätsstrasse 16, CH.8092 Zürich, Switzerland

School of Philosophy, Psychology and Language Sciences, University of Edinburgh, 3 Charles Street, Edinburgh EH8 9AD, UK

School of Biology, University of St Andrews, Harold Mitchell Building, St Andrews, Fife KY16 9TH, UK

William Paterson University of New Jersey, 300 Pompton Road, Wayne, 07470, New Jersey, USA

Department of Anthropology, 101 West Hall, University of Michigan, Ann Arbor, 48109, Michigan, USA

Department of Entomology and Department of Animal Biology, University of Illinois, Urbana, 61801, Illinois, USA

Behavioural Ecology, Institute of Ecology and Evolution, University of Bern, Wohlenstrasse 50a, CH-3032 Hinterkappelen, Switzerland

Department of Biology, University of Western Ontario, 1151 Richmond Street North, London, Ontario N6A 5B7, Canada

Department of Anthropology, University of California, Santa Barbara, 93106-3210, California, USA

Deptartment of Environmental Science, Policy and Management, 130 Mulford Hall, 3114, University of California Berkeley, Berkeley, 94720-3114, California, USA

Faculty of Agriculture, University of the Ryukyus, Okinawa 903-0213, Japan

Dipartimento di Biologia Evoluzionistica, Università degli Studi di Firenze, via Romana 17, 50125 Firenze, Italy

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Department of Entomology, Box 7613, North Carolina State University, Raleigh, 27695-7613, North Carolina, USA

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Department of Applied Mathematics, University of Western Ontario, 1151 Richmond Street North, London, Ontario N6A 5B7, Canada

Department of Human Evolutionary Biology, Harvard University, Cambridge, 02138, Massachusetts, USA

Department of Biology and Program in Ecology, Evolution and Conservation Biology, University of Nevada, Reno, 89557, Nevada, USA

David W. Zeh & Jeanne A. Zeh

Department of Biology, San Francisco State University, San Francisco, 94132, California, USA

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Contributions

All authors contributed to the planning, writing and/or revising of this paper. Several others who contributed significantly are not listed because they are named on separate comments.


Did a scientific battle about altruism just end?

Inclusive fitness was originally developed to explain eusociality, a extreme form of altruism found in social insects, where non-reproducing colony members give up their right to reproduce and devote their lives to caring for the offspring of a single reproducing member. Above, a leaf cutter ant. (Credit: Yonatan Munk/Flickr)

You are free to share this article under the Attribution 4.0 International license.

Scientific controversies don’t often end up in the New Yorker, but a 2012 article described a tempest over a biology theory.

The tempest got started with a study in the August 26, 2010 issue of Nature. Written by Harvard mathematicians Martin A. Nowak and Corina E. Tarnita and Harvard biologist Edward O. Wilson, it questions the validity of the theory of inclusive fitness.

Inclusive fitness theory, proposed by British biologist W. D. Hamilton in 1964, expanded Darwin’s definition of “fitness”—an organism’s success in passing on its genes—to include the genes of its relatives. This expansion made altruism in the service of kin a competitive strategy.

The Nature article, titled “The Evolution of Eusociality,” asserts that inclusive fitness theory, which has been a cornerstone of evolutionary biology for the past 50 years, had produced only “meagre” results and that mathematical models based on standard natural selection theory provide a “simpler and superior approach.”

This provoked a prolonged argument among evolutionary biologists that’s still going. But in a new PLOS Biology study, evolutionary biologist David C. Queller of Washington University in St. Louis suggests a way out of the impasse.

Queller, a professor in the biology department, and his coauthors adopted the model the Harvard writers had proposed as an alternative to inclusive fitness and tested it to see whether it supported the claims the authors made in the Nature paper.

“They had a modeling strategy that should work and should be fine, but they weren’t careful enough when they made claims about their models’ novel results,” Queller says. But he also argued that the two mathematical models are essentially equivalent in that they ultimately predict the same results.

Eusocial insects, for example

Inclusive fitness was originally developed to explain eusociality, a extreme form of altruism found in social insects, where non-reproducing colony members give up their right to reproduce and devote their lives to caring for the offspring of a single reproducing member.

Hamilton’s inclusive fitness theory was invented to solve this paradox, which vexed even Darwin. Hamilton calculated that sterile castes could evolve if altruistic sterility sufficiently benefited relatives also carrying the altruistic gene.

Kin selection and inclusive fitness quickly became the dominant mode of thinking about the evolution of eusocial insects and their success in this area led to their application to many other problems in social evolution.

But the Harvard authors’ article asserts that while “empirical research on eusocial organisms has flourished, revealing rich details of caste, communication, colony life cycles, and other phenomena…almost none of this progress has been stimulated or advanced by inclusive fitness theory, which has evolved into an abstract enterprise largely on its own.”

Queller saw nothing wrong with the mathematical models the Harvard authors proposed in Nature but was puzzled by some of the assertions they made.

“I went through their paper trying to pull out conclusions that appeared to be different from the conclusions you get from inclusiveness theory,” he says. “He settled on three claims, which he then tried to prove by running ‘experiments’ with the Harvard-style models.”

How does eusociality evolve?

In inclusive fitness theory, relatedness is essential to the evolution of eusociality. But the Harvard paper claims it is a consequence of eusociality rather than a cause. “Once eusociality has evolved, colonies consist of related individuals because daughters stay with their mothers to raise further offspring,” write its authors.

“Although they said relatedness was not important, in their mathematical models they didn’t actually vary relatedness,” Queller says. “To test their claim we allowed some mixing between the offspring of different mothers before the offspring decided to stay with the colony to help her or to abandon her and leave,” he says.

“When you ‘lower’ relatedness,” he says, “it makes eusociality hard to evolve, and if you make it zero, you never get eusociality. So varying relatedness in their model takes us back to what we thought we already knew from inclusive fitness theory.”

Are colony workers ‘robots’?

“It follows from inclusive fitness theory is that unless all members of a colony are genetically identical, there will be a region of the benefit/cost space where the queen and workers are in conflict,” Queller says. What’s good for the inclusive fitness of one may not be good for the inclusive fitness of the other.”

But the Harvard authors write that “the queen and her workers are not engaged in a standard cooperative dilemma.” The workers, they write, are “robots,” built by the queen as part of her reproductive strategy rather than independent agents.

But, Queller says, they tested only “offspring control models” (models where the decision to stay with the colony or to leave was controlled by genes expressed by workers). To check for conflict Queller compared models with offspring agency to ones with maternal agency (where the decision to stay to help is controlled by genes expressed by the queen).

As predicted by inclusive fitness theory, he says, the two cases evolve quite differently, and mothers benefit from stay-at-home offspring under conditions where offspring would be better off leaving.

“So as inclusive fitness theory predicts, you get regions of conflict where the queen would like her workers to stay but the workers want to leave. The mathematics says they’re not robots,” Queller says.

How hard is it to evolve eusociality?

Finally, the Harvard authors write, their model shows that it was very difficult for a solitary species to evolve to become eusocial despite the intuitive advantages of cooperation among members of a group.

This claim is less fundamental than the two others, Queller says, and it is true that eusociality has evolved only 10 or 20 times in the course of evolution.

“But we also showed that this result hinged on heavily biased assumptions,” Quellers says. “We showed that modifying either the fitness function in their model or the worker decision rule made it easier to achieve eusociality. ”

“So the essence of my paper,” Queller says, “is that there really isn’t much disagreement. The things we thought were important from inclusive fitness theory show up as important in their models as well.”

Fully aware of the irony of a fight over selflessness, he hopes his assertion that the dueling models are essentially equivalent will help resolve the debate.

Stephen Rong, who graduated from Washington University with a bachelor’s degree in math and is now a graduate student at Brown University, and Xiaoyun Liao, a former research assistant at Rice University with expertise in mathematical modeling, are Queller’s coauthors.


Social Evolution and Inclusive Fitness Theory: An Introduction

Social behavior has long puzzled evolutionary biologists, since the classical theory of natural selection maintains that individuals should not sacrifice their own fitness to affect that of others. This book argues that a theory first presented in 1963 by William D. Hamilton—inclusive fitness theory—provides the most fundamental and general explanation for the evolution and maintenance of social behaviors in the natural world. The book guides readers through the vast and confusing literature on the evolution of social behavior, introducing and explaining the competing theories that claim to pr . More

Social behavior has long puzzled evolutionary biologists, since the classical theory of natural selection maintains that individuals should not sacrifice their own fitness to affect that of others. This book argues that a theory first presented in 1963 by William D. Hamilton—inclusive fitness theory—provides the most fundamental and general explanation for the evolution and maintenance of social behaviors in the natural world. The book guides readers through the vast and confusing literature on the evolution of social behavior, introducing and explaining the competing theories that claim to provide answers to questions such as why animals evolve to behave altruistically. Using simple statistical language and techniques that practicing biologists will be familiar with, the book provides a comprehensive yet easily understandable treatment of key concepts and their repeated misinterpretations. Particular attention is paid to how more realistic features of behavior, such as nonadditivity and conditionality, can complicate analysis. The book highlights the general problem of identifying the underlying causes of evolutionary change, and proposes fruitful approaches to doing so in the study of social evolution. It describes how inclusive fitness theory addresses both simple and complex social scenarios, the controversies surrounding the theory, and how experimental work supports the theory as the most powerful explanation for social behavior and its evolution.


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