An inclusive fitness model for the evolutionary advantage of sibmating

Summary We construct an inclusive fitness model of the relative selective advantage of sibmating and outbreeding behaviour, under the assumption that inbred offspring pay a fitness penalty. We are particularly interested in the question of whether such inbreeding depression is enough to generate a stable phenotypic polymorphism, with both kinds of breeding observed. The model predicts that, under diploidy, such a polymorphism is never found, but under haplodiploidy, it exists for a narrow range of parameter values. The inclusive fitness argument is technically interesting because care must be taken with reproductive values. We also present a corrected version of a one-locus genetic model for sibmating and find that the inclusive fitness and genetic models give identical results when selection is weak.     

Unifying the theories of inclusive fitness and reciprocal altruism

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

Sibling solidarity in a polygamous community in the USA: unpacking inclusive fitness

This pilot study explores the degree of solidarity felt between full and half siblings who are raised in a Mormon Fundamentalist polygamous community. The community under study is unique in that, at the level of official culture, it actively promotes full and half sibling solidarity through an ethos that strives to downplay genetic differences in favor of a harmonious family living together in one household. This community is an ideal cultural setting in which to examine the suitability of inclusive fitness theory for understanding the factors that promote family cohesion, sibling solidarity, and rivalry. Our main question becomes: is the degree of sibling solidarity a manifestation of genetic closeness or a natural byproduct of emotional closeness that arises from being raised together? We found evidence for more solidarity between full siblings than between half siblings. Our data suggest that, despite the force of religious ideals, and notwithstanding the continued close physical proximity of half siblings in the polygamous family, there is a pronounced clustering of feeling and affection in the polygamous family that is consistent with inclusive fitness theory.     

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.     

An inclusive fitness analysis of altruism on a cyclical network

A recent model studies the evolution of cooperation on a network, and concludes with a result connecting the benefits and costs of interactions and the number of neighbours. Here, an inclusive fitness analysis is conducted of the only case solved analytically, of a cycle, and the identical result is obtained. This brings the result within a biologically familiar framework. It is notable that the benefits and costs in the inclusive fitness framework need to be derived, and are not the benefits and costs that are the parameters in the original model. The relatedness is a quadratic function of position in a cycle of size N: an individual is related by 1 to itself, by (N - 5)/(N + 1) to an immediate neighbour, and by very close to -1/2 to the most distant individuals. The inclusive fitness analysis explains hitherto puzzling features of the results.     

Extending the range of additivity in using inclusive fitness

Inclusive fitness is a concept widely utilized by social biologists as the quantity organisms appear designed to maximize. However, inclusive fitness theory has long been criticized on the (uncontested) grounds that other quantities, such as offspring number, predict gene frequency changes accurately in a wider range of mathematical models. Here, we articulate a set of modeling assumptions that extend the range of scenarios in which inclusive fitness can be applied. We reanalyze recent formal analyses that searched for, but did not find, inclusive fitness maximization. We show (a) that previous models have not used Hamilton''s definition of inclusive fitness, (b) a reinterpretation of Hamilton''s definition that makes it usable in this context, and (c) that under the assumption of probabilistic mixing of phenotypes, inclusive fitness is indeed maximized in these models. We also show how to understand mathematically, and at an individual level, the definition of inclusive fitness, in an explicit population genetic model in which exact additivity is not assumed. We hope that in articulating these modeling assumptions and providing formal support for inclusive fitness maximization, we help bridge the gap between empiricists and theoreticians, which in some ways has been widening, demonstrating to mathematicians why biologists are content to use inclusive fitness, and offering one way to utilize inclusive fitness in general models of social behavior.     

Nepotistic nosiness: inclusive fitness and vigilance of kin members' romantic relationships

The logic of inclusive fitness suggests that people should be attentive to the mating relationships of their kin—especially their genetically closest kin. This logic further suggests that people will be especially attentive to close kin members' relationships when a greater indirect fitness benefit is at stake. Three studies tested implications of this analysis. The primary results were that (a) people maintain greater vigilance over (and attempt greater influence on) the romantic relationships of genetically closer kin; (b) this effect is largely mediated by feelings of emotional closeness and perceptions of physical similarity; (c) women are more vigilant than men over their kin members' relationships; (d) people are more vigilant over the relationships of female kin, as compared to male kin, but only under conditions with especially clear implications for indirect fitness; and (e) people are more vigilant over kin members' long-term committed relationships, as compared to their casual relationships. These results indicate that a subtle form of nepotism is manifest in people's concern with their kin members' romantic relationships.     

The sociobiology of sex: inclusive fitness consequences of inter-sexual interactions

The diversity of social interactions between sexual partners has long captivated biologists, and its evolution has been interpreted largely in terms of 'direct fitness' pay-offs to partners and their descendants. Inter-sexual interactions also have 'indirect effects' by affecting the fitness of relatives, with important consequences for inclusive fitness. However, inclusive fitness arguments have received limited consideration in this context, and definitions of 'direct' and 'indirect' fitness effects in this field are often inconsistent with those of inclusive fitness theory. Here, we use a sociobiology approach based on inclusive fitness theory to distinguish between direct and indirect fitness effects. We first consider direct effects: we review how competition leads to sexual conflict, and discuss the conditions under which repression of competition fosters sexual mutualism. We then clarify indirect effects, and show that greenbeard effects, kin recognition and population viscosity can all lead to episodes of indirect selection on sexual interactions creating potential for sexual altruism and spite. We argue that the integration of direct and indirect fitness effects within a sociobiology approach enables us to consider a more diverse spectrum of evolutionary outcomes of sexual interactions, and may help resolving current debates over sexual selection and sexual conflict.     

On the relation of family structured models and inclusive fitness models for kin selection

The concept of inclusive fitness plays a key role in much of sociobiology. Yet most theoretical studies concerning the evolution of social behavior circumvent inclusive fitness by mobilizing the concept of frequencydependent individual fitness. Given certain assumptions, it is shown that models based on these two different concepts are dynamically equivalent. The models do differ, however, in bookkeeping methods which are advantageous under different circumstances. A knowledge of these circumstances should prove of value to students of social behavior.     

Hamilton goes empirical: estimation of inclusive fitness from life-history data

Hamilton's theory of kin selection is one of the most important advances in evolutionary biology since Darwin. Central to the kin-selection theory is the concept of inclusive fitness. However, despite the importance of inclusive fitness in evolutionary theory, empirical estimation of inclusive fitness has remained an elusive task. Using the concept of individual fitness, I present a method for estimating inclusive fitness and its components for diploid organisms with age-structured life histories. The method presented here: (i) allows empirical estimation of inclusive fitness from life-history data; (ii) simultaneously considers all components of fitness, including timing and magnitude of reproduction; (iii) is consistent with Hamilton's definition of inclusive fitness; and (iv) adequately addresses shortcomings of existing methods of estimating inclusive fitness. I also demonstrate the application of this new method for testing Hamilton's rule.     

An inclusive fitness model for the sex ratio in a partially sibmating population with inbreeding cost

Summary We construct an inclusive fitness model to find the evolutionarily stable sex ratios in a partially sibmating diploid or haplodiploid population. We assume a constant rate of sibmating with inbred offspring incurring a fitness penalty which, under haplodiploidy, is only suffered by females. We construct a one-locus genetic model for the same problem and observe that when selection is weak it gives the same numerical results as the inclusive fitness model.     

Group size determined by fusion and fission A mathematical modelling with inclusive fitness

We consider a mathematical model for the group size determination by the intra-reactions, self-growth, ostracism and fission within a group, and by the inter-reactions, immigration and fusion between two groups. In some group reactions, a conflict between two groups occurs about the reaction to change the group size. We construct a mathematical model to consider such conflict, taking into account the inclusive fitness of members in each group. In the conflict about the fusion between two groups, our analysis shows that the smaller group wants to fuse, while the larger does not. Also the criterion to resolve the conflict is discussed, and some numerical examples are given, too. It is concluded that, depending on the deviation in the total cost paid for the conflict by counterparts, the group reactions could result in a terminal group size different from that reached only by a sequence of outsider's immigrations into a group.     

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

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

The evolution of helping and harming on graphs: the return of the inclusive fitness effect

Evolutionary graph theory has been proposed as providing new fundamental rules for the evolution of co‐operation and altruism. But how do these results relate to those of inclusive fitness theory? Here, we carry out a retrospective analysis of the models for the evolution of helping on graphs of Ohtsuki et al. [Nature (2006) 441, 502] and Ohtsuki & Nowak [Proc. R. Soc. Lond. Ser. B Biol. Sci (2006) 273, 2249]. We show that it is possible to translate evolutionary graph theory models into classical kin selection models without disturbing at all the mathematics describing the net effect of selection on helping. Model analysis further demonstrates that costly helping evolves on graphs through limited dispersal and overlapping generations. These two factors are well known to promote relatedness between interacting individuals in spatially structured populations. By allowing more than one individual to live at each node of the graph and by allowing interactions to vary with the distance between nodes, our inclusive fitness model allows us to consider a wider range of biological scenarios leading to the evolution of both helping and harming behaviours on graphs.     

Regression,least squares,and the general version of inclusive fitness

A general version of inclusive fitness based on regression is rederived with minimal mathematics and directly from the verbal interpretation of its terms that motivated the original formulation of the inclusive fitness concept. This verbal interpretation is here extended to provide the two relationships required to determine the two coefficients and b. These coefficients retain their definition as expected effects on the fitness of an individual, respectively of a change in allelic state of this individual, and of correlated change in allelic state of social partners. The known least‐squares formulation of the relationships determining b and c can be immediately deduced and shown to be equivalent to this new formulation. These results make clear that criticisms of the mathematical tools (in particular least‐squares regression) previously used to derive this version of inclusive fitness are misdirected.     

URec: a system for unrooted reconciliation

URec is a software based on a concept of unrooted reconciliation. It can be used to reconcile a set of unrooted gene trees with a rooted species tree or a set of rooted species trees. Moreover, it computes detailed distribution of gene duplications and gene losses in a species tree. It can be used to infer optimal species phylogenies for a given set of gene trees. URec is implemented in C++ and can be easily compiled under Unix and Windows systems. Availability: Software is freely available for download from our website at http://bioputer.mimuw.edu.pl/~gorecki/urec. This webpage also contains Windows executables and a number of advanced examples with explanations.     

Sex-specific associative learning cues and inclusive fitness benefits in the Seychelles warbler

In cooperative breeding vertebrates, indirect fitness benefits would be maximized by subordinates that accurately assess their relatedness to group offspring and preferentially help more closely related kin. In the Seychelles warbler (Acrocephalus sechellensis), we found a positive relationship between subordinate-nestling kinship (determined using microsatellite marker genotypes) and provisioning rates, but only for female subordinates. Female subordinates that helped were significantly more related to the nestlings than were nonhelpers, and the decision to help appears to be based on associative learning cues. High levels of female infidelity means that subordinates cannot trust their legitimacy through the male line, consequently they appear to use the continued presence of the primary female, but not the primary male, as a reliable cue to determine when to feed nestlings. By using effective discrimination, female subordinates are able to maximize the indirect benefits gained within a cooperative breeding system otherwise driven primarily by direct breeding benefits.