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.     

Invasion fitness,inclusive fitness,and reproductive numbers in heterogeneous populations

How should fitness be measured to determine which phenotype or “strategy” is uninvadable when evolution occurs in a group‐structured population subject to local demographic and environmental heterogeneity? Several fitness measures, such as basic reproductive number, lifetime dispersal success of a local lineage, or inclusive fitness have been proposed to address this question, but the relationships between them and their generality remains unclear. Here, we ascertain uninvadability (all mutant strategies always go extinct) in terms of the asymptotic per capita number of mutant copies produced by a mutant lineage arising as a single copy in a resident population (“invasion fitness”). We show that from invasion fitness uninvadability is equivalently characterized by at least three conceptually distinct fitness measures: (i) lineage fitness, giving the average individual fitness of a randomly sampled mutant lineage member; (ii) inclusive fitness, giving a reproductive value weighted average of the direct fitness costs and relatedness weighted indirect fitness benefits accruing to a randomly sampled mutant lineage member; and (iii) basic reproductive number (and variations thereof) giving lifetime success of a lineage in a single group, and which is an invasion fitness proxy. Our analysis connects approaches that have been deemed different, generalizes the exact version of inclusive fitness to class‐structured populations, and provides a biological interpretation of natural selection on a mutant allele under arbitrary strength of selection.     

Inclusive fitness is an indispensable approximation for understanding organismal design

For some decades most biologists interested in design have agreed that natural selection leads to organisms acting as if they are maximizing a quantity known as “inclusive fitness.” This maximization principle has 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 adopt a resolution offered by Birch, who accepts the technical difficulties of establishing inclusive fitness maximization in a fully general model, while concluding that inclusive fitness is still useful as an organizing framework. We set out in more detail why inclusive fitness is such a practical and powerful framework, and provide verbal and conceptual arguments for why social biology would be more or less impossible without it. We aim to help mathematicians understand why social biologists are content to use inclusive fitness despite its theoretical weaknesses. Here, we also offer biologists practical advice for avoiding potential pitfalls.     

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.     

Much ado about nothing: Nowak et al.'s charge against inclusive fitness theory

In a recent article, Nowak et al. claim that the mathematical basis of inclusive fitness theory does not stand to scrunity and to have found an alternative explanation for eusociality. We show that these claims are based on false premises, many of which have been exposed more than 25 years ago, such as misrepresentations of the basic components of inclusive fitness and fallacious distinctions between individual fitness and inclusive fitness. Moreover, some limitations ascribed to inclusive fitness are actually limitations of current evolutionary theory, for which Nowak et al. propose no new solution. Likewise, their assertedly 'common sense' empirical alternative to estimating inclusive fitness is not applicable in cases of interest. Finally, their eusociality model merely confirms the importance of all the components of inclusive fitness. We conclude by discussing how rhetorical devices and editorial practices can impede scientific endeavours.     

Hamilton's rule,inclusive fitness maximization,and the goal of individual behaviour in symmetric two‐player games

Hamilton's original work on inclusive fitness theory assumed additivity of costs and benefits. Recently, it has been argued that an exact version of Hamilton's rule for the spread of a pro‐social allele (rb > c) holds under nonadditive pay‐offs, so long as the cost and benefit terms are defined as partial regression coefficients rather than pay‐off parameters. This article examines whether one of the key components of Hamilton's original theory can be preserved when the rule is generalized to the nonadditive case in this way, namely that evolved organisms will behave as if trying to maximize their inclusive fitness in social encounters.     

MATHEMATICS OF KIN‐ AND GROUP‐SELECTION: FORMALLY EQUIVALENT?

Evolutionary game theory is a general mathematical framework that describes the evolution of social traits. This framework forms the basis of many multilevel selection models and is also frequently used to model evolutionary dynamics on networks. Kin selection, which was initially restricted to describe social interactions between relatives, has also led to a broader mathematical approach, inclusive fitness, that can not only describe social evolution among relatives, but also in group structured populations or on social networks. It turns out that the underlying mathematics of game theory is fundamentally different from the approach of inclusive fitness. Thus, both approaches—evolutionary game theory and inclusive fitness—can be helpful to understand the evolution of social traits in group structured or spatially extended populations.     

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.     

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.     

Inclusive fitness and the sociobiology of the genome

Inclusive fitness theory provides conditions for the evolutionary success of a gene. These conditions ensure that the gene is selfish in the sense of Dawkins (The selfish gene, Oxford University Press, Oxford, 1976): genes do not and cannot sacrifice their own fitness on behalf of the reproductive population. Therefore, while natural selection explains the appearance of design in the living world (Dawkins in The blind watchmaker: why the evidence of evolution reveals a universe without design, W. W. Norton, New York, 1996), inclusive fitness theory does not explain how. Indeed, Hamilton’s rule is equally compatible with the evolutionary success of prosocial altruistic genes and antisocial predatory genes, whereas only the former, which account for the appearance of design, predominate in successful organisms. Inclusive fitness theory, however, permits a formulation of the central problem of sociobiology in a particularly poignant form: how do interactions among loci induce utterly selfish genes to collaborate, or to predispose their carriers to collaborate, in promoting the fitness of their carriers? Inclusive fitness theory, because it abstracts from synergistic interactions among loci, does not answer this question. Fitness-enhancing collaboration among loci in the genome of a reproductive population requires suppressing alleles that decrease, and promoting alleles that increase the fitness of its carriers. Suppression and promotion are effected by regulatory networks of genes, each of which is itself utterly selfish. This implies that genes, and a fortiori individuals in a social species, do not maximize inclusive fitness but rather interact strategically in complex ways. It is the task of sociobiology to model these complex interactions.     

A reconciliation of inclusive fitness and personal fitness approaches: a proposed correcting term for the inclusive fitness formula

Hamilton implicitly defined the inclusive fitness of an individual as the number of genomes, identical by descent to its own, but not in its own body, which owe their existence to expression of genes in said individual. Hamilton regarded inclusive fitness as the true metric of evolutionary success and the thin- maximized by selection. Williams, Stern and Orlove either claimed this property for mean reproductive success, or stated that expected reproductive success equals expected inclusive fitness. These statements are reconciled if a correcting term is added to Hamilton's inclusive fitness formula.This change completely accounts for inclusive fitness in personal fitness terminology. The use of ? in place of r renders the new formula exact. This has less numerical impact than the addition of the correcting term to begin with, but helps show inclusive fitness theory holds exactly.     

Optimization of inclusive fitness

The first fully explicit argument is given that broadly supports a widespread belief among whole-organism biologists that natural selection tends to lead to organisms acting as if maximizing their inclusive fitness. The use of optimization programs permits a clear statement of what this belief should be understood to mean, in contradistinction to the common mathematical presumption that it should be formalized as some kind of Lyapunov or even potential function. The argument reveals new details and uncovers latent assumptions. A very general genetic architecture is allowed, and there is arbitrary uncertainty. However, frequency dependence of fitnesses is not permitted. The logic of inclusive fitness immediately draws together various kinds of intra-genomic conflict, and the concept of 'p-family' is introduced. Inclusive fitness is thus incorporated into the formal Darwinism project, which aims to link the mathematics of motion (difference and differential equations) used to describe gene frequency trajectories with the mathematics of optimization used to describe purpose and design. Important questions remain to be answered in the fundamental theory of inclusive fitness.     

Detecting kin selection at work using inclusive fitness

A recent model shows that altruism can evolve with limited migration and variable group sizes, and the authors claim that kin selection cannot provide a sufficient explanation of their results. It is demonstrated, using a recent reformulation of Hamilton's original arguments, that the model falls squarely within the scope of inclusive fitness theory, which furthermore shows how to calculate inclusive fitness and the relevant relatedness. A distinction is drawn between inclusive fitness, which is a method of analysing social behaviour; and kin selection, a process that operates through genetic similarity brought about by common ancestry, but not by assortation by genotype or by direct assessment of genetic similarity. The recent model is analysed, and it turns out that kin selection provides a sufficient explanation to considerable quantitative accuracy, contrary to the authors' claims. A parallel analysis is possible and would be illuminating for all models of social behaviour in which individuals' effects on each other's offspring numbers combine additively.     

Taming fitness: Organism‐environment interdependencies preclude long‐term fitness forecasting

Fitness is a central but notoriously vexing concept in evolutionary biology. The propensity interpretation of fitness is often regarded as the least problematic account for fitness. It ties an individual's fitness to a probabilistic capacity to produce offspring. Fitness has a clear causal role in evolutionary dynamics under this account. Nevertheless, the propensity interpretation faces its share of problems. We discuss three of these. We first show that a single scalar value is an incomplete summary of a propensity. Second, we argue that the widespread method of “abstracting away” environmental idiosyncrasies by averaging over reproductive output in different environments is not a valid approach when environmental changes are irreversible. Third, we point out that expanding the range of applicability for fitness measures by averaging over more environments or longer time scales (so as to ensure environmental reversibility) reduces one's ability to distinguish selectively relevant differences among individuals because of mutation and eco‐evolutionary feedbacks. This series of problems leads us to conclude that a general value of fitness that is both explanatory and predictive cannot be attained. We advocate for the use of propensity‐compatible methods, such as adaptive dynamics, which can accommodate these difficulties.     

Kinship,sex, and fitness in a Caribbean community

Patterns of human kinship commonly involve preferential treatment of relatives based on lineal descent (lineages) rather than degree of genetic relatedness (kindreds), presenting a challenge for inclusive fitness theory. Here, we examine effects of lineage and kindred characteristics on reproductive success (RS) and number of grandchildren for 130 men and 124 women in a horticultural community on Dominica. Kindreds had little effect on fitness independently of lineage characteristics. Fitness increased with the number of lineal relatives residing in the community but decreased beyond an apparently optimal lineage size, suggesting resource enhancement and competition among kin. Female-biased patrilineage sex ratio was positively associated with men’s fitness, while male-biased matrilineage sex ratio was positively associated with women’s fitness. Number of brothers in the community was negatively associated with men’s, but not women’s, fitness. Parents and number of sisters had no effect on either male or female reproduction; however, women with younger sisters had higher RS, suggesting benefits of kin support for childcare. In sum, imposed norms for lineage social organization may enhance lineal ancestors’ inclusive fitness at a cost to individual inclusive fitness. Research was supported by grants from the National Science Foundation (BNS 8920569 and SBR 9205373); the University of Missouri Research Board to MVF; the Earthwatch Center for Field Research to MVF, Marsha B. Quinlan, and RJQ; and the B.S.U. Center for International Programs and Office of Academic Research and Sponsored Programs to RJQ. Marsha Quinlan and Napoleon Chagnon provided valuable advice on earlier drafts. Ed Hagen gave generous help with Descent software for kinship analysis. Many friends, teachers, and consultants in Bwa Mawego contributed generously to this study: the Durand clan—Juranie, Jonah, Elford, Induria, Margelia, Eugenia, Lillia, Elquimedo, Zexia, Delfine, Wilford, Nathalie, and Sarah; the Warringtons—Martina, Amatus, Onia, Belltina, Zabius, Sarah-Gene, and Heckery; the Laudats—Eddie, Benedict, and Dellie; the Laurents—Aron and Tito; the Lewises—Eddie, Melanie, Eulina, Spliffy, Ganjala, Julina, Jalina, and Marietta; Franklin Vigilante; Lawrence Prosper; Edmund Sanderson; Alex and Tita Alie; and especially Mistress Didi and Mr. McField Coipel. Rob Quinlan is Assistant Professor of Anthropology at Ball State University. His main interests include human evolutionary ecology, reproductive development, parental care, kinship, and medical anthropology. He has conducted fieldwork in Dominica since 1993. Mark Flinn is Associate Professor of Anthropology and Psychological Sciences at the University of Missouri-Columbia. His main interests include evolutionary theory, childhood stress, family relationships, and health. He has conducted fieldwork in Dominica every year since 1987.     

Group selection, kin selection, altruism and cooperation: When inclusive fitness is right and when it can be wrong

Group selection theory has a history of controversy. After a period of being in disrepute, models of group selection have regained some ground, but not without a renewed debate over their importance as a theoretical tool. In this paper I offer a simple framework for models of the evolution of altruism and cooperation that allows us to see how and to what extent both a classification with and one without group selection terminology are insightful ways of looking at the same models. Apart from this dualistic view, this paper contains a result that states that inclusive fitness correctly predicts the direction of selection for one class of models, represented by linear public goods games. Equally important is that this result has a flip side: there is a more general, but still very realistic class of models, including models with synergies, for which it is not possible to summarize their predictions on the basis of an evaluation of inclusive fitness.     

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.     

Hamilton's inclusive fitness in finite-structured populations

Hamilton''s formulation of inclusive fitness has been with us for 50 years. During the first 20 of those years attention was largely focused on the evolutionary trajectories of different behaviours, but over the past 20 years interest has been growing in the effect of population structure on the evolution of behaviour and that is our focus here. We discuss the evolutionary journey of the inclusive-fitness effect over this epoch, nurtured as it was in an essentially homogeneous environment (that of ‘transitive’ structures) having to adapt in different ways to meet the expectations of heterogeneous structures. We pay particular attention to the way in which the theory has managed to adapt the original constructs of relatedness and reproductive value to provide a formulation of inclusive fitness that captures a precise measure of allele-frequency change in finite-structured populations.     

Reverse evolution of fitness in Drosophila melanogaster

Abstract The evolution of fitness is central to evolutionary theory, yet few experimental systems allow us to track its evolution in genetically and environmentally relevant contexts. Reverse evolution experiments allow the study of the evolutionary return to ancestral phenotypic states, including fitness. This in turn permits well‐defined tests for the dependence of adaptation on evolutionary history and environmental conditions. In the experiments described here, 20 populations of heterogeneous evolutionary histories were returned to their common ancestral environment for 50 generations, and were then compared with both their immediate differentiated ancestors and populations which had remained in the ancestral environment. One measure of fitness returned to ancestral levels to a greater extent than other characters did. The phenotypic effects of reverse evolution were also contingent on previous selective history. Moreover, convergence to the ancestral state was highly sensitive to environmental conditions. The phenotypic plasticity of fecundity, a character directly selected for, evolved during the experimental time frame. Reverse evolution appears to force multiple, diverged populations to converge on a common fitness state through different life‐history and genetic changes.     

On the assignment of fitness to parents and offspring: whose fitness is it and when does it matter?

There has been a long‐standing conceptual debate over the legitimacy of assigning components of offspring fitness to parents for purposes of evolutionary analysis. The benefits and risks inherent in assigning fitness of offspring to parents have been given primarily as verbal arguments and no explicit theoretical analyses have examined quantitatively how the assignment of fitness can affect evolutionary inferences. Using a simple quantitative genetic model, we contrast the conclusions drawn about how selection acts on a maternal character when components of offspring fitness (such as early survival) are assigned to parents vs. when they are assigned directly to the individual offspring. We find that there are potential shortcomings of both possible assignments of fitness. In general, whenever there is a genetic correlation between the parental and direct effects on offspring fitness, assigning components of offspring fitness to parents yields incorrect dynamical equations and may even lead to incorrect conclusions about the direction of evolution. Assignment of offspring fitness to parents may also produce incorrect estimates of selection whenever environmental variation contributes to variance of the maternal trait. Whereas assignment of offspring fitness to the offspring avoids these potential problems, it introduces the possible problem of missing components of kin selection provided by the mother, which may not be detected in selection analyses. There are also certain conditions where either model can be appropriate because assignment of offspring fitness to parents may yield the same dynamical equations as assigning offspring fitness directly to offspring. We discuss these implications of the alternative assignments of fitness for modelling, selection analysis and experimentation in evolutionary biology.