There is no fitness but fitness,and the lineage is its bearer

Inclusive fitness has been the cornerstone of social evolution theory for more than a half-century and has matured as a mathematical theory in the past 20 years. Yet surprisingly for a theory so central to an entire field, some of its connections to evolutionary theory more broadly remain contentious or underappreciated. In this paper, we aim to emphasize the connection between inclusive fitness and modern evolutionary theory through the following fact: inclusive fitness is simply classical Darwinian fitness, averaged over social, environmental and demographic states that members of a gene lineage experience. Therefore, inclusive fitness is neither a generalization of classical fitness, nor does it belong exclusively to the individual. Rather, the lineage perspective emphasizes that evolutionary success is determined by the effect of selection on all biological and environmental contexts that a lineage may experience. We argue that this understanding of inclusive fitness based on gene lineages provides the most illuminating and accurate picture and avoids pitfalls in interpretation and empirical applications of inclusive fitness theory.     

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.     

Inclusive fitness arguments in genetic models of behaviour

My purpose here is to provide a coherent account of inclusive fitness techniques, accessible to a mathematically literate graduate student in evolutionary biology, and to relate these to standard one-locus genetic models. I begin in Sect. 2 with a general formulation of evolutionary stability; in Sect. 3 and Sect. 4 I interpret the basic stability conditions within genetic and inclusive fitness models. In Sect. 5 I extend these concepts to the case of a class-structured population, and in Sect. 6 I illustrate these notions with a sex ratio example. In Sect. 7 I give a proof of the result that under additive gene action and weak selection, an inclusive fitness argument is able to verify an important stability condition (2.5) for one-locus genetic models. Most of these results have been published.     

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.     

Darwinism without populations: a more inclusive understanding of the "Survival of the Fittest"

Following Wallace's suggestion, Darwin framed his theory using Spencer's expression "survival of the fittest". Since then, fitness occupies a significant place in the conventional understanding of Darwinism, even though the explicit meaning of the term 'fitness' is rarely stated. In this paper I examine some of the different roles that fitness has played in the development of the theory. Whereas the meaning of fitness was originally understood in ecological terms, it took a statistical turn in terms of reproductive success throughout the 20th Century. This has lead to the ever-increasing importance of sexually reproducing organisms and the populations they compose in evolutionary explanations. I will argue that, moving forward, evolutionary theory should look back at its ecological roots in order to be more inclusive in the type of systems it examines. Many biological systems (e.g. clonal species, colonial species, multi-species communities) can only be satisfactorily accounted for by offering a non-reproductive account of fitness. This argument will be made by examining biological systems with very small or transient population structures. I argue this has significant consequences for how we define Darwinism, increasing the significance of survival (or persistence) over that of reproduction.     

Quantitative genetic versions of Hamilton's rule with empirical applications

Hamilton''s theory of inclusive fitness revolutionized our understanding of the evolution of social interactions. Surprisingly, an incorporation of Hamilton''s perspective into the quantitative genetic theory of phenotypic evolution has been slow, despite the popularity of quantitative genetics in evolutionary studies. Here, we discuss several versions of Hamilton''s rule for social evolution from a quantitative genetic perspective, emphasizing its utility in empirical applications. Although evolutionary quantitative genetics offers methods to measure each of the critical parameters of Hamilton''s rule, empirical work has lagged behind theory. In particular, we lack studies of selection on altruistic traits in the wild. Fitness costs and benefits of altruism can be estimated using a simple extension of phenotypic selection analysis that incorporates the traits of social interactants. We also discuss the importance of considering the genetic influence of the social environment, or indirect genetic effects (IGEs), in the context of Hamilton''s rule. Research in social evolution has generated an extensive body of empirical work focusing—with good reason—almost solely on relatedness. We argue that quantifying the roles of social and non-social components of selection and IGEs, in addition to relatedness, is now timely and should provide unique additional insights into social evolution.     

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.     

Superorganismality and caste differentiation as points of no return: how the major evolutionary transitions were lost in translation

More than a century ago, William Morton Wheeler proposed that social insect colonies can be regarded as superorganisms when they have morphologically differentiated reproductive and nursing castes that are analogous to the metazoan germ‐line and soma. Following the rise of sociobiology in the 1970s, Wheeler's insights were largely neglected, and we were left with multiple new superorganism concepts that are mutually inconsistent and uninformative on how superorganismality originated. These difficulties can be traced to the broadened sociobiological concept of eusociality, which denies that physical queen–worker caste differentiation is a universal hallmark of superorganismal colonies. Unlike early evolutionary naturalists and geneticists such as Weismann, Huxley, Fisher and Haldane, who set out to explain the acquisition of an unmated worker caste, the goal of sociobiology was to understand the evolution of eusociality, a broad‐brush convenience category that covers most forms of cooperative breeding. By lumping a diverse spectrum of social systems into a single category, and drawing attention away from the evolution of distinct quantifiable traits, the sociobiological tradition has impeded straightforward connections between inclusive fitness theory and the major evolutionary transitions paradigm for understanding irreversible shifts to higher organizational complexity. We evaluate the history by which these inconsistencies accumulated, develop a common‐cause approach for understanding the origins of all major transitions in eukaryote hierarchical complexity, and use Hamilton's rule to argue that they are directly comparable. We show that only Wheeler's original definition of superorganismality can be unambiguously linked to irreversible evolutionary transitions from context‐dependent reproductive altruism to unconditional differentiation of permanently unmated castes in the ants, corbiculate bees, vespine wasps and higher termites. We argue that strictly monogamous parents were a necessary, albeit not sufficient condition for all transitions to superorganismality, analogous to single‐zygote bottlenecking being a necessary but not sufficient condition for the convergent origins of complex soma across multicellular eukaryotes. We infer that conflict reduction was not a necessary condition for the origin of any of these major transitions, and conclude that controversies over the status of inclusive fitness theory primarily emanate from the arbitrarily defined sociobiological concepts of superorganismality and eusociality, not from the theory itself.     

Fitness,inclusive fitness,and optimization

Individual-as-maximizing agent analogies result in a simple understanding of the functioning of the biological world. Identifying the conditions under which individuals can be regarded as fitness maximizing agents is thus of considerable interest to biologists. Here, we compare different concepts of fitness maximization, and discuss within a single framework the relationship between Hamilton’s (J Theor Biol 7:1–16, 1964) model of social interactions, Grafen’s (J Evol Biol 20:1243–1254, 2007a) formal Darwinism project, and the idea of evolutionary stable strategies. We distinguish cases where phenotypic effects are additive separable or not, the latter not being covered by Grafen’s analysis. In both cases it is possible to define a maximand, in the form of an objective function ?(z), whose argument is the phenotype of an individual and whose derivative is proportional to Hamilton’s inclusive fitness effect. However, this maximand can be identified with the expression for fecundity or fitness only in the case of additive separable phenotypic effects, making individual-as-maximizing agent analogies unattractive (although formally correct) under general situations of social interactions. We also feel that there is an inconsistency in Grafen’s characterization of the solution of his maximization program by use of inclusive fitness arguments. His results are in conflict with those on evolutionary stable strategies obtained by applying inclusive fitness theory, and can be repaired only by changing the definition of the problem.     

An inclusive fitness analysis of synergistic interactions in structured populations

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or ‘synergistic’ fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term—that is, over all possible allele frequencies—and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects—for example, hawk–dove and prisoner''s dilemma games—frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p. We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk–dove game.     

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.     

Analytical Results for Individual and Group Selection of Any Intensity

The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory.     

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.     

Sulfur Isotope Fractionation during the Evolutionary Adaptation of a Sulfate-Reducing Bacterium

Dissimilatory sulfate reduction is a microbial catabolic pathway that preferentially processes less massive sulfur isotopes relative to their heavier counterparts. This sulfur isotope fractionation is recorded in ancient sedimentary rocks and generally is considered to reflect a phenotypic response to environmental variations rather than to evolutionary adaptation. Modern sulfate-reducing microorganisms isolated from similar environments can exhibit a wide range of sulfur isotope fractionations, suggesting that adaptive processes influence the sulfur isotope phenotype. To date, the relationship between evolutionary adaptation and isotopic phenotypes has not been explored. We addressed this by studying the covariation of fitness, sulfur isotope fractionation, and growth characteristics in Desulfovibrio vulgaris Hildenborough in a microbial evolution experiment. After 560 generations, the mean fitness of the evolved lineages relative to the starting isogenic population had increased by ∼17%. After 927 generations, the mean fitness relative to the initial ancestral population had increased by ∼20%. Growth rate in exponential phase increased during the course of the experiment, suggesting that this was a primary influence behind the fitness increases. Consistent changes were observed within different selection intervals between fractionation and fitness. Fitness changes were associated with changes in exponential growth rate but changes in fractionation were not. Instead, they appeared to be a response to changes in the parameters that govern growth rate: yield and cell-specific sulfate respiration rate. We hypothesize that cell-specific sulfate respiration rate, in particular, provides a bridge that allows physiological controls on fractionation to cross over to the adaptive realm.     

The extended evolutionary synthesis: its structure,assumptions and predictions

Scientific activities take place within the structured sets of ideas and assumptions that define a field and its practices. The conceptual framework of evolutionary biology emerged with the Modern Synthesis in the early twentieth century and has since expanded into a highly successful research program to explore the processes of diversification and adaptation. Nonetheless, the ability of that framework satisfactorily to accommodate the rapid advances in developmental biology, genomics and ecology has been questioned. We review some of these arguments, focusing on literatures (evo-devo, developmental plasticity, inclusive inheritance and niche construction) whose implications for evolution can be interpreted in two ways—one that preserves the internal structure of contemporary evolutionary theory and one that points towards an alternative conceptual framework. The latter, which we label the ‘extended evolutionary synthesis'' (EES), retains the fundaments of evolutionary theory, but differs in its emphasis on the role of constructive processes in development and evolution, and reciprocal portrayals of causation. In the EES, developmental processes, operating through developmental bias, inclusive inheritance and niche construction, share responsibility for the direction and rate of evolution, the origin of character variation and organism–environment complementarity. We spell out the structure, core assumptions and novel predictions of the EES, and show how it can be deployed to stimulate and advance research in those fields that study or use evolutionary biology.     

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.     

Resolving the evolution of sterile worker castes: a window on the advantages and disadvantages of monogamy

Many social Hymenoptera species have morphologically sterile worker castes. It is proposed that the evolutionary routes to this obligate sterility must pass through a ‘monogamy window’, because inclusive fitness favours individuals retaining their reproductive totipotency unless they can rear full siblings. Simulated evolution of sterility, however, finds that ‘point of view’ is critically important. Monogamy is facilitating if sterility is expressed altruistically (i.e. workers defer reproduction to queens), but if sterility results from manipulation by mothers or siblings, monogamy may have no effect or lessen the likelihood of sterility. Overall, the model and data from facultatively eusocial bees suggest that eusociality and sterility are more likely to originate through manipulation than by altruism, casting doubt on a mandatory role for monogamy. Simple kin selection paradigms, such as Hamilton''s rule, can also fail to account for significant evolutionary dynamics created by factors, such as population structure, group-level effects or non-random mating patterns. The easy remedy is to always validate apparently insightful predictions from Hamiltonian equations with life-history appropriate genetic models.     

An evolutionary analysis of psychological pain following rape:: I. The effects of victim's age and marital status

The typical approach used to identify and characterize adaptations is discussed briefly, and then it is applied to psychological changes associated with the psychological pain experienced by rape victims. It has been hypothesized that mental pain may reflect psychological adaptation that is designed to detect and cope with the occurence of social problems that reduce an individual's inclusive fitness in human evolutionary history. According to the hypothesis, mental pain is brought about by social tragedies in the lives of individuals and focuses the attention of individuals on the events surrounding the pain, promoting correction of the pain-causing events and their avoidance in the future. The hypothesis applied to rape victims proposes that in human evolutionary history raped females had increased fitness as a result of mental pain, because the pain forced them to focus attention on the fitness-reducing circumstances surrounding rape, which are discussed. Some of the hypothesis' predictions about the psychological pain of rape victims are examined using a data set of 790 rape victims in Philadelphia (USA) who were interviewed about their psychological traumatization within five days after the assault. The analyses indicate that, as predicted, a victim's age and marital status are proximate causes of the magnitude of psychological pain following rape. Reproductive-aged women appear to be more severely traumatized by rape than older women or girls and married women more than unmarried women. The results presented suggest that the psychology that regulates mental pain processes information about age and mateship status in the event of a women's rape.     

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.     

Inclusive fitness and differential productivity across the life course determine intergenerational transfers in a small-scale human society

Transfers of resources between generations are an essential element in current models of human life-history evolution accounting for prolonged development, extended lifespan and menopause. Integrating these models with Hamilton''s theory of inclusive fitness, we predict that the interaction of biological kinship with the age-schedule of resource production should be a key driver of intergenerational transfers. In the empirical case of Tsimane’ forager–horticulturalists in Bolivian Amazonia, we provide a detailed characterization of net transfers of food according to age, sex, kinship and the net need of donors and recipients. We show that parents, grandparents and siblings provide significant net downward transfers of food across generations. We demonstrate that the extent of provisioning responds facultatively to variation in the productivity and demographic composition of families, as predicted by the theory. We hypothesize that the motivation to provide these critical transfers is a fundamental force that binds together human nuclear and extended families. The ubiquity of three-generational families in human societies may thus be a direct reflection of fundamental evolutionary constraints on an organism''s life-history and social organization.