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.     

Procedures for reliable estimation of viral fitness from time-series data

In order to develop a better understanding of the evolutionary dynamics of HIV drug resistance, it is necessary to quantify accurately the in vivo fitness costs of resistance mutations. However, the reliable estimation of such fitness costs is riddled with both theoretical and experimental difficulties. Experimental fitness assays typically suffer from the shortcoming that they are based on in vitro data. Fitness estimates based on the mathematical analysis of in vivo data, however, are often questionable because the underlying assumptions are not fulfilled. In particular, the assumption that the replication rate of the virus population is constant in time is frequently grossly violated. By extending recent work of Marée and colleagues, we present here a new approach that corrects for time-dependent viral replication in time-series data for growth competition of mutants. This approach allows a reliable estimation of the relative replicative capacity (with confidence intervals) of two competing virus variants growing within the same patient, using longitudinal data for the total plasma virus load, the relative frequency of the two variants and the death rate of infected cells. We assess the accuracy of our method using computer-generated data. An implementation of the developed method is freely accessible on the Web (http://www.eco.ethz.ch/fitness.html).     

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.     

The evolution of fitness in life-history theory

Theory concerning the evolution of life history (the schedule of reproduction and survival) focuses on describing the life history which maximises fitness. Although there is an intuitive link between life history and fitness, there are in fact several measures of the 'black box' concept of fitness. There has been a debate in the bio-mathematical literature on the predictive difference between the two most commonly used measures; intrinsic rate of increase r and net reproductive ratio R0. Although both measures aim to describe fitness, models using one of the measures may predict the opposite of similar models using the other measure, which is clearly undesirable. Here, I review the evolution of these fitness measures over the last four decades, the predictive differences between these measures and the resulting shift of the fitness concept. I focus in particular on some recent developments, which have solved the dilemma of predictive differences between these fitness measures by explicitly acknowledging the game-theoretical nature of life-history 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.     

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.     

Evolution of monogamous marriage by maximization of inclusive fitness

The majority of human societies allow polygynous marriage, and the prevalence of this practice is readily understood in evolutionary terms. Why some societies prescribe monogamous marriage is however not clear: current evolutionary explanations—that social monogamy increases within‐group co‐operation, giving societies an advantage in competition with other groups—conflict with the historical and ethnographic evidence. We show that, within the framework of inclusive fitness theory, monogamous marriage can be viewed as the outcome of the strategic behaviour of males and females in the allocation of resources to the next generation. Where resources are transferred across generations, social monogamy can be advantageous if partitioning of resources among the offspring of multiple wives causes a depletion of their fitness value, and/or if females grant husbands higher fidelity in exchange for exclusive investment of resources in their offspring. This may explain why monogamous marriage prevailed among the historical societies of Eurasia: here, intensive agriculture led to scarcity of land, with depletion in the value of estates through partitioning among multiple heirs. Norms promoting high paternity were common among ancient societies in the region, and may have further facilitated the establishment of social monogamy. In line with the historical and ethnographic evidence, this suggests that monogamous marriage emerged in Eurasia following the adoption of intensive agriculture, as ownership of land became critical to productive and reproductive success.     

Unifying life-history analyses for inference of fitness and population growth

The lifetime fitnesses of individuals comprising a population determine its numerical dynamics, and genetic variation in fitness results in evolutionary change. This dual importance of individual fitness is well understood, but empirical fitness records generally violate the assumptions of standard statistical approaches. This problem has undermined comprehensive study of fitness and impeded empirical synthesis of the numerical and genetic dynamics of populations. Recently developed aster models remedy this problem by explicitly modeling the dependence of later-expressed components of fitness (e.g., fecundity) on those expressed earlier (e.g., survival to reproduce). Moreover, aster models employ different sampling distributions for different components of fitness (e.g., binomial for survival over a given interval and Poisson for fecundity). Analysis is done by maximum likelihood, and the resulting distributions for lifetime fitness closely approximate observed data. We illustrate the breadth of aster models' utility with three examples demonstrating estimation of the finite rate of increase, comparison of mean fitness among genotypic groups, and analysis of phenotypic selection. Aster models offer a unified approach to addressing the breadth of questions in evolution and ecology for which life-history data are gathered.     

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.     

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.     

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.     

Caste fate conflict in swarm-founding social hymenoptera: an inclusive fitness analysis

A caste system in which females develop into morphologically distinct queens or workers has evolved independently in ants, wasps and bees. Although such reproductive division of labour may benefit the colony it is also a source of conflict because individual immature females can benefit from developing into a queen in order to gain greater direct reproduction. Here we present a formal inclusive fitness analysis of caste fate conflict appropriate for swarm-founding social Hymenoptera. Three major conclusions are reached: (1) when caste is self-determined, many females should selfishly choose to become queens and the resulting depletion of the workforce can substantially reduce colony productivity; (2) greater relatedness among colony members reduces this excess queen production; (3) if workers can prevent excess queen production at low cost by controlled feeding, a transition to nutritional caste determination should occur. These predictions generalize results derived earlier using an allele-frequency model [Behav. Ecol. Sociobiol. (2001) 50: 467] and are supported by observed levels of queen production in various taxa, especially stingless bees, where caste can be either individually or nutritionally controlled.     

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.     

Directionality theory: an empirical study of an entropic principle in life-history evolution

Understanding the relationship between ecological constraints and life-history properties constitutes a central problem in evolutionary ecology. Directionality theory, a model of the evolutionary process based on demographic entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn, provides an analytical framework for addressing this problem. The theory predicts that in populations that spend the greater part of their evolutionary history in the stationary growth phase (equilibrium species), entropy will increase. Equilibrium species will be characterized by high iteroparity and strong demographic stability. In populations that spend the greater part of their evolutionary history in the exponential growth phase (opportunistic species), entropy will decrease when population size is large, and will undergo random variation when population size is small. Opportunistic species will be characterized by weak iteroparity and weak demographic stability when population size is large, and random variations in these attributes when population size is small. This paper assesses the validity of these predictions by employing a demographic dataset of 66 species of perennial plants. This empirical analysis is consistent with directionality theory and provides support for its significance as an explanatory and predictive model of life-history evolution.     

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.     

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.     

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.     

Selective pressures for accurate altruism targeting: evidence from digital evolution for difficult-to-test aspects of inclusive fitness theory

Inclusive fitness theory predicts that natural selection will favour altruist genes that are more accurate in targeting altruism only to copies of themselves. In this paper, we provide evidence from digital evolution in support of this prediction by competing multiple altruist-targeting mechanisms that vary in their accuracy in determining whether a potential target for altruism carries a copy of the altruist gene. We compete altruism-targeting mechanisms based on (i) kinship (kin targeting), (ii) genetic similarity at a level greater than that expected of kin (similarity targeting), and (iii) perfect knowledge of the presence of an altruist gene (green beard targeting). Natural selection always favoured the most accurate targeting mechanism available. Our investigations also revealed that evolution did not increase the altruism level when all green beard altruists used the same phenotypic marker. The green beard altruism levels stably increased only when mutations that changed the altruism level also changed the marker (e.g. beard colour), such that beard colour reliably indicated the altruism level. For kin- and similarity-targeting mechanisms, we found that evolution was able to stably adjust altruism levels. Our results confirm that natural selection favours altruist genes that are increasingly accurate in targeting altruism to only their copies. Our work also emphasizes that the concept of targeting accuracy must include both the presence of an altruist gene and the level of altruism it produces.     

Implications of empirical data quality to metapopulation model parameter estimation and application

Parameter estimation is a critical step in the use of any metapopulation model for predictive purposes. Typically metapopulation studies assume that empirical data are of good quality and any errors are so insignificant that they can be ignored. However, three types of errors occur commonly in metapopulation data sets. First, patch areas can be mis-estimated. Second, unknown habitat patches may be located within or around the study area. Third, there may be false zeros in the data set, that is, some patches were observed to be empty while there truly was a population in the patch. This study investigates biases induced into metapopulation model parameter estimates by these three types of errors. It was found that mis-estimated areas influence the scaling of extinction risk with patch area; extinction probabilities for large patches become overestimated. Missing patches cause overestimation of migration distances and colonization ability of the species. False zeros can affect very strongly all model components, the extinction risk in large patches, intrinsic extinction rates in general, migration distances and colonization ability may become all overestimated. Biases in parameter estimates translate into corresponding biases in model predictions, which are serious particularly if metapopulation persistence becomes overestimated. This happens for example when the migration capability of the species is overestimated. Awareness of these biases helps in understanding seemingly anomalous parameter estimation results. There are also implications for field work: it may be reasonable to allocate effort so that serious errors in data are minimized. It is particularly important to avoid observing false zeros for large and/or isolated patches.