Using the Price equation to detect inclusive fitness in class-structured populations

Key Variables ◽

Hamilton's Rule ◽

Simple Regression

AbstractInclusive fitness theory has transformed the study of adaptive evolution since 1964, contributing to significant empirical findings. However, its status as a theory has been challenged by the proposals of several alternative frameworks. Those challenges have been countered by analyses that use the Price equation and the regression method. The Price equation is a universal description of evolutionary change, and the partitioning of the Price equation using the regression method immediately yields Hamilton’s rule, which embodies the main tenets of inclusive fitness. Hamilton’s rule captures the intensity and direction of selection acting on social behaviour and its underlying causal structure. Recent work, however, has suggested that there is an anomaly in this approach: in some cases, the regression method fails to estimate the correct values of the variables in Hamilton’s rule and the causal structure of the behaviour. Here, I address this apparent anomaly. I argue that the failure of the simple regression method occurs because social players vary in baseline fecundity. I reformulate the Price equation and regression method to recover Hamilton’s rule and I show that the method correctly estimates its key variables. I show that games where baseline fecundity varies among individuals represent a more general set of games that unfold in class-structured populations. This framework supports the robustness and validity of inclusive fitness.

Inclusive Fitness and Hamilton’s Rule

10.23943/princeton/9780691161563.003.0004 ◽

2015 ◽

Author(s):

James A.R. Marshall

Keyword(s):

Sex Allocation ◽

Charles Darwin ◽

Inclusive Fitness ◽

Price Equation ◽

Additive Effects ◽

Eusocial Insect ◽

Hamilton’S Rule ◽

Biological Phenomena ◽

This chapter examines how the logic of inclusive fitness theory can be mathematically formalized using the Price equation, and how that formalization can be used to derive Hamilton's rule in its simplest form, as applied to unconditional behaviors having additive effects on fitness. Various biological phenomena, such as sex allocation and working policing within eusocial insect colonies, have been analyzed by considering what strategies maximize individuals' inclusive fitness, and how observed social behaviors should correlate with quantities such as relatedness. The chapter derives Hamilton's rule by introducing some notation for the effects of behaviors on fitnesses of individuals that interact socially, to make explicit precisely how genes (and later phenotypes) affect fitness, and to give a general form of Hamilton's rule that will apply to any (unconditional, additive) behavior regardless of its details. It shows that inclusive fitness is a genuinely novel extension of the classical fitness studied by Charles Darwin, R. A. Fisher, and others.

Social Evolution, Hamilton’s Rule, and Inclusive Fitness

10.1093/oso/9780198815082.003.0006 ◽

2018 ◽

Author(s):

Samir Okasha

Keyword(s):

Social Behaviour ◽

Social Evolution ◽

Inclusive Fitness ◽

Popular Approach ◽

Hamilton’S Rule ◽

The Social ◽

Social Encounters ◽

The Individual ◽

Inclusive fitness theory, originally due to W. D. Hamilton, is a popular approach to the study of social evolution, but shrouded in controversy. The theory contains two distinct aspects: Hamilton’s rule (rB > C); and the idea that individuals will behave as if trying to maximize their inclusive fitness in social encounters. These two aspects of the theory are logically separable but often run together. A generalized version of Hamilton’s rule can be formulated that is always true, though whether it is causally meaningful is debatable. However, the individual maximization claim only holds true if the payoffs from the social encounter are additive. The notion that inclusive fitness is the ‘goal’ of individuals’ social behaviour is less robust than some of its advocates acknowledge.

Helping in cooperatively breeding long-tailed tits: a test of Hamilton's rule

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2013.0565 ◽

2014 ◽

Vol 369 (1642) ◽

pp. 20130565 ◽

Cited By ~ 34

Author(s):

Ben J. Hatchwell ◽

Philippa R. Gullett ◽

Mark J. Adams

Keyword(s):

Social Evolution ◽

Inclusive Fitness ◽

Empirical Studies ◽

Alloparental Care ◽

Hamilton’S Rule ◽

Long Term Study ◽

Cooperatively Breeding ◽

Helping Behaviour ◽

Inclusive fitness theory provides the conceptual framework for our current understanding of social evolution, and empirical studies suggest that kin selection is a critical process in the evolution of animal sociality. A key prediction of inclusive fitness theory is that altruistic behaviour evolves when the costs incurred by an altruist ( c ) are outweighed by the benefit to the recipient ( b ), weighted by the relatedness of altruist to recipient ( r ), i.e. Hamilton's rule rb > c . Despite its central importance in social evolution theory, there have been relatively few empirical tests of Hamilton's rule, and hardly any among cooperatively breeding vertebrates, leading some authors to question its utility. Here, we use data from a long-term study of cooperatively breeding long-tailed tits Aegithalos caudatus to examine whether helping behaviour satisfies Hamilton's condition for the evolution of altruism. We show that helpers are altruistic because they incur survival costs through the provision of alloparental care for offspring. However, they also accrue substantial benefits through increased survival of related breeders and offspring, and despite the low average relatedness of helpers to recipients, these benefits of helping outweigh the costs incurred. We conclude that Hamilton's rule for the evolution of altruistic helping behaviour is satisfied in this species.

Nonadditive Interactions and Hamilton’s Rule

10.23943/princeton/9780691161563.003.0005 ◽

2015 ◽

Author(s):

James A.R. Marshall

Keyword(s):

Replicator Dynamics ◽

Structured Populations ◽

The Other ◽

Price Equation ◽

Costs And Benefits ◽

Partial Regression ◽

Selective Pressures ◽

Hamilton’S Rule ◽

Hamilton's Rule ◽

Synergistic Coefficient

This chapter examines what happens in nonadditive interactions when such interactions take place between relatives, and how Hamilton's rule can be extended in two different ways to accommodate such nonadditivity. It first considers the selective pressures on nonadditive behaviors directed towards relatives by making use of the replicator dynamics to capture interactions within structured populations, so that on average, interactions within the population occur between relatives. It then describes two extensions to Hamilton's rule to deal with nonadditive interactions. One approach takes deviations from additivity and accounts for them all in a single synergistic coefficient. The other approach applies partial regression to keep a version of Hamilton's rule with only three parameters, in which costs and benefits vary according to the frequency of social individuals in a population. The chapter also explains the use of the Price equation to study nonadditive social interactions between relatives.

On Hamilton’s Rule and Inclusive Fitness Theory with Nonadditive Payoffs

Philosophy of Science ◽

10.1086/687871 ◽

2016 ◽

Vol 83 (5) ◽

pp. 873-883 ◽

Cited By ~ 5

Author(s):

Samir Okasha

Keyword(s):

Inclusive Fitness ◽

Hamilton’S Rule ◽

Inclusive Fitness and Hamilton’s Rule

10.1093/oso/9780198862260.003.0005 ◽

2021 ◽

pp. 116-150

Author(s):

J. Arvid Ågren

Keyword(s):

Reproductive Success ◽

Inclusive Fitness ◽

Formal Darwinism ◽

Formal Equivalence ◽

Hamilton’S Rule ◽

Intimate Association ◽

Close Relatives ◽

This chapter evaluates the long and intimate association between the gene’s-eye view and the work of W.D. Hamilton. Hamilton’s key insight was that individual organisms can affect the transmission of their genes through personal reproductive success, as well as through the success of close relatives. Inclusive fitness provides a way to view this process from the perspective of individual organisms, but it can also be seen from a gene’s-eye view. Dawkins and others have repeatedly emphasized the formal equivalence of the two perspectives. Yet, this chapter shows there is an underappreciated tension between the two perspectives. It demonstrates how this tension is expressed in both the current kerfuffle over the value of inclusive fitness theory stemming from Martin Nowak and colleagues and in Alan Grafen’s ongoing Formal Darwinism Project. The chapter ends by discussing two recent attempts to resolve this tension.

Quantitative genetic versions of Hamilton's rule with empirical applications

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2013.0358 ◽

2014 ◽

Vol 369 (1642) ◽

pp. 20130358 ◽

Cited By ~ 26

Author(s):

Joel W. McGlothlin ◽

Jason B. Wolf ◽

Edmund D. Brodie ◽

Allen J. Moore

Keyword(s):

Quantitative Genetics ◽

Social Evolution ◽

Inclusive Fitness ◽

Good Reason ◽

Empirical Work ◽

Critical Parameters ◽

Simple Extension ◽

Hamilton’S Rule ◽

Quantitative Genetic ◽

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.

Evidence, Other Approaches, and Further Topics

10.23943/princeton/9780691161563.003.0010 ◽

2015 ◽

Author(s):

James A.R. Marshall

Keyword(s):

Social Evolution ◽

Inclusive Fitness ◽

Kin Recognition ◽

Replicator Dynamics ◽

Empirical Support ◽

Natural World ◽

Price Equation ◽

Evolution Theory ◽

The Many

This book has examined the genesis, the logic, and the generality of social evolution theory. In particular, it has presented evolutionary explanations of the many social behaviors we observe in the natural world by showing that William D. Hamilton's inclusive fitness theory provides the necessary generalization of classical Darwin–Wallace–Fisher fitness. This concluding chapter discusses the limitations of the analyses presented in this book and assesses the empirical support for inclusive fitness theory, focusing on microbial altruism, help in cooperative breeders, reproductive restraint in eusocial species, and the evolution of eusociality and cooperative breeding. It also considers more advanced topics in social evolution theory, including sex allocation, genetic kin recognition, spite, and the evolution of organismality. Finally, it reviews theoretical approaches to studying social evolution other than replicator dynamics and the Price equation, such as population genetics, class-structured populations, and maximization approaches.

Conditional Behaviors and Inclusive Fitness

10.23943/princeton/9780691161563.003.0006 ◽

2015 ◽

Author(s):

James A.R. Marshall

Keyword(s):

Genetic Relatedness ◽

Inclusive Fitness ◽

Social Behaviors ◽

Phenotypic Assortment ◽

Hamilton’S Rule ◽

Implicit And Explicit ◽

This chapter examines social behaviors that are expressed conditional on the phenotype of others. David Queller argued that inclusive fitness analyses need to be done on a per-behavior basis, citing as an example the decision over whether to reproduce directly, and whether to aid a reproductive. Queller showed that inclusive fitness predictions are only sensible when one analyzes what an individual should do, given it finds itself in a particular behavioral role. The chapter first provides an overview of implicit and explicit conditionality and presents two classic examples: William D. Hamilton's greenbeard traits and Robert Trivers's theory of reciprocal cooperation. It also introduces an extension of Hamilton's rule to deal with explicitly conditional behaviors; this extension features a measure of phenotypic assortment that appears not to be the classic genetic relatedness of Hamilton's rule.

Social Behavior and Evolutionary Thought

10.23943/princeton/9780691161563.003.0001 ◽

2015 ◽

Author(s):

James A.R. Marshall

Keyword(s):

Natural Selection ◽

Mathematical Theory ◽

Group Selection ◽

Inclusive Fitness ◽

Price Equation ◽

Evolutionary Thought ◽

Multilevel Selection Theory ◽

The Individual ◽

Evolutionary Explanations

This book demonstrates the generality of inclusive fitness theory, with particular emphasis on its fundamental evolutionary logic. It presents the basic mathematical theory of natural selection and shows how inclusive fitness theory deals with more complicated social scenarios. Topics include the Price equation, Hamilton's rule, nonadditive interactions, conditional behaviors, heritability, and maximization of inclusive fitness. This chapter provides a brief historical introduction to the problem of apparent design in biology, evolutionary explanations of this, and in particular, evolutionary explanations of individual behaviors that appear designed to benefit not the individual themselves, but other members of their species. It examines how social behaviors can be shaped by natural selection and discusses the problem of providing an evolutionary explanation of self-sacrifice by individuals, altruism in group selection, and multilevel selection theory.