scholarly journals Can Hamilton’s rule be violated?

eLife ◽  
2018 ◽  
Vol 7 ◽  
Author(s):  
Matthijs van Veelen
Keyword(s):  
Statistical Models ◽  
General Model ◽  
Fitness Function ◽  
Regression Method ◽  
Costs And Benefits ◽  
Hamilton’S Rule ◽  
Empirical Tests ◽  
Group Compositions ◽  
Hamilton's Rule

How generally Hamilton’s rule holds is a much debated question. The answer to that question depends on how costs and benefits are defined. When using the regression method to define costs and benefits, there is no scope for violations of Hamilton’s rule. We introduce a general model for assortative group compositions to show that, when using the counterfactual method for computing costs and benefits, there is room for violations. The model also shows that there are limitations to observing violations in equilibrium, as the discrepancies between Hamilton’s rule and the direction of selection may imply that selection will take the population out of the region of disagreement, precluding observations of violations in equilibrium. Given what it takes to create a violation, empirical tests of Hamilton’s rule, both in and out of equilibrium, require the use of statistical models that allow for identifying non-linearities in the fitness function.

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

2020 ◽  
Author(s):  
António M. M. Rodrigues
Keyword(s):  
Inclusive Fitness ◽  
Causal Structure ◽  
Regression Method ◽  
Structured Populations ◽  
Price Equation ◽  
Hamilton’S Rule ◽  
Inclusive Fitness Theory ◽  
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.

Nonadditive Interactions and Hamilton’s Rule

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.

scholarly journals The causal meaning of Hamilton’s rule

2016 ◽  
Vol 3 (3) ◽  
pp. 160037 ◽  
Author(s):  
Samir Okasha ◽  
Johannes Martens
Keyword(s):  
Social Action ◽  
Biological Significance ◽  
Costs And Benefits ◽  
Partial Regression ◽  
Hamilton’S Rule ◽  
Hypothetical Experiment ◽  
The Cost ◽  
Original Derivation ◽  
Hamilton's Rule ◽  
Exact Version

Hamilton’s original derivation of his rule for the spread of an altruistic gene ( rb > c ) assumed additivity of costs and benefits. Recently, it has been argued that an exact version of the rule holds under non-additive pay-offs, so long as the cost and benefit terms are suitably defined, as partial regression coefficients. However, critics have questioned both the biological significance and the causal meaning of the resulting rule. This paper examines the causal meaning of the generalized Hamilton’s rule in a simple model, by computing the effect of a hypothetical experiment to assess the cost of a social action and comparing it to the partial regression definition. The two do not agree. A possible way of salvaging the causal meaning of Hamilton’s rule is explored, by appeal to R. A. Fisher’s ‘average effect of a gene substitution’.

scholarly journals Oblique Transmission, Conformity, and Preference in the Evolution of Altruism

2020 ◽  
Author(s):  
Kaleda K Denton ◽  
Yoav Ram ◽  
Marcus W Feldman
Keyword(s):  
Kin Selection ◽  
Cultural Transmission ◽  
Costs And Benefits ◽  
Fitness Components ◽  
Genetic Transmission ◽  
Hamilton’S Rule ◽  
Genetic Components ◽  
Random Assortment ◽  
Invasion Threshold ◽  
Hamilton's Rule

The evolution of altruism is frequently studied using models of non-random assortment, including kin selection. In genetic kin selection models, under certain assumptions including additive costs and benefits, the criterion for altruism to invade a population is Hamilton's rule. Deviations from Hamilton's rule occur when vertical transmission has cultural and genetic components, or when costs and benefits are combined multiplicatively. Here, we include oblique and vertical cultural transmission and genetic transmission in four models--two forms of parent-to-offspring altruism, sibling-to-sibling altruism, and altruism between offspring that meet assortatively--under additive or multiplicative assumptions. Oblique transmission may be conformist (anti-conformist), where the probability that an individual acquires a more common cultural variant is greater (less) than its frequency. Inclusion of conformist or anti-conformist oblique transmission may reduce or increase the threshold for invasion by altruism relative to Hamilton's rule. Thresholds for invasion by altruism are lower with anti-conformity than with conformity, and lower or the same with additive rather than multiplicative fitness components. Invasion by an allele that increases the preference for altruism does not depend on oblique phenotypic transmission, and with sibling-to-sibling altruism, this allele's invasion threshold can be higher with additive rather than multiplicative fitnesses.

Social Evolution, Hamilton’s Rule, and Inclusive Fitness

2018 ◽  
Author(s):  
Samir Okasha
Keyword(s):  
Social Behaviour ◽  
Social Evolution ◽  
Inclusive Fitness ◽  
Popular Approach ◽  
Hamilton’S Rule ◽  
Inclusive Fitness Theory ◽  
The Social ◽  
Social Encounters ◽  
The Individual ◽  
Hamilton's Rule

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.

Hamilton’s rule and kin competition in a finite kin population

2021 ◽  
pp. 110862
Author(s):  
Qiao-Qiao He ◽  
Xiu-Deng Zheng ◽  
Ruth Mace ◽  
Yi Tao ◽  
Ting Ji
Keyword(s):  
Kin Competition ◽  
Hamilton’S Rule ◽  
Hamilton's Rule

scholarly journals Quantitative genetic versions of Hamilton's rule with empirical applications

2014 ◽  
Vol 369 (1642) ◽  
pp. 20130358 ◽  
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 Rule

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.

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