Hamilton's rule

Veelen, Matthijs van; Allen, Benjamin; Hoffman, Moshe; Simon, Burton; Veller, Carl

doi:10.1016/j.jtbi.2016.08.019

Cited by 37 publications

(58 citation statements)

References 140 publications

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“…That HRG has no predictive power has been previously noted by ourselves (22) and others (12,23,24), yet HRG is credited with making a variety of empirical predictions (7,9,14).…”

Section: Discussionmentioning

confidence: 88%

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The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Nowak

McAvoy

Allen

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Hamilton's rule asserts that a trait is favored by natural selection if the benefit to others, B, multiplied by relatedness, R, exceeds the cost to self, C. Specifically, Hamilton's rule states that the change in average trait value in a population is proportional to BR − C. This rule is commonly believed to be a natural law making important predictions in biology, and its influence has spread from evolutionary biology to other fields including the social sciences. Whereas many feel that Hamilton's rule provides valuable intuition, there is disagreement even among experts as to how the quantities B, R, and C should be defined for a given system. Here, we investigate a widely endorsed formulation of Hamilton's rule, which is said to be as general as natural selection itself. We show that, in this formulation, Hamilton's rule does not make predictions and cannot be tested empirically. It turns out that the parameters B and C depend on the change in average trait value and therefore cannot predict that change. In this formulation, which has been called "exact and general" by its proponents, Hamilton's rule can "predict" only the data that have already been given.amilton's rule is a widely known concept in evolutionary biology. It has become standard textbook knowledge and is encountered in undergraduate education. For many, Hamilton's rule expresses the intuition that cooperation evolves more easily when there are frequent interactions among relatives, because relatives are likely to share the cooperative trait. However, Hamilton's rule goes beyond this intuition by positing a quantitative condition, BR − C > 0, which is said to predict whether or not a trait will be selected. Specifically, it is claimed that the change in average trait value from one time point to the next is proportional to BR − C .We immediately encounter the question of how the "benefit," B , the "relatedness," R, and the "cost," C , are calculated for a given system. Surprisingly, there is no consensus about the correct method. A variety of derivations have been proposed over the years (1-10), which define B , R, and C in distinct (nonequivalent) ways. In the empirical literature, peer reviewers often disagree over which method should be used in a particular manuscript (11).A number of recent papers (7, 9, 10) have endorsed a particular formulation (4, 5) as the exact, general, and even "canonical" version of Hamilton's rule. This formulation, called "Hamilton's rule-general" (HRG) (12, 13), is claimed to be as general as natural selection itself (7,14). The derivation, which we recapitulate below, is simple and contains only a few steps.The mathematical investigation of HRG reveals three astonishing facts. First, HRG is logically incapable of making any prediction about any situation because the benefit, B , and the cost, C , cannot be known in advance. They depend on the data that are to be predicted. At the outset of an experiment, B and C are unknown, and so there is no way to say what Hamilton's rule would predict. Once the experiment is ...

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“…That HRG has no predictive power has been previously noted by ourselves (22) and others (12,23,24), yet HRG is credited with making a variety of empirical predictions (7,9,14).…”

Section: Discussionmentioning

confidence: 88%

“…For example, benefit and cost can be properties of individual phenotypes, and relatedness can be defined using common ancestry (1,3,12,13,24,28). This approach, "Hamilton's rule-special" (HRS) (12,13), has the advantage of making testable predictions, because the benefit and cost of a phenotype can be determined in advance.…”

Section: Discussionmentioning

confidence: 99%

The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Nowak

McAvoy

Allen

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

View full text Add to dashboard Cite

show abstract

“…; Allen ; Allen and Nowak ; Nowak and Allen ; van Veelen et al. ). However, none of these authors provide (i) an alternative explanation for design, (ii) a consistent, unified way to generate predictions, or (iii) an adaptive principle that can be tested in the field and the laboratory.…”

Section: Practicalities For Behavioral Ecologistsmentioning

confidence: 99%

“…; Allen ; Allen and Nowak ; Nowak and Allen ; Akçay and Van Cleve ; van Veelen et al. ) have suggested abandoning inclusive fitness for what they refer to as “standard natural selection” models, which track gene frequencies. This approach is good at predicting gene frequency change in mathematical models.…”

Section: The Challenge Of Nonadditivitymentioning

confidence: 99%

“…The limitations of inclusive fitness have led some authors to call for abandoning an individual level design principle altogether (Nowak et al 2010;Doebeli 2010;Allen et al 2013;Allen 2015;Allen and Nowak 2015;Nowak and Allen 2015;van Veelen et al 2017). However, none of these authors provide (i) an alternative explanation for design, (ii) a consistent, unified way to generate predictions, or (iii) an adaptive principle that can be tested in the field and the laboratory.…”

Section: Abandon Designmentioning

confidence: 99%

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Inclusive fitness is an indispensable approximation for understanding organismal design

Levin

Grafen

2019

Evolution

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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.

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Extending the range of additivity in using inclusive fitness

Levin

Grafen

2021

Ecology and Evolution

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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.

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Hamilton's rule

Cited by 37 publications

References 140 publications

The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Inclusive fitness is an indispensable approximation for understanding organismal design

Extending the range of additivity in using inclusive fitness

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