Extending the range of additivity in using inclusive fitness

Abstract

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.

Multiple social encounters can eliminate Crozier’s paradox and stabilise genetic kin recognition

“…the fitness consequences of defecting 1 ). For more discussion of our inclusive fitness payoff measure, and how it relates to a recent paper by Levin and Grafen 48 , see the aside at the end of this section (‘Individual-level analysis (finding the right area of parameter space)’).…”

“…We note as an aside that, when calculating the inclusive fitness payoff of a given action (trait), we followed Hamilton in measuring the fitness consequences of the trait relative to the hypothetical scenario where the actor does not express the trait 1 . A recent paper argues that, instead, when calculating the inclusive fitness payoff of a given action (trait), the fitness consequences of the trait should be measured relative to the population average trait value 48 . For instance, this proposed amendment to the calculation of inclusive fitness payoffs would mean, contrary to what we said in the above analysis, that indiscriminate defection could have an inclusive fitness payoff that is different from zero, because defection could still have fitness consequences relative to the population average trait value.…”

“…Secondly, the equations are simpler and the mathematical argument is easier to follow when inclusive fitness calculations are made relative to case where the trait is absent (Hamilton’s definition), rather than to the population average trait value (proposed amendment). More broadly, the two formulations are likely to give identical results in most models, with Hamilton’s original definition only leading to potential pitfalls, and requiring amendment, in models where fitness effects combine non-additively 48 , 53 , 54 .…”

Realistic genetic architecture enables organismal adaptation as predicted under the folk definition of inclusive fitness

“…Recently, Lehmann and Rousset (2020) A similar half-marginal formulation of IF, with similar drawbacks, was proposed by Levin and Grafen (2021). Their version sums three components, namely 'baseline asocial fitness, the difference to personal fitness as a result of the strategy, and relatedness weighted difference to social partners' fitnesses as a result of the strategy' (Ibid., p. 5).…”

Bacterial cooperation through horizontal gene transfer

“…Through his inclusive fitness theory, Hamilton first proposed that relatedness between interacting organisms can favor cooperation even when costly to the individual [78,79]. Inclusive fitness theory has since been expanded to include general models taking individual genes into account [80,81]. Spatial structure of a population can also allow cooperation to evolve [56,57], even without considering relatedness [7,80].…”