Hamilton

Hamilton's theory of kin selection is the best-known framework for understanding the evolution of social behavior but has long been a source of controversy in evolutionary biology. A recent critique of the theory by Nowak, Tarnita, and Wilson sparked a new round of debate, which shows no signs of abating. In this overview, we highlight a number of conceptual issues that lie at the heart of the current debate. We begin by emphasizing that there are various alternative formulations of Hamilton's rule, including a general version, which is always true; an approximate version, which assumes weak selection; and a special version, which demands other restrictive assumptions. We then examine the relationship between the neighbor-modulated fitness and inclusive fitness approaches to kin selection.

Finally, we consider the often-strained relationship between the theories of kin and multilevel selection. Relatedness leads to indirect reproduction. An altruist (black) confers a fitness benefit ( b) on a related recipient (white) at a cost ( c) to itself. The recipient does not express the altruistic phenotype. However, it possesses conditionally expressed genes for altruism, which it transmits to some of its offspring (indicated by the dotted lines, which show the genetic similarity between the actor and the recipient's offspring). The recipient thereby provides the actor with a means of indirect reproduction—that is, an indirect route to genetic representation in the next generation. Relatedness leads to indirect reproduction.

An altruist (black) confers a fitness benefit ( b) on a related recipient (white) at a cost ( c) to itself. The recipient does not express the altruistic phenotype. However, it possesses conditionally expressed genes for altruism, which it transmits to some of its offspring (indicated by the dotted lines, which show the genetic similarity between the actor and the recipient's offspring). The recipient thereby provides the actor with a means of indirect reproduction—that is, an indirect route to genetic representation in the next generation.The first perspective is captured in the neighbor-modulated fitness framework (figure ), which looks at the correlations between an individual's genotype and its social neighborhood and helps predict when these correlations will make the bearers of the genes for altruism fitter, on average, than nonbearers (Hamilton, Taylor PD and Frank, Frank, ).

Kin

The second perspective is captured in the inclusive fitness framework (figure ), which adds up all the fitness effects causally attributable to a social actor, weighting each component by the relatedness between the actor and the recipient, in order to calculate the net effect of a social behavior on the actor's overall genetic representation in the next generation (Hamilton, Frank, Grafen ). Inclusive fitness. In an inclusive fitness analysis, fitness effects are assigned to the actors whose behavior was causally responsible for them.

A therefore retains the effect –c for which it responsible but loses the 3b units of personal fitness it received by virtue of its interactions with B, C, and D. In compensation, it gains 3b units taken from the reproductive output of B, C, and D. To calculate A's inclusive fitness, these new slices are weighted by the actor's relatedness to the recipient. (1)This is a version of the Price equation (Price ); the full version includes an extra term, but we are entitled to drop that term here because our assumptions guarantee the unbiased transmission of alleles. The equation tells us that the allele—and, therefore, the social behavior that it codes for—will spread so long as cov( w i, p i) is greater than 0 (i.e., there is a positive covariance between an individual's fitness and its genetic value).

Kin Selection Definition

This simply formalizes the core neo-Darwinian idea that genes associated with higher individual fitness will increase in frequency.is always true but not always useful, becauase the covariance term will often lack a natural biological interpretation (Grafen, Okasha ). Kin and multilevel selection can be regarded as alternative ways of decomposing the covariance term in into more meaningful components. According to the kin selection approach, we use a linear regression model to split the covariance term into components attributable to the direct and indirect fitness effects of the social behavior under consideration (Queller, Gardner et al.

This allows us to derive HRG, the generalized version of Hamilton's rule discussed above, in a straightforward manner. According to the multilevel selection approach, we split the covariance term into components attributable to selection within groups and selection between groups (Price, Okasha ). This allows us to derive a principle that closely parallels HRG, according to which a costly social behavior can spread by natural selection only if the selection for the trait between groups is stronger than the selection against the trait within groups. The details of these derivations are spelled out in boxes.

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