Inclusive fitness

Inclusive fitness is a conceptual framework in evolutionary biology first defined by W. D. Hamilton in 1964. It is primarily used to aid the understanding of how social traits are expected to evolve in structured populations. It involves partitioning an individual's expected fitness returns into two distinct components: direct fitness returns - the component of a focal individual’s fitness that is independent of who it interacts with socially; and indirect fitness returns - the component that is dependent on who it interacts with socially. The direct component of an individual's fitness is often called its personal fitness, while an individual’s direct and indirect fitness components taken together are often called its inclusive fitness.

Under an inclusive fitness framework, direct fitness returns are realised through the offspring a focal individual produces independent of who it interacts with, while indirect fitness returns are realised by adding up all the effects our focal individual has on the (number of) offspring produced by those it interacts with weighted by the relatedness of our focal individual to those it interacts with. Hamilton's theory, alongside reciprocal altruism, is considered one of the two primary mechanisms for the evolution of social behaviors in natural species and a major contribution to the field of sociobiology, which holds that some behaviors can be dictated by genes, and therefore can be passed to future generations and may be selected for as the organism evolves.

Belding's ground squirrel provides an example; it gives an alarm call to warn its local group of the presence of a predator. By emitting the alarm, it gives its own location away, putting itself in more danger. In the process, however, the squirrel may protect its relatives within the local group (along with the rest of the group). Therefore, if the effect of the trait influencing the alarm call typically protects the other squirrels in the immediate area, it will lead to the passing on of more copies of the alarm call trait in the next generation than the squirrel could leave by reproducing on its own. In such a case natural selection will increase the trait that influences giving the alarm call, provided that a sufficient fraction of the shared genes include the gene(s) predisposing to the alarm call.

Synalpheus regalis, a eusocial shrimp, is an organism whose social traits meet the inclusive fitness criterion. The larger defenders protect the young juveniles in the colony from outsiders. By ensuring the young's survival, the genes will continue to be passed on to future generations.

Inclusive fitness is more generalized than strict kin selection, which requires that the shared genes are identical by descent. Inclusive fitness is not limited to cases where "kin" ('close genetic relatives') are involved.

Hamilton's rule

Hamilton's rule is most easily derived in the framework of neighbour-modulated fitness, where the fitness of a focal individual is considered to be modulated by the actions of its neighbours. This is the inverse of inclusive fitness where we consider how a focal individual modulates the fitness of its neighbours. However, taken over the entire population, these two approaches are equivalent to each other so long as fitness remains linear in trait value. Relatedness here can vary between a value of 1 (only interacting with individuals of the same trait value) and -1 (only interacting with individuals of a [most] different trait value), and will be 0 when all individuals in the population interact with equal likelihood.

Fitness in practice, however, does not tend to be linear in trait value -this would imply an increase to an infinitely large trait value being just as valuable to fitness as a similar increase to a very small trait value. Consequently, to apply Hamilton's rule to biological systems the conditions under which fitness can be approximated to being linear in trait value must first be found. There are two main methods used to approximate fitness as being linear in trait value; performing a partial regression with respect to both the focal individual's trait value and its neighbours average trait value, or taking a first order Taylor series approximation of fitness with respect to trait value. They suggest that one should "use standard population genetics, game theory, or other methodologies to derive a condition for when the social trait of interest is favoured by selection and then use Hamilton's rule as an aid for conceptualizing this result". In other words, while inclusive fitness theory specifies a set of necessary criteria for the evolution of altruistic traits, it does not specify a sufficient condition for their evolution in any given species. More primary necessary criteria include the existence of gene complexes for altruistic traits in gene pool, as mentioned above, and especially that "a suitable social object is available", as Hamilton noted. The American evolutionary biologist Paul W. Sherman gives a fuller discussion of Hamilton's latter point:

The occurrence of sibling cannibalism in several species underlines the point that inclusive fitness theory should not be understood to simply predict that genetically related individuals will inevitably recognize and engage in positive social behaviours towards genetic relatives. Only in species that have the appropriate traits in their gene pool, and in which individuals typically interacted with genetic relatives in the natural conditions of their evolutionary history, will social behaviour potentially be elaborated, and consideration of the evolutionarily typical demographic composition of grouping contexts of that species is thus a first step in understanding how selection pressures upon inclusive fitness have shaped the forms of its social behaviour. Richard Dawkins gives a simplified illustration:

Evidence from a variety of species including primates and other social mammals suggests that contextual cues (such as familiarity) are often significant proximate mechanisms mediating the expression of altruistic behaviour, regardless of whether the participants are always in fact genetic relatives or not. This is nevertheless evolutionarily stable since selection pressure acts on typical conditions, not on the rare occasions where actual genetic relatedness differs from that normally encountered.

Such misunderstandings of inclusive fitness' implications for the study of altruism, even amongst professional biologists utilizing the theory, are widespread, prompting prominent theorists to regularly attempt to highlight and clarify the mistakes.

Green-beard effect

As well as interactions in reliable contexts of genetic relatedness, altruists may also have some way to recognize altruistic behaviour in unrelated individuals and be inclined to support them. As Dawkins points out in The Selfish Gene and The Extended Phenotype, this must be distinguished from the green-beard effect.

The green-beard effect is the act of a gene (or several closely linked genes), that:

Produces a phenotype.
Allows recognition of that phenotype in others.
Causes the individual to preferentially treat other individuals with the same gene.

The green-beard effect was originally a thought experiment by Hamilton in his publications on inclusive fitness in 1964, although it hadn't yet been observed. As of today, it has been observed in few species. Its rarity is probably due to its susceptibility to 'cheating' whereby individuals can gain the trait that confers the advantage, without the altruistic behaviour. This normally would occur via the crossing over of chromosomes which happens frequently, often rendering the green-beard effect a transient state. However, Wang et al. has shown in one of the species where the effect is common (fire ants), recombination cannot occur due to a large genetic transversion, essentially forming a supergene. This, along with homozygote inviability at the green-beard loci allows for the extended maintenance of the green-beard effect.

Equally, cheaters may not be able to invade the green-beard population if the mechanism for preferential treatment and the phenotype are intrinsically linked. In budding yeast (Saccharomyces cerevisiae), the dominant allele FLO1 is responsible for flocculation (self-adherence between cells) which helps protect them against harmful substances such as ethanol. While 'cheater' yeast cells occasionally find their way into the biofilm-like substance that is formed from FLO1 expressing yeast, they cannot invade as the FLO1 expressing yeast will not bind to them in return, and thus the phenotype is intrinsically linked to the preference.

Parent–offspring conflict and optimization

Early writings on inclusive fitness theory (including Hamilton 1964) used K in place of B/C. Thus Hamilton's rule was expressed as

is the necessary and sufficient condition for selection for altruism.

Where B is the gain to the beneficiary, C is the cost to the actor and r is the number of its own offspring equivalents the actor expects in one of the offspring of the beneficiary. r is either called the coefficient of relatedness or coefficient of relationship, depending on how it is computed. The method of computing has changed over time, as has the terminology. It is not clear whether or not changes in the terminology followed changes in computation.

Robert Trivers (1974) defined "parent-offspring conflict" as any case where to say that nothing is being maximized.

According to Trivers, if Sigmund Freud had tried to explain intra-family conflict after Hamilton instead of before him, he would have attributed the motivation for the conflict and for the castration complex to resource allocation issues rather than to sexual jealousy.

Incidentally, when k=1 or k=2, the average number of offspring per parent stays constant as time goes by. When k<1 or k>2 then the average number of offspring per parent increases as time goes by.

The term "gene" can refer to a locus (location) on an organism's DNA—a section that codes for a particular trait. Alternative versions of the code at that location are called "alleles." If there are two alleles at a locus, one of which codes for altruism and the other for selfishness, an individual who has one of each is said to be a heterozygote at that locus. If the heterozygote uses half of its resources raising its own offspring and the other half helping its siblings raise theirs, that condition is called codominance. If there is codominance the "2" in the above argument is exactly 2. If by contrast, the altruism allele is more dominant, then the 2 in the above would be replaced by a number smaller than 2. If the selfishness allele is the more dominant, something greater than 2 would replace the 2. Gardner in turn was critical of the paper, describing it as "a really terrible article", and along with 136 co-authors wrote a reply, submitted to Nature. The disagreement stems from a long history of confusion over what Hamilton's rule represents. Hamilton's rule gives the direction of mean phenotypic change (directional selection) so long as fitness is linear in phenotype, and the utility of Hamilton's rule is simply a reflection of when it is suitable to consider fitness as being linear in phenotype. The primary (and strictest) case is when evolution proceeds in very small mutational steps. Under such circumstances Hamilton's rule then emerges as the result of taking a first order Taylor series approximation of fitness with regards to phenotype. This assumption of small mutational steps (otherwise known as δ-weak selection) is often made on the basis of Fisher's geometric model and underpins much of modern evolutionary theory.

In work prior to Nowak et al. (2010), various authors derived different versions of a formula for <math>r</math>, all designed to preserve Hamilton's rule. Orlove noted that if a formula for <math>r</math> is defined so as to ensure that Hamilton's rule is preserved, then the approach is by definition ad hoc. However, he published an unrelated derivation of the same formula for <math>r</math> – a derivation designed to preserve two statements about the rate of selection – which on its own was similarly ad hoc. Orlove argued that the existence of two unrelated derivations of the formula for <math>r</math> reduces or eliminates the ad hoc nature of the formula, and of inclusive fitness theory as well. The derivations were demonstrated to be unrelated by corresponding parts of the two identical formulae for <math>r</math> being derived from the genotypes of different individuals. The parts that were derived from the genotypes of different individuals were terms to the right of the minus sign in the covariances in the two versions of the formula for <math>r</math>. By contrast, the terms left of the minus sign in both derivations come from the same source. In populations containing only two trait values, it has since been shown that <math>r</math> is in fact Sewall Wright's coefficient of relationship.

Engles (1982) suggested that the c/b ratio be considered as a continuum of this behavioural trait rather than discontinuous in nature. From this approach fitness transactions can be better observed because there is more to what is happening to affect an individual's fitness than just losing and gaining.

Inclusive fitness

Hamilton's rule

Green-beard effect

Parent–offspring conflict and optimization

See also

References

Further reading