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; 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 offspring produced by those it interacts with weighted by the relatedness of our focal individual to those it interacts with. This can be visualised in a sexually reproducing system by saying that an individual's own child, who carries one half of that individual's genes, represents one offspring equivalent. A sibling's child, who will carry one-quarter of the individual's genes, will then represent 1/2 offspring equivalent.
Neighbour-modulated fitness is the conceptual inverse of inclusive fitness. Where inclusive fitness calculates an individual’s indirect fitness component by summing the fitness that focal individual receives through modifying the productivities of those it interacts with, neighbour-modulated fitness instead calculates it by summing the effects an individual’s neighbours have on that focal individual’s productivity. When taken over an entire population, these two frameworks give functionally equivalent results. Hamilton’s rule is a particularly important result in the fields of evolutionary ecology and behavioral ecology that follows naturally from the partitioning of fitness into direct and indirect components, as given by inclusive and neighbour-modulated fitness. It enables us to see how the average trait value of a population is expected to evolve under the assumption of small mutational steps.
Kin selection is a well known case whereby inclusive fitness effects can influence the evolution of social behaviours. Kin selection relies on positive relatedness to enable individuals who positively influence the fitness of those they interact with at a cost to their own personal fitness, to outcompete individuals employing more selfish strategies. It is thought to be one of the primary mechanisms underlying the evolution of altruistic behaviour, alongside the less prevalent reciprocity, and to be of particular importance in enabling the evolution of eusociality among other forms of group living. Inclusive fitness has also been used to explain the existence of spiteful behaviour, where individuals negatively influence the fitness of those they interact with at a cost to their own personal fitness.
Inclusive fitness and neighbour-modulated fitness are both frameworks that leverage the individual as the unit of selection. It is from this that the gene-centered view of evolution emerged: a perspective that has facilitated much of the work done into the evolution of conflict.
Overview
The British evolutionary biologist W. D. Hamilton showed mathematically that, because other members of a population may share one's genes, a gene can also increase its evolutionary success by indirectly promoting the reproduction and survival of other individuals who also carry that gene. This is variously called "kin theory", "kin selection theory" or "inclusive fitness theory". The most obvious category of such individuals is close genetic relatives, and where these are concerned, the application of inclusive fitness theory is often more straightforwardly treated via the narrower kin selection theory. 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. 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 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" 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. A simple derivation of Hamilton's rule can be gained via the Price equation as follows. If an infinite population is assumed, such that any non-selective effects can be ignored, the Price equation can be written as:Where represents trait value and represents fitness, either taken for an individual or averaged over the entire population. If fitness is linear in trait value, the fitness for an individual can be written as:
Where is the component of an individual's fitness which is independent of trait value, parameterizes the effect of individual 's phenotype on its own fitness, is the average trait value of individual 's neighbours, and parameterizes the effect of individual 's neighbours on its fitness. Substituting into the Price equation then gives:
Since by definition does not covary with, this rearranges to:
Since this term must, by definition, be greater than 0. This is because variances can never be negative, and negative mean fitness is undefined. It can then be said that that mean trait value will increase when:
or
Giving Hamilton's rule, where relatedness is a regression coefficient of the form, or. Relatedness here can vary between a value of 1 and -1, 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. Performing a partial regression requires minimal assumptions, but only provides a statistical relationship as opposed to a mechanistic one, and cannot be extrapolated beyond the dataset that it was generated from. Linearizing via a Taylor series approximation, however, provides a powerful mechanistic relationship, but requires the assumption that evolution proceeds in sufficiently small mutational steps that the difference in trait value between an individual and its neighbours is close to 0 : although in practice this approximation can often still retain predictive power under larger mutational steps.
As a first order approximation, Hamilton's rule can only inform about how the mean trait value in a population is expected to change. It contains no information about how the variance in trait value is expected to change. As such it cannot be considered sufficient to determine evolutionary stability, even when Hamilton's rule predicts no change in trait value. This is because disruptive selection terms, and subsequent conditions for evolutionary branching, must instead be obtained from second order approximations of fitness.
Gardner et al. suggest that Hamilton's rule can be applied to multi-locus models, but that it should be done at the point of interpreting theory, rather than the starting point of enquiry. 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". It is now becoming increasingly popular to use adaptive dynamics approaches to gain selection conditions which are directly interpretable with respect to Hamilton's rule.
Altruism
The concept serves to explain how natural selection can perpetuate altruism. If there is an "altruism gene" that influences an organism's behaviour to be helpful and protective of relatives and their offspring, this behaviour also increases the proportion of the altruism gene in the population, because relatives are likely to share genes with the altruist due to common descent. In formal terms, if such a complex of genes arises, Hamilton's rule specifies the selective criteria for such a trait to increase in frequency in the population. Hamilton noted that inclusive fitness theory does not by itself predict that a species will necessarily evolve such altruistic behaviours, since an opportunity or context for interaction between individuals is a more primary and necessary requirement in order for any social interaction to occur in the first place. As Hamilton put it, "Altruistic or selfish acts are only possible when a suitable social object is available. In this sense behaviours are conditional from the start." 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 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. Inclusive fitness theory thus does not imply that organisms evolve to direct altruism towards genetic relatives. Many popular treatments do however promote this interpretation, as illustrated in a review:
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. An example of attempted clarification is West et al. :