Inclusive fitness

In evolutionary biology and evolutionary psychology, inclusive fitness is the sum of an organism's classical fitness (how many of its own offspring it produces and supports) and the number of equivalents of its own offspring it can add to the population by supporting others.

Belding's ground squirrel provides an example. The ground squirrel 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 protects its relatives within the local group (along with the rest of the group). Further study has shown that the squirrel's willingness to put itself at risk is directly proportional to how closely related it is to members of the local group. Therefore, if protecting the other squirrels in the immediate area will lead to the passing on of more of the squirrel’s own genes than the squirrel could leave by reproducing on its own, then natural selection will favor giving the alarm call, provided that a sufficient fraction of the shared genes include the gene(s) predisposing to the alarm call.

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

From the gene's point of view, evolutionary success ultimately depends on leaving behind the maximum number of copies of itself in the population. Until 1964, it was generally believed that genes only achieved this by causing the individual to leave the maximum number of viable offspring. However, in 1964 W. D. Hamilton proved mathematically that, because close relatives of an organism share some identical genes, a gene can also increase its evolutionary success by promoting the reproduction and survival of these related or otherwise similar individuals. Hamilton claimed that this leads natural selection to favor organisms that would behave in ways that maximize their inclusive fitness. It is also true that natural selection favors behavior that maximizes personal fitness.

Hamilton's rule describes mathematically whether or not a gene for altruistic behaviour will spread in a population: :$rb\; >\; c\; \backslash$ where

$c\; \backslash$ is the reproductive cost to the altruist,

$b\; \backslash$ is the reproductive benefit to the recipient of the altruistic behavior, and

$r\; \backslash$ is the probability, above the population average, of the individuals sharing an altruistic gene – commonly viewed as "degree of relatedness".

In a recent paper, Gardner et al suggest that Hamilton's rule can be applied to multi-locus models, but that it should be done so 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 favored by selection and then use Hamilton’s rule as an aid for conceptualizing this result,". A recent paper by Nowak et al. suggested that standard natural selection theory is superior to inclusive fitness theory, stating that the the interactions between cost and benefit can not be explained only in terms of relatedness. This, Nowak said, makes Hamilton's rule at worst superfluous and at and best ad hoc. Gardner in turn was critical of the paper, describing it as "a really terrible article", and along with other co-authors has written a reply paper, submitted to Nature..

Inclusive fitness and altruism

The concept serves to explain how natural selection can perpetuate altruism. If there is an '"altruism gene"' (or complex of genes) that influences an organism's behavior to be helpful and protective of relatives and their offspring, this behavior 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. Altruists may also have some way to recognize altruistic behavior in unrelated individuals and be inclined to support them. As Dawkins points out in The Selfish Gene (Chapter 6) and The Extended Phenotype (Chapter 9), this must be distinguished from the green-beard effect. The proposal that altruists who support other altruists who are not their kin will encourage the evolution of altruism requires that altruists recognize and choose to support others predisposed toward altruism whom they have detected by their past altruistic behavior, not on the observation of some temporarily correlated characteristic (e.g., green beards). If the green beard effect were the mechanism, some non-altruistic individuals would evolve to mimic the label and would receive the benefits of support from altruists. This would happen quickly due to crossing over of chromosomes; it would not require waiting for the rare event of a mutation. The mimics would receive the benefits but would not incur the costs of caring for others, and so would out-compete the true altruists.

Inclusive fitness and parental care

Some might express concern that parental investment (parental care) is said to contribute to inclusive fitness. The distinctions between the kind of beneficiaries nurtured (collateral versus descendant relatives) and the kind of fitnesses used (inclusive versus personal) in our parsing of nature are orthogonal concepts. This orthogonality can best be understood in a thought experiment: Consider a model of a population of animals such as crocodiles or tangle web spiders. Among these spiders and reptiles, some species or populations exhibit parental care, while closely-related species or populations lack it. Assume that in these creatures a gene, called a, codes for parental care, and its other allele, called A, codes for an absence thereof. The aa homozygotes care for their young, and AA homozygotes don't, and the heterozygotes behave like aa homozygotes if a is dominant, and like AA homozygotes if A is dominant, or exhibit some kind of intermediate behaviour if there is partial dominance. Other kinds of animals could be considered in which all individuals exhibit parental care, but variation among them would be in the quantity and quality thereof.

Calculating personal and inclusive fitness

There is a theoretical and methodological distinction to be made concerning another type of fitness, personal fitness. In the terminology used by Richard Dawkins in his 1976 book, The Selfish Gene, with personal fitness, the increments of fitness are counted with the bearers, and with inclusive fitness they are counted with the carers.

If we parse nature such that life begins at conception, then, other things being equal, the only differences between how well different individuals fare will be based on how much care they got as pre-weaned babies, because all mothers will conceive the same number of kids, but some will take care of them, or care for them better, and thus more of them will live, but the differences in mortality will count as part of the offsprings' fitnesses. Thus the variations in fitness among the animals will be part of their L(x) curves.

But if we parse nature such that life begins at weaning, and the pre-weaned offspring is part of the mother until weaned, sort of like a fetus, then the number of offspring weaned successfully, will be sort of a littersize, and the variations in success among individuals will be considered part of the mother's M(x) curve.

L(x) is the probability of still being alive at age = x, and M(x) is fecundity at age x. These are just two ways of keeping track of the bookkeeping, and the animals are exactly the same regardless how we keep track of them. However, if we regard life as beginning at weaning, the heterozygote will have the same fitness as the homozygote with the dominant gene, and it would be reasonable to assume that fitness will be a constant function of genotype (Provided that the relatedness coefficient does not change from one generation to the next; during weak selection where the relatedness coefficient changes only slightly, the assumption will be approximately true). If life begins at conception, it would be reasonable to assume that the three kinds of genotyped individuals will have different fitnesses, not only from each other but from generation to generation.

Fitnesses calculated in the life-begins-at-conception world will be examples of "personal fitnesses" or reproductive successes, whereas fitnesses calculated in the life-begins-at-weaning world will be examples of "inclusive fitnesses." This understanding is identical to that of W. D. Hamilton, whose philosophy is embodied in this discussion and terminology.

The size of the increment is always one in a personal-fitness parsing, but can be some fraction less than one during an inclusive-fitness parsing. A cousin, for example, has some copies of one's own genes in the manner that an offspring does, although not as many of them. Because first cousins are related by approximately 1/8 on average, raising one kid for your first cousin automatically increments your inclusive fitness by approximately 1/8, but indicates a probability of approximately 1/8 of incrementing your personal fitness by 1. This is because the probability is approximately 1/8 your cousin will rear a child of yours for you if you rear one offspring for any of your cousins. (This is a statement of probability, not of deliberate intention on the part of you or your cousin.) There are complicating factors. One is that in order to determine the value of inclusive fitness it is necessary to know the exact value of the relatedness coefficient, which will rarely be exactly 1/8. Another is that there are two kinds of inclusive fitness, "corrected" and "uncorrected" (Orlove 1979).

When personal fitness is being considered we are using a reciprocal altruism approach. In inclusive fitness parsing we are using a kin-theoretical approach. This is so regardless of whether the individuals are actually related, or as-if related because they share the same altruism genes (as indicated by past behavior).

These probabilities of reciprocity will be coefficients of relatedness in species where there is only altruism toward relatives, but when strangers are involved they can be estimates of reciprocation, which depend on being, as if, more closely related than average at the altruism influencing portions of the genome, based on past behaviour, in a stranger. Sometimes the altruistic act benefits non-relatives for other reasons. For example, members of many species will take care of unrelated youngsters. This may be because the evolved mechanism is not sensitive enough to make fine discriminations. . The possibility of this being the cause of the altruistic behavior is implicitly incorporated into the definition of the relatedness coefficient. Any particular interaction between individuals may be analyzed by either the reciprocal altruism or inclusive fitness approach. Depending on the situation, one or the other may make the analysis easier. The animals do what they do and we analyze it one way or the other.

See also

Gene-centered view of evolution

Kin selection

Reproductive success

r/K selection theory

External links

Test simulations:

:* http://www.simtel.net/free/Biology-programs/wasps004zip/24173.html :* http://www.simtel.net/product.rate.php%5BproductId%5D14756%5BSiteID%5Dsimtel.net

Sources

Campbell, N., Reece, J., et al. 2002. Biology. 6th ed. San Francisco, California. pp. 1145-1148.

Rheingold, Howard, “Technologies of cooperation” in Smart Mobs. Cambridge, MA : Perseus Publishing, 2002 (Ch. 2:pp 29-61)

Dawkins, Richard C. 1976 The Selfish Gene, Oxford University Press (Discussion of carers and bearers in relation to inclusive and personal fitnesses, and the bugbear of parental investment as part of inclusive fitness occurs herein)

Hamilton, W. D. 1964 The Genetical Evolution of Social Behaviour I and II, J. Theor. Biol. v7, pp 1-16, and 17-52

Hamilton, W. D. 1975, Innate Social Aptitudes of Man: an Approach from Evolutionary Genetics, in Robin Fox (ed.), Biosocial Anthropology, Malaby Press, London, 133-153 (IF including altruism to fellow altruists among strangers discussed herein)

Hamilton, W. D. Narrow Roads of Geneland I and II, 1995 Freeman I 2001 Oxford Press II (biography of WDH and anthology of his writings)

Orlove, M. J. 1975 A Model of Kin Selection not Invoking Coefficients of Relationship J. Theor. Biol. v49 pp289-310 (Isomorphism between Karma and Kin Theories discussed herein)

Orlove, M. J. 1979 A Reconciliation of Inclusive Fitness and Personal Fitness Approaches: a Proposed Correcting Term for the Inclusive Fitness Formula, J. Theor. Biol. v81 pp577-586 (Karma-Theory/Kin-Theory equivalence moves from conjecture to theorem status here)

Trivers, R. L. 1971 The Evolution of Reciprocal Altruism, Quarterly Review of Biology 46: 35-57

Trivers, R. L. 1972 Parental Investment and Sexual Selection in B. Campbell (ed.), Sexual Selection and the Descent of Man, 1871-1971 (pp. 136-179) Chicago, Il: Aldine

Trivers, R. L. 1974 Parent/Offspring Conflict, American Zoologist, 14 249-264 (Bigtime importance of If in understanding intra-family conflict)

Sherman, P.W. 2001. “Squirrels” (pp. 598-609, with L. Wauters) and “The Role of Kinship” (pp. 610-611) in Encyclopedia of Mammals, D.W. Macdonald (Ed.). Andromeda, UK.

Category:Evolutionary biology