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In evolutionary biology and evolutionary psychology, inclusive fitness refers to an organism's classical fitness (how many of its own offspring it produces and supports) plus the number of equivalents of its own offspring it can add to the population by supporting others. ^[1]

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 possible. However, in 1964 W. D. Hamilton proved mathematically that because close relatives of an organism have some replica genes, the gene can also increase its evolutionary success by promoting the reproduction and survival of these related or otherwise similar individuals. This leads individuals to behave in a manner maximising their inclusive fitness, rather than their individual fitness.

This model is more generalized than kin selection (in the strict sense), which requires that the shared genes are identical by descent. Inclusive fitness is not limited to cases where kin are involved. Kin selection theory has been treated as synonymous with inclusive fitness theory because the most common historical context for modeling inclusive fitness has been in groups of organisms with a kin-relation.

An example of inclusive fitness is when Belding's ground squirrel gives an alarm call to warn its group of the presence of a predator. By emitting the alarm, the squirrel puts itself into increased danger by giving away its location. In the process, however, the squirrel protects its relatives that live within the population (along with the rest of the population). In further studies, it has been shown that willingness of the squirrel to put itself at risk is directly proportional to how closely related it is to members of its population. 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, the squirrel is willing to risk sacrificing itself which leads to greater inclusive fitness. ^[2]

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. Altruists may also have some way to recognize altruistic behavior in completely unrelated individuals and be inclined to support them. Inclusive fitness encompasses both of these phenomena.

Contents 1 Hamilton's equation 2 Evidence of inclusive fitness in humans 3 Inclusive fitness in the family structure 4 See also 5 External links 6 Sources

[edit] Hamilton's equation

Hamilton's equation describes mathematically whether or not a gene for altruistic behaviour will spread in a population:

where

• is the reproductive cost to the altruist,
• is the reproductive benefit to the recipient of the altruistic behavior, and
• is the probability, above the population average, of the individuals sharing an altruistic gene – commonly viewed as "degree of relatedness".

[edit] Evidence of inclusive fitness in humans

Human behavior is generally much more complicated than the behavior of other organisms, making it difficult to define human behavior in general organism terms. However, evidence for human altruistic behavior leading to increased inclusive fitness has been observed. While there exists clear evidence towards increased inclusive fitness through altruistic behaviors on behalf of parents and children, much sacrificial behavior by humans is generally done in the hope of reciprocation at some point in the future. Therefore, increasing inclusive fitness in humans is not necessarily dependent upon relatedness. Rather, it is commonly based on reciprocal altruism.

[edit] Inclusive fitness in the family structure

Inclusive fitness may also be applied to the familial structure. Parents are frequently self-sacrificing towards their children with the hope that children will carry on the family genes. Frequently, the amount of altruistic behavior displayed by parents to increase their inclusive fitness is related to the amount of parental investment initially involved.

It is common for some people to express concern when parental investment (parental care) is said to contribute to inclusive fitness. This concern exemplifies the surprisingly large degree of confusion and obfuscation over such a profound and fundamental concept as IF. The distinctions between, kind of beneficiaries nurtured (collateral versus descendant relatives), and, kind of fitnesses used in our parsing events in nature to understand the goings on, are orthogonal concepts. This orthogonality, can best be understood in a thought experiment in which we consider a model of a population of animals such as tangle web spiders or crocodiles in which a gene, called a, codes for parental care, and its other allele, called A, codes for an absence thereof, thus 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. Among these spiders and reptiles, some species or populations exhibit parental care, while closely-related species or populations lack it, so this is somewhat reasonable. However, 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.

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."

Both kinds of fitnesses can be used to parse reality in models or real populations with or without altruism toward collateral relatives. An older kind of fitness, called "classical fitness", doesn't consider social interactions at all. Altruistically-reared offspring aren't counted here as incrementing the fitness of the altruist or the beneficiary, but classical fitness, is simply, a carryover from earlier days when thought didn't go this deep in this direction.

This understanding is identical to that of W. D. Hamilton, whose philosophy is embodied in this discussion and terminology.

As enunciated 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.

The mathematics simply becomes easier to use inclusive fitnesses, when studying model or real populations in which altruism toward collateral relatives is common or present, but the use of an inclusive fitness approach doesn't ipso facto imply collateral altruism is occurring, nor the use of personal fitnesses imply it isn't.

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. For example, because first cousins are related by approximately 1/8 on average, raising one kid for your first cousin automatically increments your inclusive fitness by 1/8, but indicates a probability of 1/8 of incrementing your personal fitness by 1. This is because the probability is 1/8 your cousin will rear a child of yours for you if you rear one offspring for one of your cousins. There are complicating factors. One is that the relatedness coefficient will rarely be exactly 1/8. Another is that there are two kinds of inclusive fitness, "corrected" and "uncorrected," explained in the reference below (Orlove 1979). This is because 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. 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).

Corrected and uncorrected inclusive fitness, along with other concepts, are verbally explained, however in: Stories with Bill Hamilton in them. (This account was written in the spirit of the Pliny the Younger letter to Tacitus when he said "You will use the important bits, for it is one thing to write a letter, another to write history, one thing to write to a friend, another to write for the public. Farewell." Eyewitness Account of the Disaster at Pompeii. And it wasn't expected to be published verbatim in an anthology, so you will have to read around the typos.)

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. ^[3]. The possibility that this is the cause of the altruistic behavior is implicitly incorporated into the definition of the relatedness coefficient. Again, whether inclusive fitness or reciprocal altruism approaches are used affects the observers not a jot, but the observer's comprehension a great deal.

If any of this seems weird or counter-intuitive, you might want to take a look at a less involved at-first-counterintuitive mathematical problem called the Monty Hall problem.

Some people would consider IF fundamentally important, which it is, but it might be claimed that the ultimate test for whether someone is a true mutualist or not, i.e., a true friend, would be based on whether they were increasing your inclusive fitness or not. Others might say it is based on whether they are increasing your personal fitness. Sometimes increasing one would decrease the other, but advocates for these ideas would say someone was purloining you if they were decreasing your fitness. Some would argue it doesn't matter which kind of fitness they choose to increase, as long as it is one of them and consistent. Many would argue that such a value system should not be based on fitness at all. This line of thought leads to many other, more sophisticated conundrums.

Another spin-off of IF Theory is parent-offspring conflict as discovered by Robert L. Trivers 1974 and popularised and reviewed by Dawkins in The Selfish Gene.

Basically, a parent is trying to maximise its number of grandchildren, but one of its offspring would give up the chance to have "n" children only if the benefit to one of its siblings for doing so provided more than 2n nieces or nephews. Thus, Trivers hypothesised that when the benefit-to-cost ratio is between 2 and 1 there is a parent-offspring conflict: The parent will want an offspring who is less effective at producing children to become a helper for another who is more effective, but the offspring will selfishly want to devote its resources to raising its own children.

Trivers' theory predicts that, for example, if the parent can't be around forever to coerce an offspring into being a worker, aka a helper, at a sibling's nest, then the parent needs to get its expected benefit-to-cost ratio higher than 2 by creating a situation in which the offspring will be stimulated to be a voluntary worker.

One outcome of this process is that since increasing the productivity of the more productive child is impractical (and unlikely to be selected for), the parents' best bet is to lower the reproductive capability of the offspring, without harming its somatic skills, such as walking or finding food.

Trivers argues that if Sigmund Freud had lived after 1964, he would have explained intra-family conflict, and castration complex as resulting from resource-sharing issues and economics rather than sexual or incestuous jealousy.'

[edit] See also

• Gene-centered view of evolution
• Kin selection
• Reproductive success

[edit] 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

[edit] 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.