Inclusive fitness

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Inclusive fitness encompasses conventional Darwinian fitness with the addition of behaviors that contribute to an organism’s individual fitness through altruism. An organism’s ultimate goal is to leave the maximum number of viable offspring possible, thereby keeping their genes present within a population. Since relatives of an organism are likely to share common genes, an organism may increase its own fitness by keeping its relatives and offspring viable. Kin selection results from this altruistic behavior towards relatives leading to increased fitness in an organism. Inclusive fitness therefore takes into account both the passing of genes from an organism to its offspring and the inheritance of the same genes among relatives and their offspring.

The most obvious examples of increased inclusive fitness can be observed in the altruistic behaviors of parents. To ensure that their genes remain in the gene pool, organisms attempt to give rise to the maximum number of offspring that are sure to survive. Once the offspring are produced, the parents’ reproductive success is determined by the number of offspring that can then procreate and carry on the family genes. Natural selection therefore favors any genes that code for behaviors that lend themselves to increased fitness. Possibly having a genetic basis, innate behaviors that cause parents to sacrifice their well-being, either in the actual birthing process or in aiding their young, increase the parents’ fitness, which makes them more reproductively successful and therefore favored by natural selection.

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.

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). 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. Further study has shown that the self-reported likelihood of risking one's life to save others' life is directly a function of the degree of genetic relatedness to the helper (Burnstein et al., 1994)

Synalpheus regalis, a eusocial shrimp, also is an example of an organism that seeks to increase its inclusive fitness. 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

In the context of sociobiology, which holds that some behavior can be influenced by genes and therefore can evolve by natural selection, Hamilton proposed that inclusive fitness offers a mechanism for the evolution of altruism. He claimed that this leads natural selection to favor organisms that would behave in ways that maximize their inclusive fitness.

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

$rb > c \$

where

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

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 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 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 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, submitted to Nature. In work prior to Nowak various authors derived different versions of a formula for r, all designed to preserve Hamilton's rule. Orlove noted that if a formula for r 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 $r$ – 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 $r$ 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 the fact that corresponding parts of the two identical formulae for $r$ are 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 $r$. By contrast, the terms left of the minus sign in both derivations come from the same source.

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. In formal terms, if such a complex of genes arises, Hamilton's rule (rb>c) specifies the selective criteria (in terms of cost, benefit and relatedness) 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 behaviors, 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.” (Hamilton 1987, 420). In other words, whilst 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. Paul Sherman, who has contributed much research on the ground squirrels mentioned above, gives a fuller discussion of Hamilton's latter point:

To understand any species’ pattern of nepotism, two questions about individuals’ behavior must be considered: (1) what is reproductively ideal?, and (2) what is socially possible? With his formulation of “inclusive fitness,” Hamilton suggested a mathematical way of answering (1). Here I suggest that the answer to (2) depends on demography, particularly its spatial component, dispersal, and its temporal component, mortality. Only when ecological circumstances affecting demography consistently make it socially possible will nepotism be elaborated according to what is reproductively ideal. For example, if dispersing is advantageous and if it usually separates relatives permanently, as in many birds (Nice 1937: 180-187; Gross 1940; Robertson 1969), on the rare occasions when nestmates or other kin live in proximity, they will not preferentially cooperate. Similarly, nepotism will not be elaborated among relatives that have infrequently coexisted in a population’s or a species’ evolutionary history. If an animal’s life history characteristics (Stearns 1976; Warner this volume) usually preclude the existence of certain relatives, that is if kin are usually unavailable, the rare coexistence of such kin will not occasion preferential treatment. For example, if reproductives generally die soon after zygotes are formed, as in many temperate zone insects, the unusual individual that survives to interact with its offspring is not expected to behave parentally. (Sherman 1980, 530, underlining in original)

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 behaviors 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 behavior 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 behavior. Dawkins gives a simplified illustration:

If families [genetic relatives] happen to go around in groups, this fact provides a useful rule of thumb for kin selection: ‘care for any individual you often see’.” (Dawkins 1979, 187)

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 behavior, regardless of whether the participants are always in fact genetic relatives or not. This is nevertheless evolutionarily stable since selection pressure acts on the typical conditions, not on the rare occasions where actual genetic relatedness differs from that normally encountered (see Sherman above). 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 recent review:

[M]any misunderstandings persist. In many cases, they result from conflating “coefficient of relatedness” and “proportion of shared genes,” which is a short step from the intuitively appealing—but incorrect—interpretation that “animals tend to be altruistic toward those with whom they share a lot of genes.” These misunderstandings don’t just crop up occasionally; they are repeated in many writings, including undergraduate psychology textbooks—most of them in the field of social psychology, within sections describing evolutionary approaches to altruism. (Park 2007, p860)

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. Here is one recent example of attempted clarification from West et al. (2010):

In his original papers on inclusive fitness theory, Hamilton pointed out a sufficiently high relatedness to favour altruistic behaviours could accrue in two ways —kin discrimination or limited dispersal ( Hamilton, 1964, 1971,1972, 1975). There is a huge theoretical literature on the possible role of limited dispersal reviewed by Platt & Bever (2009) and West et al. (2002a), as well as experimental evolution tests of these models (Diggle et al., 2007; Griffin et al., 2004; Kümmerli et al., 2009 ). However, despite this, it is still sometimes claimed that kin selection requires kin discrimination (Oates & Wilson, 2001; Silk, 2002 ). Furthermore, a large number of authors appear to have implicitly or explicitly assumed that kin discrimination is the only mechanism by which altruistic behaviours can be directed towards relatives... [T]here is a huge industry of papers reinventing limited dispersal as an explanation for cooperation. The mistakes in these areas seem to stem from the incorrect assumption that kin selection or indirect fitness benefits require kin discrimination (misconception 5), despite the fact that Hamilton pointed out the potential role of limited dispersal in his earliest papers on inclusive fitness theory (Hamilton, 1964; Hamilton, 1971; Hamilton, 1972; Hamilton, 1975). (West et al. 2010, p.243 and supplement)

Green-Beard effects

See also: kin recognition

As well as interactions within reliable contexts of genetic relatedness, 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, 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., altruists have 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. Green-Beard transfers thus have a negative affect on the evolution of altruistic behaviors.

Inclusive fitness and parental care

Template:Section OR 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. Some species or populations of these spiders and reptiles exhibit parental care, while closely related species or populations lack it. Assume that in these animals 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 behavior 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.

If we consider a lifecycle as extending from conception to conception, and an animal is an offspring of parents with poor parental care, the higher mortality with poor care could be considered a dimunition of the offspring's expected fitness.

Alternatively, if we consider the lifecycle as extending from weaning to weaning, the same mortality would be considered a dimunition in the parents' fecundity, and therefore a dimunition of the parent's fitness.

In Hamilton's paradigm fitnesses calculated according to in the weaning to weaning perspective are inclusive fitnesses, and fitnesses calculated in the conception to conception perspective are personal fitnesses. This distinction is independent of whether the altruism involved in child rearing is toward descendents or toward collateral relatives, as when aunts and uncle rear their nieces and nephews.

Inclusive fitness theory was developed in order to better understand collateral altruism, but this does not mean that it is limited to collateral altruism. It applies just as well to parental care. Which perspective we choose does not affect the animals but just our understanding.

Evidence of Inclusive Fitness in Humans

Human behavior is generally much more complicated than 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.

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, a, codes for parental care, and its other allele, 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, whilst 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 how much, or well, they do.

If we parse nature such that life begins at conception, then, other things being equal, the only differences between how well different individuals do will be based on how much care they got as pre-weaned babies, since 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 M(x) curves.

Simply put, l(x) is the probability of still being alive at age = x, and m(x) is fecundity at age x.

These are just 2 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 fitness will be a constant function of genotype. If life begins at conception, the 3 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 completely 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-fitnesses-parsing, but a fraction between zero and one during an inclusive-fitness parsing.

Since 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 has 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 kid of yours, for you, if you rear one for one of your cousins. This is not reciprocity, but rather just due to the laws of statistics.

There are complicating factors so this number will not be exactly 1/8, see below.

This concept is exactly equivalent to the law of karma in Vedic (Hindu, Buddhist, Jaine) Philosophy.

The increment to inclusive fitness is valuable for its own sake, not necessarily because it is a promise of a higher personal fitness.

This is because a cousin (say) has copies of one's own genes every bit as much as an offspring does, just not as many of them.

The mathematical account, especially as given by Hamilton (1964) can look quite daunting, however, it isn't so bad if you keep trying to read it.

it can be verbally explained however, as in: Stories with Bill Hamilton in them. However, 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.

You can also find the simulations to test these thoughts at the website Simtel.net, and download the package with the simulations: [1], and to decompress the source code should you ever wish to read it, using: [2]

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. Again whether personal- or inclusive fitness approaches are used affects the observees, 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 for a reason, some of them would question and many wouldn't, which is that they believe that the ultimate test for whether some one is a true mutualist, i. e., a true friend, would be based on whether they were increasing your inclusive fitness. Others might say it is based on whether they are increasing your personal fitness. Sometime increasing one would decrease the other, but advocates for these ideas would say someone was purloining you if they were decreasing your fitness. Some wound argue it doesn't matter which kind of fitness they choose to increase as long as it is one of them and consistent. And many would argue such a value system shouldn't be based on fitness at all.

Complicating factors would include, what if you include the meme as well as the gene in your argument?

What about conflicts within individuals between genes, between memes, and between genes and memes?

From thoughts along these lines we might derive the test as to whether humans are spiritual beings, or mere automata. If some person or organisation of persons had an endeavour which generated a pollutant, a chemical, or waste product laden with parasites or pathogens.

In order to clean up their operation they have two choices:

• 1. nutralise the pollutant, rendering it harmless, or

• 2. dilute it so thoroughly as to equally distribute it in the atmosphere, or ocean, where it would harm people slightly, or alternatively, not so slightly but randomly and rarely, but the harm or risk would be equally distributed around the world.

In order to be consistent, a believer in Inclusive fitness, in the sense as a utility function, but one with a moral imperative, would argue that if people based the choice of pollution control on which was cheaper, then the chooser would be an automaton without a spirit. Similarly, if a person were willing to pay extra to go for the nutralisation option, then spiritual humanity exists.

Considering IF at all opens moral dilemmas in slightly, but only slightly, less grand questions, like, "Do you inform a person who has been sterilised that it isn't so bad, if their identical twin is still alive?" If you don't tell them they may die forlorn. If you do what would it do to the twin's marriage?

Some people might look down on celibate people as inferior; a positive spin-off of IF Theory is that their ammunition evaporates under it.

Another positive spin-off of IF would be to challenge those among us who would have considered people from India as savages, or primitive, and Karma as a mumbo-jumbo concept, but praise Bill Hamilton as if he were Einstein or Darwin, which he deserves, but there is no place for putting down people of foreign cultures. William Provine, In a lecture, and an attempt to present a cynical view of the cosmos, told his audience that only one to 3 of them would have their bloodlines extant in a thousand years thence, due to random events. IF Theory shows this doesn't matter another jot. The explanation is simply that if bad luck eliminates some bloodlines, it will enhance others, and if it is truly random, if you lose your bloodline, other ones carrying the same genes in the same numbers will exist somewhere. And if you believe genes don't matter, then there is no reason to get upset from the onset.

Another spin-off of IF Theory is parent-offspring conflict as discovered by Robert L. Trivers in 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 kids only if the benefit to one of its siblings for doing so provided more than 2n nieces or nephews. So if the benefit to cost ratio is between 2 and 1 there is a conflict.

Trivers predicts that 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 if the benefit to cost ratio is between 2 and 1, the parent needs to get it higher than 2, so the offspring will be a voluntary worker.

Since increasing the productivity of the more productive child is impractical, 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.

See also

• Evolution
  • Natural selection
  • Sexual selection
  • Kin selection
• Gene-centered view of evolution
  • Parental investment
  • Parent-offspring conflict
  • Trivers-Willard hypothesis
  • Reciprocal altruism
• Group selection
• Life-history theory
• Reproductive success
• r/K selection theory

Also, applications to the study of human behavior:

• Dual inheritance theory
• Evolutionary psychology
  • Evolutionary developmental psychology
  • Evolutionary educational psychology
  • Criticism of evolutionary psychology
• Human behavioral ecology
• List of publications on evolution and human behavior

References

• 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 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 beween 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, U.K.

Further reading

• Helle, S., Lummaa, V. & Jokela J. (2004). Selection for increased brood size in pre-industrial humans. Evolution, 52, 430-436. Full text

External links

• Test simulations:

• http://web.archive.org-main.us/web/20120621125750/http://www.simtel.net/free/Biology-programs/wasps004zip/24173.htmlTemplate:Archive link
• http://web.archive.org-main.us/web/20050328021932/http://www.simtel.net/product.rate.php%5BproductId%5D14756%5BSiteID%5Dsimtel.netTemplate:Archive link