On the (un)importance of kin selection

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While writing a recent short note on Richard Dawkins and kin selection, I looked through my previous posts on the subject, and found what I thought was a blunder in an old post from 2004. To avoid misleading anyone who came across it in a search, I deleted it from the archive. But on further reflection I have concluded that there was no blunder after all…

My original post was a critique of an argument used by an anthropologist against the importance of kin selection in human social evolution. I did not mention the anthropologist’s name, and I do not now recall it, so I will refer to him simply as ‘Anthropologist’. Anthropologist’s argument was, in essence, that kin selection cannot be important because (a) for relatives beyond the closest it is too weak to be effective, and (b) in the human species (unlike, say, ants) an individual has few close relatives.

As it happens, I am sceptical about the importance of kin selection in human social evolution, and I agree with Anthropologist that kin selection is too weak to be important in relationships more distant than (roughly) uncle-nephew. (I will not consider Anthropologist’s second point, that there are too few close relatives.) According to Hamilton’s Rule, the value (to the relevant gene in the donor) of providing benefits to a relative is proportional to the coefficient of relatedness, and this declines rapidly with each extra degree of remoteness in the relationship: 1/2 for siblings, 1/8 for first cousins, 1/32 for second cousins and so on (or half of these figures if the relationship is through a single common ancestor, and not a pair). The problem with giving benefits to distant relatives is not just that beyond first cousins the relatedness is weak in absolute terms, but that it will usually be possible to give the benefit to a closer relative. Other things being equal, it is better to give a benefit to a sibling than a nephew, a nephew than a cousin, and so on. The circumstances in which it is advantageous to give benefits to a distant relative are probably rare.

So I agree with Anthropologist that kin selection in favour of helping distant relatives is unlikely to be important. But Anthropologist went beyond this qualitative conclusion, and attempted to quantify the importance of kin selection at each degree of relatedness in a way that I originally believed – and now believe again – is fallacious.

The importance of kin selection at any given degree of relatedness depends on the number of relatives helped and the inclusive fitness benefit of helping them. The number of relatives actually helped is an empirical matter, but it is possible to set an approximate upper limit to the number of relatives in any given degree who may be helped. In a stable or slowly changing population, each individual (or monogamous pair) will on average have 2 offspring, and the number of descendants after n generations will be approximately 2^n. Anthropologist takes this as his figure for the number of relatives in any given degree that can be helped. Even if we only count the descendants of a single ancestor, this is not strictly correct. For each individual ancestor, only about half of its descendants after n generations will have the most distant degree of relatedness to each other (e.g. second cousins, if they are descended from a common great-grandparent), while the other half will be more closely related (e.g. first cousins), because they have a more recent common ancestor. But it is true that on average the number of relevant descendants approximately doubles with each generation.

The selective value to a donor of giving benefits to a particular relative in any given degree depends on the coefficient of relatedness, or some similar measure, as used in Hamilton’s Rule. This may be calculated by tracing the connection between two relatives through their nearest common ancestor or ancestors, and taking a factor of 1/2 for each link in the chain. For example, for second cousins linked through a single great-grandparent, there are three links in the chain up from one cousin to the great-grandparent, and another three links in the chain down to the other cousin, so the coefficient of relatedness is (1/2)^6 = 1/64. More generally, if n is the number of steps back to the common ancestor, the relatedness is (1/2)^2n. Relatedness therefore declines by a factor of 1/4 for each unit increase in n.

So far, so good. But here comes the problematic part. Anthropologist calculates the (potential) importance of kin selection in each degree of relatedness by multiplying the estimated number of descendents from a single ancestor (or pair) by the coefficient of relatedness appropriate to that degree of relatedness. As already noted, one of these numbers increases by a factor of 2 with each generation, while the other declines by a factor of 1/4. Since 2 x 1/4 = 1/2, Anthropologist concludes that the potential aggregate value of helping relatives in any given degree is halved with each step of distance in relatedness, and rapidly becomes negligible.

In my 2004 post I raised several objections of detail to Anthropologist’s calculations, which I will not repeat here. But my more fundamental objection was that Anthropologist had taken into account only the relatives descended from a single pair of ancestors, for example second cousins descended from a single pair of great-grandparents. This underestimates the number of relatives an individual is likely to have in any given degree, since he or she may have such relatives by several different lines of descent. For example, excluding inbreeding, an individual will have 8 great-grandparents, and may have second-cousins descended from any of them. When this is taken into account, the number of relatives in any given degree increases in the same ratio as genetic relatedness declines. With each step back, the number of ancestors doubles (ignoring inbreeding) which exactly cancels out the alleged decline in the importance of kin selection.

Why then on re-reading my post did I think I had blundered?

In dealing with kin selection it is essential to take a gene’s-eye-view. If we focus on the particular gene of interest, kin selection only promotes it by increasing the fitness of genes that are identical by descent (IBD) with it. Since IBD genes are, by definition, derived by replication from a single common ancestor’s gene, IBD genes can only be found in the descendants of that ancestor, such as the descendants of a common great-grandparent. Other individuals may be equally closely related to the donor in the conventional sense – e.g. they may also be second-cousins – but their genes cannot be IBD with the gene of interest. The relevant number of relatives – those who can possess IBD copies of the gene of interest – is therefore confined to the descendants of a single common ancestor. On re-reading my post I thought I must have overlooked this, and that Anthropologist was right to count only the descendants of a single ancestor (or pair).

But on further reflection, I think I was right first time. (Indeed, on checking my old working papers I find that I considered this objection and dismissed it, unfortunately without mentioning it in my post.)

What is relevant to kin selection is the probability that a relative will have a copy of the gene that is IBD with the copy possessed by the actor. This probability is conventionally measured by the coefficient of relatedness, r. But probabilities are relative to the statistical ‘population’ under consideration, and this depends on the information available to us. For example, if all we know about an individual is that he is a white American male, and we wish to know the probability that he will die within a year, the relevant population consists of all white American males. If on the other hand we also know that he has been diagnosed with cancer, then the relevant population consists of all white American males who have been diagnosed with cancer. In the case of relatedness, the usual calculation of r assumes that the ancestral source of a gene is unknown, and that it may with equal probability have come from any ancestor at the appropriate distance. If on the other hand we know (or assume) that the source is some particular ancestor, then the usual calculation of r is not appropriate to determine the probability that another descendant of that ancestor has inherited the same gene. If that ancestor is definitely the source of the gene in one descendant, then the probability that it is IBD in another descendent is simply 1/2^n, where n is the number of generations from the common ancestor. It is easy to see that this probability is greater than r (as normally calculated) by a factor of 2^n.

We may therefore legitimately measure the potential importance of kin selection among relatives of a given degree in two ways. Either we may take account of all the relatives in that degree descended from all ancestors at the appropriate distance back, and multiply their number by the usual r, or we may take the number of relatives descended from a particular ancestor and multiply by (2^n)r. The result by both methods is the same. What we cannot legitimately do is to take the descendants of a single ancestor (or pair) and multiply their number by the usual r, as done by Anthropologist.

In my original post I made various more technical points. The only one worth mentioning here is that a randomly selected individual is more likely to come from a large, flourishing lineage than from a small, declining one. He certainly does not come from an extinct one! The average number of relatives in a given degree, for a randomly selected individual in the present generation, may therefore be significantly larger than the simple 2^n formula would suggest. However, I doubt that this consideration is enough to make kin selection in favour of distant relatives a major factor in human evolution. I agree with Anthropologist that this is unlikely, even if I disagree with the reasoning by which he reached this conclusion.

19 Comments

  1. I think I was able to find your old post through google’s cache.

  2. Yes, that’s it. I have deleted my old text which you included in your comment, because it is (a) very long, and (b) very boring. I think (or hope, anyway) that the point is made more clearly in my new post. It is alarming, incidentally, to find that things you thought had been deleted are still out there somewhere on the net. Sometimes there might be much stronger reasons for wanting to remove something from the public record; e.g. you find that something was inadvertently libellous.

  3. Doesn’t the importance of relatedness also depend on how related you are to the average person you deal with? So relatedness would matter less in a highly inbred village?

    What is the expected level of altruism for close kin when the average person in your vicinity has cousin-level relatedness?

  4. ben g: I replied to your comment earlier, but for some reason my reply has not appeared, and it wasn’t very good anyway. The points you raised are tricky, and even W. D. Hamilton himself was sometimes unclear on how to deal with them. It is usually tacitly assumed that randomly selected members of a population are unrelated, but this is never strictly true, and sometimes far from true. However, the general level of relatedness between random members acts as a kind of baseline against which any more specific relationship can be measured. So, for example, if the general level of relatedness is equivalent to that of first cousins, then true first cousins will have that degree of relatedness *plus* the normal relatedness of cousins, and brothers will have an even closer relatedness. It is the difference between the total relatedness of two individuals and the average level of relatedness in the relevant population (roughly, the population within which interactions take place) that determines whether ‘altruism’ is worthwhile. There is a discussion of this issue under point 6 of the article by Dawkins which I linked to in my earlier post.

  5. Reading this post, I had the impression you changed your mind about deleting your old post.

    Personally, I’m more enthusiastic about information being preserved forever through efforts like the internet archive. I haven’t given it Steve Dutch levels of thought though.

  6. TGGP: I haven’t given it much thought either, but my gut feeling is to go to the opposite extreme: everything placed online should ‘expire’ after a standard period unless someone (either the author or someone who has found value in it) takes a conscious decision to preserve it. Otherwise, we will be drowned in a rising tide of intellectual garbage.

    ben g: I didn’t really answer your second question, because I wasn’t quite sure whether the motivation for altruism is weakened in this situation. But on further reflection I think the answer is as follows. Suppose that in a community the average level of relatedness is equivalent to that of first cousins. Suppose now that A and B are brothers – full siblings with both parents in common. Assuming that their parents have mated at random, then the parents will, on average, be related to each other as closely as first cousins. A and B will therefore be related to each other via their parents’ relationship, but in addition they will be related as full siblings. I will call this additional relatedness their ‘surplus’. Now the question is, does this surplus give them a motivation to be altruistic to each other, and if so is this motivation stronger, weaker, or equal to that of full siblings whose parents are not related? I think the short answer is that the motivation is equal. If we consider it from the point of view of a gene in A, that gene has a strategic choice between helping A produce more offspring, or inducing A to help B to produce more offspring. In both cases there is some selective advantage for the gene in question, since either A’s or B’s offspring will have the gene in question with higher probability than in the general population, but the advantage – the ‘surplus’ probability – is twice as great for A’s offspring as for B’s. So it will not ‘pay’ the gene to induce A to be altruistic to B unless, for some reason, the increase in offspring would be twice as great for B as for A. Which is precisely the usual result of Hamilton’s Rule. At least, that is what I think at the moment, but these issues are tricky, and I’m open to correction.

  7. I suppose the question of being drowned in data depends on how good our filters are.

  8. “Other things being equal, it is better to give a benefit to a sibling than a nephew, a nephew than a cousin, and so on.”

    But what if your sister asks you to give a benefit to her son?

  9. Steve: If your sister uses the resources herself she can make more nephews. If her son (your nephew) uses the resources, you only get more great-nephews, who are genetically worth half as much as nephews. Of course, ‘other things being equal’ may come into play: e.g. if your sister is past child-bearing, the nephew may be the best investment.

    (I’m not sure if ‘great-nephew’ is a recognised term, like great-aunt and great-uncle. I wonder why we have grand-fathers but not grand-uncles?)

  10. The costs and benefits of helping people, relatives or not, depends on the base population. There is no such thing as ‘true’ relationship. So we could if we were crazy calculate our relationship with an onion.

    If I help my brother in a highly inbred population, it doesn’t help him as much _with respect to that population_ as it would if in a population of random people. On the other hand _with respect to the species_ it helps him a whole lot more. Two random humans from the same group have an underlying relationship of about 25%, so _with respect to the world_ my brother is worth about 75%, not 50%.

    Relationship as Hamilton used it is not very well defined anywhere, and thinking about it in terms of pedigree relationship has not helped much. The 25% I use above comes from the world Fst (i.e. kinship) of about 1/8 and doubling 1/8 gives 25%.

    There are pages and pages of wordspeak in the literature since the 1980s about whether or not group selection and kin selection are the same thing. They certainly are, the only difference is how one writes the models.

    Henry Harpending

  11. “If your sister uses the resources herself she can make more nephews.”

    Okay, but I’m not clear on real world examples where this distinction is all that distinct.

    Say your sister confides in you that her marriage is stressed by the financial and energy burdens of providing and entertaining for her young daughter, your niece. You offer to take little Jenny off their hands for a week and you take her to Disneyland. Nine months after her trip to Disneyland, little Jenny gets a baby brother.

    Did you give the benefit to your sister or your niece or your new nephew?

  12. Steve: you have increased the reproductive fitness of your sister. That is a benefit to her. From your own point of view it is (genetically) worthwhile provided you do not reduce your own fitness by half a child!

    I don’t see any fitness benefit to your niece or your nephew, unless conceivably your niece narrowly avoids being strangled by her mother (or, more broadly, benefits from the relief in family stress.)

    I am thinking about Henry Harpending’s comment.

  13. This seems to me overly complicated and out of touch with the real-world. Who calculates their degree of kinship before deciding how altruistic to be to another person? How could such a calculator even evolve?

    Shouldn’t we focus on the behaviors that could conceivably evolve and work from there? That is, relatedness could be a consequence of these (altruistic-like) behaviors rather than the cause of these behaviors.

    Living cooperatively in groups for example helps an individual survive, hence it makes sense cooperative behaviors would evolve. Moreover, although we may have bygones ago been largely around close kin, the evolved behavior could just as easily encourage us to cooperative with non-kin as well (sometimes even against kin) given a different context.

    Maybe helping a cousin benefits some genes of yours but in reality nobody is going to think that way. Whether you help or not will be decided on very different terms.

    I guess what I’m trying to say is that reciprocal altruism or game theory would seem to provide a better explanation of human behavior than kinship calculations (beyond immediate family) and that such calculations beyond that point seem rather meaningless.

  14. gnome: I agree with some of what you say, from a common-sense point of view, but with one major difference: no-one argues that individuals ‘calculate’ their genetic relatedness and decide whether to be altruistic on that basis. This is one of Dawkins’s ’12 Misunderstandings of Kin Selection’. The theory of kin selection applies not just to animals but to plants and bacteria, which are presumably not even conscious. Altruistic behaviour, if it exists, would be based on non-conscious factors such as chemical similarity (e.g. pheromones) or mere proximity.

  15. Hi DavidB, thanks for the reply. You are correct, I am approaching this from a common-sense perspective but I’m kind of struggling to articulate what I mean exactly. I guess I’m questioning the direction of the arrow of causation (trying to arrive at the “correct” way of thinking about the problem) and whether it’s useful to think in terms of kin selection at all.

    I am in part responding to that misunderstanding of kin-selection you pointed out but doesn’t thinking in terms of kin-selection/inclusive fitness lend itself so easily to such a misunderstanding? Not only that, but more extreme jumps in thought too such as supposing genes are sentient beings. You can defend this by saying its not the fault of the theory that people misunderstand it but it seems to me that even on its own terms it encourages people to think about evolution from the wrong angle.

    The way I see it is this: the altruistic-like behaviors we see are not “designed” to further the shared-genes of other family members or anybody else although that sometimes happens as a consequence given a certain context. (That is, it is not the cause or purpose of said behaviors.) It is simply that pro-social behaviors encourage cooperation/reduce conflict which encourages the survival of an organism hence said behaviors evolved. And that is all that is needed to explain why it is that way it is.

  16. gnome: I agree that pro-social behaviour often has advantages of its own, and that the appearance of kin selection may be just a side effect of that. But I think you may be thinking too much in terms of social mammals (including humans), which have relatively sophisticated intelligence, memory, communication, etc. The theory of kin selection (or inclusive fitness) is applicable to the whole range of organisms, including insects, plants, bacteria, slime moulds, etc. In many of these a general ‘pro-social’ strategy is not very plausible. For example, it would hardly explain why most bees or termites are non-reproductive.

    [I am still mulling over Henry Harpending's comments.]

  17. DavidB: Good point.

    I’ve always just assumed that in those other cases, for example, a bee-hive, that the hive itself should be seen as the organism and the bees as simply cell-like constituents of that hive organism.

  18. Re Henry Harpending’s comments: I am not sure if we disagree on matters of substance or just on methods and terminology. Hamilton’s Rule still seems to me to provide the best conceptual framework for analysing these problems, despite the various complications that have been raised (many of them by Hamilton himself).

    “There is no such thing as ‘true’ relationship.”

    I agree that the relatedness between the members of a population will vary according to how the base population is defined, but in addressing any specific evolutionary problem the choice of base population is not arbitrary. For some purposes it may legitimately be the entire global population of a species, but for others it will be more limited. If what we want to know is whether altruism will evolve, it will be limited to those individuals who are capable of influencing each other’s fitness by social interaction or competition for resources. Presumably in general the relevant population will be quite localised. An individual will interact and compete mainly with local population members, to a lesser extent with nearby populations, and to a very limited extent with more distant members of the species. Ideally I suppose one should calculate a weighted average which takes account of the frequency and nature of interactions. Individuals outside the range of interaction and competition can be disregarded.

    “If I help my brother in a highly inbred population, it doesn’t help him as much _with respect to that population_ as it would if in a population of random people.”

    This brings us back to ben_g’s question about altruism in a highly inbred population. My own gut feeling was originally that inbreeding must weaken the benefit of altruism towards close relatives, since the contrast between ‘related’ and ‘unrelated’ members of the population is flattened out. But on further reflection this makes no difference to the key question, which is whether it is better to give resources to a relative or to keep them for oneself. In a sense it is true that the ‘worth’ of a relative is reduced if the surrounding population is genetically similar, but for the same reason the ‘worth’ of one’s own offspring is also reduced. On working through the algebra, the balance of advantage between helping oneself (i.e. creating more offspring) and helping a relative is unaffected. Hamilton’s Rule still applies, even in an inbred population.

    “Relationship as Hamilton used it is not very well defined anywhere, and thinking about it in terms of pedigree relationship has not helped much. ”

    It is unfortunate that in his original formulation W. D. Hamilton referred simply to ‘related’ and ‘unrelated’ members of a population, without (I think) defining what he meant by ‘unrelated’. But on a sympathetic reading of the context, it is fairly clear that what he meant by ‘unrelated’ members of the population was that they are no more (or less) likely to share the allele of interest than individuals selected randomly. Of course, if we go back far enough, ‘unrelated’ individuals may share alleles by virtue of descent from the same ancestor. We can even assume that each distinct allele in the population is derived ultimately from a single mutation event, in which case all copies of that allele are ‘identical by descent’. The allele may, by selection and/or drift, have reached a high frequency in the population. But the beauty of Hamilton’s treatment (as Dawkins emphasised in his ‘Twelve misunderstandings of kin selection’) is that Hamilton’s Rule still applies regardless of the frequency (short of fixation, at least). All we need for the validity of the Rule is that any ‘relatedness’ not covered by the explicitly worked-out pedigree is neither higher nor lower than the ‘baseline’ level in the relevant population. It makes no difference, as far as I can see, whether that baseline level is the result of long-continued selection or drift, or of comparatively recent inbreeding. But as I’ve said before, it’s a tricky subject. Hamilton himself fell into fallacy in his 1975 paper, (though Dawkins was too charitable – or nervous – to put it quite that bluntly in his discussion of ‘Misunderstanding 6′), so I will not be surprised if I have overlooked something.

  19. Just discovered this post – a bit late, heh. I’m no academic but I am quite interested in that classic anthropological/historical phenomenon whereby the relations within ancestral population groups have tended to exhibit high levels of altrusim, trust and cooperativeness while the relations BETWEEN groups have mostly tended toward the opposite. Certainly, if we choose to limit our explanation of the evolution of this system to the simple Hamiltonian model of kin selection, David B. and Henry Harpending must be correct. Kin selection alone can’t possibly account for it. However, it has long seemed pretty obvious to me that OF COURSE kin selection can only ever be a part of the story. That’s why I think this focus on genes that are IBD with one another kind of misses the point.

    Would it not also be possible that our brains have evolved additional cognitive adaptations which are designed to construct some sort of “self-recognition template” and then compare this template against the actual gradients of phenotypic differences found in the world around us? Indeed, the evidence for this appears to be mounting. Way back in 1987, Irwin found that increases in in-group favoritism appear when Eskimos observe other Eskimos with the same accent (Irwin, C. 1987. ‘A study in the evolution of ethnocentrism’ in V. Reynolds, V. S. E. Falger
    and I. Vine (eds.), The Sociobiology of Ethnocentrism: Evolutionary Dimensions of Xenophobia, Discrimination, Racism, and Nationalism. London: Croom Helm, 131–56). Then in 2002, DeBruine found that levels of trust are elevated when people play trust games against composite human faces made by averaging the player’s face into the composite. (DeBruine, L., 2002. “Facial resemblance enhances trust”, Proceedings of the Royal Society of London B, 269(1498): 1307-1312). Also, Park and Schaller recently found that attitude similarity is interpreted as a cue for kinship. (Park, J. et. al “Does attitude similarity serve as a heuristic cue for kinship? Evidence of an implicit cognitive association”. Evolution and Human Behavior, 26, 158-170. Finally, Bressan (2009) found that “Human Kin Recognition is Self-rather than Family-Referential”, Biol. Lett Vol. 5 no. 3, 336-3385.

    It seems that all these converging lines of evidence are trying to tell us something, and it’s not to “count the generations” for measuring degrees of relatedness. Nor is it any sort of “Green Beard Effect”. And if such an adaptation (or set of adaptations) does exist, why would that be? Frequent human encounters with other archaic hominid species back in the mists of time? Maybe partly due to the evolution of language and thus reflecting a natural process separating mutually-unintelligible populations? Any thoughts guys?

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