In defense of evolutionary psychology, part 3: Hamilton’s rule and reciprocal altruism

Hume once said that “A man naturally loves his children better than his nephews, his nephews better than his cousins, his cousins better than strangers, where every thing else is equal.” When I first found this quote from Hume, I was quite impressed, because it anticipates an idea that wouldn’t be formulated until roughly 200 years after Hume lived: Hamilton’s rule.

I’ve been meaning to restart my series defending evolutionary psychology for some time (see part 1 and part 2). Initially, I was thinking part 3 would be about sex differences in behavior, but ever since I saw this post by Stephanie Zvan, I’ve wanted to respond to it and the post at another site it was promoting, “Altruism — can we do good just for the sake of it, after all?” by Anne Buchanan. I’ll quoting Buchanan’s explanation of Hamilton’s rule:

Evolutionary biologist, William Hamilton, formalized the idea in an equation published in 1975, in what came to be called inclusive fitness:

      rb > c


      is “degree of relatedness”,
      is the reproductive benefit to the recipient of the altruistic behavior, and
      is the reproductive cost to the altruist.

In very basic terms, you and your sib, parent, or child share half your genes.  This is on average and it’s statistical.  You can’t say in advance which genetic variants you’ll share, just that overall it’ll be half of them.  That’s because everyone gets half their genes from their father, half from their mother.   So, if you do something for your sib that puts you at risk, say, of having one of your own children, but your assistance leads your sib to have at least 2 children s/he that wouldn’t have had without your help, then the genetic variants you carry will, on average, proliferate–via your sib’s children who will carry those variants.

This is exactly right. It’s worth explaining that we share 50% of our genes with our siblings, parents, and offspring; 25% of our genes with our aunts, uncles, nieces, and nephews; and 12.5% (1/8th) of our genes with our cousins. And the key thing here is that this number is the same as the probability of sharing any one gene. So a relative-helping gene will be promoting a copy of itself 1 out of every 2 times it helps an immediate relative, 1 out of every 4 times it helps a niece, nephew, etc., and 1 out of every 8 times it helps a cousin.

I hope that makes sense. If not, Richard Dawkins has a brilliant explanation of Hamilton’s rule starting on p. 90 of The Selfish Gene, and this is one of several reasons I recommend everyone read the book. Though his explanation is longer than the one I just gave, so I won’t try to quote it; read it for yourselves.

I should mention that Buchanan describe’s Hamilton’s rule as a formalization of the idea that “altruism is selfish after all.” It can be tempting to think that way, but I agree with Hume (at least I think he also said this, can someone find the quote for me?) that concern for family is not part of what we normally mean by “selfishness.” Nor, to update Hume, is promoting one’s genes what we normally mean by “selfishness.”

Now for Buchanan’s argument that Hamilton’s rule isn’t relevant to explaining human behavior:

Under these conditions, if a variant in question leads you to this helpful rescuing behavior, the variant will (statistically) proliferate, because helping your sib to have more children than you give up will increase the frequency of those helping-variants in the next generation.  Likewise, you share 1/8 of your variants with your cousins, so to give up a child of your own by helping your cousin, that cousin would have to have at least 8 more children than without your help.  That’s what Haldane meant.  This may make little sense in slow reproducers like humans, but could actually work, in principle at least, in fast reproducers who produce hundreds or thousands of offspring–like ants.

So, Hamilton’s rule seemed to explain why vampire bats feed each other, why bees will sting, and die, to defend the hive, and why Ken dove into a pool to save a drowning stranger years ago.  It even came to explain things that had nothing to do with altruism, such as homosexuality, which could evolve because homosexuals cared for the offspring of their kin, thus perpetuating their own genes even if they themselves didn’t reproduce.

This would seem to show clearly that, by itself, Hamilton’s rule simply cannot explain human (or even primate) sociality.  In all human societies people routinely help their cousins and other more lineally distant relatives.  But primates simply cannot have 8 or more additional children as a result of being helped.

This is a mistake. Thinking in terms of whole offspring may be useful for introducing Hamilton’s rule, but it’s not true that sacrificing one offspring is the minimum cost of actions we take to benefit relatives. For example: a stone-age hunter kills a large animal, and he and his immediate family eat as much of it as they possibly can. But there are leftovers, and without refrigeration or even salt, it will rot before the immediate family can eat any more.

Hamilton’s rule suggests that in this situation, the hunter will give the meat away to his more distant relatives. Because the meat will rot otherwise and be of no use to the hunter, the cost (“c”) is basically zero. Because of that, even a slight positive benefit to the distant relatives, a slight positive increase in their reproductive chances, will be a “b” large enough to make the action satisfy Hamilton’s rule.

Or, to use the historical example that gave us the word “nepotism,” if you’re a medieval Pope, handing out church offices to your nephews might cost you very little if the people surrounding you in the Catholic hierarchy don’t care that you do it. If you’re following your vows of chastity (though not all historical Popes did so), the reproductive cost to you might be zero. So the reproductive benefit to your nephew doesn’t need to be very large to satisfy Hamilton’s rule.

Back to Buchanan:

So those who have thought about this have had to devise various escape-value explanations to preserve the essence of Hamilton’s rule; one is ‘generalized reciprocity’ the idea that I may help you because some day you may return the favor.  But with such escape valves, and the complexity of society, it should long ago have been clear that all bets are off.

Stephanie comments on this in her own blog post:

In other words, in order to tweak the model to accommodate actual, observed social behavior in primates, it becomes so squishy that it loses its predictive power. That, of course, is where it stops being science. It certainly isn’t impossible that someone will come along and add complexity to the basic model in a way that allows it to become predictive again, but the idea isn’t at that point at the moment.

First of all, Buchanan is wrong that the idea of reciprocity was added as an “escape valve” to avoid the “cannot have 8 or more additional children” probablem, because that “probem” isn’t one. But it’s also not true that taking reciprocity into account makes the model “squishy.” It very clearly cannot explain any altruism whatsoever; it wouldn’t for example explain a willingness to be repeatedly taken advantage of by non-relatives. And it wouldn’t change the fact that we should expect animals to be more altruistic towards relatives than towards non-relatives. (By the way, The Selfish Gene is also excellent on explaining reciprocal altruism.)

I’m going to pass over some of her complaints about the fact that E. O. Wilson has changed his mind on some issues, as well as the question of whether haploidity explains eusociality in insects. Even if Buchanan had a point about those things, it wouldn’t settle more general issues about the evolution of altruism (though the eusociality issue is interesting, and I may try to write about it later). Instead, I want to deal with this part from the end of the essay:

Why is the demise of Hamilton’s rule as Gospel such a big deal?  Because it shouldn’t have been a Big Deal in the first place.  And yet why should we care what Wilson says this time around anyway?

The problem with all of this is the desire or even deep hunger, to find some precise, competition-centered pat explanation for observations about life. Anything that looks organized is assumed to be due to systematic, force-like Darwinian competition.  Even group selection, which Wilson is now advocating, is a simplistic notion, that orthodox Darwinians cannot accept because it doesn’t work strictly at the level of the individual which they insist, for some good reasons, it must, since it is only individuals who carry genes and either do or don’t reproduce.  From that point of view, everything that looks cooperative simply must have arisen and/or work strictly to the advantage of the individual.  Or, to be even more precise, it has to work at the level of individual genes.  It has to, to seem like real science!

This is a reverse kind of logic.  If you view the world as horribly selfish and cruel, then of course anything can be explained by selfishness.  On the other hand, if you see cooperation as being important, you can argue that things good for a group advance even if genetically they arise only in one member of the group.  You can argue that over time, the kindliness genes will spread and advance: each kindliness mutation will add to the group’s success.  Even those without kindliness variants will do well, but they won’t out-do their nicer peers.  Arch Darwinists who seem to be convinced the world is full of cheaters (does this imply that they know they’re cheaters themselves, and is some sort of tacit confession?), will always devise (again post hoc) reasons why kindness for unselfish reasons will never win.  Or they will always be able to find reasons why kindness is just competition in disguise.

Again, first of all Buchanan is wrong about the demise of Hamilton’s rule. But the reason theories like kin altruism and reciprocal altruism have gained widespread accepted in the scientific community is not because of a mysterious “deep hunger” to find competition-centered explanations. It’s because the alternative explanations don’t work (and these theories do).

If there ever were a population of organisms with genes for behaving altruistically towards non-relatives, regardless of whether the non-relatives responded in kind, it should be easy to see that those genes could be quickly replaced by variants for behaving more selfishly, as long as the variants were able to arise in the first place. One strategy would be to benefit from other’s altruism while displaying none of it yourself. Though in many situations, a better strategy might be to go tit for tat, helping those who’ve helped you in the past and not helping those who’ve refuse to do so.

Can we, as the title of Buchanan’s post suggests, do good just for the sake of it? Perhaps in a sense. But not in any sense that helps with understanding the evolution of animal behavior (human behavior included), at least not until someone explains how “good just for the sake if it” could impact gene frequencies. By the way, if you get thinking about group selection here, the consensus seems to be that it doesn’t work. I may devote post to the subject in the future but for how, I recommend Steven Pinker (actually a great article on the evolution of altruism in general) and this this more narrowly focused piece by Eliezer Yudkowsky.

Final point: the last of the paragraphs I’ve quoted is one bit of data that confirms my general impression that discomfort with evolutionary psychology tends to be driven not by the science, but by confused moral objections to the ideas. Buchanan doesn’t exactly say that the ideas she criticizes are immoral, but she does speculate that the reason people hold them is because they’re bad people. To which I reply: evolutionary psychologists may not behave very altruistically towards non-relatives when they don’t stand to gain anything in return, but then neither does the vast majority of the rest of humanity.

Case in point: in the past, I’ve made efforts to donate money to charities that will actually help other people the most with that money, and encouraged other people to do the same. And I intend to do more of that in the future. But there are plenty of petty things I spend my money on much more readily on than that. And I haven’t empited my savings to save strangers from malaria, whereas if my little brother desperately needed money for a life-saving medical treatment, it would be an easy decision to empty my savings for his sake. And yet my tendencies in that regard are not especially selfish or nepotistic for a Homo sapiens.

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  • Peter Hurford

    If you’re planning on donating a significant amount of money to Givewell, consider joining Giving What We Can if you haven’t already.

  • khms

    This is exactly right. It’s worth explaining that we share 50% of our genes with our siblings, parents, and offspring; 25% of our genes with our aunts, uncles, nieces, and nephews; and 12.5% (1/8th) of our genes with our cousins

    I’m pretty certain these numbers are drastically wrong – because they assume that the four sets of genes our parents have do not share anything, which is clearly nonsense: if they didn’t actually share most of those genes, reproduction would be impossible.

    Then, there’s the point that humans are not particularly good at evaluating relatedness in another, except by way of bookkeeping, which I’m pretty sure during most of our evolutionary history didn’t exist outside of maybe the immediate family. So if you want a mechanism to make altruism happen for close relatives, it is rather probable that this will spill over to anything that matches closely enough under whatever rules you apply to recognize relatedness. As a concrete example, see the cuckoo, or experiments to show birds trying to breed larger wooden eggs in preference to their own. Or, for that matter, see the human desire to keep pets.

    Incidentally, this also speaks to how complicated behavior can be a side-effect of something else – given intelligence (or even instinct), all sorts of behavior can be applied in situations quite different from what it was selected for in the first place.

    • Daniel Engblom

      I thought that these misconceptions were dead! Guess I was too optimistic about progress in understanding…

      First, the calculation is correct, but it is not based on between species calculation, in which yes, members of a species are all very similar to each other and share most of their genes with their co-members.
      The prosentiles refer to the sliver of nonstandard genes between individuals; how much of variation can there be in a gene pool.

      Second, I cannot believe that you think that not being able to calculate relatedness is an objection to Hamilton’s rule! Evolution does not work like that: Evolution is not a conscious prosess making individuals think: “Her waist-to-hip ration is is nearly perfectly in the .7 range, her behaviour appears lively, she appears parasite-free, coupled with her age, she’ll provide good genes for my offspring.” NO! Evolution builds rules of thumbs that are operated by emotional pulls, like: “Damn! did it just get hot in here? She’s smoking!”
      See this article by Dawkins:

      Plus the point of spilling over altruism is something hypothesized by evo-psych (Dawkins has expressed this view also very often; In the God Delusion for instance, as a parsimonious explanation counter to group selection), so it seems that as a criticism, it fails due to ignorance of what is actually being said by theorists.

      • Daniel Engblom

        Actually, what I said about nonstandard genes is false – It can be interpreted as “rare genes”, and so best to just say it’s false. But within gene-pool probabilities is still a good way to think about it. The article (PDF link) I posted talks about this misconception as well.

  • Iamcuriousblue

    It looks like in a couple of places Buchanan is starting with ethical implications of the idea and working backwards from that, with some gratuitous digs at “Arch Darwinists” for good measure. I’m not familiar with Weiss and Buchanan’s book, but I would hope they are advancing more scientifically sound arguments for the their cooperative model of evolution there.

    Joan Roughgarden and Lynn Margulis have similarly authored books rejecting key aspects of the Darwininan selection model (on differing grounds), and you didn’t have to look far for them to be making essentially political arguments against the competitive nature of selection theory. Especially from Roughgarden, to the point where her political commitments compromise the quality of her science.

    That EO Wilson has arrived at a group selectionist model now *is* intriguing, since I remember that he was a major critic of that idea when Stephen Jay Gould and Richard Lewontin were advocating it. He’s long been an advocate of “strong Darwinism”, which leads me to think that if he’s changed his mind now, it’s because that’s where the science has lead him, rather than politics or moralism leading him to that point. Still, I have yet to read the details of his hypothesis, so I can’t argue for it one way or the other.

    The thing is, there has long been a very interesting and long standing debate on “levels of selection”, between advocates of gene-centered selection vs. organism-centered selection vs. group-centered selection, or even selection working at multiple levels. And that’s where I feel a bit cheated in my university science education. When I first took a course in evolutionary biology (in the mid 90s), I was told flatly that group selection was a “myth” and was given no exposure to the “levels of selection” debate. Also no mention when I took population genetics in grad school. Levels of selection debate, along with novel ideas of evolutionary mechanisms like epigenetics, horizontal gene transfer, and evo-devo were ideas I was only exposed to later. Perhaps these ideas were considered just too fringe at the time of my education and current students would get more exposure to them – I’m not sure, though I know the “levels of selection” debate goes at least back to the 1970s.

  • Iamcuriousblue

    “‘This is exactly right. It’s worth explaining that we share 50% of our genes with our siblings, parents, and offspring; 25% of our genes with our aunts, uncles, nieces, and nephews; and 12.5% (1/8th) of our genes with our cousins’

    I’m pretty certain these numbers are drastically wrong – because they assume that the four sets of genes our parents have do not share anything, which is clearly nonsense: if they didn’t actually share most of those genes, reproduction would be impossible.”

    Strictly speaking, those numbers are for genes that are polymorphisms with in the family line in question. Obviously, we must share a huge number of invariant non-polymorphic genes to be in the same species. But kin selection arguments hold true when you’re talking about a larger number of shared polymorphic genes the closer your relatedness is.

    The above numbers for shared polymorphic genes are accurate in a general sense based on Hardy-Weinberg assortment (and assuming no inbreeding). Obviously, statistical variance is going to alter the absolute number of shared polymorphic genes, as will factors like genetic linkage and mutation.

    • windy

      Actually, those numbers refer only to those allele copies that are “identical by descent”. That is also a bit misleading since apart from rare convergent mutations, all identical alleles in a population are so “by descent”: in kin selection situations the altruistic variants are identical by recent descent.

  • Bronze Dog

    Psychology in general seems like a messy field to me. There are a lot of “fuzzy” rules and priorities governing people’s behavior, often in conflicting directions. Since evolution is what produced us, there’s certainly plenty of reason to look at psychology from an evolutionary perspective. Actions often result from multiple motives, and evolution can enlighten us on the “rationale” behind various instincts and tendencies that aren’t learned.

    The sad thing, though, is that there are a lot of people using evolutionary psychology as a buzz phrase to “justify” racism, sexism, or anti-social behavior, especially in a lot of cases where better behavior can be learned.

    • mikespeir

      I agree. But it’s just as sad that there are those who will automatically dismiss anything that smells of “evo psych” without examination. Granted, much of it will never be proven to everyone’s satisfaction. But, like you say, ultimately evolution has shaped what we are. Somewhere within that “fuzzy” nimbus must lie the truth.

    • Iamcuriousblue

      “The sad thing, though, is that there are a lot of people using evolutionary psychology as a buzz phrase to “justify” racism, sexism, or anti-social behavior”

      “A lot of people” being mostly non-scientists who are using appeals to mangled third-hand evpsych. But how many in the field of evolutionary psychology itself? Even really strong evolutionary psychologists like Steven Pinker are a great deal more nuanced about the conclusions of research in that field, and are careful to make is/ought distinctions. I’ve certainly heard absolutely nothing from Pinker and the like that would suggest they endorse racism, The Bell Curve, etc. On the subject of sexism, that’s more ambiguous. Pinker and other evolutionary psychologists certainly claim that there’s evidence for innate sex differences, which some people find inherently sexist. Still, that does not mean that evolutionary psychologists advocate sending women back to the kitchen, etc.

  • jaxkayaker

    “I’m going to pass over some of her complaints about the fact that E. O. Wilson has changed his mind on some issues, as well as the question of whether haploidity [sic] explains eusociality in insects.”

    The word you’re looking for is haplodiploidy, which refers to the sex determination system wherein females are diploid and males are haploid, exhibited by many, if not all, hymenopterans (ants, bees and wasps). Termites exhibit eusociality without exhibiting haplodiploid sex determination, which demonstrates that haplodiploidy is not a necessary condition for the evolution of eusociality.

    • Chris Hallquist

      Oops, I knew that sounded wrong when I typed it.

  • DMark

    Hi, I´d like to ask: Is Hamilton´s rule specifically used only for when one individial helps/saves exactly one individual? I got across the example when one brother saves the other one from drowning. The rule was applied like this: B=2 (average number of offspring for humans), r=0.5 (since they are brothers) and C = 0.25 (probability the brother will drown if the other will not save him) times 2 (the number of expected offspring if the altruist had stayed on the shore). Thus, it is beneficial for one brother to save the other. But, what would happen if two of his brothers were drowning (and he could save both)? I realize that if it is beneficial to save one, then it follows that it is advantageous to save both, but how would the rule be applied? How would it be like mathematically? When it comes to the cost of the provider, you can figure out the average probability they both will die, but how woulf “the-benefit-to-the-recipients” side of the inequality look like? Because, I don´t think you can just sum it up (or, to say it differently, multiply the benefit of one brother by two) as 50% of genes they share with the altruist is (if only in the minor part) different set of 50% (thus – if we think of drowning brothers in the terms of genes, he will – in total – save more than 50%…be it even 50.00000001%)…So? I am curious to know how this works.

    • windy

      Yes, you could have several recipients – the fitness benefit is calculated over the altruist’s lifetime so that would be a common situation. The recipients can have different relatedness values, and in theory you could sum them up, for example: (0.5*benefit to brother)+(0.25*benefit to niece)+…, except in reality the benefits are not likely to be independent of each other (for example, if the relatives are competing for food.) It doesn’t matter that the relatives share slightly different sets of genes, what matters is how likely they are to pass on the gene for the altruistic behavior – relatedness gives us an estimate of that probability.

      • DMark

        Hey, thanks for reply! (I wasn´t hopeful:)). I´d like to propose this example. Imagine parent can save its children (as you said, we think of a parent in the terms of his life-time) by dying hismelf. In this case, the “cost of parent” (as I understand it) can be measured as the probability of offspring´s death as a result of loss of parental care (x) times the number of potential offspring (y). For species needing parental care, the probability of death of offspring in rearing period (depending on stage) will be approximately 1. However, parent will also have mature offspring in whose case the probability will be 0. x will be the sum of all “death probabilities” (∑x) divided by the number of born offspring (z; y >z). Logically, ∑x will be less than 1. With r being 0.5 and B being the same for both parent and offspring (B; y=B; B1=B2=…=Bz), the adjusted formula would look like as follows:

        (r1B1 + r2B + …+ rzBz) > C

        rBz > C

        0.5Bz > ((∑x)/z)y

        0.5Bz(squared) > (∑x)B

        0.5 z(squared) > (0;1)

        So can we do that? The inequality assumes r1=r2=..=rz, which is correct mathemetically (r = 0.5), but not biologically (it is possible to use range, suggesting more than 50% will be passed – ‹0,5;1)- but that does not overcome “the bio problem”). Therefore, can this formula be used it this way? Based on what you said, this should be correct…I have not studied the theoretical basis of the rule, I only have “the general (one-sentence) knowledge” of what the rule represents, thus I am not sure what are its implications (and what I can do with it/how to use it…)

        • windy

          If you’re still following this post – yes, you could use it that way. I wouldn’t worry so much about relatedness deviating from 0.5, since it’s an approximation (but if you’re interested there’s literature estimating relatedness in real life populations: search for articles by David Queller’s group, for example). It would be unlikely that the benefits would be equal for all individuals, though, and I’m not sure if your cost calculation works as intended (looks to me that the left side of your inequality assumes that all offspring 1-z survive since they all contribute to the benefit, while the right side assumes that some of them die?)

          Another possible quibble about your example is that a parent choosing to die to save its own children can be explained even under “classical” definitions of fitness without kin selection. However, kin selection theory has been applied to similar cases, such as the proposed “grandmother effect” in humans – where the parent doesn’t die, but sacrifices her own future reproduction potential in order to help her children reproduce (or her grandchildren survive), so the end result is similar to your proposed example.

          • DMark

            Thanks for the reply. To “the left/right-side-equation thing” – I thought this is how you would calculate it. Following the example, “offspring die if parent does not save them”, therefore you compare “parent does not save offspring scenario (born offspring die, parent lives)” (C/cost to the individual/ – right side of the inequality) to “parent saves offspring scenario (born offspring survive, parent dies)” (Br/benefit to the individual/ – left side of the equation). Is this incorrect? To the “second quibble”, I realize it can be explained under classical definitions of fitness, but was curious, whether I can use mathematics (i.e. Hamilton´s rule), “to support” that death of a parent can be beneficial to offspring independent of its care. In Cambell, the definition of Hamilton´s inclusive fitness is: “the total effect an individual has on proliferating its genes is by producing its own offspring and by providing aid that enables other close relatives who share many of those genes, to produce offspring”. So, could we not make “a special use” of Hamilton´s rule and not think just about individual producing offspring and aiding to non-offspring (other close relatives), but about individual producing offspring and ading to offspring as is the case in our example (parent “aids” offspring by dying)? Anyway, thanks again for your help, I will try to find some evolutionary biologists and ask about this in more depth…I just have to know:)! Cheers!