On Kinship

On Facebook one of my friends posted that they were attending a conference on reconceptualizing kinship, and of course, I responded that it was tempting to put in my two cents worth on the subject. To my shock another commenter asked me to do just that. SO, given that I have been absolutely swamped since getting back from sabbatical, I figure I ought to at least pretend to have a blog (I actually have a couple of other issues that really need to be addressed. Maybe in a few weeks). In any case, here goes.

Of course, kinship means many things in different contexts. Colloquially kin can mean relatives, as in my cousin is kin. From a genetic perspective, the classic use of kinship is in inbreeding coefficients, and thus it is the probability that two individuals share common genes. Finally, kinship was coopted by Maynard-Smith to describe the “r” term of Hamilton’s rule.

Colloquially we can use kinship in a more general sense. Thus, a person might describe themselves as having kinship with others of a similar political view, or a group fighting for a cause may consider their fellow members as kin.


Sisterhood: 1) A bond between two or more girls or women not necessarily related by blood. 2) An association, society, or community of women linked by a common interest, religion, or trade. (Image from http://www.thismorleylife.com/wp-content/uploads/2013/09/25473872sisterhood.jpg, definition from Google.com, and Urban dictionary.com)

Of particular importance here from a genetic perspective is that the inbreeding coefficient definition of kinship is very consistent with the colloquial definition of kinship as relatives. This is not true of Maynard-Smith’s definition of kinship as the r term in Hamilton’s rule. In fact, Maynard-Smith’s definition comes much closer to the social extension of kinship as two individuals that share a common bond, regardless of the cause of that bond. I would suggest that Maynard-Smith made a mistake here. In common culture we make a distinction between kin as in relatives and kin as in shared interest. For example, we have no problem referring to relatives strictly as “kin”, but for those with a shared interest we are likely to put in a modifier – brother in arms, brother from another mother, BFF. I would argue that Hamilton’s r is actually a combination of these two colloquial concepts of kinship. Sharing of genes in an additive sense, and other forms of sharing of phenotypes.

The reason I say this comes from contextual analysis. First, in one of my papers (Goodnight 2013, Evolution 67:1539) I show that the mathematics of kin selection can be directly translated into the mathematics of contextual analysis. The basic process is that Hamilton’s inclusive fitness can be translated into the direct, or neighborhood fitness approach (Taylor and Frank 1996 JTB180:27 for the neighborhood fitness approach, Taylor, Wild and Gardner 2007 J. Evol. Biol. 20301 for the equivalence of inclusive fitness and direct fitness). The neighborhood fitness approach in turn is based on EXACTLY the same equation as inclusive fitness (fun fact: Contextual analysis predates neighborhood fitness by a lot. It has precedence, and I think a strong argument could be made that the neighborhood fitness approach should be re-named contextual analysis).

It is worth emphasizing that there are significant differences between kin selection and multilevel selection, and these are the basis for my reasoning behind why I don’t like kin selection. However, given the close mathematical association between contextual analysis and neighborhood fitness it is hardly surprising that it is possible to derive Hamilton’s rule using contextual analysis (Goodnight Schwartz and Stevens 1992.  American Naturalist 140:743) :

Hamiltons rule

This formulation differs from the classic kin selection version in several important regards. The first, a bit irrelevant, but something I personally can’t ignore, is that CA is treating Hamilton’s rule as a competing rates problem. That is, altruism will evolve when group selection is stronger than individual selection, and this can happen either due to differences in the intensity of selection (measured in genetic standard deviations at the two levels), or in the relative magnitudes of the variances in the group and individual trait (measured as the proportion of variance that is among groups).  In contrast, neighborhood fitness is providing the optimality solution.  This difference rather fades away when applied to contextual analysis, but it is a big difference in philosophy.

Much more important, however, is that using contextual analysis it is clear that Hamilton’s “r” is the fraction of the total variance that is among groups. This is an important point.   In an additive world where nobody interacts with anybody kinship, as measured by Wright’s FST, is exactly equal to the variance among groups. However, in a world in which interactions occur this will no longer be the case. Consider:

If there is epistasis is gene interation: For epistasis, the variance among groups will roughly be proportional to FSTN, where N is the order of the interaction. For example if there is two-locus epistasis the fraction of variance among groups will go up roughly as FST2. This is really only strictly true for additive by additive epistasis, nevertheless it makes the point that relatedness and variance among groups are not necessarily the same thing.

If there are interactions among individuals: This can be indirect genetic effects, but it can also be non-genetic effects. One of the very common features of social groups is some form of policing behavior. For example, in bees workers typically destroy worker laid eggs. Thus, even if there is genetic variation among workers in their propensity to lay eggs, it doesn’t matter since all of this variation is suppressed by the policing behavior. On an emphatically non-genetic scale, musical bands work together to enforce a steady rhythm on the band members. This rhythm produces a product (music) that is appealing, and, if the stories about rock bands are correct, has a definite effect on fitness. Similar stories can be made about everything from sports teams to military organizations. These interactions affect the heritable variation among groups, but have no effect on the heritable variation within groups. They simply are not in kin selection models, and as such they represent a complete wild card that will nearly always make altruism easier to evolve.

The point is Hamilton was thinking about a linear additive world when he was talking about the r term in his rule. This was perfectly reasonable in 1964 when he published his work. That was before the days of computers, before any math around gene interactions had been developed, and before there was any data to suggest that group selection could act on interactions among individuals. It was also over 50 years ago. I think it is probably time we considered moving on!

So, what should we do: Recognize that Maynard-Smith was incorrect to call Hamilton’s rule it kin selection. Hamilton’s r DOES NOT refer to kinship, or at least not kinship in the narrow genetic sense. Rather it refers to the ratio of the variance among groups to the total phenotypic variance. Given what we know about gene interactions and social interactions we are long past the time when we should have abandoned Hamilton’s simplistic view of the cause of the variance among groups. I leave it to the reader to decide whether kinship applies to individuals related by social interactions. Maybe we should have a “grouphood of the interacting genes”?


Is a Grouphood of traveling genes a form of kinship? (http://trailers.apple.com/trailers/wb/thesisterhoodofthetravelingpants/images/sisterhood_01.jpg)

One Response to “On Kinship”

  1. Tim Tyler says:

    In the “Why I Don’t like Kin Selection” article you argued:

    “Soldiers are famous for acts of altruism among genetically unrelated members of the same unit. What makes them similar is culture not genes. Genic models cannot handle this, and kin selection is no exception.”

    The existence of cultural kin selection – based on shared memes rather than shared genes – would seem to invalidate this objection. Cultural kinship has long been recognized by anthropologists. Now that knowledge about cultural inheritance and cultural evolution is becoming more widespread, it is about time for evolutionary biologists to start treating it more seriously too.

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