Kin selection: a worked example


Group selection is frequently cited as a source of altruistic behaviour. One common line of reasoning for group selection is that within a group of animals, breeding largely amongst themselves, the members of the group will share a great majority of their genes, so group-altruistic actions will be selected for. By acting on behalf of the group, they will enhance the survival of the genes common to the group. This reasoning is falacious. If you are an atheist who believes in this form of group selection, I hope to convince you in this article that you need to find a better reason for being a good person.

Kin selection on the other hand, holds that altruism occurs between related individuals in proportion to the number of genes they share by descent. Kin selection is a real phenomenon, with some fascinating consequences, but makes much weaker claims than group selection.

When a gene is rare, kin selection and the form group selection discussed here make equivalent predictions. In the more difficult case of a common gene, they differ. Richard Dawkins popularized kin selection in his book "The Selfish Gene", but only really explained the rare gene case, referring the reader in the more difficult case to some densely mathematic papers.

In this article I will give a worked example of the more difficult case, showing that in this example kin selection makes the correct prediction and group selection is in error.

Consider a population of 1000 animals. These animals have a particular gene governing altruism towards first cousins, which comes in two variants (alleles):

500 of these animals have the Nice variant, and 500 the Nasty.

We shall assume that animals interbreed randomly within this population. So a sibling has a 75% chance of having the same allele, and a cousin has a 62.5% chance of having the same allele. Thus group selection sees saving three cousins at the cost of oneself as a net win of (on average) 0.875 copies of a gene, and predicts that the Nice allele should therefore become more common over time.

Kin selection however only counts relatedness of genes by descent. A sibling has a 50% chance of having the same allele by descent, and a cousin has a 25% chance of having the same allele by descent. Kin selection therefore sees saving three cousins as a net loss (on average) of 0.25 copies of a gene, and predicts that the Nice allele should become less common over time.

What actually happens?

In the case of a Nice animal the population will be reduced by one, and the number of animals with the Nice gene will be reduced by one. The proportion of animals with the Nice gene will go from 50% to 49.95%, a reduction of 0.05%.

In the case of a Nasty animal the population will be reduced by three, comprising, on the average, 1.875 Nasty cousins and 1.125 Nice cousins. The proportion of animals with the Nasty gene will go from 50% to 49.96%, a reduction of 0.04%.

The difference is slight since we are talking about a small change in a large population, but in percentage terms the Nasty allele wins.

You can confirm for yourself that an animal sacrificing themself for four cousins has no effect on the proportions, and that sacrificing themself for five or more is beneficial.

But wait, are percentage terms really the best measure of success for a gene? In absolute terms, the Nice gene's choice lost is only one copy where the Nasty allele's choice lost it 1.875 copies.

Consider three situations.

The population can grow without bound. Both Nice and Nasty animals breed at the same rate. Although proportionately the Nasty allele comes to outnumber the Nice, the Nice allele still increases in number.

Success of a kind for the Nice, but not realistic in the long term. Any species is going to eventually be bound by available resources:

The population increases until it reaches the limits of the resources available. Nice and Nasty animals then individually stand the same chance of starving. The population stays constant while the proportions swing towards Nasty, and the Nice allele is eventually wiped out.

There's also a third, disturbing, possibility:

The population is initially able to reproduce fast enough to maintain itself. However, as the Nasty allele comes to dominate, a greater number of animals start dying, and the group wipes itself out.

Isn't this another way to get group selection? Yes but it's very fragile, you need nearly complete isolation of groups within a species. Humans, for example, are far too gregarious for this to be an effect. Obliteration by Nasty genes, if it happens to humans, is going to be a species-wide, not group-wide effect.

I hope this has helped your understanding of kin selection, rather than inducing terminal confusion. It always seemed like a hole in "The Selfish Gene" to me that this more difficult case wasn't covered. If I've misrepresented group selection, my apologies. The concept is somewhat nebulous, and if you think about it hard enough you end up at... kin selection. The form I've given here is one I encounter fairly often (and held myself before I saw the light).