The question of altruistic acts poses a serious question in the field of evolutionary biology. Altruism occurs when an individual does an act which gives benefit to others at a cost to itself. Natural selection, on the other hand, states that the traits which give an individual the greatest benefit are the ones that will spread in a population. So then how does altruism spread within a population? It seems contrary to natural selection. Many explanation have been used to explain the evolution of altruism, from the lionized (kin selection) to the marginalized (group selection). But a paper by Jeff A. Fletcher of Portland State University and Michael Doebeli of the University of British Columbia that I’m about to describe to you cuts through all the bullshit. It shows that there is only one characteristic that is needed for altruism to spread in a population: positive assortment.
Positive assortment is a fancy word of saying like attracts like. And that simple attraction is all their needs to be for altruism to spread in a population. How? Well, imagine two individuals in a two different groups; the first individual is a cooperator (altruist) and the other is a defector (non-altruist). Cooperators contribute some benefit to a common pool and pay an individual cost for their actions. Defectors do not give the benefit and have no cost to them. After all cooperators contribute, the amount in the common pool is now divided equally among all members, including defectors. So if a k number of cooperators in a group of N members contribute a benefit of reward b individually to a pool with cost c, then our cooperator gets a payment of k*b/N-c, while our defector gets a payoff of k*b/N. In this case, the defector always does better than the cooperator, and therefore, altruism will not spread within the population.
The first model I described to you assumes that both groups have the same number of cooperators. Let’s assume that the groups each have a different number of cooperators, ec for the first group and ed for the second group (Qualification: this is different from the paper. There is a whole other discussion in their paper. I am just simplifying things for sake of this blog post). Then the payoff for our cooperator is ec*b/N-c while our defector gets ed*b/N. Now this is where things get interesting. Altruism evolves when ec*b/N-c>ed*b/N. Assuming that ec is sufficiently more numerous than ed (specifically ec>c*N/b+ed), then altruism can evolve. To put it in another way, cooperators must clump together to have altruism become beneficial.
So why is this result so important? Because it generalizes the mechanism for the evolution of altruism. In essence, kin selection, reciprocal altruism, and group selection all give a specific mechanism for positive assortment. In fact, we can show that kin selection is nothing but a mere mechanism. If we take the inequality ec*b/N-c>ed*b/N, we can do some algebra and get (ec-ed)*b/N>c. This is an equivalent (not equal!) equation to the one used by WD Hamilton, r*b>c. Here the parameter r is replaced by the parameter (ec-ed)/N. Such is the power of this basic equation and this basic paper, one which I feel is the most important paper on the evolution of altruism.
Citation: Fletcher, J.A. and Doebeli, M. 2009. A simple and general explanation for the evolution of altruism. Proceedings of the Royal Society B. 276:13-19