Hamilton had predicted that close relatives would cooperate - since helping relatives helps copies of your genes inside them. Price pointed out that another way of helping your genes was killing off the least-closely related individuals in the population - that kin selection had an dark side: spite.
Spite was an interesting idea - but not a terribly practical one. The effort and risk involved in harming large numbers of non-relatives seemed highly unlikely to result in a payoff to the actor.
Price's equation allowed for a fairly simple derivation of Hamilton's rule. It was rather like the relationship between Newton's model and Einstein's. Price had a more general model that made almost all the same predictions as Hamilton's model - but handled a few extreme cases better.
However, Price's equation was to have other effects - besides its predictions about spite. Essentially Price modeled the effect of natural selection and persistence on the frequency of a trait in a population. It had two terms, one representing the persistence of the trait and the other representing the change caused by selection. It more-or-less ignored drift by dealing with expected values: stochastic forces would average out. Price had provided the logic of Universal Darwinism - and showed how the mathematics of selection could be applied to practically anything. Its generality reinforced the idea that blood relatedness was only one factor that could be responsible for trait correlations between generations. Many interpreted this to mean that the idea of "kin" was out - and that we needed a more general theory.
One of the things that the Price equation could be applied to was entire groups. You could split a population into groups (however you liked) and apply the Price equation to those groups. You could also apply the equation to individuals within those groups. That quickly led to a model of group selection. The change in frequency of a trait could be modeled as being divided into a component due to natural selection within groups, and a component due to natural selection between groups.
Price's maths could have led to a rapid reconciliation between kin selection and group selection proponents. However, that isn't quite what happened, as we will see.
- Gardner, A. (2008) The Price equation.
- Jones, James Holland (2008) Notes on the Price Equation
- Frank, Steven A. (2012) The Price Equation.
- Frank, Steven A. (1995) George Price's contributions to Evolutionary Genetics.
- Grafen, A. (2000) Developments of the Price equation and natural selection under uncertainty.