The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Abstract

Hamilton's rule asserts that a trait is favored by natural selection if the benefit to others, [Formula: see text], multiplied by relatedness, [Formula: see text], exceeds the cost to self, [Formula: see text] Specifically, Hamilton's rule states that the change in average trait value in a population is proportional to [Formula: see text] This rule is commonly believed to be a natural law making important predictions in biology, and its influence has spread from evolutionary biology to other fields including the social sciences. Whereas many feel that Hamilton's rule provides valuable intuition, there is disagreement even among experts as to how the quantities [Formula: see text], [Formula: see text], and [Formula: see text] should be defined for a given system. Here, we investigate a widely endorsed formulation of Hamilton's rule, which is said to be as general as natural selection itself. We show that, in this formulation, Hamilton's rule does not make predictions and cannot be tested empirically. It turns out that the parameters [Formula: see text] and [Formula: see text] depend on the change in average trait value and therefore cannot predict that change. In this formulation, which has been called "exact and general" by its proponents, Hamilton's rule can "predict" only the data that have already been given.