The general form of Hamilton’s rule makes no predictions and cannot be tested empirically
Martin A. Nowak a,b,c, Alex McAvoy a, Benjamin Allen a,d, and Edward O. Wilson e,1
Author Affiliations
aProgram for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138;
bDepartment of Mathematics, Harvard University, Cambridge, MA 02138;
cDepartment of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138;
dDepartment of Mathematics, Emmanuel College, Boston, MA 02115;
eMuseum of Comparative Zoology, Harvard University, Cambridge, MA 02138
Contributed by Edward O. Wilson, April 13, 2017 (sent for review February 2, 2017; reviewed by Michael Doebeli and Jan Rychtar)
Significance
Hamilton’s rule is a well-known concept in evolutionary biology. It is usually perceived as a statement that makes predictions about natural selection in situations where interactions occur between genetic relatives. Here, we examine what has been called the “exact and general” formulation of Hamilton’s rule. We show that in this formulation, which is widely endorsed by proponents of inclusive fitness theory, Hamilton’s rule does not make any prediction and cannot be tested empirically. This formulation of Hamilton’s rule is not a consequence of natural selection and not even a statement specifically about biology. We give simple and transparent expressions for the quantities of benefit, cost, and relatedness that appear in Hamilton’s rule, which reveal that these quantities depend on the data that are to be predicted.
Abstract
Hamilton’s rule asserts that a trait is favored by natural selection if the benefit to others, [Math Processing Error]B, multiplied by relatedness, [Math Processing Error]R, exceeds the cost to self, [Math Processing Error]C. Specifically, Hamilton’s rule states that the change in average trait value in a population is proportional to [Math Processing Error]BR−C. 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 [Math Processing Error]B, [Math Processing Error]R, and [Math Processing Error]C 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 [Math Processing Error]B and [Math Processing Error]C 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.
evolution cooperation kin selection sociobiology
Footnotes
1To whom correspondence should be addressed. Email: ewilson@oeb.harvard.edu.
Author contributions: M.A.N., A.M., B.A., and E.O.W. designed research, performed research, analyzed data, and wrote the paper.
Reviewers: M.D., University of British Columbia; and J.R., The University of North Carolina at Greensboro.
The authors declare no conflict of interest.
Freely available online through the PNAS open access option.
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