martin_nowak's picture
Professor of Biology and Mathematics, Harvard University; Co-author, SuperCooperators
Inclusive Fitness

This year marks the 50th anniversary of the introduction of inclusive fitness, the highly influential idea which supposedly explains how insects evolve complex societies, and how natural selection can lead to altruism among relatives.

This mainstay of sociobiology is based on the 1964 work of the English evolutionary biologist, William Hamilton, who coined the following definition:

Inclusive fitness may be imagined as the personal fitness which an individual actually expresses in its production of adult offspring as it becomes after it has been first stripped and then augmented in a certain way. It is stripped of all components which can be considered as due to the individual’s social environment, leaving the fitness which he would express if not exposed to any of the harms or benefits of that environment. This quantity is then augmented by certain fractions of the quantities of harm and benefit which the individual himself causes to the fitnesses of his neighbours. The fractions in question are simply the coefficients of relationship appropriate to the neighbours whom he affects: unity for clonal individuals, one-half for sibs, one-quarter for half-sibs, one-eighth for cousins,… and finally zero for all neighbours whose relationship can be considered negligibly small. 

Modern formulations of inclusive fitness theory use different relatedness coefficients but all other aspects of Hamilton's definition remain intact.

Leaving aside the inelegance of Hamilton's original formulation, there is a basic problem with inclusive fitness: you can prove mathematically that inclusive fitness does not apply to the vast majority of evolutionary processes. The reason is simple. Fitness effects cannot in general be written as the sum of components caused by pairwise interactions. This loss of additivity typically occurs when the outcome of a social interaction depends on the strategies of more than one individual. All mathematically meaningful approaches to inclusive fitness realize these limitations. Thus, inclusive fitness becomes a very particular way to calculate evolution: it works in some cases, but not in general. Moreover, if an inclusive fitness calculation can be performed, it gives the same answer as a standard calculation of fitness and natural selection. The latter approach is usually simple and direct.

These mathematical facts make uncomfortable reading for overly enthusiastic proponents of inclusive fitness. In the most extreme cases, they come over as followers of a cult who believe that inclusive fitness is an important extension of the theory of evolution and "always true." In order to maintain the idea that inclusive fitness can always be calculated, a method has been devised that casts any evolutionary change in terms of virtual cost and benefit parameters, which appear as regression coefficients in a statistical analysis. The problem with adopting this statistical approach is that the resulting cost and benefit parameters are meaningless quantities in the sense that they do not explain what is going on in a theoretical model or in empirical data.

Why do we have inclusive fitness? Hamilton's original goal was to find a quantity that is maximized by evolution. This view is attractive: winners of the evolutionary process should be individuals with the highest inclusive fitness. But such an attempt is very much in the spirit of the linear thinking of the 1960s before the likes of Robert May showed us how nonlinear phenomena apply to ecology, population genetics, and evolutionary game theory. From the 1970s onwards we actually understood that evolution does not permit a single quantity that is always maximized. This fact still has to sink in with many in the inclusive fitness community.

What shall we use instead of inclusive fitness? Inclusive fitness seeks to explain social evolution on the level of the individual. For most evolutionary processes, however, the individual is the wrong unit of analysis, because the population structure is complicated and the same genes are present in different types of individuals. Therefore, we have to go to the level of genes. A straightforward approach is to calculate how natural selection changes the frequency of genetic mutations that affect social behavior. These calculations, which do not use inclusive fitness, can identify the key parameters that need to be measured to improve understanding. On the level of genes there is no inclusive fitness.

We have a strong and meaningful mathematical theory of evolution. Natural selection, mutation and population structure are concepts that can be clearly investigated with mathematical formalism. Everyone who understands the mathematical theory of evolution realizes that there is no problem that would require the calculation of inclusive fitness. Calculating inclusive fitness is an optional exercise, one that is best done when a problem is already completely understood. Then in some cases, inclusive fitness can be used to re-derive the same result.

To be fair, over the years inclusive fitness has stimulated much empirical and theoretical work, some of which has been useful. It has induced a discussion of cost, benefit and relatedness in sociobiology, which has some merit. But the dominant and unfortunate impact has been the suppression of meaningful mathematical theories in wide areas of sociobiology.

Contrary to what is often claimed there exists no empirical test of inclusive fitness theory; nobody has ever performed an actual inclusive fitness calculation for a real population. Inclusive fitness was originally understood as a crude heuristic that can guide intuition in some cases, but not in general. It is only in recent years that inclusive fitness has been elevated—mostly by mediocre theoreticians—to a religious belief, which is universal, unconstrained and always true. Understanding the limitations of inclusive fitness gives us now the opportunity to develop mathematical descriptions of key phenomena in social evolution. It is time to abandon inclusive fitness and focus on a meaningful interaction between theory and experiment in sociobiology.