Modelling social evolution: the relative merits and limitations of a Hamilton's rule-based approach

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Lehmann & Keller (2006) convincingly argue that cooperation or altruism can evolve only when at least one of the following conditions are met: (i) cooperation has direct personal benefits, (ii) individuals are genetically related, (iii) individuals have information on the likely behaviour of others or (iv) individuals recognize other cooperators through a phenotypic label (green beard recognition). The first condition is quite obvious. The three others are also intuitive, given that they provide various conditions under which interacting individuals are positively related, meaning more likely than chance to interact with fellow cooperators (Frank, 1998; Pepper & Smuts, 2002; Foster & Wenseleers, 2006; Foster et al., 2006). By focusing on costs and benefits and relatedness, Lehmann and Keller (2006) are adopting an inclusive fitness or Hamilton’s rule-based approach to classify social evolution models (Hamilton, 1964). Personally, I believe a Hamiltonian perspective is indeed a very intuitive one, and should be adopted more widely. This is true particularly in the area of game theory, where currently little effort is made to interpret results this way, and models are frequently simulation-based, making general, intuitive interpretation of results difficult. In fact, in my own work, Hamilton’s rule has always taken a central place in the derivation and interpretation of model results (e.g. Wenseleers et al., 2003, 2004a, b; Ratnieks et al., 2006). At the same time, however, one may also wonder whether it is possible to translate every single social evolution model into the form of Hamilton’s rule. Here, I am skeptical, the reason being that Hamilton’s rule has well-known limitations. In particular, Hamilton’s rule only works correctly under weak selection and additive gene action (Cavalli-Sforza & Feldman, 1978; Michod, 1982; Grafen, 1985; Bulmer, 1994; Hamilton, 1964, 1995; Frank, 1997; Roze & Rousset, 2003; Rousset, 2004). In addition, evolution is normally assumed to be close to equilibrium, with most of the population fixed for a single type (Frank, 1998). Finally, with Hamilton’s rule being a deterministic equation, it entirely neglects stochasticity, and thus ignores the possibility for deleterious altruistic genotypes to go to fixation as a result of drift (Frank, 1997), which models have shown to be quite possible in small populations (Eshel, 1972; Rousset, 2004). In the section below I will give two worked-out examples where some of these limitations come into play and where, due to violations of assumptions, Hamilton’s rule does not correctly predict evolutionary change. The implication is that partitioning selection into direct and indirect fitness components is not always as straightforward as Lehmann and Keller make out. In many cases, the conditions under which a cooperative genotype would spread relative to a noncooperative one simply cannot be written in the form of Hamilton’s rule. In such situations, the inclusive fitness framework of Lehmann and Keller cannot be used to accurately classify models.