- A rule is not a rule if it changes from case to case (a reply to Marshall's comment)
- Journal of Theoretical Biology
- Volume | Issue number
- 270 | 1
- Pages (from-to)
- Document type
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
This is a reply to "Queller's rule ok: Comment on van Veelen ‘when inclusive fitness is right and when it can be wrong’ " by James Marshall in the Journal of Theoretical Biology, in this issue. In order to circumvent the disagreement about the Price equation and focus on the issue of the predictive power of inclusive fitness for group selection models, I derive Queller's and Marshall's rule without the Price equation. Both rules however need a translation step in order to be able to link them to the group selection model in van Veelen (2009). Queller's rule applies to games with 2 players and 2 strategies, and is general. Marshall's rule on the other hand applies only to a small subset of 3-player games. His rule is correct, but for other, similarly small subsets we would get other rules. This implies that if we want a rule that applies to all symmetric games with 3 players and 2 strategies, it will have to use a vector of dimension 2 that represents population structure. More in general: for group selection models with groups of size n, a correct and general prediction will need to use a vector of dimension n−1 that represents population structure.
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