*British Journal for the Philosophy of Science* 67, 1025-55

Final Draft (Open Access)

doi.org/10.1093/bjps/axv008 (Published Version - Requires Subscription)

**Abstract**: Do multi-level selection explanations of the evolution of social traits deepen the understanding provided by single-level explanations? Central to multi-level explanations is a mathematical theorem, the multi-level Price decomposition. I build a framework through which to understand the explanatory role of such non-empirical decompositions in scientific practice. Applying this general framework to the present case places two tasks on the agenda. The first task is to distinguish the various ways by which one might suppress within-collective variation in fitness, or indeed between-collective variation in fitness. I distinguish five such ways: increasing retaliatory capacity; homogenising assortment; collapsing either fitness structure or character distribution to a mean value; and boosting fitness uniformly within collectives. I then evaluate the biological interest of each of these hypothetical interventions. The second task is to discover whether one of the right-hand terms of the Price decomposition measures the effect of any of these interventions. On this basis I argue that the multi-level Price decomposition has explanatory value primarily when the sharing-out of collective resources is 'subtractable'. Thus its value is more circumscribed than its champions Sober and Wilson (1998) suppose.