Most attempts to answer the question of whether populations of groups can undergo natural selection focus on properties of the groups themselves rather than the dynamics of the population of groups. Those approaches to group selection that do emphasize dynamics lack an account of the relevant notion of equivalent dynamics. I show that the theory of ‘dynamical kinds’ I proposed in Jantzen :3617–3646, 2014) can be used as a framework for assessing dynamical equivalence. That theory is based upon the notion (...) of a dynamical symmetry, a transformation of a system that commutes with its evolution through time. In the proposed framework, structured sets of dynamical symmetries are used to pick out equivalence classes of systems. These classes are large enough to encompass the range of phenomena we associate with natural selection, yet restrictive enough to guarantee a sort of causal homogeneity. By characterizing dynamical kinds via symmetry structures in this way, the question of levels of selection becomes a precise question about which populations respect the dynamical symmetries of Darwinian evolution. Standard population genetic models suggest that populations undergoing evolution by natural selection are partially characterized by a group of fitness-scaling symmetries. I demonstrate conditions under which these symmetries may be satisfied by populations of individuals, populations of groups of individuals, or both simultaneously. (shrink)