A unifying framework reveals key properties of multilevel selection

• A ball-and-urn system is presented as a conceptual tool for understanding multilevel selection.
• General properties of multilevel selection with minimal dependence on parameter values are derived.
• Fast group-level events relative to individual-level events enhances group-level selection.
• Mutation enhances individual-level selection.
• Smaller group sizes or a larger number of groups enhance group-level selection.

Natural selection can act at multiple biological levels, often in opposing directions. Viral evolution is an important example, with selection occurring both within infected hosts and between hosts via transmission. A fast-replicating virus may outcompete a slower strain within the same host, however, if rapid viral replication incapacitates the host, this fast-replicating virus may not be transmitted as frequently as its slower counterpart. Such examples of antagonistic multilevel selection arise across biological taxa and scales, from microbial public goods production to male mating strategies. A general formalism for describing and analyzing these diverse systems can identify their common underlying properties. Here I introduce such a unifying framework, which can be intuitively visualized as a stochastic ball-and-urn process. This ball-and-urn process illustrates the dynamics of antagonistic selective forces and allows the systematic derivation of properties with little or no dependence on model parameterization. These properties are consistent with previous studies, both theoretical and empirical, of multilevel selection. In particular I show that selection at the group level is favored when group-level events occur frequently relative to individual-level events, when there is little or no mutation, and when there are many groups relative to the number of individuals in each group. This approach demonstrates how multilevel selection can be understood as a general biological phenomenon, and identifies recurring characteristics that may be independent of specific biological contexts.