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Multilevel mutation-selection systems and set-valued duals

A class of measure-valued processes which model multilevel populations undergoing mutation, selection, genetic drift and spatial migration is considered. We investigate the qualitative behaviour of models with multilevel selection and the interaction between the different levels of selection. The basic tools in our analysis include the martingale problem formulation for measure-valued processes and a generalization of the set-valued dual representation introduced in Dawson-Greven (2014). In particular we describe the ergodic behaviour of these processes and review some situations under which deme level selection determines the long-time behaviour.