Generalized gradient structures for measure-valued population dynamics and their large-population limit

Abstract We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations Bolker–Pacala–Dieckmann-Law model. Under assumption detailed balance, we provide rigorous generalized gradient structure, incorporating fluxes arising birth and death particles. Moreover, large limit, show convergence Liouville equation, which is transport associated with mean-field limit underlying process. In addition, structures sense Energy-Dissipation Principles, establish propagation chaos result for system derive gradient-flow formulation limit.