Graphical representation of some duality relations in stochastic population models

Abstract

We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. ) and for the self-duality of Feller's branching diffusion with logistic growth (cf. ). The two dual processes are approximated by particle processes which are forward and backward processes in a graphical representation. We identify duality relations between the basic building blocks of the particle processes which lead to the two dualities mentioned above.