Replicated point processes with application to population dynamics models

In this paper we study spatially clustered distribution of individuals using point process theory. In particular we discuss the spatially explicit neutral model of population dynamics of Shimatani (2010) which extends previous works on Malécot theory of isolation by distance. We reformulate Shimatani model of replicated Neyman-Scott process to allow for a general dispersal kernel function and we show that the random migration hypothesis can be substituted by the long dispersal distance property of the kernel. Moreover, the extended framework presented here is fit to handle spatially explicit statistical estimators of genetic variability like Moran autocorrelation index or Sørensen similarity index. We discuss the pivotal role of the choice of dispersal kernel for the above estimators in a toy model of dynamic population genetics theory.