Skew-normality for climatic data and dispersal models for plant epidemiology: When application fields drive spatial statistics

Developments in spatial statistics have a long standing tradition of being drawn out by specific applications. In this paper we illustrate this point by showing how research driven by two specific areas, namely the sensitivity of agriculture to climate change and plant epidemiology, has led to new developments in two branches of spatial statistics, respectively random field theory and spatio-temporal point processes. In a first part, it is shown how skew-normal distributions allow one to define skew-normal random fields and how these can be used to build a weather generator. In a second part, models for dispersal of propagules that can account for rough anisotropies and a model for group dispersal are presented. The distribution of the farthest dispersed point, a quantity of great interest for assessing expansion speed, is derived.