A phenomenological model without dispersal kernel to model species migration

Phenomenological approaches to model species migration are usually based on kernel-based methods. These methods require a good knowledge of the dispersal agent behaviour for a given species. They also calculate the location of individuals independently to each other (except the mother plant) and then suppress some of them according to additional interactions such as competition, facilitation and recruitment. In this paper, we propose to use a new phenomenological method, the Gibbs method, to model tree species migration at large scale. The Gibbs method handles the location of adult individuals in terms of pairwise interactions described by a potential function. This function summarizes the set of known and unknown factors determining the spatial distribution of the individuals (or cohorts). The principle of the Gibbs method is to minimize the sum of all pairwise interactions, also called the cost function, in order to optimize the spatial point pattern according to the chosen potential function.