A phenomenological model without dispersal kernel to model species migration
Résumé
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. We compared dispersal models based on the non-homogeneous Gibbs method to several models based on kernel methods, and in detail with a leptokurtic kernel-based model. An elasticity test of the Gibbs-based dispersal model showed a strong dependence among the parameters and the key role of the potential of interaction in the dispersion obtained. We found important differences in the resulting patterns of migration between Gibbs-based and kernel-based models: Gibbs-based model generated more random point patterns, leading to more diversified migration pathways than kernel-based model. Finally, a semi-realistic application to paleo-landscapes showed that the Gibbs-based model was able to simulate the migration pathways of Fagus sylvatica during the Holocene more realistically than kernel-based models.