A diffusive logistic growth model to describe forest recovery

Abstract

Land-use and land-cover change (LUCC) has broad implications for biodiversity, climate and ecosystem services. Even though LUCC often focuses on forest fragmentation, forest recovery is another form of LUCC that is becoming increasingly common. Understanding the process of forest recovery is a conservation and management priority; however, it is a difficult process to understand given the large number of factors that interact in a complex spatio-temporal setting. Reaction diffusion models provide an appropriate framework to study the complex dynamics of forest recovery because they account for both spatial structure and the dynamics of land-cover classes. Here, we describe a diffusive logistic growth (DLG) model to quantify forest recovery. We define a system in which forest diffuses through a non-forest matrix. The model consists of a diffusion term that describes the spread of forest in continuous space and time, and a logistic growth reaction that describes change in the proportion of forest. To illustrate model parameterization, we used the DLG approach to describe forest recovery in Puerto Rico from 1951 to 1991–1992. The model showed that forest recovery in Puerto Rico was explained by a positive intrinsic growth rate of forest and relatively slow diffusion. This mechanistic modeling approach presents a novel way to study forest recovery in continuous space and time while accounting for spatial dependency.