Ivric Valaire Yatat Djeumen

Forest encroachment over savannahs has been recurrently reported in the tropics over the last few decades, especially in northern tropical Africa. However, process-based, spatially explicit modelling of the phenomenon is still trailing broad-scale empirical observations. In this paper, we use remotely sensed diachronic data from Central Cameroon to calibrate a simple reaction–diffusion model, embodying dynamical interactions between grass and woody biomasses in the savannah biome. Landsat satellite image series over the Mpem and Djim National Park (MDNP) (Cameroon) witnessed a dramatic extension of forest over the last five decades, and our estimates of forest front speeds based on randomly sampled transects indeed yield higher values (5–7 m yr-1) than in the existing literature (0.5–2 m yr-1). We use model simulations to provide the first estimates of woody biomass dispersal coefficients. Since the study region did not provide examples of savannah progression, estimates of grass dispersal proved inconsistent and we reverted to literature-based historical data to reach rough estimates. We demonstrate that broad-scale remote sensing data allows for calibrating simple reaction–diffusion models of vegetation dynamics in the savannah biome. Such calibrated models become a general baseline of expected changes and a valuable tool to understand how spatial environmental factors may locally modulate the overall dynamics.

Anthropisation and excessive hunting in tropical forests threaten biodiversity, ecosystem maintenance, and human food security. In this article, we focus on the issue of coexistence between humans and wildlife in an anthropised environment. Assuming that humans move daily between their residential area and the surrounding forest to hunt, we study a resource‐consumer model with consumer migration. A comprehensive analysis of the system is carried out using classical theory and monotone systems theory. We show that the possibilities for long‐term coexistence between human populations and wildlife populations are determined by hunting rate thresholds. Depending on the level of anthropisation and the hunting rate, the system may converge towards a limit cycle or a co‐existence equilibrium. However, the conditions for coexistence become more difficult as anthropisation increases. Numerical simulations are provided to illustrate the theoretical results.

Many systems in life sciences have been modeled by reaction–diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events, etc) such that an appropriate formalism like impulsive reaction–diffusion equations is necessary to analyze them. While several works tackled the issue of traveling waves for monotone reaction–diffusion equations and the computation of spreading speeds, very little has been done in the case of monotone impulsive reaction–diffusion equations. Based on vector-valued recursion equations theory, we aim to present in this paper results that address two main issues of monotone impulsive reaction–diffusion equations. Our first result deals with the existence of traveling waves for monotone systems of impulsive reaction–diffusion equations. Our second result tackles the computation of spreading speeds for monotone systems of impulsive reaction–diffusion equations. We apply our methodology to a planar system of impulsive reaction–diffusion equations that models tree–grass interactions in fire-prone savannas. Numerical simulations, including numerical approximations of spreading speeds, are finally provided in order to illustrate our theoretical results and support the discussion.