A predator-prey model based on the principle of biomass conversion with dynamic use of refuge in prey

Intraspecific and interspecific interactions are of great interest in population ecology, as the trophic positioning of organisms, both as consumers and as resources, influences the corresponding population dynamics. This is particularly relevant to the feedback between demographic processes, such as birth and death rates, and the life-history functions related to reproduction and survival. Specifically, in the case of prey, the use of refuge has been reported as an evasion strategy that stabilizes predator-prey interaction. However, this remains a subject of theoretical debate. This study examines predator-prey interactions through a mathematical model based on the principle of biomass conversion, incorporating the adaptive use of refuge by prey. Analytical and numerical results establish the existence of a locally asymptotically stable co-existence equilibrium, contingent on meeting a threshold condition that links predator birth and death rates to the fraction of prey in a refuge. Introducing a dynamic component for the fraction of prey in refuge enhances persistence and stability in the predator-prey interaction compared to traditional non-dynamic models.