A nonlinear model for stage-structured population dynamics with non local density-dependent regulation: an application to the fall armyworm moth

The assessment and the management of the risks linked to insect pests can be supported by the use ofphysiologically-based demographic models. These models are useful in population ecology to simulate thedynamics of stage-structured populations, by means of functions (e.g., development, mortality and fecundityrate functions) realistically representing the nonlinear individuals physiological responses to environmentalforcing variables. Since density-dependent responses are important regulating factors in population dynamics,we propose a nonlinear physiologically-based Kolmogorov model describing the dynamics of a stage-structuredpopulation in which a time-dependent mortality rate is coupled with a nonlocal density-dependent term. Weprove existence and uniqueness of the solution for this resulting highly nonlinear partial differential equation.Then, the equation is discretized by finite volumes in space and semi-implicit backward Euler scheme intime. The model is applied for simulating the population dynamics of the fall armyworm moth (Spodopterafrugiperda), a highly invasive pest threatening agriculture worldwide