A novel PDE model to describe terrestrial arthropods considering physiological age, reproduction rate, and body mass

Abstract

Modelling the life cycle of terrestrial arthropods at multiple trophic levels and their interactions with the surrounding environment aids to understand the evolution of the populations living in the different ecological niches. The need to predict the future scenarii in a precision agriculture and forestry framework is pushing even more the development of models that can support and be supported by measurements. Although the theoretical developments of the last decades provided interesting solutions, the growth in terms of biomass has still not been properly included in physiologically based models. Modelling the biomass component of insect populations is of wide importance, given the growing availability of measurement systems that provide the biomass reduction in agriculture and forest environments. This work, hence, proposes a novel physiologically based model describing populations of terrestrial arthropods considering time, physiological age, and biomass as independent variables. The theoretical formulation led to a partial differential equation describing the population dynamics which includes, as “rate functions”, a series of sub-models that can be developed independently. These sub-models relate a specific aspect of the development of arthropods, mostly depending on the species, with the external environment and with the food resources available. A potential application to the case of the corn leafhopper Dalbulus maidis was considered as a secondary step of this study, to explore the model behaviour.