A novel version of the Von Foerster equation to describe poikilothermic organisms including physiological age and reproduction rate

Abstract

The mathematical description of poikilothermic organisms’ life cycle, of insects in particular, is a widely discussed argument, above all for its application in decision support systems. The increasing interest among agricultural industries in obtaining products with minor quantities of chemical inputs has led entomologists and model scientists to study in greater depth not only the biology and behaviour of the insects, but also the way to translate these mechanisms into mathematical language. The aim of this work is to provide a new instrument to describe insect pests’ population density. In particular, the study analyses insects’ development through the life stages driven by environmental factors. This has led researchers to consider physiological age, instead of the more widely used chronological age. In addition to mortality and fertility rates, the possibility of improving the simulation by inserting as a boundary condition results from previous field monitoring or the links with diapause models has been considered. The work is validated in the case of the European grapevine moth Lobesia botrana.