A general DDE framework to describe insect populations: Why delays are so important?

Physiologically-based models are a valuable tool to describe the biology of terrestrial arthropods, as it is the case of insects. These models represent the division of the life cycle in various discrete stages and provide explicit connections with the external environment, making them good candidates for decision support system tools. However, despite the current literature offering good theoretical frameworks, most of them lack of a description of the minimum time required by the organisms to develop to the next life stage. This problem leads to an overestimation of the population and to a compression of the peaks of the generations, hindering their application in real scenarios. In this study we provide a new general model based on Delay Differential Equations (DDE) that overcomes the problem of the minimum development time by introducing time-dependent delays. Those delays generally depend not only on the biology of the species, but on time and on the environmental conditions. This theoretical extension has new implications from the parameter estimation point of view, which are discussed with the support of a case study of agronomic relevance: the brown marmorated stink bug Halyomorpha halys. Besides supporting the description of the model, the case of H. halys was also considered to validate the model using datasets from two geographical locations, for an overall of 5 fields. Simulations showed that the DDE model describes the experimental data better than its previous version based on ordinary differential equations. The model represents an overall step forward in theory development and can be of great support to describe multivoltine species.