A dynamically-structured matrix population model based on renewal processes for accumulative development under variable environmental conditions

Arthropod vectors are responsible for the transmission of pathogens in humans and other species. The transmission rate depends on the size and activity of the vector population, factors which are in turn strongly affected by environmental conditions. Therefore, in order to develop realistic representations of vector population dynamics, it is necessary to properly account for the impact of a changing environment on the duration of life processes. Here, we use a pseudo-stage-structured population to model the accumulative process of development as a renewal process with a variable rate that depends on the environment. We incorporate this into sPop, formerly an age-structured population dynamics model. This framework allows the modeller to represent realistic life stage durations by choosing from three alternative probability schemes: an Erlang distribution, a Pascal distribution, or a fixed duration, while enabling the model to respond appropriately to variations in stage duration characteristics. Using this approach, we demonstrate that introducing random variation into the environmental conditions, which results in fluctuating development rates, on average decreases the time required for stage completion. An exception to this is an already optimum development rate being perturbed by noise towards a less efficient course. The proposed framework is suitable for performing inverse modelling with data collected from highly variable environmental conditions, the results of which can be used to develop realistic climate-driven population dynamics models.