Mathematical Bases for 2D Insect Trap Counts Modelling

Abstract

AbstractPitfall trapping is a predominant sampling method in insect ecology, invasive species and agricultural pest management. Once samples are collected, their content is analyzed, different species are identified and counted and then used to provide reliable estimates of relative population abundance. Such estimates are essential for a variety of reasons, such as the general survey of insect diversity, detection of new insect invasions or simply for monitoring population levels. However, interpreting trap counts is a challenging task, since captures can depend on a variety of factors, such as environmental conditions, trap or survey design, insect movement behaviour, etc. Mathematical models provide an extremely useful description of how insects move in the field and in turn, can simulate the trapping process. In this chapter, we present the mathematical bases for 2D insect trap counts modelling, at the mean-field level using the diffusion equation and on an individual level using random walks. We reveal the intricacies of the trap counts dynamics, with details on how trap geometries and movement types can affect captures. We also describe the mathematical details for other trapping methods, such as baited trapping, where an attractant is used to lure the insects towards the trap location.