Estimating insect population density from trap counts

Time Dependent Diffusion as a Mean Field Counterpart of Lévy Type Random Walk

“…The Mean Field Approach (MFA) and Individual Based Model (IBM) have been shown to be consistent in the context of estimating trap counts [46,50], for a system whose movement dynamics are of a Brownian nature, corresponding to the constant diffusion case. Individual based models provide information on the fluctuations in the system and provide a basis for the study of the stochasticity of the system.…”

“…The assumption that subsequent steps are uncorrelated, is not viable for a sufficiently small value of Δt. The movement direction of the preceding step is preferred for the next step, resulting in the expected values of direction to be centered about zero, [46]. The corresponding random process is known as the correlated random walk (CRW), [31].…”

“…Currently, the list of complex systems displaying anomalous diffusion behaviour is quite extensive [4,35,59,75,77], and the problem of trapping (more commonly known as system flux) is well known in physics. However, most studies are concerned with large-time asymptotics whilst for insect monitoring short time dynamics are of primary concern [46,50].…”

“…Furthermore, experimental trap counts can be simulated via computer algorithms where the properties of the individual movement are fully determined by the step distributions and turning angle distribution. A comprehensive mathematical framework for individual based modelling can be found in [46] and also presented below in §(2.2).…”

“…In another ecological context, accurate information about population abundance is required to trace the spread of harmful invading species. In the case of insects, their density is usually estimated based on trap counts [45,46]. One way to look at the dynamics of trap counts is to simulate them by modelling the movement of each individual in the field.…”