Numerica lstudy of pest population size at various diffusion rates

Estimating population size from spatially discrete sampling data is a routine task of ecological monitoring. This task may however become challenging in the case that the spatial data are sparse. The latter often happens in nationwide pest monitoring programs where the number of samples per field or area can be reduced to just a few due to resource limitation and other reasons. In this rather typical situation, the standard (statistical) approaches may become unreliable. Here we consider an alternative approach to evaluate the population size from sparse spatial data. Specifically, we consider numerical integration of the population density over a coarse grid, i.e. a grid where the asymptotical estimates of numerical integration accuracy do not apply because the number of nodes is not large enough. We first show that the species diffusivity is a controlling parameter that directly affects the complexity of the density distribution. We then obtain the conditions on the grid step size (i.e. the distance between two neighboring samples) allowing for the integration with a given accuracy at different diffusion rates. We consider how the accuracy of the population size estimate may change if the sampling positions are spaced non-uniformly. Finally, we discuss the implications of our findings for pest monitoring and control.