Understanding flying insect dispersion: Multiscale analyses of fragmented landscapes

Abstract

A multiscale model was developed to simulate the rate of landing of a winged insect, the grain aphid, Sitobion avenae F. At a large scale (kilometric scale), it is convenient to use a deterministic model of their dispersion, based upon diffusion–advection–reaction partial derivative equations. At a small scale (hectometric scale), the process of site selection (‘landing’) is only partially understood, but is known to include the perception of field colour and landscape characteristics. Several hypotheses on aphids' behaviour were tested to simulate the rate of landing: the simulation was done by a cellular automata submodel under five different hypotheses on the precise organisation of the landing behaviour. We found a strong interaction between the effect of the proportion of wheat crops in the landscape and their spatial organisation. The spatial correlation between the places occupied by wheat crops appears crucial to determine the global rate of landing of the aerial insect stock. The shape of the response surface of landing rate against the proportion of surface occupied by wheat, and the spatial autocorrelation of wheat plots, appears very regular and relatively simple to model by ad hoc mathematical functions. Large scale simulations using the results of the small scale model in a diffusion–reaction equation solved numerically, showed that, on a real landscape extracted from a GIS on the whole Brittany region (western France), the spatial pattern of the aphid landing is sensitive to the hypothesis tested on their landing behaviour. This hierarchical modelling combining two different approaches at two different scales (mathematical deterministic equations on a large multi-kilometric scale, and partly stochastic cellular automata on a small hectometric scale), requires methods to validate its results in the field, in the framework of a decision support system. Such a multiscale model has a wide field of application including not only plant protection but also management and conservancy of animal species dispersing by flight.