The effect of chemical information on the spatial distribution of fruit flies: II Parameterization, calibration, and sensitivity.

In a companion paper (Lof et al., in Bull. Math. Biol., 2008), we describe a spatio-temporal model for insect behavior. This model includes chemical information for finding resources and conspecifics. As a model species, we used Drosophila melanogaster, because its behavior is documented comparatively well. We divide a population of Drosophila into three states: moving, searching, and settled. Our model describes the number of flies in each state, together with the concentrations of food odor and aggregation pheromone, in time and in two spatial dimensions. Thus, the model consists of 5 spatio-temporal dependent variables, together with their constituting relations. Although we tried to use the simplest submodels for the separate variables, the parameterization of the spatial model turned out to be quite difficult, even for this well-studied species. In the first part of this paper, we discuss the relevant results from the literature, and their possible implications for the parameterization of our model. Here, we focus on three essential aspects of modeling insect behavior. First, there is the fundamental discrepancy between the (lumped) measured behavioral properties (i.e., fruit fly displacements) and the (detailed) properties of the underlying mechanisms (i.e., dispersivity, sensory perception, and state transition) that are adopted as explanation. Detailed quantitative studies on insect behavior when reacting to infochemicals are scarce. Some information on dispersal can be used, but quantitative data on the transition between the three states could not be found. Second, a dose-response relation as used in human perception research is not available for the response of the insects to infochemicals; the behavioral response relations are known mostly in a qualitative manner, and the quantitative information that is available does not depend on infochemical concentration. We show how a commonly used Michaelis-Menten type dose-response relation (incorporating a saturation effect) can be adapted to the use of two different but interrelated stimuli (food odors and aggregation pheromone). Although we use all available information for its parameterization, this model is still overparameterized. Third, the spatio-temporal dispersion of infochemicals is hard to model: Modeling turbulent dispersal on a length scale of 10 m is notoriously difficult. Moreover, we have to reduce this inherently three-dimensional physical process to two dimensions in order to fit in the two-dimensional model for the insects. We investigate the consequences of this dimension reduction, and we demonstrate that it seriously affects the parameterization of the model for the infochemicals. In the second part of this paper, we present the results of a sensitivity analysis. This sensitivity analysis can be used in two manners: firstly, it tells us how general the simulation results are if variations in the parameters are allowed, and secondly, we can use it to infer which parameters need more precise quantification than is available now. It turns out that the short term outcome of our model is most sensitive to the food odor production rate and the fruit fly dispersivity. For the other parameters, the model is quite robust. The dependence of the model outcome with respect to the qualitative model choices cannot be investigated with a parameter sensitivity analysis. We conclude by suggesting some experimental setups that may contribute to answering this question.