The Effect of Chemical Information on the Spatial Distribution of Fruit Flies: II Parameterization,Calibration, and Sensitivity |
| |
Authors: | Maarten de Gee Marjolein E Lof Lia Hemerik |
| |
Institution: | (1) Biometris, Department of Mathematical and Statistical Methods, Wageningen University, P.O. Box 100, 6700 AC Wageningen, The Netherlands;(2) Laboratory of Entomology, Wageningen University, P.O. Box 8031, 6700 EH Wageningen, The Netherlands |
| |
Abstract: | 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. |
| |
Keywords: | Parameterization Sensitivity analysis Chemotaxis Spatial population dynamics Integro-difference equations |
本文献已被 PubMed SpringerLink 等数据库收录! |
|