Modelling the impact of GM plants and insecticides on arthropod populations of agricultural interest

Matrix population models (MPM) are nowadays not widely used to simulate arthropod population dynamics with applications to risk assessment. However, an increasing body of studies are prompting the finding of optimization techniques to reduce uncertainty in matrix parameters estimation. Indeed, uncertainty in parameters estimates may lead to significant management implications. Here we present two case studies where MPM are used for assessing the potential impact of genetically modified (GM) plants on beneficial insect species (the coccinellid Adalia bipunctata) and for evaluating spider mites (the two-spotted spider mite Teranychus urticae) resurgence after insecticide application. In both studies the data obtained, consisting of population time series, were used to generate a stage-classified projection matrix. The general model used to simulate population dynamics consists of a matrix containing (i) survival probabilities (the probability of growing and moving to the next stage and the probability of surviving and remaining in the same stage), and (ii) fecundities of the population. Most of the methods utilized for estimate the parameter values of stage-classified models rely on following cohorts of identified individuals [1]. However in these studies the observed data consisted of a time-series of population vectors n(t), for t = T0, T1, …, Tn, where individuals are not distinguished. The relationship between the observed data and the values of the matrix parameters that produced the series involves an estimation process called inverse problem. The set of parameters that minimize the residual between the collected data and the model output for the two studies presented here was estimated using the quadratic programming method [2]. The set of estimated parameters for the A. bipunctata Rhopalosiphum maidis maize tritrophic system model supports the hypothesis that GM maize does not negatively influences A. bipunctata population growth in the tritrophic system studied [3]. Otherwise, in the case of the two-spotted spider mite resurgence, some insecticides, namely etofenprox, deltamethrin and betacifluthrin, fostered a higher mite population growth than the untreated control. This was principally due to higher adult fecundity and egg fertility, clearly explained by Life Table Response Experiments, performed starting from estimated matrices, indicating a likely trophobiotic effect. A variety of inverse modelling approaches have been applied to demographic models other than quadratic programming. Bayesian approaches [4] and evolutionary algorithms, such as Genetic Algorithms [5] have also been used for inverse modelling and parameters fitting. In order to find a better model fit for the observed stage class distributions on two case studies, we would like to explore Neural Networks or more generally machine learning possibilities in finding a set of parameter values that successfully describes observed data.