Modelling populations ofLygus hesperuson cotton fields in the San Joaquin Valley of California: the importance of statistical and mathematical model choice

Abstract

Understanding the population dynamics of herbivorous insects is critical to developing and implementing effective pest control protocols. In the context of inverse problems, we explore the dynamic effects of pesticide treatments on Lygus hesperus, a common pest of cotton in the western United States. Fitting models to field data, we explore the topic of model selection for an appropriate mathematical model and corresponding statistical models, and use techniques including ANOVA-based model comparison tests and residual plot analysis to make the best selections. In addition we explore the topic of data information content: in this example, we are testing the question of whether data, as it is currently collected, can support time-dependent parameter estimation. Furthermore, we investigate the statistical assumptions often haphazardly made in the process of parameter estimation and consider the implications of unfounded assumptions. ARTICLE HISTORY

Modelling Pesticide Treatment Effects on Lygus hesperus in Cotton Fields

“…The data used came from a database consisting of approximately 1500 replicates of L. hesperus density counts, using sweep counts, in over 500 Pima or Acala cotton fields in 1997-2008 in the San Joaquin Valley of California. This data is described more fully in [2]. We selected subsets to analyze using the following criteria:…”

“…In most cases, this includes selection of both statistical and mathematical models in fits-to-data -something that is not always fully explicitly addressed in the ecological literature. We first addressed this gap in [1,2] using data from pest population counts of Lygus hesperus Knight (Hemiptera: Meridae) feeding on pesticide-treated cotton fields in the San Joaquin Valley of California [22].…”

“…In particular, in [1,2] we investigated the effect of pesticide treatments on the growth dynamics of Lygus hesperus. This was done by constructing mathematical models and then fitting these models to field data so as to estimate growth rate parameters of Lygus hesperus both in the absence and in the presence of pesticide application.…”

“…In the present effort we further examine the importance of model selection and demonstrate how optimal selection of both statistical and mathematical models is crucial for accuracy in parameter estimation and uncertainty quantification in fitting data to models. This report further investigates these issues by testing different data sets from the same database as in [1,2] but with a varied number of pesticide applications in treated fields.…”

Parameter Estimation for an Allometric Food Web Model

“…Our experiences [4,3,5,6] with other ecological and population modeling efforts involving population counts have suggested that some type of error process depending on the size of the population is likely to be most appropriate. This motivates our choice of statistical model in (2).…”