Modelling populations of Lygus hesperus on 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.

KEYWORDS:

• Inverse problem
• ordinary least squares
• generalized least squares
• model selection
• information content
• bootstrapping
• residual plots
• linear splines
• hemiptera
• herbivory
• pest suppression
• pesticide

Acknowledgments

J.E. Banks thanks J.A. Rosenheim for hosting him during his sabbatical, and also extends thanks to the University of Washington, Tacoma for providing support for him during his sabbatical leave. The authors wish to acknowledge the efforts of two referees of an earlier version of this ms. whose comments resulted in improvements in the current version of this ms.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Air Force Office of Scientific Research under grant number [AFOSR FA9550-12-1-0188].