Analysis of Variance of Integro-Differential Equations with Application to Population Dynamics of Cotton Aphids Academic Article uri icon


  • The population dynamics of cotton aphids is usually described by mechanistic models, in the form of integro-differential equations (IDEs), with the IDE parameters representing some key properties of the dynamics. Investigation of treatment effects on the population dynamics of cotton aphids is a central issue in developing successful chemical and biological controls for cotton aphids. Motivated by this important agricultural problem, we propose a framework of analysis of variance (ANOVA) of IDEs. The main challenge in estimating the IDE-based ANOVA model is that IDEs usually have no analytic solution, and repeatedly solving IDEs numerically leads to a high computational cost. We propose a penalized spline method in which spline functions are used to estimate the IDE solutions and the penalty function is defined by the IDEs. The estimated IDE solutions, as implicit functions of the parameters, are inputs in a nonlinear least squares criterion, which in turn is minimized by a Gauss-Newton algorithm. The proposed method is illustrated using simulation and an observed cotton aphid data set. © 2013 International Biometric Society.

author list (cited authors)

  • Wang, X., Cao, J., & Huang, J. Z.

citation count

  • 2

publication date

  • December 2013