Modelling mortality of a stored grain insect pest with fumigation: probit, logistic or Cauchy model?

Computer simulation models can provide a relatively fast, safe and inexpensive means to judge and weigh the merits of various pest control management options. However, the usefulness of such simulation models relies on the accurate estimation of important model parameters, such as the pest mortality under different treatments and conditions. Recently, an individual-based simulation model of population dynamics and resistance evolution has been developed for the stored grain insect pest Rhyzopertha dominica, based on experimental results showing that alleles at two different loci are involved in resistance to the grain fumigant phosphine. In this paper, we describe how we used three generalized linear models, probit, logistic and Cauchy models, each employing two- and four-parameter sub-models, to fit experimental data sets for five genotypes for which detailed mortality data was already available. Instead of the usual statistical iterative maximum likelihood estimation, a direct algebraic approach, generalized inverse matrix technique, was used to estimate the mortality model parameters. As this technique needs to perturb the observed mortality proportions if the proportions include 0 or 1, a golden section search approach was used to find the optimal perturbation in terms of minimum least squares (L2) error. The results show that the estimates using the probit model were the most accurate in terms of L2 errors between observed and predicted mortality values. These errors with the probit model ranged from 0.049% to 5.3%, from 0.381% to 8.1% with the logistic model and from 8.3% to 48.2% with the Cauchy model. Meanwhile, the generalized inverse matrix technique achieved similar results to the maximum likelihood estimation ones, but is less time consuming and computationally demanding. We also describe how we constructed a two-parameter model to estimate the mortalities for each of the remaining four genotypes based on realistic genetic assumptions.