Mortality estimation for individual-based simulations of phosphine resistance in lesser grain borer (Rhyzopertha dominica)

Abstract

There is a world-wide need for the development of sustainable management strategies to control the development of phosphine (PH3) resistance in lesser grain borer (Rhyzopertha dominica). Computer simulation models can provide a relatively fast, safe and inexpensive way to weigh the merits of various management options. However, the usefulness of simulation models relies on the accurate estimation of important model parameters. Concentration and time of exposure are both important in determining the intensity of response to a toxic agent. The ability to estimate mortality or survival rate (1 - mortality) at a range of concentrations and exposure times based on experimental data is critical for the development of an accurate simulation of the evolution of resistance to phosphine. Our individual-based simulation model required predictions of finite daily survival rates at different concentrations for each of nine possible genotypes in our two-locus model. In this paper we briefly described how we used a two-parameter probit model Y = a + b log(Ct) and a fourparameter probit model Y = a + b 1 log(t) + b 2 log(C) + b 3 log(t) log(C) to fit three sets of experimental data (Collins et al, 2002, 2005; Daglish, 2004). Here C (mg/l) is the PH3 concentration, t (hour) is the exposure time and Y is the probit (= "probability unit") mortality, which is the probability of mortality transformed by the inverse cumulative distribution function (CDF) associated with the standard normal distribution. The data sets of Collins et al. (2002, 2005) and Daglish (2004) are observed from five available strains of lesser grain borer, associated with five different genotypes. We still needed to construct a model predicting finite daily survival at different concentrations for the remaining four genotypes. As a step towards achieving this, we first estimated the resistance factors for the first five genotypes (strains) based on our fitted models. The resistance factor of a genotype x for a given fumigation duration is defined as the ratio between the PH 3 concentration that achieves 50% mortality in a sub-population of genotype x and the lower PH 3 concentration that achieves 50% mortality in a susceptible sub-population. We then estimated the resistance factors for the other four genotypes by making some basic assumptions regarding genetic interactions; log-transformed resistance factors for the nine genotypes can be expressed in terms of five parameters which represent respectively the strength and the dominance of the 1 st and 2 nd genes, and the synergism between the two genes. Finally we modelled survival rates for the other four genotypes using the two-parameter probit model. We assumed that the parameter b for these genotypes was the same as the b value for one of the five strains. Finally, the value for parameter a for each of the four genotypes could then be obtained by direct substitution of the related values C, t and Y into the two-parameter probit model. Having constructed the probit models we obtained estimates of finite daily survival rates in two ways with the same total survival rate for each of the nine genotypes.