Fumigation of stored-grain insects - a two locus model of phosphine resistance

Abstract

The standard pest control methodology for insect pests in grain storage is fumigation with phosphine gas. However phosphine resistance is a serious problem which threatens Australia's grain industries. There are several questions regarding how to determine the most effective strategies for fumigation using phosphine to prevent the emergence of resistant strains. Linkage analysis and molecular techniques have provided strong evidence that resistance is conferred by two genes on separate chromosomes for the insect species Rhyzopertha dominica. For this species resistance for those homozygous with both copies of the sensitive gene has been determined to be well over 250× those with no copies of the resistance genes, whereas there is a resistance factor of 2.5× to 30× if the resistance genes are present in only one of the two locations, depending on which location. A further important question arises as to whether single-locus population genetics models are adequate to give an accurate representation of the population dynamics under fumigation or whether two-locus models are needed. This paper describes the development of a two-locus model for the population genetics for R. dominica for fumigation under a given concentration of phosphine gas. The mathematical model consists of nine sub-populations, corresponding to the nine genotypes, modelled by a system of nonlinear ordinary differential equations. These are solved numerically using standard techniques. Using the model, some different fumigation strategies are investigated; for fumigation switched on for a given period and switched off for a given period. The two-locus model is compared with a single-locus model. Preliminary results of this model have identified situations where a single-locus model gives different qualitative conclusions to the two-locus model.