Modelling the effects of the sterile insect technique applied to Eldana saccharina Walker in sugarcane

Abstract

A mathematical model is formulated for the population dynamics of an Eldana saccharina Walker infestation of sugarcane under the influence of partially sterile released insects. The model describes the population growth of and interaction between normal and sterile E.saccharina moths in a temporally variable, but spatially homogeneous environment. The model consists of a deterministic system of difference equations subject to strictly positive initial data. The primary objective of this model is to determine suitable parameters in terms of which the above population growth and interaction may be quantified and according to which E.saccharina infestation levels and the associated sugarcane damage may be measured. Although many models have been formulated in the past describing the sterile insect technique, few of these models describe the technique for Lepidopteran species with more than one life stage and where F1-sterility is relevant. In addition, none of these models consider the technique when fully sterile females and partially sterile males are being released. The model formulated is also the first to describe the technique applied specifically to E.saccharina, and to consider the economic viability of applying the technique to this species. Pertinent decision support is provided to farm managers in terms of the best timing for releases, release ratios and release frequencies.

Population dynamics of Eldana saccharina Walker (Lepidoptera: Pyralidae): application of a biophysical model to understand phenological variation in an agricultural pest

“…When more than one season's phenological and abundance responses are captured, it will likely sketch a better picture about the long-term stressors that work on the species in a particular environment. From a broader point of view, sophisticated models that have been developed to predict the outcomes of IPM intervention (Potgieter et al, 2012(Potgieter et al, , 2013(Potgieter et al, , 2016 provide excellent insight into temporal population responses in the light of future pest management plans. Nevertheless, the mechanism-based model applied in this study provided novel insights into the effect of newly-invaded cold climates on E. saccharina survival and adult relative abundance.…”

The role of heterogeneous agricultural landscapes in the suppression of pest species following random walk dispersal patterns

“…Growth, maturation and mortality parameters are assumed similar to those used in the study by Potgieter et al (2012). Each life stage of E. saccharina has unique maturation and mortality rates which depend on the daily average temperature (Way, 1995).…”

“…Assuming that infestation occurs only at randomly selected points in a newly planted/harvested area, corresponds to a scenario where not all E. saccharina are removed at the time of harvest, where some of the planted seed cane is infested with E. saccharina, or where some moths not only spread gradually along the edges of fields, but also fly longer distances to infest neighbouring fields within-field. The initial infestation levels of older sugarcane fields at the start of simulations are estimated by the mean-field model of Potgieter et al (2012). 1.…”

“…The population dynamics of the pest species Eldana saccharina Walker (Lepidoptera: Pyralidae) in sugarcane (Saccharum officinarum L.) is taken as application scenario in this study, with the model presented in this paper similar to the models discussed and validated by Potgieter et al (2012Potgieter et al ( , 2013, but excluding the effect of the sterile insect technique.…”

Overview of Technological Advances Toward Greater Efficiency and Efficacy in Sterile Insect-Inherited Sterility Programs Against Moth Pests

“…The first mathematical model described the population growth and the interaction between wild and sterile moths in a temporally variable but spatially homogeneous environment. The primary objective of this model was to determine suitable parameters that allowed quantification of population growth and interactions between released and wild moths (Potgieter et al 2012). The second model, a reaction-diffusion model, described the growth of the wild population and the interaction between wild and sterile E. saccharina moths in a temporally variable and spatially heterogeneous environment.…”