Mathematical Modeling of Population Dynamics of Trogoderma granarium (Coleoptera: Dermistidae)

Abstract

Khapra beetle, Trogoderma granarium Everts, is one of the economically important quarantine pests that mainly feeds on food grain and proteinaceous materials. Its total development time lasts approximately 40-45 d under favorable environmental conditions. Extreme temperatures, high relative humidity (RH), high larval densities, or low food quality can induce a larval diapause, where the insect can survive for up to a few years, occasionally feeding and molting. Ecological modeling is a helpful tool to study the population dynamics of biological systems. Physi-Biological age method is based on temperature-driven development rate, and factors such as RH and food quality were considered as multipliers. The objective of this study was to develop mathematical models to calculate the survival and development of adults, eggs, larvae, pupae, and oviposition and diapause under different environmental conditions such as temperature, RH, and food quality. Algorithms were developed to simulate the population dynamics for each day and coded in C++. The developed models were validated against the literature data and evaluated using linear regression, R2, and MSE. Population dynamics were simulated under Canadian grain storage conditions, and the developed models predicted that the diapausing larvae survived the extremely cold conditions found in Canadian grain. In contrast, other stages did not survive. The surviving larvae developed to pupae and adults, and females began laying eggs once the temperature became warmer in the grain bins.

Keywords: Khapra beetle; mathematical modeling; physi-biological age; population dynamics; same shape concept.