Mathematical modelling of population dynamics of khapra beetle (Trogoderma granarium)
Trogoderma granarium Everts (Coleoptera: Dermestidae), generally known as the khapra beetle, is found in the hot and dry regions of North Africa, the Middle East, and India. It is not established elsewhere and is classified as a quarantine pest in Canada and several other countries. It is one of the economically important quarantine pests that mainly feeds on food grain and proteinaceous materials. Its total lifespan lasts approximately 40 to 45 d under favourable environmental conditions. Extreme temperatures, high 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. The diapausing larvae are resistant to heat, cold, and insecticides, that aids in surviving the adverse conditions. Ecological modelling is a helpful tool to study the population dynamics of biological systems. The objective of this study was to develop mathematical models to calculate the survival and development of the khapra beetle under different environmental conditions such as temperature, RH, and food quality. The developed models were used to estimate the development and survival of the khapra beetle under Canadian grain storage conditions. The factors affecting the development and mortality of the khapra beetle were reviewed, and appropriate assumptions were made for developing the mathematical equations using the Physi-Biological age method. This method is based on temperature-driven development rate, and factors such as RH and food quality were considered as multipliers. Mathematical equations were developed to calculate the development and mortality of adults, eggs, larvae, pupae, and oviposition and diapause under different environmental conditions. 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 it was found that the diapausing larvae survived the extremely cold conditions found in Canadian grain. In contrast, insects in 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.
Trogoderma granarium, Mathematical modelling, Physi-Biological age, Population dynamics, Same shape concept