Abstract
We study population biology of eusocial insects such as Ropalidia marginata through a stochastic model based on random (matrix) difference equations. This facilitates a study of dynamics of such populations when the survival and other rates vary randomly over time. The worker–brood relatedness, which is a function of the underlying population structure, can be used to explain theories on the evolution of altruism. The effect of demographic parameters and the queen takeover probabilities on the worker–brood relatedness has been studied. Based on the proposed model, we simulate insect colonies where queens are replaced. Simulation results help us to study the effect of various factors on the worker–brood relatedness. Further, we study two estimators of the worker–brood relatedness and suggest procedures for estimating their standard errors. Approximate confidence intervals for the same can be constructed with the help of these results.
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