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Many areas of agriculture rely on honey bees to provide pollination servicesand any decline in honey bee numbers can impact on global food security. Inorder to understand the dynamics of honey bee colonies we present a discretetime marked renewal process model for the size of a colony. We demonstrate thatunder mild conditions this attains a stationary distribution that depends onthe distribution of the numbers of eggs per batch, the probability an egghatches and the distributions of the times between batches and bee lifetime.This allows an analytic examination of the effect of changing these quantities.We then extend this model to cyclic annual effects where for example thenumbers of eggs per batch and {the probability an egg hatches} may vary overthe year.

A marked renewal process model for the size of a honey bee colony