Modelling honey bee queen mating as a measure of feral colony density

Robust estimates of feral and wild honey bee (Apis mellifera) colony densities are essential for the understanding of the role of honey bees in an ecosystem, and for planning responses to an incursion of an exotic honey bee disease or pest. New genetic methods make it possible to identify the number of feral colonies with which a test queen mates. We present an agent-based model of the spatial process of honey bee mating that describes the relationship between feral colony densities and the number of unique colonies with which a queen mates. This model incorporates random, aggregated and overdispersed spatial distributions of feral colonies and drone congregation areas. We model different densities of feral colonies and drone congregation areas with various numbers of test queens and determine the range of counts of matings with drones from unique colonies. The model shows that the range of counts for a given set of parameters is consistent with a Poisson distribution, and that the most significant explanatory variable is density of the feral colonies. The results obtained reveal that 10 or more test queens may be needed in field studies to resolve order of magnitude differences in feral colony densities. We conclude that the new genetic methods provide a powerful tool for making indirect inferences about feral colony densities, so long as the field survey results are treated as outcomes of a stochastic spatial process.