Unbiased estimation of foraging range and disease incidence from social bee genotypes
Social bees such as bumble bees (Bombus spp.) and stingless bees (Meliponini) are essential pollinators in natural and agricultural landscapes. Estimation of quantities which are relevant to the conservation of these insects, such as population densities, foraging ranges, and disease incidence, relies on accurate assignment of individuals to colonies. However, colonies are extremely difficult to locate in the wild. Frequently, bees collected in the wild are genotyped at multiple unlinked loci, and a sibship configuration is found by maximizing a likelihood derived from Mendelian inheritance probabilities. Conditional on this optimal sibship configuration, population and colony-level quantities are estimated.
However, under moderate genotyping error and polyandry, an optimal sibship configuration will be ill-defined. Estimates of quantities derived from sibships, but which ignore uncertainty in the sibships, will be overconfident and potentially biased. Here we present a semi-parametric Bayesian method which allows joint inference about sibship-derived quantities and the sibship configuration; thus providing unbiased estimates of the former, while appropriately accounting for uncertainty in the estimation of the latter. We validate this method with real and simulated datasets, and provide an example application with field collections of Bombus vosnesenskii carrying the trypanosome parasite Crithidia bombi, to infer the influence of parasitism on bee foraging range.
When only a fraction of the bees at a site are sampled, the maximum likelihood estimate of the sibship configuration is likely to mis-identify half-sib singletons as novel colonies. On simulated data sets, we find that mis-assignments of half-sib singletons bias estimates of colony densities upward, and the bias increases as the number of singleton half-sibs increases. Until a site is sampled thoroughly enough to find siblings for the majority of half-sibs, the number of half-sibs will increase with the number of sampled bees. This equates to increasing bias with increasing sample size.
Our model gives unbiased estimates of population-level statistics under moderate-or-greater polyandry and colony densities, relative to estimates calculated using a single, optimal sibship configuration. In cases where the foraging areas of colonies were not identical (where spatial location was informative as to colony membership), including spatial information in the model resulted in improved estimation of the sibship configuration, and was robust to the choice of foraging kernel. In our real-world application, we estimate a weak decrease in foraging range associated with Crithidia infection.