Bayes-optimal estimation of overlap between populations of fixed size

摘要

Author summary Understanding when two populations are composed of similar species is important for ecologists, epidemiologists, and population geneticists, and in principle it is easy: just sample the two populations, compare the sets of species identified in each, and count how many appear in both populations. In practice, however, this is difficult because sampling methods typically produce only a random subset of the total population, leaving current population overlap estimates biased. Knowing only the number of shared members between two of these partial population samples, this paper shows how we can nevertheless estimate the true overlap between the full populations, when those full populations sizes are known. Using Bayesian statistics, we can also compute credible intervals to produce error bars. We show that using this unbiased approach has a dramatic impact on the conclusions one might draw from previously published studies in the malaria literature, which used simple but biased methods. Because the method in this paper quantifies the tradeoff between sampling effort and uncertainty, we also show how to compute the number of samples required to ensure high-confidence results, which may be useful for planning future studies or budgeting lab reagents and time.