Revealing the range of equally likely estimates in the admixture model

Many ancestry inference tools, including Structure and Admixture, rely on the admixture model to infer both, allele frequencies p and individual admixture proportions q for a collection of individuals relative to a set of hypothetical ancestral populations. We show that under realistic conditions the likelihood in the admixture model is typically flat in some direction around a maximum-likelihood estimate (q^,p^). In particular, the maximum-likelihood estimator is nonunique and there is a complete spectrum of possible estimates. Common inference tools typically identify only a few points within this spectrum. We provide an algorithm which computes the set of equally likely (q~,p~), when starting from (q^,p^). It is analytic for K=2 ancestral populations and numeric for K>2. We apply our algorithm to data from the 1000 genomes project, and show that inter-European estimators of q can come with a large set of equally likely possibilities. In general, markers with large allele frequency differences between populations in combination with individuals with concentrated admixture proportions lead to small areas with a flat likelihood. Our findings imply that care must be taken when interpreting results from STRUCTURE and ADMIXTURE if populations are not separated well enough.