A central limit theorem concerning uncertainty in estimates of individual admixture

The concept of individual admixture (IA) assumes that the genome of individuals is composed of alleles inherited from K ancestral populations. Each copy of each allele has the same chance qk to originate from population k, and together with the allele frequencies p in all populations at all M markers, comprises the admixture model. Here, we assume a supervised scheme, i.e. allele frequencies p are given through a reference database of size N, and q is estimated via maximum likelihood for a single sample. We study laws of large numbers and central limit theorems describing effects of finiteness of both, M and N, on the estimate of q. We recall results for the effect of finite M, and provide a central limit theorem for the effect of finite N, introduce a new way to express the uncertainty in estimates in standard barplots, give simulation results, and discuss applications in forensic genetics.