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A central limit theorem concerning uncertainty in estimates of individual admixture

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  • Pfaffelhuber, Peter
  • Rohde, Angelika

Abstract

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.

Suggested Citation

  • Pfaffelhuber, Peter & Rohde, Angelika, 2022. "A central limit theorem concerning uncertainty in estimates of individual admixture," Theoretical Population Biology, Elsevier, vol. 148(C), pages 28-39.
    • Handle: RePEc:eee:thpobi:v:148:y:2022:i:c:p:28-39
    DOI: 10.1016/j.tpb.2022.09.003
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