A likelihood-free estimator of population structure bridging admixture models and principal components analysis

Irineo Cabreros, John D. Storey

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We introduce a simple and computationally efficient method for fitting the admixture model of genetic population structure, called AL Structure. The strategy of AL Structure is to first estimate the low-dimensional linear subspace of the population admixture components, and then search for a model within this subspace that is consistent with the admixture model’s natural probabilistic constraints. Central to this strategy is the observation that all models belonging to this constrained space of solutions are risk-minimizing and have equal likelihood, rendering any additional optimization unnecessary. The low-dimensional linear subspace is estimated through a recently introduced principal components analysis method that is appropriate for genotype data, thereby providing a solution that has both principal components and probabilistic admixture interpretations. Our approach differs fundamentally from other existing methods for estimating admixture, which aim to fit the admixture model directly by searching for parameters that maximize the likelihood function or the posterior probability. We observe that AL Structure typically outperforms existing methods both in accuracy and computational speed under a wide array of simulated and real human genotype datasets. Throughout this work, we emphasize that the admixture model is a special case of a much broader class of models for which algorithms similar to ALStructure may be successfully employed.

Original languageEnglish (US)
Pages (from-to)1009-1029
Number of pages21
Issue number4
StatePublished - Aug 2019

All Science Journal Classification (ASJC) codes

  • Genetics


  • Admixture
  • Genetic structure
  • Logistic factor analysis
  • Method of moments
  • Nonparametric
  • PCA
  • Population stratification
  • Population structure
  • Unifying


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