Informativeness of Genetic Markers for Inference of Ancestry

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https://www.sciencedirect.com/science/article/pii/S0002929707639901
Table 1. Measures of Marker Information Content

Criterion Description Features Limitations
Absolute allele frequency difference (δ) |p11−p21| Is related to amount of linkage disequilibrium in an admixture model (Chakraborty and Weiss 1988); is related to probability of correct assignment in a multilocus no-admixture model (Risch et al. 2002); is related to Fisher information curvature criterion for K=2 (eq. [18]); is related to ORCA for K=2 (eq. [11]) Requires that only two populations be possible sources; does not take into account all available information about allele frequencies (Stephens et al. 1999; Campbell et al. 2003); statistical features do not apply to the Shriver et al. (1997) multiallelic extension of δ
Fst Excess in probability of identity of alleles from the same population compared with randomly chosen alleles (Excoffier 2001, for example) Is related, for biallelic markers, to the quotient of expected posterior and prior variance of ancestry in a population equally admixed from two sourcesa (McKeigue 1998; Molokhia et al. 2003) Performs only slightly better than random markers (Rosenberg et al. 2001)
Expected heterozygosityb 1-Σj=1Np2j (bias correction can be applied in estimation from data) Performs better than random markers (Rosenberg et al. (2001) and fig. 3) Measures the amount of variation but not the differences across populations
Number of allelesb N Performs better than random markers (Rosenberg et al. 2001) Measures the amount of variation but not the differences across populations; is useful only for multiallelic markers that have variation in number of alleles
Fisher information curvature criterion Reciprocal of the largest eigenvalue of the information matrix for maximum-likelihood estimation of ancestry coefficients (Gomulkiewicz et al. 1990; Millar 1991) Enables predictions about approximate variances of ancestry estimates (see “Number of Markers” subsection of the “Theory” section); information matrix is additive across loci that are independent within populations Depends on unknown ancestry coefficients and requires computation for many possible parameter values; largest eigenvalue gives an upper bound that might not be generally applicable across the parameter space
Pairwise Kullback-Leibler divergencec Brenner 1998; Smith et al. 2001; Anderson and Thompson 2002) Provides a natural measure, for K=2, of average potential for assignment of an allele to one population compared with the other; has a natural multilocus extension; enables measurement of contributions of specific alleles Requires that only two populations be possible sources; has upwardly biased estimates in small samples
Informativeness for assignment (In) Equation (4) Provides a natural measure of potential for assignment of an allele to one population compared with the “average” population; has a natural multilocus extension; enables measurement of contributions of specific alleles or populations; performs better than random or highly heterozygous markers (fig. 3) Has upwardly biased estimates in small samples
Informativeness for ancestry coefficients (Ia) Equation (14) Provides a natural measure of potential for assignment of an allele to a point on the set of all possible ancestry coefficient vectors; has a natural multilocus extension; enables measurement of contributions of specific alleles Has upwardly biased estimates in small samples; is difficult to compute in samples with populations of equal sample size
Optimal rate of correct assignment (ORCA) Equation (10) Gives the probability of correct assignment of an allele using the decision rule with lowest risk; has a natural multilocus extension (eq. [12]); enables measurement of contributions of specific alleles Has upwardly biased estimates in small samples