Supplementary Note: Analysis of Latino populations from GALA and MEC reveals genomic loci with biased local ancestry estimation

Transcription

1 Supplementary Note: Analysis of Latino populations from GALA and MEC reveals genomic loci with biased local ancestry estimation Bogdan Pasaniuc, Sriram Sankararaman, et al. 1 Relation between Error Rate in local ancestry estimation and MI- LANC Consider a single SNP at which local ancestry is inferred. The error rate in the local ancestry at this SNP is drawn from some distribution F with mean µ 6 and standard deviation σ 6. Given a trio of individuals and assuming that the errors in inferring the local ancestry of each allele in this trio are independent, the probability of at least a single local ancestry error in this trio is denoted ǫ. For small local ancestry error rates, the distribution ofǫacross SNPs has meanµand standard deviation σ. Under the assumption of an uncorrelated error process across trios, the number of ancestry errors at this SNP for n trios is given by O Bin(n,ǫ). Assume that a fraction α of these errors lead to mendelian inconsistencies. ThusM, the MILANC, at this SNP follows M O Bin(O,α) for someα. We want to compute the population correlation ρ = ρ(m,o). Some results, we ll use Then, using the tower property of expectation E[M O] = Oα Var[M O] = Oα(1 α) E[O ǫ] = nǫ Var[O ǫ] = nǫ(1 ǫ) E[M ǫ] = E[E[M O] ǫ] = E[Oα ǫ] = nǫα 1

2 and the variance decomposition Var[M ǫ] = Var[E[M O] ǫ]+e[var[m O] ǫ] = Var[Oα ǫ]+e[oα(1 α) ǫ] = nα 2 ǫ(1 ǫ)+nα(1 α)ǫ = nαǫ(1 αǫ) Applying this again E[O] = E[E[O ǫ]] = E[nǫ] = ne[ǫ] = nµ Var[O] = Var[E[O ǫ]]+e[var[o ǫ]] = Var[nǫ]+E[nǫ(1 ǫ)] = n 2 σ 2 +n ( µ (µ 2 +σ 2 ) ) = n 2 σ 2 +n ( µ (µ 2 +σ 2 ) ) E[M] = E[E[M ǫ]] = E[nǫα] = nαe[ǫ] = nαµ Var[M] = Var[E[M ǫ]]+e[var[m ǫ]] = Var[nǫα]+E[nαǫ(1 αǫ)] = n 2 α 2 σ 2 +nα(µ α(µ 2 +σ 2 )) E[MO] = E[E[MO O]] = E[OE[M O]] = E [ αo 2] = αe[o 2 ] = α ( n 2 (σ 2 +µ 2 )+n ( µ (µ 2 +σ 2 ) )) 2

3 cov(m,o) = E[MO] E[M]E[O] = E[MO] αn 2 µ 2 = α ( n 2 σ 2 +n ( µ (µ 2 +σ 2 ) )) Finally, ρ 2 = cov(m,o)2 Var[O]Var[M] ( ( α n 2 σ 2 +n ( µ (µ 2 +σ 2 ) ))) 2 = (n 2 σ 2 +n(µ (µ 2 +σ 2 )))(n 2 α 2 σ 2 +nα(µ α(µ 2 +σ 2 ))) = α2( n 2 σ 2 +n ( µ (µ 2 +σ 2 ) )) (n 2 α 2 σ 2 +nα(µ α(µ 2 +σ 2 ))) (1) Consider two cases. 1. σ 2 = 0: Then Equation 1 becomes ρ 2 = α2 nµ(1 µ) nαµ(1 αµ) = α(1 µ) (1 αµ) 2. σ 2 > 0: Then Equation 1 becomes ρ 2 = ( 1+ 1 µ(1 µ) n σ ( 2 µ(1 µα) ασ n ) 1 ) 1 For n, we then haveρ 2 1. There are several assumptions underlying our result. 1. Independence of local ancestry estimation errors across the trios at a given SNP. 2. Independence of estimation errors across the alleles within a trio. The above assumptions can be violated in practice. Assumption 1 will be violated due to more distant relatedness amongst the trios. The effect of violating assumption a) is that the effective number of trios is less than n. Nevertheless, the asymptotic result will continue to hold although the rate will be slower. Assumption 2 is likely to be violated when, for example, the offspring is expected to share ancestry with its parents and this increases the correlation of local ancestry errors. Violating assumption 2 can be considered equivalent to having a factor smaller than 6 for the error rates ( µ 6, σ 6 ). It will also change α, the fraction of errors that lead to a MILANC. While this changes the quantitative value of the correlation, the qualitatitive result that the correlation tends to 1 for large sample sizes only whenσ 2 > 0 still holds. 3

4 The result does not assume independence across loci however. The reason is that we are considering the population correlation between the marginal MILANC rate and the marginal true error rate at a locus. The estimation of this correlation will need to deal with non-independence but, here, the bigger problem is that the true error rates for empirical data are unknown. 4

5 Figure 1: Histogram of MILANC rates across the genome in 232 Mexican (left) and 257 Puerto Rican (right) trios showing variability of error rate across genome. LAMP-LD was used for local ancestry estimation using 600k reference panel. Similar results are obtained for other methods (Supplementary Note). 5

6 Figure 2: Histogram of MILANC across the genome in 232 Mexican (left) and 257 Puerto Rican (top) trios, using European(top) or Spanish reference panels (down), showing variability of error rate across genome. LAMP-LD was used for local ancestry estimation using 300k reference panel (see Main text). 6

7 Figure 3: MILANC across the genome in 232 Mexican (left) and 257 Puerto Rican (top) trios, using European(top) or Spanish reference panels (down), showing variability of error rate across genome. Every point denotes average across 1Mb region. LAMP-LD was used for local ancestry estimation using 300k reference panel (see Main text). Horizontal lines denote 3 (4) standard deviations from the mean. 7

8 s Figure 4: Histogram of MILANC across the genome in 232 Mexican (left) and 257 Puerto Rican (top) trios, using European(top) or Spanish reference panels (down), showing variability of error rate across genome. WINPOP was used for local ancestry estimation using 600k reference panel (see Main text). 8

9 Figure 5: MILANC in 232 Mexican (left) and 257 Puerto Rican (right) trios computed when ancestral LD is not modeled (WINPOP) in local ancestry estimation procedure. Horizontal lines denote 3 (4) standard deviations from the mean. 9

10 Figure 6: MILANC versus genome-wide African ancestry proportion showing correlation between genome-wide amount of African Ancestry and Error rate. 10

11 Figure 7: Histogram of MILANC rate in 366 Latino trio families of GALA when either standard (light color) or new reference panels built from the remaining 123 trios (darker color) are used. We observe a significant decrease in average MILANC rate. 11

12 Figure 8: Average local ancestry in 3204 Latino Mexican ancestry samples of MEC data set. Red denotes results for cosmopolitan reference panels while blue denotes results when the reference panels built from GALA trios are also provided. The increase in African average local ancestry at the HLA locus on chromosome 6 is the only genome-wide significant deviations in average local ancestry in this sample. 12

13 Figure 9: Average MILANC in 366 trios across using different sets of reference panels for the European and Native American components (chromosome 6 and 7). We note the significant reduction in MILANC in chromosome 6 locus 20Mb suggesting a much better representation of the true ancestral European and Native American ancestries at this locus. Results are binned into averages across 1Mb regions for better visualization. 13

14 Figure 10: Deviation (in stdevs) of the average local ancestry (European, Native American and African) in 3204 MEC samples versus observed MILANC rate in the 232 Mexican trio families of GALA. Every dot denotes the average values across 1 Mb contiguous genomic region. We observe significant correlation of MILANC rate to decreases in Native American ancestry and increases in European ancestry suggesting that when errors are made in local ancestry inference they are more likely to miscall true Native American chromosomes as European. 14

15 Figure 11: Deviation (in stdevs) of the average local ancestry (European, Native American and African) in 3204 MEC samples versus observed MILANC rate in the 232 Mexican trio families of GALA when the new reference panels are employed in addition to the cosmopolitan panels. Every dot denotes the average values across 1 Mb contiguous genomic region. We observe significant correlation of MILANC to decreases in Native American ancestry and increases in European ancestry, albeit at a much smaller decrease than when the cosmopolitan reference panels are used. 15

16 Figure 12: Haploid Error Rate (number of allele miscalled from total number of alleles) versus MILANC rate as obtained by LAMP-LD in 1,000 simulated Latinos (chromosome 1). 16

17 YRI AFR PR AFR MEX AFR MEX 2.43% 0.62% AFR PR 1.64% 0.62% CEU EUR PR EUR MEX EUR MEX 1.05% 0.43% EUR PR 0.91% 0.43% NA NA PR NA MEX NA MEX 1.40% 2.57% NA PR 2.96% 2.57% Table 1: F ST estimates between inferred ancestral segments in Mexicans and Puerto Ricans and different ancestral panels computed on the 600k set of SNPs. 17

18 Population (European, Native American) (European,African) (Native American, African) Mexicans 77% 12% 11% Puerto Ricans 54% 32% 14% Table 2: Proportion of trio families showing one MILANC clustered according to the pair of ancestries that are inconsistent between parent and child. LAMP-LD (CEU-600k) was used for local ancestry inference. 18

19 Method Correlation MILANC rate to Local Ancestry European Native American African GALA Mexican WINPOP LAMP-LD ALLOY PCAdmix GALA Puerto Rican WINPOP LAMP-LD ALLOY PCAdmix Table 3: Correlation of MILANC rate to local ancestry across the genome. 19

20 Window Number of Correlation MILANC rate to Local Ancestry Size Windows European Native American African GALA Mexican 10Kb Kb Kb Kb Mb M b Mb Mb GALA Puerto Rican 10Kb Kb Kb Kb Mb Mb Mb Mb Table 4: Robustness to window size. We plot the correlation between MILANC and Average local ancestry in the local ancestry estimates of LAMP-LD in the GALA study across various window sizes. Overall the results are insensitive to window size, although we note a slight increase in correlation as windows size increases across all ancestries due to averaging within a windows that removes part of the sampling noise in local ancestry and MILANC estimation. All results reported use a 1Mb window size. 20