2.3 Data analysis methods
2.3.3 Methods for assessment of population structure
A panel of 30 SNPs, developed by the laboratory of Professor Andrés Ruiz Linares at UCL GEE, was used to estimate ancestry proportions in Latin American admixed populations, assuming a tri–hybrid admixture model of African, European and Native American parents. The development of this panel was based on the selection of unlinked markers with pronounced differences in fre- quencies among the parent populations.
Ancestry proportions were calculated with Admixture 1.23 (Alexander et al., 2009), which uses a maximum likelihood method adapted from the algorithm used in STRUCTURE (Pritchard et al., 2000). A dataset of the genotypes of these 30 markers in 876 individuals from parental popula- tions (169 Africans, 299 Europeans and 408 Native Americans) was kindly provided by Andrés Ruiz Linares group. These individuals of known ancestry were used as parental reference by Admixture and all their alleles are considered to come from the same population.
The estimated ancestry proportion q(i)k, is the proportion of alleles in individual i inherited from an ancestor from population k. The estimation procedure considers independently a population of origin for each allele, so the population of origin of the allele a in individual i at locus l is z(i,a)l . Therefore, individual i has a proportion of ancestry from population k equals to the probability of each allele to be drawn independently from k (Falush et al., 2003), or formally,
Pr[z(i,a)l = k] = q(i)k
All the individuals with less than 80% of genotyping success were excluded from this analysis. Results, expressed as a proportion of ancestry for each parental population (i.e. African, European and Native American), were used to control for ancestry as a confounding variable in relevant regression models (see section 2.3.4).
2.3.3.2 Highly variable autosomal STR identification markers
The inclusion of closely related individuals in our sample presents the problem of potential distor- tion introduced in all associations. The small population size of these villages (see section 2.1.1) led us to expect high degrees of inbreeding and relatedness. This assumption was also suggested by close family connections observed ethnographically.
2.3. Data analysis methods 77 otype 15 microsatellite markers. Using STRUCTURE 2.3.4 (Falush et al., 2003, 2007; Hubisz et al., 2009; Pritchard et al., 2000), i individuals were assigned with different levels of membership into kdifferent clusters, generating a matrix Q, of i rows and k columns. The value of k was determined using the method developed by Evanno et al. (2005).
Several studies (Cardoso et al., 2012; Yu et al., 2006; Zhao et al., 2007) have pointed out that this Qmatrix cannot capture deep levels of cryptic relatedness and have proposed the use of different relatedness matrices as interacting random effects in regression models. Following Zhao et al. (2007) and Cardoso et al. (2012) we employed the STR genotypes to build a matrix of pairwise proportion of shared alleles (PSA) (Chakraborty & Jin, 1993), and mixed models were formulated using this PSA matrix as random effects in conjunction with the Q matrix generated by STRUCTURE as fixed effects.
Additionally, estimations of inbreeding were computed from the genotyped STR markers. Inbreed- ing was evaluated using the inbreeding coefficient Fis, a measure based in the comparison of means
of expected and observed values of heterozygosity, in this case for all 15 loci, with a paired t-test after testing for homogeneity of variances using Barlett test9. F
iswere estimated using the GNU R
package “adegenet” (Jombart, 2008; Jombart & Ahmed, 2011), which employs the same prin- ciple originally formulated by Wright (1922). An excess of homozygosity across several loci in a single individual can be the result of a shared ancestry of their parents, Fisis the likelihood of being
homozygous due to relatedness of the parents: if piis the frequency of allele i, the probability of
an individual of being homozygous at one locus in random mating is, Pr(homozygote) = X
i
p2i
Then, the probability in presence of inbreeding is,
Pr(homozygote) = Fis+ (1 − Fis) X i
p2i
The estimation of inbreeding is obtained by drawing a random sample from the log-likelihood function of homozygosity summed across all 15 loci (Jombart, 2008; Wright, 1922). A value Fj,
defined as the chances of individual j of being homozygous through inheritance from a common ancestor of their parents, was computed for each individual to estimate inbreeding (Curik, 2003).
9Several alternatives to the methods used here (comparing simple heterozygosity) have been developed to take advant-
age of stepwise mutation models using STRs, such as Rstand d2(Coltman, 1998; Curik, 2003). While popular in studies of
inbreeding depression in animal breeds, “simple heterozygosity outperforms them detecting differences over short time periods”, as pointed out by Neff (2004), making Fismore suited for our purposes.
2.3. Data analysis methods 78
2.3.3.3 Haplotype inference
Gametic phase of 27 SNPs surrounding LCT enhancer region was elucidated to test the hypothesis of homogeneous European-like haplotypic backgrounds in segments carrying −13,910*T (due to their European origin) and heterogeneous haplotypic backgrounds in segments carrying −13,910*C (of both European and Native American origin).
Haplotypes were inferred using PHASE 2.1.1 (Crawford et al., 2004; Li & Stephens, 2003; Stephens & Donnelly, 2003; Stephens & Scheet, 2005; Stephens et al., 2001), which uses data on linked genotypes to estimate haplotypes of each individual taking into account recombination and decay in linkage desequilibrium. This is described by the authors as “A Bayesian method with approximate ‘coalescent with recombination’ prior, capturing the fact that each sampled haplotype tends to be similar to another haplotype or to a mosaic of other haplotypes”(Stephens & Scheet, 2005). PHASE starts assuming unknown haplotypes (Z) to be similar to unambiguous haplotypes (G) or to a mosaic of recombinations of them. It randomly choose an unresolved haplotype from individual i (Zi) and
calculates its probability to be like any of the already known haplotypes from their frequencies estimated so far, then the newly estimated haplotype is moved to the group of known haplotypes and used to estimate the next unresolved haplotype, assuming all the estimations to be correct until going through all the unknown haplotypes. This process is repeated iteratively creating a set of all the estimations in each iteration: During the (k + 1)thiteration STRUCTURE samples an
haplotype of the individual i, corresponding to that iteration (Zi(k+1)). The haplotype is drawn from a set of all the previously phased genotypes excluding those for the individual i itself, i.e. P(zi| G, Z−ik )
(Niu, 2004; Stephens & Scheet, 2005).
PHASE was run five times with 150 iterations using different random seeds on each run to check for consistency between estimations. A dataset of 190 individuals from different Old World popula- tions genotyped for the same variants, kindly provided by Anke Liebert, was included in the PHASE run to compare their haplotypic backgrounds with those estimated for our samples. This was done comparing the extension of the European haplotypes carrying −13,910*T with the extension of the −13,910*Thaplotypes in our sample, using extended haplotype homozygosity (EHH) implemented in Sweep 1.1 (Sabeti et al., 2002).
2.3.3.4 Differentiation and distances by groups
Traditionally, Fsthas been used as a measure of population differentiation between a subpopulation
sand the metapopulation t. It was defined for biallelic loci by Wright (1949) as,
Fst=
Vp p(1 − p)
2.3. Data analysis methods 79 Were p is the mean frequency of one of the alleles and Vp is its variance over all subpopulations. It ranges from 0 (absence of differentiation) to 1 (complete differentiation). This measure is used in this thesis fo evaluate differentiation between groups (as defined in section 2.3.2.1), for −13,910 C/T. However, there are difficulties to interpret this measure for multiallelic markers, such as the forensic identification STRs.
An alternative measure aims to apply Fst to multiallelic loci. Firstly proposed by (Nei, 1973), Gst
is based on mean heterozygosity calculated for any number of alleles across all subpopulations (Ht = 1 − Pi¯p2i, see section 2.3.3.2). This idea was later adapted by Hedrick (2005) to force the
result to fall between 0 and 1 regardless the number of alleles, making it easily comparable with biallelic Fst. Hedrick’s Gst0 is defined as,
G0st =Gst(1 + Hs) (1 − Hs)
It has been demonstrated that G0
stfails to identify differentiation when there are various exclusive
alleles within subpopulations (Jost, 2008). This is a likely scenario using markers as polymorphic as the STRs employed in this thesis. Jost (2008) proposed an approach that takes into account the proportion of alleles that are common to n subpopulations, and the proportion of alleles in a given subpopulation that only occur on it (Jost, 2008, 2009),
D= (H t− Hs) (1 − Hs) · n (n − 1)
In this thesis, Jost’s D is employed as the preferred method to measure of differentiation between groups when using highly variable STR markers.
Measures of population differentiation are regularly used to evaluate genetic distances between groups through pairwise comparison, and to compare them with the differences of individuals within each group. However, several other methods are available to consider differences across all groups rather than the pair population–subpopulation. The methods proposed by Cavalli-Sforza & Edwards (1967), Nei (1972), Reynolds et al. (1983), and Chakraborty & Jin (1993), are among the most popular. Each of this methods has its own assumptions about the influence of genetic drift and mutation in the change of frequencies, and most are developed under the ideal scenario of no selection, no inbreeding, and no migration between groups. A geometric approximation without biological assumptions uses Euclidean distances,
Deucl= v u u t L X i=1 (pji− pki)2
2.3. Data analysis methods 80 Where pjiand pkiare the frequencies of allele i in populations j and k respectively, summed across
all loci L.
Choosing the right distance measure based on incomplete knowledge of the population history is difficult. These different measures were compared using visualisation techniques based on Prin- cipal Components, Neighbour Joining Trees, and Hierarchical clustering to illustrate their differ- ences in the resulting distance matrices in Chapter 4. These analyses were performed using GNU R packages “gstudio” (Dyer, 2014), “ape” (Paradis et al., 2004), and “adegenet” (Jombart, 2008; Jombart & Ahmed, 2011).