we used a gwas dataset for height , generated from the giant consortium , as our source for per snp association statistics .
the height - increasing allele was defined as the allele that is associated with increased height in the giant dataset .
we were concerned that imputation using the hapmap ceu panel as the reference panel would bias our analyses , which focus on intra - european differences .
therefore , we only examined snps directly genotyped in migen or popres for our analysis . in order to determine
if the allele frequency of the height - increasing alleles are systematically increased or decreased in either the northern- or southern - european populations , we compared the northern- and southern - european allele frequencies for three different classes of snps in our analyses : ( 1 ) the 180 known height - associated snps identified by giant ; ( 2 ) sets of frequency - matched snps to the height - associated snps ; and ( 3 ) sets of independent snps genome - wide . a fourth class of snps consisting of ~1,400 independent snps most strongly associated with height , for which the effect size estimates are similar between giant and a family - based analysis , was also defined and used for much of the later analyses presented in the manuscript ( see definitions and descriptions below ) .
intra - european differences in allele frequencies were assessed using sign tests , which tested whether the proportion of snps with the height - increasing allele was significantly more common in northern vs. southern europeans compared with a 50/50 expectation , and paired t - tests , which tested whether the mean northern - european to southern - european allele frequency differences were significantly different from zero .
for the 180 known height - associated snps , the allele frequency for only 139 and 109 snps were analyzed in migen and popres , respectively , due to our restriction of using only directly genotyped snps .
these groups of snps include 55 and 30 height snps that were directly genotyped , and 84 and 79 proxies that were in high ld ( r0.8 in ceu ) with an original height snp , in migen and popres , respectively . in the case that multiple proxy snps were available in ceu , we selected the snp with the lowest p - value for height association in giant .
our analysis showed similar patterns in the directly genotyped snps and proxies , and mean allele frequency differences remained significant for both subsets of snps ( supplementary table 13 ) .
for the sets of matched snps , randomly drawn snps were matched to the height - associated snps on ancestral european allele frequency ( estimated as the average allele frequency of northern- and southern - european populations ) .
the genome - wide data used had been pruned by clumping snps in high ld ( r0.8 ) into a single cluster so to avoid drawing highly correlated snps .
clumping was done by first randomly choosing a snp as the index snp , then clustering all snps within 0.5 mb of the index snp that had a pairwise r0.8 based on hapmap phase 2 ceu data . in total 10,000 sets of matched snps
for the set of independent snps genome - wide , we calculated the mean northern- to southern - european allele frequency differences of the predicted height - increasing alleles in successive groups of 500 independent variants , sorted by their giant height association p - value starting from the most strongly associated snp . here
, snps were clumped using the method described above but with an r threshold of  0.1 to ensure that each clump of snps is nearly or completely independent from each other . in total , 73,657 snps and 54,542 snps genome - wide were used from the migen and popres datasets , respectively , to estimate northern- and southern - european allele frequency .
curves of best fit were determined using a smooth splined approach with spar parameter equal to 0.75 in r-2.11 . for each snp ,
the allele that is more common in northern europe than in southern europe is defined as the northern - predominant allele . to test whether northern - predominant alleles are associated with increased height in a family - based test that is immune to stratification
, we conducted a within - sibship test using data from the family - based framingham heart study .
the number of snps genotyped in fhs and used in these analyses ( after clumping to remove correlated snps ) was 55,927 and 52,680 for the migen and popres allele frequency data sets , respectively .
for each individual within a sibship and for each independent snp ( r < 0.1 ) , we designated the genotype as the number of northern - predominant alleles carried by that individual .
missing genotypes were skipped and treated as neither a northern- or southern - predominant allele .
we then adjusted the genotype at each snp within each sibship by subtracting from the observed number of northern - predominant alleles the average number of northern - predominant alleles for that snp in that sibship . similarly , we adjusted the age- and sex - corrected height values within each sibship by subtracting the sibship mean .
then , across all individuals ( each adjusted by the means in his / her own sibship ) , we regressed the sibship - adjusted height values against the sibship - adjusted genotypes , producing a pure family - based test immune to stratification .
the family - based effect size estimates ( i.e. , the regression coefficients ) were compared with the effect sizes estimated by the giant consortium .
we note that fhs was one of the cohorts included in the giant meta - analysis .
we therefore removed the fhs results from the giant data and repeated the giant meta - analysis in order to generate new giant estimates that are completely independent of our family - based test . from this comparison
, we identified a set of ~1,400 most strongly associated and clearly independent snps for which the effect sizes are similar in giant and in our family - based test .
this latter snp set was determined by first clumping the above - mentioned genome - wide datasets according to the giant height association p - value , using an r0.1 .
the top 5,000 snps from this list were then further pruned by requiring that no two snps occupy the same 1 mb window , preferentially keeping snps more strongly associated with height .
these snps have comparable effect sizes between our fhs within - sibship regression coefficients and giant effect sizes ( p = 0.36 and 0.89 for migen and popres , respectively , by paired t - test ; supplementary figure 3 ) .
thus , the height effect size estimates for this set of ~1,400 snps are not inflated by stratification . in our subsequent analyses
, we use these sets of ~1,400 snps , as well as the genome - wide data from which the ~1,400 snps were selected . for within - sibship analyses using genome - wide sets of snps , running averages of regression coefficients were also determined by successively calculating regression coefficients for each group of 500 snps and then calculating a running average of all regression coefficients up to and including that group of snps . to determine the significance of these running averages ,
simulations were conducted by randomly redistributing the height values within each sibship 1,000 times , and calculating the regression coefficients and running averages for each simulation .
the observed running average regression coefficients were considered significant if none of the simulations had as large a running average regression coefficient at that point in the genome as the observed values . to calculate the relative likelihoods that the observed northern- and southern - european allele frequency data for height - increasing alleles is consistent with a model with genetic drift alone or with models that incorporate selection , we used a likelihood ratio test , and modeled drift according to the methods outlined in ayodo et al . to model the effects of drift alone , the allele frequency difference between two populations was estimated as a random normal variable with mean 0 and variance equal to p(1p)(c + 1/n1 + 1/n2 ) , where p is the ancestral allele frequency ( the average of the two populations ) , c is a genetic drift parameter equal to 2  fst , where fst is determined using the genome - wide data ( fst = 0.0019 for migen and 0.0031 for popres ) , and n1 and n2 are total chromosome counts for each of our two populations .
the negative log likelihoods of observing the northern - european southern - european allele frequency difference was calculated using r , and summed over all independent snps ( r < 0.1 ) genome - wide or in groups of 500 independent snps sorted by giant height association p - value . to model the effect of drift and selection on the observed northern - european southern - european allele frequency differences , we first estimated the expected amount of allele frequency differences that could be attributed to selection using the following equation ( see section 4.1 for derivation ) : 
 afselt(wp2+wp+p1 + 2wp - p ) where p is the ancestral allele frequency ( estimated as the average of northern- and southern - european allele frequencies ) , t is the number of generations since the two populations have split , and w is the selective pressure experienced by the population under different models of ongoing selection .
a number of additional biases could have influenced our results , including ascertainment bias due to giant cohort collection , hapmap snp ascertainment , and our choice for phenotype .
please refer to the supplementary note for a detailed description of analyses demonstrating that these potential ascertainment biases of our study design did not influence our results .
we used a gwas dataset for height , generated from the giant consortium , as our source for per snp association statistics .
the height - increasing allele was defined as the allele that is associated with increased height in the giant dataset .
we were concerned that imputation using the hapmap ceu panel as the reference panel would bias our analyses , which focus on intra - european differences .
therefore , we only examined snps directly genotyped in migen or popres for our analysis . in order to determine
if the allele frequency of the height - increasing alleles are systematically increased or decreased in either the northern- or southern - european populations , we compared the northern- and southern - european allele frequencies for three different classes of snps in our analyses : ( 1 ) the 180 known height - associated snps identified by giant ; ( 2 ) sets of frequency - matched snps to the height - associated snps ; and ( 3 ) sets of independent snps genome - wide . a fourth class of snps consisting of ~1,400 independent snps most strongly associated with height , for which the effect size estimates are similar between giant and a family - based analysis , was also defined and used for much of the later analyses presented in the manuscript ( see definitions and descriptions below ) .
intra - european differences in allele frequencies were assessed using sign tests , which tested whether the proportion of snps with the height - increasing allele was significantly more common in northern vs. southern europeans compared with a 50/50 expectation , and paired t - tests , which tested whether the mean northern - european to southern - european allele frequency differences were significantly different from zero .
for the 180 known height - associated snps , the allele frequency for only 139 and 109 snps were analyzed in migen and popres , respectively , due to our restriction of using only directly genotyped snps .
these groups of snps include 55 and 30 height snps that were directly genotyped , and 84 and 79 proxies that were in high ld ( r0.8 in ceu ) with an original height snp , in migen and popres , respectively . in the case that multiple proxy snps were available in ceu , we selected the snp with the lowest p - value for height association in giant .
our analysis showed similar patterns in the directly genotyped snps and proxies , and mean allele frequency differences remained significant for both subsets of snps ( supplementary table 13 ) .
for the sets of matched snps , randomly drawn snps were matched to the height - associated snps on ancestral european allele frequency ( estimated as the average allele frequency of northern- and southern - european populations ) .
the genome - wide data used had been pruned by clumping snps in high ld ( r0.8 ) into a single cluster so to avoid drawing highly correlated snps .
clumping was done by first randomly choosing a snp as the index snp , then clustering all snps within 0.5 mb of the index snp that had a pairwise r0.8 based on hapmap phase 2 ceu data . in total 10,000 sets of matched snps were generated .
for the set of independent snps genome - wide , we calculated the mean northern- to southern - european allele frequency differences of the predicted height - increasing alleles in successive groups of 500 independent variants , sorted by their giant height association p - value starting from the most strongly associated snp . here
, snps were clumped using the method described above but with an r threshold of  0.1 to ensure that each clump of snps is nearly or completely independent from each other . in total , 73,657 snps and 54,542 snps genome - wide were used from the migen and popres datasets , respectively , to estimate northern- and southern - european allele frequency .
curves of best fit were determined using a smooth splined approach with spar parameter equal to 0.75 in r-2.11 .
for each snp , the allele that is more common in northern europe than in southern europe is defined as the northern - predominant allele . to test whether northern - predominant alleles are associated with increased height in a family - based test that is immune to stratification
, we conducted a within - sibship test using data from the family - based framingham heart study .
the number of snps genotyped in fhs and used in these analyses ( after clumping to remove correlated snps ) was 55,927 and 52,680 for the migen and popres allele frequency data sets , respectively . for each individual within a sibship and for each independent snp ( r < 0.1 ) , we designated the genotype as the number of northern - predominant alleles carried by that individual .
missing genotypes were skipped and treated as neither a northern- or southern - predominant allele .
we then adjusted the genotype at each snp within each sibship by subtracting from the observed number of northern - predominant alleles the average number of northern - predominant alleles for that snp in that sibship . similarly ,
we adjusted the age- and sex - corrected height values within each sibship by subtracting the sibship mean . then , across all individuals ( each adjusted by the means in his / her own sibship ) , we regressed the sibship - adjusted height values against the sibship - adjusted genotypes , producing a pure family - based test immune to stratification . the family - based effect size estimates ( i.e. , the regression coefficients )
we note that fhs was one of the cohorts included in the giant meta - analysis .
we therefore removed the fhs results from the giant data and repeated the giant meta - analysis in order to generate new giant estimates that are completely independent of our family - based test . from this comparison
, we identified a set of ~1,400 most strongly associated and clearly independent snps for which the effect sizes are similar in giant and in our family - based test .
this latter snp set was determined by first clumping the above - mentioned genome - wide datasets according to the giant height association p - value , using an r0.1 .
the top 5,000 snps from this list were then further pruned by requiring that no two snps occupy the same 1 mb window , preferentially keeping snps more strongly associated with height .
these snps have comparable effect sizes between our fhs within - sibship regression coefficients and giant effect sizes ( p = 0.36 and 0.89 for migen and popres , respectively , by paired t - test ; supplementary figure 3 ) .
thus , the height effect size estimates for this set of ~1,400 snps are not inflated by stratification . in our subsequent analyses
, we use these sets of ~1,400 snps , as well as the genome - wide data from which the ~1,400 snps were selected . for within - sibship analyses using genome - wide sets of snps , running averages of regression coefficients were also determined by successively calculating regression coefficients for each group of 500 snps and then calculating a running average of all regression coefficients up to and including that group of snps . to determine the significance of these running averages ,
simulations were conducted by randomly redistributing the height values within each sibship 1,000 times , and calculating the regression coefficients and running averages for each simulation .
the observed running average regression coefficients were considered significant if none of the simulations had as large a running average regression coefficient at that point in the genome as the observed values .
to calculate the relative likelihoods that the observed northern- and southern - european allele frequency data for height - increasing alleles is consistent with a model with genetic drift alone or with models that incorporate selection , we used a likelihood ratio test , and modeled drift according to the methods outlined in ayodo et al . to model the effects of drift alone , the allele frequency difference between two populations was estimated as a random normal variable with mean 0 and variance equal to p(1p)(c + 1/n1 + 1/n2 ) , where p is the ancestral allele frequency ( the average of the two populations ) , c is a genetic drift parameter equal to 2  fst , where fst is determined using the genome - wide data ( fst = 0.0019 for migen and 0.0031 for popres ) , and n1 and n2 are total chromosome counts for each of our two populations .
the negative log likelihoods of observing the northern - european southern - european allele frequency difference was calculated using r , and summed over all independent snps ( r < 0.1 ) genome - wide or in groups of 500 independent snps sorted by giant height association p - value . to model the effect of drift and selection on the observed northern - european southern - european allele frequency differences , we first estimated the expected amount of allele frequency differences that could be attributed to selection using the following equation ( see section 4.1 for derivation ) : 
 afselt(wp2+wp+p1 + 2wp - p ) where p is the ancestral allele frequency ( estimated as the average of northern- and southern - european allele frequencies ) , t is the number of generations since the two populations have split , and w is the selective pressure experienced by the population under different models of ongoing selection .
a number of additional biases could have influenced our results , including ascertainment bias due to giant cohort collection , hapmap snp ascertainment , and our choice for phenotype .
please refer to the supplementary note for a detailed description of analyses demonstrating that these potential ascertainment biases of our study design did not influence our results .
 strong signatures of positive selection at newly arising genetic variants are well - documented in humans18 , but this form of selection may not be widespread in recent human evolution9 . because many human traits are highly polygenic and partly determined by 
 common , ancient genetic variation , an alternative model for rapid genetic adaptation has been proposed : weak selection acting on many pre - existing ( standing ) genetic variants , or polygenic adaptation1012 . by studying height , a classic polygenic trait 
 , we demonstrate the first human signature of widespread selection on standing variation . 
 we show that frequencies of alleles associated with increased height , both at known loci and genome - wide , are systematically elevated in northern europeans compared with southern europeans ( p<4.3104 ) . 
 this pattern mirrors intra - european height differences and is not confounded by ancestry or other ascertainment biases . 
 the systematic frequency differences are consistent with the presence of widespread weak selection ( selection coefficients ~103105 per allele ) rather than genetic drift alone ( p<1015 ) . 
Online Methods
Study Cohorts
Defining classes of height-associated SNPs for sign tests and mean allele frequency difference analyses
Within-sibship association test of Northern-predominant alleles and increased height
Modeling genetic drift and selection
Ruling out potential ascertainment biases
Supplementary Material