Ancestryrelated assortative mating in Latino populations
 Neil Risch^{1, 2, 3}Email author,
 Shweta Choudhry^{4},
 Marc Via^{1, 4},
 Analabha Basu^{1},
 Ronnie Sebro^{1},
 Celeste Eng^{4},
 Kenneth Beckman^{5},
 Shannon Thyne^{1},
 Rocio Chapela^{6},
 Jose R RodriguezSantana^{7},
 William RodriguezCintron^{8},
 Pedro C Avila^{9},
 Elad Ziv^{1, 4} and
 Esteban Gonzalez Burchard^{1, 4}
DOI: 10.1186/gb20091011r132
© Risch et al.; licensee BioMed Central Ltd. 2009
Received: 2 September 2009
Accepted: 20 November 2009
Published: 20 November 2009
Abstract
Background
While spouse correlations have been documented for numerous traits, no prior studies have assessed assortative mating for genetic ancestry in admixed populations.
Results
Using 104 ancestry informative markers, we examined spouse correlations in genetic ancestry for Mexican spouse pairs recruited from Mexico City and the San Francisco Bay Area, and Puerto Rican spouse pairs recruited from Puerto Rico and New York City. In the Mexican pairs, we found strong spouse correlations for European and Native American ancestry, but no correlation in African ancestry. In the Puerto Rican pairs, we found significant spouse correlations for African ancestry and European ancestry but not Native American ancestry. Correlations were not attributable to variation in socioeconomic status or geographic heterogeneity. Past evidence of spouse correlation was also seen in the strong evidence of linkage disequilibrium between unlinked markers, which was accounted for in regression analysis by ancestral allele frequency difference at the pair of markers (European versus Native American for Mexicans, European versus African for Puerto Ricans). We also observed an excess of homozygosity at individual markers within the spouses, but this provided weaker evidence, as expected, of spouse correlation. Ancestry variance is predicted to decline in each generation, but less so under assortative mating. We used the current observed variances of ancestry to infer even stronger patterns of spouse ancestry correlation in previous generations.
Conclusions
Assortative mating related to genetic ancestry persists in Latino populations to the current day, and has impacted on the genomic structure in these populations.
Background
Mating patterns and preferences have been an active area of research for population geneticists, sociologists, and anthropologists for more than a century. On both a global and local scale, mating does not occur at random. On the larger scale, geographic constraints, such as great distances, high mountains and bodies of water, create local isolation, differentiation and endogamy. The influence of local geography has also been extensively studied [1, 2]. However, on a local level, nongeographic factors have greater importance in mate selection. In racially/ethnically heterogeneous societies that characterize the Western hemisphere, race and ethnicity have played a major role in mate selection [3], although interracial mating is on the incline. Within racial/ethnic groups and within racially/ethnically homogenous societies, factors such as age, education, occupation, socioeconomic status (SES), height, weight and religious background influence the choice of a mating partner [4–9]. Specific behavioral characteristics are also known to correlate between spouses [10].
Population structure and assortative mating have implications in a wide variety of fields, ranging from genetics to sociology and anthropology. From the perspective of population genetics, the impact depends on the source of the nonrandom mating. Generally, assortative mating does not affect the frequency of alleles involved with the choice process unless assortment is linked with natural selection or differential reproduction. These are referred to as first moment effects [11]. By contrast, genotype frequencies may be altered by assortative mating, specifically leading to a positive allelic correlation or homozygote excess for loci that are correlated with the mate selection process [4]. These have been referred to as second moment effects [11]. Second moment effects, or correlations, also occur between alleles at different loci, a phenomenon characterized as linkage disequilibrium (LD). Such LD will occur for all pairs of loci that correlate with the source of nonrandom mating. In the case of multifactorial traits, Crow and Felsenstein [12] have shown that the increase in locus homozygosity is relatively small while the increase in trait variance can be large. The trait variance increase is due primarily to the myriad LD effects among loci.
Assortative mating can also create correlations between previously unrelated traits when these traits are involved in the mating partner selection [4]. These correlations between previously unrelated traits can also have an impact on casecontrol association studies, significantly increasing type I error rates with loci involved in the assortative mating process [13].
Populations of the Western hemisphere, and particularly Latin America, provide unique opportunities to study population structure and nonrandom mating, due to the historical confluence of three major racial groups over the past five centuries. Mating among the various migrant and local populations has given rise to new population groups characterized by genetic admixture. During the Spanish colonial period, Spanish colonialists taking Native American or Africandescent women as sexual partners was a common practice as early as in the first decades of the 16th century, although social pressure prevented interethnic marriages from becoming widespread [14]. In 1776, the Royal Pragmatic on Marriage was enacted due to 'unequal marriages on account of their size and the diversity of classes and castes of their inhabitants' [15]. The primary purpose of this law was to avoid 'inequality' in the marriage based on an overall assessment not only of skin color, but also of wealth and social status. This 'pigmentocracy' is still observed in some Latin American countries, where the resistance to interethnic marriage is greater among individuals of higher socioeconomic status [3, 16].
Within the populations of Latin America, assortative mating has been described to occur based on a variety of factors, including education level, religion, age, family values, anthropometric measurements, and skin pigmentation [16–21]. There has also been debate regarding the degree to which spouse correlations for physical traits such as skin color and anthropometric traits reflect partner selection based on perceived 'race' or selection based on socioeconomic position [16, 22], although the two may be confounded in certain settings.
The most significant studies of mating patterns in Latin America have been conducted by Newton Morton and his colleagues in northeastern Brazil [23–25]. These authors studied 1,068 spouse pairs and their offspring of rural origin identified from government records. Subjects were evaluated on an eightpoint scale of ancestry based on physical characteristics such as skin pigment, hair color and type, and facial features. The scale reflects the degree of African versus European ancestry. At the same time, the investigators tested 17 blood group and protein markers to genetically estimate African, European and Native American ancestry, within each of the scale categories described above. They found evidence of ancestry correlation between spouses, although they concluded that it was modest [24].
The advent of DNAbased markers now allows us to address the question of nonrandom mating in Latino populations in a comprehensive way. We use ancestry informative genetic markers (AIMs) to study spouse correlations in two Latino populations, Mexicans and Puerto Ricans. To contrast indigenous versus migrant patterns, we study spouse pairs recruited both from the country/territory of origin (Mexico, Puerto Rico) as well as from the US. We show directly through ancestry estimation that significant spouse correlations in ancestry persist at a high level in all populations, leading to significant LD between unlinked markers, the strength of which is directly related to ancestral allele frequency differences. While both populations show strong assortative mating, the patterns are different, with Mexicans showing spouse correlations in European and Native American ancestry, while Puerto Ricans show spouse correlations in European and African ancestry.
Results
Mean (standard deviation) ancestries for Latino spouses by recruitment site
Wives  Husbands  

Ethnicity  Site  Number  African  European  Native American  African  European  Native American 
Mexican  All  285  0.078 (0.040)  0.437 (0.175)  0.485 (0.180)  0.080 (0.044)  0.425 (0.171)  0.495 (0.180) 
Mexico City  91  0.064 (0.034)  0.322 (0.165)  0.615 (0.172)  0.061 (0.034)  0.322 (0.181)  0.617 (0.194)  
Bay Area  194  0.084 (0.040)  0.491 (0.152)  0.425 (0.150)  0.089 (0.045)  0.473 (0.143)  0.438 (0.142)  
Puerto Rican  All  377  0.237 (0.141)  0.622 (0.145)  0.141 (0.061)  0.229 (0.127)  0.623 (0.139)  0.148 (0.070) 
Puerto Rico  223  0.232 (0.142)  0.625 (0.148)  0.143 (0.060)  0.223 (0.129)  0.629 (0.140)  0.149 (0.069)  
New York  154  0.244 (0.138)  0.618 (0.141)  0.138 (0.063)  0.238 (0.125)  0.615 (0.138)  0.147 (0.071) 
In Mexicans, the predominance of Native American and European ancestry is also reflected in the variances of the three ancestries, where the standard deviation for Native American and European ancestry is large at approximately 0.16, while for African ancestry the standard deviation is much smaller at approximately 0.04. By contrast, in Puerto Ricans, where European and African ancestry are dominant, the variance of African and European ancestry are large (standard deviations approximately 0.14) and the variance of Native American ancestry less (standard deviation 0.065). These variances also have implications for correlations in ancestry within individuals. As expected (Table S1 in Additional data file 1), the correlation between Native American and European ancestry in Mexicans is extremely strong (0.97). There is also a moderately negative correlation observed between African and Native American ancestry (0.28). In Puerto Ricans, the correlation between African and European ancestry is strong (0.89). Because European is the predominant ancestry in the Puerto Ricans, there is also a moderate negative correlation between European and Native American ancestry (0.35).
Results of ttests comparing average ancestries between spouses, and recruitment site within ethnic group, are given in Table S2 in Additional data file 1. As is apparent in Table 1, there are no significant differences in ancestry between the wives and husbands within any category. There are also no significant differences between the Puerto Ricans recruited from Puerto Rico and those recruited from New York. However, there are substantial ancestry differences between the Mexicans from Mexico City and those from the Bay Area, reflecting a migrant effect. The Bay Area Mexicans have significantly more European and African ancestry and less Native American ancestry compared to the Mexicans from Mexico City (Table S2 in Additional data file 1). This difference may reflect specific geographical or socioeconomic origins of the Mexican migrants to the Bay Area.
To examine a possible role of socioeconomic status on further analyses of these subjects, we examined average ancestries within SES categories for the subset of subjects on whom we had such information (Table S3 in Additional data file 1). Linear regression analysis of ancestry on SES (coded as 1 for low, 2 for moderate, 3 for middle and 4 for upper) was also performed separately for the sexes and ethnicities. There was a nonsignificant trend towards increased European and decreased Native American ancestry with SES among the Mexican wives but not husbands. However, there was a significant positive relationship of African ancestry with SES and negative relationship of SES with European ancestry among the Puerto Rican wives. SES trends were less clear among the Puerto Rican fathers. We note that because SES was measured based on censusbased location information rather than personal information, there may be a loss of sensitivity in these results.
Between spouse correlations (95% confidence interval) in ancestry, by ethnicity, recruitment site and socioeconomic status
Ancestry  

Ethnicity  Site  SES  Number  African  European  Native American 
Mexican  All  All  285  0.068  0.577  0.586 
(0.048,0.183)  (0.494,0.649)  (0.505,0.658)  
Mexico  All  91  0.030  0.564  0.568  
City  (0.234,0.177)  (0.405,0.689)  (0.411,0.693)  
Bay Area  All  194  0.003  0.430  0.392  
(0.138,0.144)  (0.308,0.538)  (0.266,0.505)  
Low  42  0.131  0.233  0.280  
(0.180,0.419)  (0.077,0.501)  (0.026,0.538)  
Moderate  75  0.048  0.518  0.501  
(0.181,0.272)  (0.330,0.667)  (0.310,0.654)  
Middle  39  0.268  0.409  0.384  
(0.052,0.538)  (0.107,0.642)  (0.078,0.624)  
Puerto Rican  All  All  377  0.328  0.237  0.003 
(0.235,0.416)  (0.139,0.330)  (0.098,0.104)  
New York  All  154  0.314  0.252  0.146  
(0.164,0.450)  (0.098,0.395)  (0.012,0.297)  
Puerto  All  223  0.335  0.226  0.103  
Rico  (0.213,0.446)  (0.097,0.347)  (0.231,0.029)  
Moderate  56  0.426  0.122  0.165  
(0.184,0.620)  (0.146,0.373)  (0.410,0.102)  
Middle  67  0.281  0.265  0.111  
(0.043,0.488)  (0.026,0.475)  (0.133,0.342)  
Upper  59  0.458  0.260  0.361  
(0.229,0.639)  (0.004,0.484)  (0.564,0.115) 
An important question is the source of the ancestry correlation between spouses. One possible factor is SES. Therefore, for the Mexicans from the Bay Area and the Puerto Ricans from Puerto Rico, for whom we had such information, we also examined spouse correlations within SES categories (Table 2). The spouse correlations in ancestry persisted within SES categories both in Mexicans and Puerto Ricans, and there was no apparent pattern of increase or decline with SES. As an additional evaluation of the impact of SES, we performed a linear regression analysis, with wife's individual ancestry (IA) as dependent variable and husband's IA and SES as the independent variables. These analyses were performed separately for each of the three ancestry components (Table S4 in Additional data file 1). Here again, we find no attenuation of the significant spouse relationship in European or Native American ancestry in the Mexicans when allowing for SES in the regression model. Similarly, we find no attenuation of African or European ancestry spouse correlation in the Puerto Ricans when including SES in the regression model. SES was not a significant predictor of wife's ancestry in any of the analyses of Mexicans; however, as noted previously, there was a significant positive regression of SES on African ancestry and negative regression of SES on European ancestry among the Puerto Rican wives.
We next evaluated the impact of assortative mating on genotype distributions at individual loci. First, we noted no significant differences in allele frequencies between spouses within recruitment sites, either for the Mexicans or Puerto Ricans (Table S5 in Additional data file 1). However, we did find a large excess of significant allele frequency differences between the Mexican and US recruitment sites for the Mexicans (69% of loci significant at P < 0.05). This pattern is consistent with what we previously observed for sitespecific ancestry differences for the Mexicans. To determine whether the Mexico City versus Bay Area allele frequency differences were entirely attributable to the ancestry difference between the two sites, we performed a regression analysis of the allele frequency difference chisquare on δ_{ij}^{2}/p*q*, where δ_{ij} represents the allele frequency difference between ancestral populations i and j, and p* is the allele frequency in the admixed population, q* = 1  p* (see Materials and methods). The results are given in Table S6 in Additional data file 1. We observed a highly significant regression coefficient for the EuropeanNative American δ (0.0339 ± 0.0037), while neither of the other coefficients was statistically significant, nor was the intercept significantly different from 1. Similarly, in an analysis where the intercept term was fixed at 1, the regression coefficients were very close to the unconstrained analysis. Thus, the entire excess of significant allele frequency differences between Mexico City and Bay Area can be attributed to the EuropeanNative American δ values at the markers, consistent with the European/Native American ancestry difference between the two sites being the source of site allele frequency differences. As described in Materials and methods, the pairwise sums of regression coefficients provide estimates of the squared difference in ancestry between the two sites. From the regression coefficients in Table S6 in Additional data file 1, we estimate the following ancestry differences between Mexico City and the Bay Area: Native American, √(0.0315 + 0.0025) = 0.184; European, √(0.0315  0.0018) = 0.172; African, √(0.0025  0.0018) = 0.026. From Table 1, the corresponding numbers are 0.184, 0.160 and 0.024, respectively. Thus, the regression results agree remarkably well with the observed site ancestry differences.
To explore the effect of assortative mating on individual loci, we calculated F values, both for the spouses themselves (within individual correlation) and between spouses (between spouse correlation), as described in Materials and methods. The value F_{1} represents the within spouse allelic correlation, which is derived from the excess of homozygosity among the spouses. The value F_{2} represents the between spouse allelic correlation obtained by sampling one allele from each parent at random, which is also an estimate of the expected value of F_{1} for the children of these spouse pairs (see Materials and methods). Thus, the two values of F allow us to compare the effect of assortative mating across two generations.
Mean (standard error) values of allelic correlation within spouses (F_{1}) and between spouses (F_{2})
Ethnicity  Site  F_{1}  F_{2} 

Mexican  Mexico City  0.0183 (0.0080)^{†}  0.0255 (0.0050)^{‡} 
Bay Area  0.0150 (0.0055)^{†}  0.0117 (0.0036)^{‡}  
All  0.0161 (0.0047)^{†}  0.0172 (0.0029)^{‡}  
Puerto Rican  Puerto Rico  0.0268 (0.0047)^{‡}  0.0068 (0.0039)* 
New York  0.0239 (0.0060)^{‡}  0.0105 (0.0042)*  
All  0.0256 (0.0036)^{‡}  0.0085 (0.0030)^{†} 
We next undertook an analysis to determine the degree to which the significant F values could be attributed to ancestry assortative mating. We did so by linear regression, allowing the F value to be the dependent variable and three independent variables denoted as δ_{ij}^{2}/p*q*, where the i, j subscripts refer to the three possible combinations of the ancestral African, European and Native American populations and p* is the allele frequency in the admixed population (see Materials and methods).
Regressions of F_{1} on δ^{2}/p*q*
F_{1}  

Ethnicity  Site  δ_{AE}^{2}/p*q*  δ_{AN}^{2}/p*q*  δ_{EN}^{2}/p*q*  Intercept 
Mexican  Mexico City  0.0052 (0.0049)  0.0066 (0.0047)  0.0187 (0.0110)  0.0127 (0.0174) 
0.0047 (0.0048)  0.0054 (0.0043)  0.0125 (0.0069)  0.0 (fixed)  
Bay Area  0.0028 (0.0039)  0.0056 (0.0037)  0.0274 (0.0086)^{‡}  0.0216 (0.0144)  
0.0038 (0.0039)  0.0033 (0.0033)  0.0168 (0.0049)^{‡}  0.0 (fixed)  
All  0.0037 (0.0034)  0.0054 (0.0032)  0.0236 (0.0074)^{‡}  0.0160 (0.0124)  
0.0039 (0.0032)  0.0038 (0.0028)  0.0155 (0.0042)^{‡}  0.0 (fixed)  
Puerto Rican  Puerto Rico  0.0035 (0.0057)  0.0014 (0.0036)  0.0007 (0.0048)  0.0249 (0.0136) 
0.0110 (0.0041)^{†}  0.0015 (0.0032)  0.0054 (0.0041)  0.0 (fixed)  
New York  0.0077 (0.0074)  0.0074 (0.0045)  0.0028 (0.0061)  0.0289 (0.0175)  
0.0165 (0.0051)^{‡}  0.0040 (0.0041)  0.0082 (0.0052)  0.0 (fixed)  
All  0.0050 (0.0044)  0.0037 (0.0027)  0.0014 (0.0036)  0.0265 (0.0104)^{†}  
0.0131 (0.0031)^{‡}  0.0006 (0.0025)  0.0064 (0.0031)^{†}  0.0 (fixed) 
Regressions of F_{2} on δ^{2}/p*q*
F_{2}  

Ethnicity  Site  δ_{AE}^{2}/p*q*  δ_{AN}^{2}/p*q*  δ_{EN}^{2}/p*q*  Intercept 
Mexican  Mexico City  0.0018 (0.0031)  0.0009 (0.0030)  0.0013 (0.0071)  0.0260 (0.0112)^{†} 
0.0028 (0.0031)  0.0034 (0.0029)  0.0141 (0.0045)^{‡}  0.0 (fixed)  
Bay Area  0.0002 (0.0026)  0.0024 (0.0025)  0.0075 (0.0057)  0.0123 (0.0096)  
0.0004 (0.0026)  0.0011 (0.0022)  0.0135 (0.0033)^{‡}  0.0 (fixed)  
All  0.0015 (0.0021)  0.0012 (0.0020)  0.0039 (0.0046)  0.0202 (0.0078)^{†}  
0.0008 (0.0020)  0.0010 (0.0017)  0.0140 (0.0027)^{‡}  0.0 (fixed)  
Puerto Rican  Puerto Rico  0.0029 (0.0047)  0.0043 (0.0029)  0.0008 (0.0039)  0.0063 (0.0111) 
0.0029 (0.0047)  0.0043 (0.0029)  0.0008 (0.0039)  0.0 (fixed)  
New York  0.0065 (0.0051)  0.0015 (0.0032)  0.0026 (0.0042)  0.0043 (0.0122)  
0.0052 (0.0035)  0.0010 (0.0028)  0.0018 (0.0035)  0.0 (fixed)  
All  0.0044 (0.0036)  0.0030 (0.0022)  0.0007 (0.0030)  0.0051 (0.0086)  
0.0028 (0.0025)  0.0024 (0.0020)  0.0002 (0.0025)  0.0 (fixed) 
Regression analyses on Puerto Rican F_{1} values yielded less clearcut results. As expected, the largest regression coefficients were for AfricanEuropean delta terms, although none were formally significant, in the analyses of single sites or for the two sites combined. Also, it appears that the ancestral deltas do not fully explain the excess of homozygosity at these markers. As seen in Tables 4 and 5, the F_{2} values were not as extreme as the F_{1} values, and none of the regression coefficients were significant, although again the largest regression coefficient tended to be for AfricanEuropean delta terms. After regression, there was no significant intercept term remaining.
As described in Materials and methods, the pairwise sums of regression coefficients provide estimates of the three spouse covariances in ancestry. For the Mexicans we analyzed the two recruitment sites separately, to avoid inflation of spouse covariance due to average ancestry differences between sites. From Table 4, for the regression analysis on F_{1} we estimate the following ancestry covariances for Mexico City: Native American, 0.0125 + 0.0054 = 0.0179; European, 0.0125  0.0047 = 0.0078; African, 0.0054  0.0047 = 0.0007. For the regression analysis on F_{2}, the corresponding covariance estimates are: Native American, 0.0141 + 0.0034 = 0.0175; European, 0.0141  0.0028 = 0.0113; African, 0.0034  0.0028 = 0.0006. The corresponding observed spouse covariances in ancestry derived from Tables 1 and 2 for Mexico City are: Native American, 0.0190; European, 0.0168; African, 0.0001. Thus, the regressionbased estimates for Native American ancestry spouse covariance are quite close to the observed, but the regressionbased estimate for European ancestry covariance is somewhat below the observed. For the Bay Area Mexicans, the regressionbased covariance estimates for F_{1} are: Native American, 0.0168 + 0.0033 = 0.0201; European, 0.0168  0.0038 = 0.0130; African, 0.0033  0.0038 = 0.0005. For the corresponding regression analysis on F_{2}, we estimate: Native American, 0.0135  0.0011 = 0.0124; European, 0.0135 + 0.0004 = 0.0139; African, 0.0004  0.0011 = 0.0007. The corresponding observed spouse covariances for Bay Area Mexicans are: Native American, 0.0083; European, 0.0093; African, 0. Here the regressionbased estimates appear to somewhat overestimate the actual covariances for Native American and European ancestry. All analyses regarding covariances for African ancestry are consistent in showing no evidence of correlation.
We repeated the same analysis in the Puerto Ricans, but for the two recruitment sites combined. From Table 4, for the regression analysis on F_{1} we estimated the following ancestry covariances: African, 0.0131  0.0006 = 0.0125; European, 0.0131 + 0.0064 = 0.0195; Native American, 0.0064  0.0006 = 0.0058. For the regression analysis on F_{2}, the corresponding covariance estimates are: African, 0.0028 + 0.0024 = 0.0052; European, 0.0028  0.0002 = 0.0026; Native American, 0.0024  0.0002 = 0.0022. The corresponding observed spouse covariances in ancestry from Tables 1 and 2 for Puerto Ricans are: African, 0.0059; European, 0.0048; Native American, 0. The F_{2} regressionbased estimates of spouse covariance for African and European ancestry are comparable to the observed (with a somewhat underestimated European ancestry correlation), while the F_{1} regressionbased estimates are higher. This suggests (as does the overall higher mean value for F_{1} than F_{2}) that the assortative mating in Puerto Ricans was stronger in the prior generation than in the current one.
To determine whether the excess average F_{1} and F_{2} values might be attributable to specific genomic locations, we created a QQ (quantilequantile) plot of regression residuals against a normal distribution (Figure S1a for Mexicans and S1b for Puerto Ricans in Additional data file 2). In both figures the observed distributions match closely to the expected. Hence, the homozygote excess appears to be a global phenomenon.
Chisquare tests of linkage disequilibrium between pairs of markers for spouses combined
Ethnicity  Site  Mean chisquare*  % (N) with P< 0.05 

Mexican  Mexico City  1.80  0.146 (782) 
Bay Area  1.47  0.105 (564)  
All  3.27  0.152 (814)  
Puerto Rican  Puerto Rico  1.95  0.161 (861) 
New York  1.43  0.100 (534)  
All  3.38  0.173 (925) 
Regression of linkage disequilibrium parameter D on δ_{1}δ_{2}
δfor:  

Ethnicity  Site  AfricanEuropean  AfricanNative American  EuropeanNative American  Intercept 
Mexican  Mexico City  0.0042 (0.0009)*  0.0044 (0.0006)*  0.0519 (0.0010)^{†}  0.0003 (0.0002) 
Bay Area  0.0004 (0.0007)  0.0006 (0.0004)  0.0322 (0.0007)^{†}  0.0002 (0.0001)  
All  0.0011 (0.0006)  0.0018 (0.0003)*  0.0385 (0.0006)^{†}  0.000 (0.0001)  
Puerto Rican  Puerto Rico  0.0298 (0.0006)^{†}  0.0016 (0.0004)*  0.0010 (0.0007)  0.000 (0.0001) 
New York  0.0260 (0.0008)^{†}  0.0020 (0.0005)*  0.0009 (0.0009)  0.0001 (0.0002)  
All  0.0283 (0.0005)^{†}  0.0018 (0.0003)*  0.0010 (0.0005)*  0.000 (0.0001) 
To determine the compatibility of the curves in Figure 4 with our own data, we calculated V_{t}/V_{0} and r_{t} for the current generation of spouses. From the means (α) and standard deviations (√V) in Table 1, we derived values of V_{t}/V_{0} of approximately 0.11 for European and Native American ancestry in Mexicans and 0.08 for African and European ancestry in Puerto Ricans. By contrast, the proportion of original variance for African ancestry in Mexicans is only 0.02, and for Native American ancestry in Puerto Ricans the value is 0.03. These lower values are consistent with the more modest spouse correlations observed for these ancestry components. All these variance ratios may be slightly inflated due to statistical noise in ancestry estimation. Because there was no correlation of African ancestry in the Mexican spouses, we assumed that the variance observed for African ancestry (0.0016) was primarily due to estimation error, since the actual variance would have decreased rapidly by this point in time. Adjusting the values of V_{t}/V_{0} given above for this amount of error variance (an upper bound) reduced the ratios to 0.10 for European and Native American ancestry in Mexicans, and 0.07 for African and European ancestry in Puerto Ricans.
To estimate r_{t}, we need to project the value of the LD parameter D to marker loci that are completely informative for ancestry (that is, allele frequency of 1 in one ancestral population and 0 in the other), which corresponds to δ values of 1 for both markers. From the regression results presented in Table 7, we can estimate D for δ = 1 by simply using the regression coefficient of δ_{1}δ_{2}. For Mexicans combined, D = 0.0402. To obtain the value of r_{t}, we then need to divide D by α(1  α), because α and 1  α correspond to the allele frequencies for a marker that is completely informative for ancestry (δ = 1). Using the mean ancestry values of Table 1 as α, we derive an approximate r_{t} value of 0.16. For Puerto Ricans, the value of D is 0.0283; dividing by α(1  α), we obtain a value of 0.12. We can rearrange the formula for V_{t} given in Materials and methods to V_{t}/V_{0} = r_{t}/(2  c_{t}) and c_{t} = 2  r_{t}/(V_{t}/V_{0}). Using the values above for V_{t}/V_{0} and r_{t}, for Mexicans we obtain c_{t} = 2  0.16/0.10 = 0.40; for Puerto Ricans we obtain c_{t} = 2  0.12/0.07 = 0.29. These values are close to the observed spouse correlations in ancestry in Table 2. Referring back to Figure 4, we see that our results are consistent with a model of decreasing spouse ancestry correlation over a period of about 9 to 13 generations for Mexicans and 10 to 14 generations for Puerto Ricans. The same formulas given above can also be adapted for linked markers [26]. The assortative mating we observed is expected to enhance the LD between linked markers to an even greater extent than for unlinked markers.
Discussion
It is of interest to compare our results to those of prior authors who have studied triracial populations of northeastern Brazil. Although Krieger et al. [24] studied 17 genetic polymorphisms, they did not estimate ancestry at an individual level, but rather within 7 'racial classes' based on a graded scale from 0 to 8 of physical characteristics. However, based on their compilation of spouse pairs for the 7 categories [24] and their estimates of genetic ancestry within each of these categories, we obtained a spouse correlation of 0.46 for African ancestry and 0.45 for European ancestry. These results are comparable to what we observed among the Puerto Ricans, although the Brazilian correlations are somewhat higher. These spouse correlations are also similar to a correlation between spouses of the scale scores derived based on physical characteristics (0.46). This is not surprising, given the very strong correlation between genetically estimated African (European) ancestry and their eightpoint scale (correlation = 0.98).
A more recent study by Azevêdo et al. [20] examined subjects from the same region of northeastern Brazil, but only used a fivepoint observed scale of ancestry without genetic markers. However, the spouse correlation in the fivepoint scale in their data (correlation = 0.47) is quite comparable to that observed in the earlier study from the same region [24].
An important question relates to the actual trait or traits underlying mate selection leading to the spouse correlation in ancestry in these populations. Ancestry is not directly observed, but estimated from genetic markers. One possibility is social, whereby ancestry is associated with social position, and marriages occur within social strata. However, we found only a modest relationship, at best, between SES and ancestry in our study, and the regression of wife's ancestry on husband's ancestry was undiminished when SES was included in the model. Another possibility is geographic origins. If mates are preferentially chosen locally, an ancestry correlation would be induced if ancestry varies geographically. However, among the Puerto Ricans in our study, we found no significant difference between those from New York City and those from Puerto Rico, and also previously found only modest ancestral variation across recruitment sites in Puerto Rico [27]. Reexamining the geographic variation in ancestry in our Puerto Rican subjects [27], we estimate that a spouse correlation of 6 to 8% in African or European ancestry could be induced by such variation; however, this is far short of what we observed, although geographic ancestry variation could be one modest contributor to the observed spouse correlation, assuming that mating preferentially occurs locally.
Among the Mexicans in our study, we noted greater European and lower Native American ancestry among those recruited in the Bay Area than those recruited in Mexico City. Because of this, combining all Mexicans together did increase somewhat the spouse correlations in ancestry; however, the spouse correlations within recruitment sites were nearly as strong. Thus, it appears that geographic heterogeneity in ancestry alone cannot explain the spouse correlations. Another possibility involves physical characteristics, such as skin pigment, hair texture, eye color, and other physical features. Certainly, these traits are correlated with ancestry and are likely to be factors in mate selection. However, the spouse correlation for these traits must be high and the correlation of these traits with ancestry must also be high to explain the observed ancestry correlations. For example, denote the spouse correlation in ancestry by c, the spouse trait correlation by u, and the ancestrytrait correlation by w; then w = √(c/u). If the spouse trait correlation is 0.6 (a reasonably high value), then for a spouse ancestry correlation of 0.3 (Puerto Ricans), the traitancestry correlation is 0.7; for a spouse ancestry correlation of 0.4 (Mexicans), the traitancestry correlation is 0.8. Previous studies on assortative mating in Latin American groups have retrieved correlation coefficients of 0.29 to 0.46 for education level, 0.48 for skin reflectance, 0.07 to 0.18 for eye and hair color, and 0.16 to 0.24 for different anthropometric measurements [17, 18, 21].
We also note that the spouses in our study were parents of children with asthma. However, it is unlikely that this selection process has contributed to the spouse correlation because the correlation of genetic ancestry with asthma is only modest, at best [28]. A final assessment of the degree to which these and/or other physical traits may underlie the spouse ancestral correlations observed here requires assessment of these traits within spouse pairs along with ancestry informative markers.
The number of generations since admixing we derived from models allowing for a decrease in spouse ancestry correlation over time is clearly more consistent with the known demographic history of Mexicans and Puerto Ricans [29], and suggests that ancestry assortative mating was even stronger historically than observed in the most recent generations. Although admixing between the indigenous American, European and African populations started to occur in the centuries after the arrival of Columbus and the subsequent importation of slaves from Africa, continuous and large scale migrations to the Americas from Europe continued through the 17th, 18th and 19th centuries. Similarly, the slave trade from Africa continued through the 18th and 19th centuries. Thus, 9 to 14 generations, which corresponds approximately to 225 to 350 years, appears consistent with the general time frame over which the admixing started to occur in substantial numbers, giving rise to the admixed Mestizo populations of Mexico and Puerto Rico [14, 30, 31].
Conclusions
We have shown that mating within contemporary Latino populations does not occur at random with regard to ancestry. While both Mexicans and Puerto Ricans show positive assortative mating for ancestry, the pattern between the two populations is quite different. Among Mexicans, the strongest spouse correlations relate to the proportion of Native American and European ancestry, while amount of African ancestry appears to have little impact on mate choice. This is not surprising, given the modest overall level of African ancestry in this population. By contrast, among Puerto Ricans, the strong assortative mating relates to African and European ancestry, while Native American ancestry appears not to contribute to the correlation. While Native American in this population is the smallest ancestral component on average (14%), it is not dramatically less than the average of African ancestry (23%), yet the spouse correlations for these ancestries is dramatically different. Moreover, we did not find any evidence of ancestry asymmetry in the mating patterns. Some authors have described assortative mating by skin color in Latin American populations but with a male preference for lighterskinned women [16–20]. In our results, there is no evidence of any directionality in partner choice. Ancestry correlation was observed to be a global phenomenon of the genome and not restricted to a few loci.
Our results also reiterate that ancestry variation in Latino populations can be a strong confounder in genetic association studies [32]. As we have shown above, the amount of LD between unlinked markers is directly related to both the ancestry delta values and the variance in ancestry. Assortative mating in these Latino populations will continue to maintain both the ancestry variance and LD over time. However, the patterns observed in these two Latino populations are quite distinct, reflecting strong LD between markers that differentiate Europeans and Native Americans among the Mexicans, versus strong LD between markers that differentiate Europeans and Africans among the Puerto Ricans. It will be of considerable interest to investigate other Latino populations who have varying degrees of African, European and Native American ancestry.
Materials and methods
Subjects
The subjects included in this study are part of the Genetics of Asthma in Latino Americans (GALA) study and have been described previously [33]. Subjects are of Mexican and Puerto Rican ethnicity and are parents of childhood asthma patients. Mexican spouse pairs were recruited from both Mexico City and the San Francisco Bay Area. Puerto Rican spouse pairs were recruited from both New York City and from Puerto Rico. Both spouses selfidentified as Mexican and all four parents of the spouse pair were identified as Mexican for the Mexico City and Bay Area recruitment sites. For the New York City and Puerto Rico sites, both spouses selfidentified as Puerto Rican, and all four parents of spouses were identified as Puerto Rican. The present analysis included 91 Mexican spouse pairs from Mexico City and 194 spouse pairs from the Bay Area for a total of 285 Mexican spouse pairs; there were 154 Puerto Rican spouse pairs from New York and 223 pairs from Puerto Rico, for a total of 377 Puerto Rican spouse pairs.
All subjects provided written informed consent for blood donation and genotyping. The study protocol was approved by the UCSF Committee on Human Research.
Assessment of socioeconomic status
We used census tract geocoding of income as the basis for SES characterizations of subjects as previously described [27]. The Federal Financial Institutions Examination Council has provided a geocoding/mapping system for this purpose [34]. Census tracts are characterized as low, moderate, middle or upper based on median family income for that census tract compared to median income of the entire metropolitan area. For Puerto Rican subjects from Puerto Rico, SES was defined in terms of the location of the recruitment center; for Mexican subjects from the Bay Area, SES was defined in terms of home residence location.
Selection of ancestry informative markers
AIMs were selected as described [35]. In brief, biallelic single nucleotide polymorphisms (SNPs) were chosen from an Affymetrix 100K SNP chip panel that showed large allele frequency differences (δ of at least 0.5) between pairs of African, European or Native American populations. For the present analysis 107 markers were selected that were widely spaced across all chromosomes, so as to avoid LD in the ancestral populations. A full list of these markers and corresponding chromosome location has been given [35].
Genotyping
Marker genotyping was performed at the Functional Genomics Core, Children's Hospital Oakland Research Institute as described previously [35]. Briefly, four multiplex PCR assays containing 28, 27, 26, and 26 SNPs, respectively, were performed, followed by singlebase primer extensions using iPLEX enzyme and buffers (Sequenom, San Diego, CA, USA). Primer extension products were measured with the MassARRAY Compact System (Sequenom), and mass spectra analyzed using TYPER software (Sequenom) to generate genotype calls.
Quality control was performed on the genotype calls for all Mexican and Puerto Rican subjects. Genotype call rates were generally high and reproducible. The average call rate was 97.6%, and all included markers had a call rate of at least 92%. Three markers were excluded that had call rates below 90% (rs10498919, rs2569029, rs798887), leaving 104 AIMs for subsequent analyses. The final list of markers and their chromosomal locations is given in Table S9 in Additional data file 1.
Analytic methods
Surrogate ancestral populations were used in this analysis to characterize ancestral allele frequencies for IA estimation. These samples included 37 West Africans, 42 European Americans and 30 Native Americans [35]. We calculated δ values between allele frequencies for each pair of ancestral populations for all of the markers. For the African versus European groups, the median δ value was 0.56, and 65% of values were greater than 0.30; for the African versus Native American groups, the median δ was 0.71, and 83% were greater than 0.30; for the European versus Native American populations, the median δ was 0.47, and 59% were greater than 0.30. With this number of markers and distribution of δ values, it is predicted that estimated genomewide IA values are at least 90% correlated with actual values [36].
Estimation of ancestry
To estimate individual ancestries, we used the program Structure 2.1 [37, 38] using the 104 AIMs described above. Structure was run using the admixture model with unlinked markers, with 50,000 burnin iterations and 50,000 further iterations. We assumed three ancestral populations, African, European and Native American, and included genotype data on the ancestral populations previously described. The program was run four times, once each for Mexican woman, Mexican men, Puerto Rican women and Puerto Rican men. We analyzed the men and women separately due to possible correlations between spouses. The implementation was similar to what we have done previously [27]. To confirm that the use of three ancestral populations was appropriate, we examined the distribution of LnP(D) for K = 2, 3, 4 and 5. There was a large difference in LnP(D) between K = 2 and K = 3, but not between K = 3 and K = 4 or K = 5. Thus, the optimal value of K for these data was determined to be K = 3. However, this is not surprising as the markers were AIMs and therefore specifically selected to have large allele frequency differences between the three ancestral populations.
ttests
Mean ancestries were compared across groups defined by site, gender and SES using ttests.
Interclass correlations
Pearson interclass correlations were calculated between ancestries within individuals. Similarly, interclass correlations in ancestry between spouses were calculated. Because means and variances of ancestry were similar in men and women, we also calculated intraclass correlations between spouses. However, these results were virtually identical to the interclass correlations.
Single locus analyses
where n_{2} and n_{0} are the number of homozygotes and n_{1} the number of heterozygotes observed; N = n_{2} + n_{1} + n_{0}. Under the null hypothesis of no withinlocus allelic correlation, Z has a normal distribution with mean 0 and variance 1. We chose to use a onesided test as opposed to a twosided chisquare test because we specifically were searching for an excess of homozygotes, as predicted by assortative mating.
Note that Z = F√N. Also, 1  F represents the proportionate decrease in heterozygosity versus expected under random mating. In future discussion, we refer to this value of F as F_{1}, to denote correlation within the first generation (that is, within spouses).
To examine allelic correlations between spouses, we calculated a similar statistic to F. First, we calculated the intraclass correlation ρ for the number of 'B' alleles (0, 1 or 2) in the spouse pairs (assume a biallelic locus with alleles B and b). However, because we are correlating two alleles between the spouses, this correlation is not directly comparable to the F value defined within individuals defined above. Hence, to derive a comparable statistic, we created a variable F_{2}, defined as the expected intraclass correlation for single alleles selected at random from the two spouses. It can be shown that F_{2} = ρ (1 + F_{1})/2. As F_{1} values are generally modest, often F_{2} will be approximately half the intraclass correlation ρ.
For comparison, we also calculated interclass correlations for the spouse pairs, which allows for unequal allele frequencies between the two spouses. Because the genotype distributions in wives and husbands were generally extremely similar, the interclass correlations were nearly identical to the intraclass correlations (correlation between correlations ranging from 0.997 to 0.999).
Pairwise locus analyses
For pairs of markers, we calculated nonindependence of genotype using a likelihood ratio chisquare test, where the double heterozygotes were estimated using maximum likelihood. We also calculated the LD parameter D. Both calculations were performed using the computer package PLINK [39].
Linear regressions to estimate effects of ancestry assortative mating
A major goal of this analysis was to examine how genetic structure in Latino populations is influenced by ancestryrelated assortative mating. One way to characterize the structure is by examining intralocus correlations (F statistics) and interlocus correlations, or correlations between markers (LD parameters r and D). We therefore derived formulas relating the spouse ancestry correlations to expected patterns of allele frequency difference between recruitment sites, F statistics, and D statistics.
p_{1}' and p_{2}' are the allele frequencies in groups 1 and 2, N_{1} and N_{2} are the number of individuals in groups 1 and 2, p* = (N_{1}p_{1}' + N_{2}p_{2}')/(N_{1} + N_{2}) and Var represents variance.
Equation 4 shows that Equation 3 for the expectation of χ^{2} can be fit with a linear model in terms of the three covariates, δ_{i}^{2}/Var(p_{1}'  p_{2}') for i = 1 to 3 via linear regression. If we specify the estimated regression coefficient of δ_{i}^{2}/Var(p_{1}'  p_{2}') as a_{i}, then from the derived regression coefficients we can estimate ε_{1} as √(a_{1} + a_{3}), ε_{3} as √(a_{2} + a_{3}), and ε_{2} = √(a_{1} + a_{2}).
We next consider regression analyses on the statistic F. Recall that F represents the correlation between alleles at a given locus. Consider again a locus with two alleles B and b. Define the binomial random variable S to be 1 if the maternally transmitted allele is B and 0 if b; similarly, define T to be 1 if the paternally transmitted allele is B and 0 if b. Then F can be defined as Cov(S, T)/p*q* where p* is the frequency of B in the combined set of parents and q* = 1  p* and Cov is covariance. In the analysis of F_{1}, p* simply represents the frequency of allele B in the pool of individuals; in the analysis of F_{2}, p* represents the frequency of allele B in the pool of spouses combined. Next define the random variable X_{i} as the proportionate ancestry from population i in the wife and Y_{i} as the proportionate ancestry from population i in the husband, where i ranges from 1 to 3. Note that X_{1} + X_{2} + X_{3} = Y_{1} + Y_{2} + Y_{3} = 1. Then the random variables S and T can be defined as S = π_{1}X_{1} + π_{2}X_{2} + π_{3}X_{3} and T = π_{1}Y_{1} + π_{2}Y_{2} + π_{3}Y_{3}, respectively. Then, because π_{2} is constant, Cov(S, T) = Cov(π_{1}X_{1} + π_{2}X_{2} + π_{3}X_{3}, π_{1}Y_{1} + π_{2}Y_{2} + π_{3}Y_{3}) = Cov(π_{1}X_{1} + π_{2}X_{2} + π_{3}X_{3}  π_{2}, π_{1}Y_{1} + π_{2}Y_{2} + π_{3}Y_{3}  π_{2}) = Cov((π_{1}  π_{2})X_{1} + (π_{3}  π_{2})X_{3}, (π_{1}  π_{2})Y_{1} + (π_{3}  π_{2})Y_{3}) = Cov(δ_{1}X_{1}  δ_{3}X_{3}, δ_{1}Y_{1}  δ_{3}Y_{3}) = δ_{1}^{2}Cov(X_{1}, Y_{1}) + δ_{3}^{2}Cov(X_{3}, Y_{3})  2δ_{1}δ_{3}Cov(X_{1}, Y_{3}), assuming Cov(X_{1}, Y_{3}) = Cov(X_{3}, Y_{1}). Now define κ_{ii} = Cov(X_{i}, Y_{i}) and κ_{ij} = Cov(X_{i}, Y_{j}) for i, j = 1 to 3. Then again noting that δ_{2} = δ_{1} + δ_{3}, we have Cov(S, T) = δ_{1}^{2}κ_{11} + δ_{3}^{2}κ_{33} + (δ_{1}^{2} + δ_{3}^{2}  δ_{2}^{2})κ_{13} = (κ_{11} + κ_{13})δ_{1}^{2} + (κ_{33} + κ_{13})δ_{3}^{2}  κ_{13}δ_{2}^{2}. Therefore, assuming the denominator p*q* is fixed, F is a linear function of the δ_{i}^{2}/p*q*, whose coefficients can be estimated by linear regression. In this case, the coefficients a_{i} of δ_{i}^{2}/p*q* are given by a_{1} = κ_{11} + κ_{13}, a_{3} = κ_{33} + κ_{13} and a_{2} = κ_{13}. Then note that a_{1} + a_{2} = κ_{11}, a_{2} + a_{3} = κ_{33}, and a_{1} + a_{3} = κ_{11} + κ_{33} + 2κ_{13} = Cov (X_{1} + X_{3}, Y_{1} + Y_{3}) = Cov(1  X_{2},1  Y_{2}) = Cov(X_{2}, Y_{2}) = κ_{22}. The same linear model and regression coefficients apply to both F_{1} and F_{2}, as defined above.
Finally, we consider regression analysis on the LD statistic D. In this case, we examine the cooccurrence of alleles at two loci. Thus, consider loci B_{1} and B_{2}, with alleles B_{1}, b_{1} at locus B_{1} and B_{2}, b_{2} at locus B_{2}. Define the random variable S corresponding to locus B_{1} so that S = 1 if allele B_{1} occurs, and 0 if allele b_{1}. Define the random variable U similarly for locus B_{2}, so that U = 1 if allele B_{2} occurs, and 0 if b_{2}. The LD parameter D is defined as Cov(S, U), and χ^{2} = N [Corr(S, U)]^{2} where N is the number of individuals and Corr is correlation. Also, Corr(S, U) = Cov(S, U)/[Var(S)Var(U)]^{1/2}, Var(S) = p*q*, Var(U) = r*s* where p* is the frequency of B_{1}, q* = 1  p*, r* is the frequency of B_{2} and s* = 1  r*. Therefore, χ^{2} = ND^{2}/p*q*r*s. For a given individual, assume her(his) three ancestry proportions are represented by the random variables X_{i}, where i ranges from 1 to 3. Assume the allele frequency of B_{1} in the three ancestral populations is represented by π_{i}, for i = 1,3; similarly, the allele frequency of B_{2} in the three ancestral populations is represented by τ_{i}, for i = 1,3. As before, let δ_{1} = π_{1}  π_{2}, δ_{2} = π_{1}  π_{3}, and δ_{3} = π_{2}  π_{3}. By analogy, we define the ancestral allele frequency differences for the B_{2} locus by φ_{1} = τ_{1}  τ_{2}, φ_{2} = τ_{1}  τ_{3}, and φ_{3} = τ_{2}  τ_{3}. Given the proportions X_{i}, D = Cov(S, U) = Cov(π_{1}X_{1} + π_{2}X_{2} + π_{3}X_{3}, τ_{1}X_{1} + τ_{2}X_{2} + τ_{3}X_{3}). As before, subtracting the constant π_{2} from the first term and τ_{2} from the second term, respectively, gives D = Cov((π_{1}  π_{2})X_{1} + (π_{3}  π_{2})X_{3}, (τ_{1}  τ_{2})X_{1} + (τ_{3}  τ_{2})X_{3}) = Cov(δ_{1}X_{1}  δ_{3}X_{3}, φ_{1}X_{1}  φ_{3}X_{3}) = δ_{1}φ_{1}Var(X_{1}) + δ_{3}φ_{3}Var(X_{3}) + (δ_{1}φ_{3} + δ_{3}φ_{1})Cov(X_{1}, X_{3}). Because Var(X_{2}) = Var(1  X_{2}) = Var(X_{1} + X_{3}) = Var(X_{1}) + Var(X_{3}) + 2Cov(X_{1}, X_{3}), and δ_{1}φ_{3} + δ_{3}φ_{1} = δ_{2}φ_{2}  δ_{1}φ_{1}  δ_{3}φ_{3}, D = δ_{1}φ_{1}Var(X_{1}) + δ_{3}φ_{3}Var(X_{3}) + (δ_{2}φ_{2}  δ_{1}φ_{1}  δ_{3}φ_{3})(Var(X_{2})  Var(X_{1})  Var(X_{3}))/2 = δ_{1}φ_{1}(Var(X_{1}) + Var(X_{2})  Var(X_{3}))/2 + δ_{3}φ_{3}(Var(X_{3}) + Var(X_{2})  Var(X_{1}))/2 + δ_{2}φ_{2}(Var(X_{1}) + Var(X_{3})  Var(X_{2}))/2. In this case, D is a linear function of the δ_{i}φ_{i} for i = 1,3; by linear regression, the coefficients of these terms can be estimated, and are notated as a_{i} for i = 1,3. As previously, the regression coefficients can be related to the variances in ancestry by the equations: a1 + a2 = Var(X_{2}); a1 + a3 = Var(X_{1}); and a2 + a3 = Var(X_{3}).
Decrease of ancestry variance over time
In theory, the variation in ancestry should decrease from one generation to the next due to recombination between loci. However, the rate of decline will be diminished when there is assortative mating in ancestry. In fact, there is a direct quantitative relationship between the strength of LD between loci, the ancestry variance, and the degree of assortative mating for ancestry over time [26]. Specifically, let c_{t} denote the spouse ancestry correlation in generation t, V_{t} denote the variance in ancestry at generation t, and r_{t} denote the correlation of alleles selected at random at two unlinked loci at generation t (equivalent to the LD parameter r). Let the average ancestry in the population be represented by α, which we assume to be unchanged over time. Note that α(1  α) represents the variance of ancestry in the generation before admixing first occurred. Then, as shown by Crow and Kimura [26], V_{t} = α(1  α)r_{t}/(2  c_{t}) and r_{t+1} = [r_{t}  1/2_{t1}(r_{t}  r_{t1})]/(2  c_{t1}). Notice from this formula that when the spouse correlation c is 0, the variance declines by a factor of 1/2 per generation, whereas when c is 1, there is no decline in variance. We iterated the formulas above over 15 generations using 3 different models for the ancestry correlation c: a model where c is constant, a model where c declines linearly over time, and a model where c decreases exponentially over time.
Additional data files
Abbreviations
 AIM:

ancestry informative marker
 Corr:

correlation
 Cov:

covariance
 Exp:

expectation
 GALA:

Genetics of Asthma in Latino Americans
 IA:

individual ancestry
 LD:

linkage disequilibrium
 QQ:

quantilequantile
 SES:

socioeconomic status
 SNP:

single nucleotide polymorphism
 Var:

variance.
Declarations
Acknowledgements
The authors would like to acknowledge the families and the patients for their participation and the numerous health care providers and community clinics for their support and participation in the GALA Study. We would like to especially thank Jeffrey M Drazen, MD, Scott Weiss, MD, Ed Silverman, MD, PhD, Homer A Boushey, MD, Jean G Ford, MD and Dean Sheppard, MD for all of their effort towards the creation of the GALA Study. We are also indebted to Dr Mark Shriver for providing ancestral allele frequency data. This work was supported by National Institutes of Health (HL078885, HL088133, U19 AI077439, ES015794), Flight Attendant Medical Research Institute (FAMRI), and the RWJ Amos Medical Faculty Development Award to EGB, American Thoracic Society 'Breakthrough Opportunities in Lung Disease' (BOLD) Award and TobaccoRelated Disease Research Program New Investigator Award (15KT0008) to SC, Beatriu de Pinos Postdoctoral Grant (2006 BPA 10144) to MV, the Ernest S Bazley Grant to PCA, and the Sandler Center for Basic Research in Asthma and the Sandler Family Supporting Foundation.
Authors’ Affiliations
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