Supplementary Discussion on Hardy-Weinberg Disequilibrium (HWD)
A female-associated allele of a SNP should be present at a higher rate in females than the general population (a natural selection), which may violate Hardy-Weinberg Equilibrium (HWE) of that SNP in females. Thus, Hardy-Weinberg Disequilibrium (HWD) of a SNP in females could be an indicator of allele-female association. Only when the marker is not associated with sex or has no LD with any sex-specific locus, i.e., the genotype frequency distributions of the marker are independent of sex, can the female group and the male group have the same genotype frequency distributions, with both in HWE. Therefore, the HWD in females in the present study suggests an association between alleles and females. Usually, female-specific loci are in HWD in females, but in HWE in males, as observed in our study. This is because a much greater sample size is needed to detect HWD of a female-specific locus in males. (Luo et al. 2008)
The HWD also reflected a recessive genetic inheritance model in females, because the HWD statistics (Δ, F and J) (Feder et al. 1996; Jiang et al. 2001; Wittke-Thompson et al. 2005) were positive (data not shown). Using the model-fitting method implemented in the Mathematica Notebooks written by Wittke-Thompson et al. (Wittke-Thompson et al. 2005) (2005), we also identified the genetic models for these female-associated loci with the best fit to a recessive model (data not shown). This model-fitting method can also tell us that other explanations for the observed HWD, including chance, genotyping errors, and/or violations of the requisite assumptions of HWE, are unlikely, when one “best-fit” model can be identified (Wittke-Thompson et al. 2005).
The following analyses further support the interpretation that other factors underlying HWD are unlikely to be important in explaining our data. We note, though, that it might take a very large sample to fully support this conclusion. Signal intensity, background noise, and clustering properties all play a role in the ability to assign genotypes correctly, and in determining the types of errors that occur (Leal 2005). Genotyping error is one of the greatest concerns for causing spurious HWD observation. First, if genotyping errors caused HWD in females, HWE would be impossibly remained in males, because females and males were genotyped on the same platforms at the same time. Second, DNA contamination can result in the lack of one homozygote, which leads to a deficiency of observed homozygotes (Leal 2005). This runs counter to our data and thus is not a possible explanation for the present study. Third, Cohort #13 was a family cohort. We assessed the family data for Mendelian consistencies by the program PEDCHECK(O'Connell and Weeks 1998), with no non-Mendelian inconsistencies detected, which suggested genotyping errors in this cohort were unlikely. Fourth, missing genotype data rate was not significantly different between females and males (data not shown). Together, the evidence suggests that genotyping error as an explanation for the observed HWD is impossible. (Luo et al. 2008)
Besides selection of alleles by sex, violation of one of the other HWE assumptions can also cause HWD. First, genetic drift can cause HWD. Genetic drift is the effect of finite population size (Hedrick 1983), such that the smaller the population, the more noticeable the effects of drift. Actually, all populations are finite and all genetic variation is subject to genetic drift at varying degree. In a finite population, allele frequencies fluctuate by chance randomly and the fluctuation leads to deviations from HWE (in this context, this is “sampling error”) (Barton and Turelli 2004). If a population is small enough, the effects of drift may overwhelm the other forces described below, even selection. In our male samples, which are smaller than females, HWE was not violated, which supports the interpretation that HWD in females is not due to a sample size issue. Second, inbreeding can cause HWD. Inbreeding is a type of positive assortative mating which is non-random. However, we have no evidence for inbreeding in the present study. Third, gene flow may result in HWD. Gene flow is the result of migration. Immigrants carrying new alleles into the population may change the genotype frequency distribution of that population with resulting HWD in that generation. However, we do not have evidence of larger immigration for females than males in our cohorts, so gene flow resulting in HWD in females is unlikely. Fourth, mutation may increase the genetic variability due to genetic drift and might cause HWD. But because change in allele frequencies induced by mutation is so small from one generation to the next, we can safely ignore mutation as a factor in HWD. In conclusion, violation of one of the above HWE assumptions causing HWD is unlikely. (Luo et al. 2008)
In addition to the factors that have been discussed, other factors can also cause HWD. For example, population stratification and admixture can cause HWD. However, the females and males were compared within the same cohorts that had the same ethnicity, and the males were in HWE, excluding the possibility that HWD in females resulted from an effect of admixture. Additionally, nonrandom patterns of missing data may also generate a relatively consistent pattern of HWD (e.g., disproportionate missing data in heterozygotes may lead to a consistent pattern of HWD, with an excess of homozygotes). This possibility is common and inevitable. However, our females and males for comparisons in the same cohorts were genotyped using same genotyping systems and their genotyping missing rates were similar (data not shown), reducing the possibility that non-random patterns of missing data cause HWD only in females but not in males. Further, if the females or males are old enough, the marker can be in HWD because a specific mortality-related allele drops out due to death associated with advancing age (Weinberg and Morris 2003). However, the ages of our subjects ranged from 17 to 80 years and the age structures were similar between both sexes, making this explanation unlikely. (Luo et al. 2008)
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