Letter to the Editor

Response to the Letter "Gametic and Zygotic Associations" by Rong-Cai Yang

Corresponding author: Chiara Sabatti, University of California, 695 Charles E. Young Dr., Los Angeles, CA 90095-7088., csabatti{at}mednet.ucla.edu (E-mail)

WE thank R.-C. YANG 2003 (this issue) for drawing attention to the connection between our work on homozygosity and linkage disequilibrium (LD; SABATTI and RISCH 2002 ) and his work on zygotic associations (YANG 2000 ). As he clearly points out in his letter (YANG 2003 ), our analyses were based on the assumption that zygotes result from the random union of gametes, while he has analyzed more general situations that include a series of nongametic disequilibria. It is useful to note that Equation 3 in our article and the generalization of it to multiallelic systems already reported in OHTA 1980 can be obtained as a special case of Yang's more general framework.

The second part of Yang's letter aims to point out possible difficulties in deriving certain LD statistics from zygotic observations in both the absence and the presence of other genic disequilibria. We limit our discussion to the first case, which is the one we analyzed. Yang proposes to derive a measure of linkage disequilibrium from Equation 3, solving for a value of D, given the observed homozygosity association . This is a substantially different procedure from the one we suggested. The role of Equation 3 in our work was to illustrate the presence of a relationship between homozygosity and D and, at the same time, the fact that this is a complex one. We did not suggest solving (3) to obtain a value of D. Although such an approach may possibly be of interest for the case of two biallelic markers, the homozygosity measure we proposed aims to deal with the more general situation of two or more multiallelic loci. Furthermore, it is clear—and Yang's numerical examples show it eloquently—that it is not possible to reconstruct the correct value of D from zygotic data without indeterminacy, even for the simple case of a 2 x 2 table. In addition, D itself is rarely, if ever, used as a measure of LD because it is unstandardized. Our suggestion was to use itself, appropriately standardized as a measure of linkage disequilibrium. Our article goes into some length to describe the limitations of such measures and the specific interpretation that is appropriate for it.

We also have a few additional comments to add regarding random mating (Hardy-Weinberg) assumptions and LD measures, the primary concern of Yang's letter. In a typical study of diploids, haplotype data are not directly observed. The homozygosity statistic we described requires no haploid data. While the expectation of the homozygosity LD statistic was based on a Hardy-Weinberg assumption, the same would also be true of other haplotype-based measures (such as D', r², and others) since haplotype frequency estimates (usually obtained by maximum likelihood) on which such measures are based inevitably invoke a Hardy-Weinberg assumption in modeling the frequency of haplotype combinations.

The roles of random mating and Hardy-Weinberg in LD analysis depend on the particular application. Two applications cited by Yang are LD analysis of candidate gene-disease association studies and estimation of genetic distances between loci in humans (ARDLIE et al. 2002 ). The primary concern in disease-gene association studies is nonrandom mating due to population structure, with latent population subgroups with limited intermating. Most such studies will stratify on major groupings such as race, but still leave the potential for substructure within a racial group. However, because Hardy-Weinberg is achieved in a single generation of random mating and deviations from Hardy-Weinberg expectations require significant structure as manifested by limited intermating and large allele-frequency differences between subgroups, significant deviations from Hardy-Weinberg expectations are rarely observed within racial/ethnic groups in practice and, when observed, are typically attributable to genotyping artifact (DEVLIN et al. 1990 ). Because of this, tests of Hardy-Weinberg are typically viewed as having very poor power to detect population substructure (LEWONTIN and HARTL 1991 ).

By contrast, linkage disequilibrium, especially between alleles at linked loci, can persist over many generations, even under random mating circumstances. This would especially be the case in a population with relatively recent admixture (for example, U.S. Hispanics), even if currently viewed as relatively "homogeneous."

Thus, for studies of LD in human populations, the primary focus of our previous discussion (SABATTI and RISCH 2002 ), deviations from Hardy-Weinberg are unlikely to confound either the zygotic statistics we described or other linkage disequilibrium statistics provided such studies at least stratify on major racial/ethnic subgroupings. Indeed, to confirm lack of bias due to Hardy-Weinberg deviations, the individual loci can also first be subjected to Hardy-Weinberg tests.

LITERATURE CITED

ARDLIE, K. G., L. KRUGLYAK, and M. SEIELSTAD, 2002  Patterns of linkage disequilibrium in the human genome. Nat. Rev. Genet. 3:299-309.[Medline]

DEVLIN, B., N. RISCH, and K. ROEDER, 1990  No excess of homozygosity at loci used for DNA fingerprinting. Science 249:1416-1420.[Abstract/Free Full Text]

LEWONTIN, R. C. and D. HARTL, 1991  Population genetics in forensic DNA typing. Science 254:1745-1750.[Abstract/Free Full Text]

OHTA, T., 1980  Linkage disequilibrium between amino acid sites in immunoglobulin genes and other multigene families. Genet. Res. 36:181-197.[Medline]

SABATTI, C. and N. RISCH, 2002  Homozygosity and linkage disequilibrium. Genetics 160:1707-1719.[Abstract/Free Full Text]

YANG, R.-C., 2000  Zygotic associations and multilocus statistics in a nonequilibrium diploid population. Genetics 155:1449-1458.[Abstract/Free Full Text]

YANG, R.-C., 2003  Gametic and zygotic associations. Genetics 165:447-450.[Free Full Text]