Accurate inference of relationships in sib-pair linkage studies.

Relative-pair designs are routinely employed in linkage studies of complex genetic diseases and quantitative traits. Valid application of these methods requires correct specification of the relationships of the pairs. For example, within a sibship, presumed full sibs actually might be MZ twins, half sibs, or unrelated. Misclassification of half-sib pairs or unrelated individuals as full sibs can result in reduced power to detect linkage. When other family members, such as parents or additional siblings, are available, incorrectly specified relationships usually will be detected through apparent incompatibilities with Mendelian inheritance. Without other family members, sibling relationships cannot be determined absolutely, but they still can be inferred probabilistically if sufficient genetic marker data are available. In this paper, we describe a simple likelihood ratio method to infer the true relationship of a putative sibling pair. We explore the number of markers required to accurately infer relationships typically encountered in a sib-pair study, as a function of marker allele frequencies, marker spacing, and genotyping error rate, and we conclude that very accurate inference of relationships can be achieved, given the marker data from even part of a genome scan. We compare our method to related methods of relationship inference that have been suggested. Finally, we demonstrate the value of excluding non-full sibs in a genetic linkage study of non-insulin-dependent diabetes mellitus.     

Identification of Mendelian inconsistencies between SNP and pedigree information of sibs

Background

Using SNP genotypes to apply genomic selection in breeding programs is becoming common practice. Tools to edit and check the quality of genotype data are required. Checking for Mendelian inconsistencies makes it possible to identify animals for which pedigree information and genotype information are not in agreement.

Methods

Straightforward tests to detect Mendelian inconsistencies exist that count the number of opposing homozygous marker (e.g. SNP) genotypes between parent and offspring (PAR-OFF). Here, we develop two tests to identify Mendelian inconsistencies between sibs. The first test counts SNP with opposing homozygous genotypes between sib pairs (SIBCOUNT). The second test compares pedigree and SNP-based relationships (SIBREL). All tests iteratively remove animals based on decreasing numbers of inconsistent parents and offspring or sibs. The PAR-OFF test, followed by either SIB test, was applied to a dataset comprising 2,078 genotyped cows and 211 genotyped sires. Theoretical expectations for distributions of test statistics of all three tests were calculated and compared to empirically derived values. Type I and II error rates were calculated after applying the tests to the edited data, while Mendelian inconsistencies were introduced by permuting pedigree against genotype data for various proportions of animals.

Results

Both SIB tests identified animal pairs for which pedigree and genomic relationships could be considered as inconsistent by visual inspection of a scatter plot of pairwise pedigree and SNP-based relationships. After removal of 235 animals with the PAR-OFF test, SIBCOUNT (SIBREL) identified 18 (22) additional inconsistent animals.Seventeen animals were identified by both methods. The numbers of incorrectly deleted animals (Type I error), were equally low for both methods, while the numbers of incorrectly non-deleted animals (Type II error), were considerably higher for SIBREL compared to SIBCOUNT.

Conclusions

Tests to remove Mendelian inconsistencies between sibs should be preceded by a test for parent-offspring inconsistencies. This parent-offspring test should not only consider parent-offspring pairs based on pedigree data, but also those based on SNP information. Both SIB tests could identify pairs of sibs with Mendelian inconsistencies. Based on type I and II error rates, counting opposing homozygotes between sibs (SIBCOUNT) appears slightly more precise than comparing genomic and pedigree relationships (SIBREL) to detect Mendelian inconsistencies between sibs.     

A test statistic to detect errors in sib-pair relationships.

Several authors have proposed algorithms to detect Mendelian errors in human genetic linkage data. Most currently available methods use likelihood-based methods on multiplex family data to identify typing or pedigree errors. These algorithms cannot be applied in many sib-pair collections, because of lack of parental-genotype information. Nonetheless, misspecifying the relationships between individuals has serious consequences for sib-pair linkage studies: false relationships bias the statistics designed to identify linkage with disease phenotypes. To test the hypothesis that two individuals are sibs, we propose a test statistic based on the summation, over a large number of genetic markers, of the number of alleles shared identical by state by a pair of individuals, for each marker. The test statistic has an approximately normal distribution under the null hypothesis, and extreme negative values correspond to nonsib pairs. Power and significance studies show that the test statistic calculated by use of 50 unlinked markers has 96% power to detect half-sibs and has 100% power to detect unrelated individuals as not full-sib pairs, with a 5% false-positive rate. Furthermore, extreme positive values of the test statistic identify sibs as MZ twins.     

The mechanism of emergenesis

Since each individual produced by the sexual process contains a unique set of genes, very exceptional combinations of genes are unlikely to appear twice even within the same family. E. O. Wilson (1978)The intraclass correlations of monozygotic twins who were separated in infancy and reared apart (MZA twins) provide estimates of trait heritability, and the Minnesota Study of Twins Reared Apart [MISTRA: Bouchard et al. (1990), The sources of human psychological differences: the Minnesota study of twins reared apart, Science 250, 223-228] has demonstrated that MZA pairs are as similar in most respects as MZ pairs reared together. Some polygenic traits--e.g. stature, IQ, harm avoidance, negative emotionality, interest in sports--are polygenic-additive, so pairs of relatives resemble one another on the given trait in proportion to their genetic similarity. But the existence and the intensity of other important psychological traits seem to be emergent properties of gene configurations (or configurations of independent and partially genetic traits) that interact multiplicatively rather than additively. Monozygotic (MZ) twins may be strongly correlated on such emergenic traits, while the similarity of dizygotic (DZ) twins, sibs or parent-offspring pairs may be much less than half that of MZ pairs. Some emergenic traits, although strongly genetic, do not appear to run in families. MISTRA has provided at least two examples of traits for which MZA twins are strongly correlated, and DZA pairs correlate near zero, while DZ pairs reared together (DZTs) are about half as similar as MZTs. These findings suggest that even more traits may be emergenic than those already identified. Studies of adoptees reared together (who are perhaps more common than twins reared apart) may help to identify traits that are emergenic, but that also are influenced by a common rearing environment.     

Familial correlations of variables from the craniofacial complex in a Venezuelan isolate of African origin

Familial aggregation for 33 different variables from the craniofacial complex was estimated through intraclass correlation coefficients for four different relationships: parent-offspring paris, sibs, cousins and unrelated pairs. The population chosen for the study was La Sabana, D.F., a Venezuelan isolate of Negroid origin. The general tendency observed among the different correlations was as anticipated: sibs show higher correlations than cousins and these were higher than for unrelated pairs. Parent-offspring correlations were lower than expected. The significant correlations observed among sibs for 17 of the variables indicate aggregation due to genetic and/or common environmental factors. On the other hand, little genetic determination was detected for sella-C point distance or for upper dental arch depth both of which show intraclass sib correlations ≤0.1.     

Genetic relationships of grizzly bears (Ursus arctos) in the Prudhoe Bay region of Alaska: inference from microsatellite DNA, mitochondrial DNA, and field observations

Grizzly bears are abundant in the region of the Prudhoe Bay oil fields in northern Alaska. We used field observations and molecular genetic data to identify parent-offspring and sibling relationships among bears in this region. We determined genotypes at 14 microsatellite DNA loci and the cytochrome b gene of mitochondrial DNA (mtDNA) for 36 bears. We identified 17 possible mother-offspring pairs and 8 possible father-offspring pairs. This includes verification of the relationships of 14 mother-offspring pairs identified from field observations. Three additional mother-offspring pairs and all eight father-offspring pairs were determined from genetic and age data. Relatedness coefficients based on numbers of shared alleles between individuals were as expected: approximately 0.50 for parent-offspring and sibling pairs and approximately 0.75 for a father-offspring pair resulting from a father-daughter mating. The level of genetic variation (mean number of alleles per locus = 6.6, mean heterozygosity = 70%) and allele frequencies in grizzly bears in the Prudhoe Bay region are similar to those in other parts of the species' range.     

Parentage in natural populations: novel methods to detect parent-offspring pairs in large data sets

Parentage analysis in natural populations presents a valuable yet unique challenge because of large numbers of pairwise comparisons, marker set limitations and few sampled true parent-offspring pairs. These limitations can result in the incorrect assignment of false parent-offspring pairs that share alleles across multi-locus genotypes by chance alone. I first define a probability, Pr(δ), to estimate the expected number of false parent-offspring pairs within a data set. This probability can be used to determine whether one can accept all putative parent-offspring pairs with strict exclusion. I next define the probability Pr(φ|λ), which employs Bayes' theorem to determine the probability of a putative parent-offspring pair being false given the frequencies of shared alleles. This probability can be used to separate true parent-offspring pairs from false pairs that occur by chance when a data set lacks sufficient numbers of loci to accept all putative parent-offspring pairs. Finally, I propose a method to quantitatively determine how many loci to let mismatch for study-specific error rates and demonstrate that few data sets should need to allow more than two loci to mismatch. I test all theoretical predictions with simulated data and find that, first, Pr(δ) and Pr(φ|λ) have very low bias, and second, that power increases with lower sample sizes, uniform allele frequency distributions, and higher numbers of loci and alleles per locus. Comparisons of Pr(φ|λ) to strict exclusion and CERVUS demonstrate that this method may be most appropriate for large natural populations when supplemental data (e.g. genealogies, candidate parents) are absent.     

The probability of dizygosity of phenotypically concordant twins.

A basic element in the determination of the zygosity of a twin pair is the proportion of genotypically concordant pairs among the dizygotic pairs. Two methods to derive this proportion are in common use: the first method requires a laborious enumeration of parental genotypic mating types, and the second method relies on a set of formulas, one for each of the possible combinations of genotypes of two full sibs. In this paper the relation between both methods is uncovered. The set of formulas of the second method is reduced to a single general formula, of which the connection with the ITO method (Li and Sacks 1954) is indicated. By applying both methods in turn to an example concerning the MNS blood group system (Fisher 1951), Fisher's way of performing the calculations according to the first method is unraveled, and the preferability of the second method is made clear. Next, formulas are derived for the probability of genotypic or phenotypic concordance of dizygotic twins when direct information on the genotype or phenotype of one of the parents is available. The case of an X-linked locus is also considered. To facilitate applications, tables are given.     

Estimation of genotyping error rate from repeat genotyping,unintentional recaptures and known parent–offspring comparisons in 16 microsatellite loci for brown rockfish (Sebastes auriculatus)

Genotyping errors are present in almost all genetic data and can affect biological conclusions of a study, particularly for studies based on individual identification and parentage. Many statistical approaches can incorporate genotyping errors, but usually need accurate estimates of error rates. Here, we used a new microsatellite data set developed for brown rockfish (Sebastes auriculatus) to estimate genotyping error using three approaches: (i) repeat genotyping 5% of samples, (ii) comparing unintentionally recaptured individuals and (iii) Mendelian inheritance error checking for known parent–offspring pairs. In each data set, we quantified genotyping error rate per allele due to allele drop‐out and false alleles. Genotyping error rate per locus revealed an average overall genotyping error rate by direct count of 0.3%, 1.5% and 1.7% (0.002, 0.007 and 0.008 per allele error rate) from replicate genotypes, known parent–offspring pairs and unintentionally recaptured individuals, respectively. By direct‐count error estimates, the recapture and known parent–offspring data sets revealed an error rate four times greater than estimated using repeat genotypes. There was no evidence of correlation between error rates and locus variability for all three data sets, and errors appeared to occur randomly over loci in the repeat genotypes, but not in recaptures and parent–offspring comparisons. Furthermore, there was no correlation in locus‐specific error rates between any two of the three data sets. Our data suggest that repeat genotyping may underestimate true error rates and may not estimate locus‐specific error rates accurately. We therefore suggest using methods for error estimation that correspond to the overall aim of the study (e.g. known parent–offspring comparisons in parentage studies).     

Use of microsatellite loci to classify individuals by relatedness

This study investigates the use of microsatellite loci for estimating relatedness between individuals in wild, outbred, vertebrate populations. We measured allele frequencies at 20 unlinked, dinucleotide-repeat microsatellite loci in a population of wild mice ( Mus musculus ), and used these observed frequencies to generate the expected distributions of pairwise relatedness among full sib, half sib, and unrelated pairs of individuals, as would be estimated from the microsatellite data. In this population one should be able to discriminate between unrelated and full-sib dyads with at least 97% accuracy, and to discriminate half-sib pairs from unrelated pairs or from full-sib pairs with better than 80% accuracy. If one uses the criterion that parent-offspring pairs must share at least one allele per locus, then only 15% of full-sib pairs, 2% of half-sib pairs, and 0% of unrelated pairs in this population would qualify as potential parent-offspring pairs. We verified that the simulation results (which assume a random mating population in Hardy-Weinberg and linkage equilibrium) accurately predict results one would obtain from this population in real life by scoring laboratory-bred full- and half-sib families whose parents were wild-caught mice from the study population. We also investigated the effects of using different numbers of loci, or loci of different average heterozygosities ( He ), on misclassification frequencies. Both variables have strong effects on misclassification rate. For example, it requires almost twice as many loci of He = 0.62 to achieve the same accuracy as a given number of loci of He = 0.75. Finally, we tested the ability of UPGMA clustering to identify family groups in our population. Clustering of allele matching scores among the offspring of four sets of independent maternal half sibships (four females, each mated to two different males) perfectly recovered the true family relationships.     

A linkage strategy for detection of human quantitative-trait loci. I. Generalized relative risk ratios and power of sib pairs with extreme trait values.

We generalize the concept of the relative risk ratio (lambda) to the case of quantitative traits, to take into account the various trait outcomes of a relative pair. Formulas are derived to express the expected proportions of genes shared identical by descent by a sib pair, in terms of the generalized lambda's for sib pairs (lambda S), parent-offspring pairs (lambda O), and monozygotic twins (lambda M) and in terms of the recombination fraction, with the assumption of no residual correlations. If residual correlations are nonzero among relative pairs, we assume that they are the same among sib pairs, parent-offspring pairs, and monozygotic twins, and we employ a slightly different definition for the generalized lambda so that the same set of formulas still hold. The power (or, the sample size necessary) to detect quantitative-trait loci (QTLs) by use of extreme sib pairs (ESPs) is shown to be a function of the three generalized lambda's. Since lambda M can be derived by use of values of lambda S and lambda O, estimates of the latter two lambda's will suffice for the analysis of power and the necessary sample sizes of ESPs, for a QTL linkage study.     

Identity-by-descent genomic selection using selective and sparse genotyping

Background

Genomic selection methods require dense and widespread genotyping data, posing a particular challenge if both sexes are subject to intense selection (e.g., aquaculture species). This study focuses on alternative low-cost genomic selection methods (IBD-GS) that use selective genotyping with sparse marker panels to estimate identity-by-descent relationships through linkage analysis. Our aim was to evaluate the potential of these methods in selection programs for continuous traits measured on sibs of selection candidates in a typical aquaculture breeding population.

Methods

Phenotypic and genomic data were generated by stochastic simulation, assuming low to moderate heritabilities (0.10 to 0.30) for a Gaussian trait measured on sibs of the selection candidates in a typical aquaculture breeding population that consisted of 100 families (100 training animals and 20 selection candidates per family). Low-density marker genotype data (~ 40 markers per Morgan) were used to trace genomic identity-by-descent relationships. Genotyping was restricted to selection candidates from 30 phenotypically top-ranking families and varying fractions of their phenotypically extreme training sibs. All phenotypes were included in the genetic analyses. Classical pedigree-based and IBD-GS models were compared based on realized genetic gain over one generation of selection.

Results

Genetic gain increased substantially (13 to 32%) with IBD-GS compared to classical selection and was greatest with higher heritability. Most of the extra gain from IBD-GS was obtained already by genotyping the 5% phenotypically most extreme sibs within the pre-selected families. Additional genotyping further increased genetic gains, but these were small when going from genotyping 20% of the extremes to all phenotyped sibs. The success of IBD-GS with sparse and selective genotyping can be explained by the fact that within-family haplotype blocks are accurately traced even with low-marker densities and that most of the within-family variance for normally distributed traits is captured by a small proportion of the phenotypically extreme sibs.

Conclusions

IBD-GS was substantially more effective than classical selection, even when based on very few markers and combined with selective genotyping of small fractions of the population. The study shows that low-cost GS programs can be successful by combining sparse and selective genotyping with pedigree and linkage information.     

Enhanced pedigree error detection

Accurate information on the relationships among individuals in a study is critical for valid linkage analysis. We extend the MLLR, EIBD, AIBS and IBS tests for detection of misspecified relationships to a broader range of relative pairs, and we improve the two-stage screening procedure for analyzing large data sets. We have developed software, PREST, which calculates the test statistics and performs the corresponding hypothesis tests for relationship misclassification in general outbred pedigrees. When a potential pedigree error is detected, our companion program, ALTERTEST, can be used to determine which relationships are compatible with the genotype data. Both programs are now freely available on the web.     

Selection and subsequent analysis of sib pair data for QTL detection.

Haseman and Elston (1972) developed a robust regression method for the detection of linkage between a marker and a quantitative trait locus (QTL) using sib pair data. The principle underlying this method is that the difference in phenotypes between pairs of sibs becomes larger as they share a decreasing number of alleles at a particular QTL identical by descent (IBD) from their parents. In this case, phenotypically very different sibs will also on average share a proportion of alleles IBD at any marker linked to the QTL that is lower than the expected value of 0.5. Thus, the deviation of the proportion of marker alleles IBD from the expected value in pairs of sibs selected to be phenotypically different (i.e. discordant) can provide a test for the presence of a QTL. A simple regression method for QTL detection in sib pairs selected for high phenotypic differences is presented here. The power of the analytical method was found to be greater than the power obtained using the standard analysis when samples of sib pairs with high phenotypic differences were used. However, the use of discordant sib pairs was found to be less powerful for QTL detection than alternative selective genotyping schemes based on the phenotypic values of the sibs except with intense selection, when its advantage was only marginal. The most effective selection scheme overall was the use of sib pairs from entire families selected on the basis of high within-family variance for the trait in question. There is little effect of selection on QTL position estimates, which are in good agreement with the simulated values. However, QTL variance estimates are biased to a greater or lesser degree, depending on the selection method.     

Excess of twins among affected sibling pairs with autism: implications for the etiology of autism

It is widely accepted that genes play a role in the etiology of autism. Evidence for this derives, in part, from twin data. However, despite converging evidence from gene-mapping studies, aspects of the genetic contribution remain obscure. In a sample of families selected because each had exactly two affected sibs, we observed a remarkably high proportion of affected twin pairs, both MZ and DZ. Of 166 affected sib pairs, 30 (12 MZ, 17 DZ, and 1 of unknown zygosity) were twin pairs. Deviation from expected values was statistically significant (P<10(-6) for all twins); in a similarly ascertained sample of individuals with type I diabetes, there was no deviation from expected values. We demonstrate that to ascribe the excess of twins with autism solely to ascertainment bias would require very large ascertainment factors; for example, affected twin pairs would need to be, on average, approximately 10 times more likely to be ascertained than affected non-twin sib pairs (or 7 times more likely if "stoppage" plays a role). Either risk factors (related to twinning or to fetal development) or other factors (genetic or nongenetic) in the parents may contribute to autism.     

Zygosity diagnosis in the absence of genotypic data: an approach using latent class analysis.

For zygosity diagnosis in the absence of genotypic data, or in the recruitment phase of a twin study where only single twins from same-sex pairs are being screened, or to provide a test for sample duplication leading to the false identification of a dizygotic pair as monozygotic, the appropriate analysis of respondents' answers to questions about zygosity is critical. Using data from a young adult Australian twin cohort (N = 2094 complete pairs and 519 singleton twins from same-sex pairs with complete responses to all zygosity items), we show that application of latent class analysis (LCA), fitting a 2-class model, yields results that show good concordance with traditional methods of zygosity diagnosis, but with certain important advantages. These include the ability, in many cases, to assign zygosity with specified probability on the basis of responses of a single informant (advantageous when one zygosity type is being oversampled); and the ability to quantify the probability of misassignment of zygosity, allowing prioritization of cases for genotyping as well as identification of cases of probable laboratory error. Out of 242 twins (from 121 like-sex pairs) where genotypic data were available for zygosity confirmation, only a single case was identified of incorrect zygosity assignment by the latent class algorithm. Zygosity assignment for that single case was identified by the LCA as uncertain (probability of being a monozygotic twin only 76%), and the co-twin's responses clearly identified the pair as dizygotic (probability of being dizygotic 100%). In the absence of genotypic data, or as a safeguard against sample duplication, application of LCA for zygosity assignment or confirmation is strongly recommended.     

Inference of kinship coefficients from Korean SNP genotyping data

The determination of relatedness between individuals in a family is crucial in analysis of common complex diseases. We present a method to infer close inter-familial relationships based on SNP genotyping data and provide the relationship coefficient of kinship in Korean families. We obtained blood samples from 43 Korean individuals in two families. SNP data was obtained using the Affymetrix Genome-wide Human SNP array 6.0 and the Illumina Human 1M-Duo chip. To measure the kinship coefficient with the SNP genotyping data, we considered all possible pairs of individuals in each family. The genetic distance between two individuals in a pair was determined using the allele sharing distance method. The results show that genetic distance is proportional to the kinship coefficient and that a close degree of kinship can be confirmed with SNP genotyping data. This study represents the first attempt to identify the genetic distance between very closely related individuals. [BMB Reports 2013; 46(6): 305-309]     

Studies of X inactivation and isodisomy in twins provide further evidence that the X chromosome is not involved in Rett syndrome.

Rett syndrome (RS), a progressive encephalopathy with onset in infancy, has been attributed to an X-linked mutation, mainly on the basis of its occurrence almost exclusively in females and its concordance in female MZ twins. The underlying mechanisms proposed are an X-linked dominant mutation with male lethality, uniparental disomy of the X chromosome, and/or some disturbance in the process of X inactivation leading to unequal distributions of cells expressing maternal or paternal alleles (referred to as a "nonrandom" or "skewed" pattern of X inactivation). To determine if the X chromosome is in fact involved in RS, we studied a group of affected females including three pairs of MZ twins, two concordant for RS and one uniquely discordant for RS. Analysis of X-inactivation patterns confirms the frequent nonrandom X inactivation previously observed in MZ twins but indicates that this is independent of RS. Analysis of 29 RS females reveals not one instance of uniparental X disomy, extending the observations previously reported. Therefore, our findings contribute no support for the hypothesis that RS is an X-linked disorder. Furthermore, the concordant phenotype in most MZ female twins with RS, which has not been observed in female twins with known X-linked mutations, argues against an X mutation.     

A low-marker density implementation of genomic selection in aquaculture using within-family genomic breeding values

Background

Genomic selection can increase genetic gain within aquaculture breeding programs, but the high costs related to high-density genotyping of a large number of individuals would make the breeding program expensive. In this study, a low-cost method using low-density genotyping of pre-selected candidates and their sibs was evaluated by stochastic simulation.

Methods

A breeding scheme with selection for two traits, one measured on candidates and one on sibs was simulated. Genomic breeding values were estimated within families and combined with conventional family breeding values for candidates that were pre-selected based on conventional BLUP breeding values. This strategy was compared with a conventional breeding scheme and a full genomic selection program for which genomic breeding values were estimated across the whole population. The effects of marker density, level of pre-selection and number of sibs tested and genotyped for the sib-trait were studied.

Results

Within-family genomic breeding values increased genetic gain by 15% and reduced rate of inbreeding by 15%. Genetic gain was robust to a reduction in marker density, with only moderate reductions, even for very low densities. Pre-selection of candidates down to approximately 10% of the candidates before genotyping also had minor effects on genetic gain, but depended somewhat on marker density. The number of test-individuals, i.e. individuals tested for the sib-trait, affected genetic gain, but the fraction of the test-individuals genotyped only affected the relative contribution of each trait to genetic gain.

Conclusions

A combination of genomic within-family breeding values, based on low-density genotyping, and conventional BLUP family breeding values was shown to be a possible low marker density implementation of genomic selection for species with large full-sib families for which the costs of genotyping must be kept low without compromising the effect of genomic selection on genetic gain.     

X inactivation as a source of behavioural differences in monozygotic female twins.

Although members of monozygotic twin pairs are identical in genome sequence, they may differ in patterns of gene expression. One early and irreversible process affecting gene expression, which can create differences within pairs of female monozygotic twins, is X inactivation - one twin can express mainly paternally-received genes on the X chromosome while the other twin expresses mainly maternally-received genes. It follows that non-identical X chromosome expression may cause female monozygotic twins to correlate less strongly than male monozygotic twins on complex behavioural traits affected by X-linked loci. We tested this hypothesis using data from around 4000 same-sex twin pairs on 9 social, behavioural and cognitive measures at ages 2, 3 and 4. Consistent with our hypothesis, monozygotic males were generally more similar than monozygotic females. Three of four significant differences were in traits showing higher correlations in males than females, and these traits - prosocial behaviour, peer problems, and verbal ability - have all been proposed previously in the literature as being influenced by genes on the X chromosome. Interestingly, dizygotic twins showed the reverse pattern of correlations for similar variables, which is also consistent with the X inactivation hypothesis; taken together, then, our monozygotic and dizygotic results suggest the presence of quantitative trait loci on the X chromosome.