N. E. Morton

The first linkage disequilibrium (LD) maps: Delineation of hot and cold blocks by diplotype analysis

Linkage disequilibrium (LD) provides information about positional cloning, linkage, and evolution that cannot be inferred from other evidence, even when a correct sequence and a linkage map based on more than a handful of families become available. We present theory to construct an LD map for which distances are additive and population-specific maps are expected to be approximately proportional. For this purpose, there is only a modest difference in relative efficiency of haplotypes and diplotypes: resolving the latter into 2-locus haplotypes has significant cost or error and increases information by about 50%. LD maps for a cold spot in 19p13.3 and a more typical region in 3q21 are optimized by interval estimates. For a random sample and trustworthy map the value of LD at large distance can be predicted reliably from information over a small distance and does not depend on the evolutionary variance unless the sample size approaches the population size. Values of the association probability that can be distinguished from the value at large distance are determined not by population size but by time since a critical bottleneck. In these examples, omission of markers with significant Hardy–Weinberg disequilibrium does not improve the map, and widely discrepant draft sequences have similar estimates of the genetic parameters. The LD cold spot in 19p13.3 gives an unusually high estimate of time, supporting an argument that this relationship is general. As predicted for a region with ancient haplotypes or uniformly high recombination, there is no clear evidence of LD clustering. On the contrary, the 3q21 region is resolved into alternating blocks of stable and decreasing LD, as expected from crossover clustering. Construction of a genomewide LD map requires data not yet available, which may be complemented but not replaced by a catalog of haplotypes.

Dominant genes for colorectal cancer are not rare

The genetic basis for colorectal cancer was investigated by complex segregation analysis of a published series of consecutive pedigrees ascertained through patients undergoing treatment for colorectal cancer. Analysis favoured a dominant gene or genes with a frequency of 0·006 with a lifetime penetrance of 0·63. These genes account for 81% of colorectal cancer in patients under 35, however, by 65 about 85% are phenocopies.

Hardy-Weinberg quality control.

An efficient test of deviation from Hardy–Weinberg frequencies with one degree of freedom was applied to 44 marker loci in a genome scan, and 7 loci had a significant excess of apparent homozygotes (χ2(1) > 6) suggestive of typing error. In this example evidence for linkage did not increase when outliers were censored. Statistical quality control is an essential part of genotyping, and the effect of mistyping and map error should be considered in evaluating any genome scan.

The optimal measure of allelic association

Allelic association between pairs of loci is derived in terms of the association probability ρ as a function of recombination θ, effective population size N, linear systematic pressure v, and time t, predicting both ρrt, the decrease of association from founders and ρct, the increase by genetic drift, with ρt = ρrt + ρct. These results conform to the Malecot equation, with time replaced by distance on the genetic map, or on the physical map if recombination in the region is uniform. Earlier evidence suggested that ρ is less sensitive to variations in marker allele frequencies than alternative metrics for which there is no probability theory. This robustness is confirmed for six alternatives in eight samples. In none of these 48 tests was the residual variance as small as for ρ. Overall, efficiency was less than 80% for all alternatives, and less than 30% for two of them. Efficiency of alternatives did not increase when information was estimated simultaneously. The swept radius within which substantial values of ρ are conserved lies between 385 and 893 kb, but deviation of parameters between measures is enormously significant. The large effort now being devoted to allelic association has little value unless the ρ metric with the strongest theoretical basis and least sensitivity to marker allele frequencies is used for mapping of marker association and localization of disease loci.

Positional Cloning by Linkage Disequilibrium

Recently, metric linkage disequilibrium (LD) maps that assign an LD unit (LDU) location for each marker have been developed (Maniatis et al. 2002). Here we present a multiple pairwise method for positional cloning by LD within a composite likelihood framework and investigate the operating characteristics of maps in physical units (kb) and LDU for two bodies of data (Daly et al. 2001; Jeffreys et al. 2001) on which current ideas of blocks are based. False-negative indications of a disease locus (type II error) were examined by selecting one single-nucleotide polymorphism (SNP) at a time as causal and taking its allelic count (0, 1, or 2, for the three genotypes) as a pseudophenotype, Y. By use of regression and correlation, association between every pseudophenotype and the allelic count of each SNP locus (X) was based on an adaptation of the Malecot model, which includes a parameter for location of the putative gene. By expressing locations in kb or LDU, greater power for localization was observed when the LDU map was fitted. The efficiency of the kb map, relative to the LDU map, to describe LD varied from a maximum of 0.87 to a minimum of 0.36, with a mean of 0.62. False-positive indications of a disease locus (type I error) were examined by simulating an unlinked causal SNP and the allele count was used as a pseudophenotype. The type I error was in good agreement with Walds likelihood theorem for both metrics and all models that were tested. Unlike tests that select only the most significant marker, haplotype, or haploset, these methods are robust to large numbers of markers in a candidate region. Contrary to predictions from tagging SNPs that retain haplotype diversity, the sample with smaller size but greater SNP density gave less error. The locations of causal SNPs were estimated with the same precision in blocks and steps, suggesting that block definition may be less useful than anticipated for mapping a causal SNP. These results provide a guide to efficient positional cloning by SNPs and a benchmark against which the power of positional cloning by haplotype-based alternatives may be measured.

Does haplotype diversity predict power for association mapping of disease susceptibility

Many recent studies have established that haplotype diversity in a small region may not be greatly diminished when the number of markers is reduced to a smaller set of “haplotype-tagging” single-nucleotide polymorphisms (SNPs) that identify the most common haplotypes. These studies are motivated by the assumption that retention of haplotype diversity assures retention of power for mapping disease susceptibility by allelic association. Using two bodies of real data, three proposed measures of diversity, and regression-based methods for association mapping, we found no scenario for which this assumption was tenable. We compared the chi-square for composite likelihood and the maximum chi-square for single SNPs in diplotypes, excluding the marker designated as causal. All haplotype-tagging methods conserve haplotype diversity by selecting common SNPs. When the causal marker has a range of allele frequencies as in real data, chi-square decreases faster than under random selection as the haplotype-tagging set diminishes. Selecting SNPs by maximizing haplotype diversity is inefficient when their frequency is much different from the unknown frequency of the causal variant. Loss of power is minimized when the difference between minor allele frequencies of the causal SNP and a closely associated marker SNP is small, which is unlikely in ignorance of the frequency of the causal SNP unless dense markers are used. Therefore retention of haplotype diversity in simulations that do not mirror genomic allele frequencies has no relevance to power for association mapping. TagSNPs that are assigned to bins instead of haplotype blocks also lose power compared with random SNPs. This evidence favours a multi-stage design in which both models and density change adaptively.

Genetic epidemiology of complex phenotypes

A theory is given for complex phenotypes represented by an ordered polychotomy separately for affected (as severity) and for normals (as diathesis), with consideration of history, ascertainment, sampling frames, and phenotype systems. Nonrandom selection of probands by severity is permitted. Both probit and logistic models are developed in a form compatible with segregation and/or linkage analysis. Probabilities are set out in detail in the Appendix. This approach avoids problems that have been encountered with quantitative traits and correlated phenotypes, although using this information.

Leukaemia and transient leukaemia in Down syndrome.

SummaryWe have reviewed 215 published cases of leukaemia and transient leukaemia in Down syndrome. There is an over-representation of mosaic trisomy 21, possibly the result, at least in part, of a survival effect. The most intriguing observation is a bimodal distribution of maternal age, produced largely because cases with true leukaemia have a significantly higher maternal age than cases with transient leukaemia (33.5 versus 29.5 years). In conjunction with evidence that meiosis I non-disjunction is infrequent in transient leukaemia, this suggests different mechanisms for the etiology of leukaemia and transient leukaemia, and favours a locus predisposing to transient leukaemia proximal to the centromere on the long arm of chromosome 21.

Genetic epidemiology of breast cancer in Britain

A complex segregation analysis was conducted on two British series (one consecutive series of probands with breast cancer and one series ascertained through a normal consultand). Altogether there were 1248 nuclear families with breast cancer. A dominant gene with a frequency of 0‐003 giving a lifetime penetrance of 0‐83 is favoured. Ovarian, endometrial and cancers associated with the SBLA syndrome, as well as benign breast disease, were significantly more common in familial breast cancer than in families of single cases. Probands in families with more than one individual with breast cancer were non‐significantly younger than isolated probands.

Linkage disequilibrium maps and association mapping

The causal chain between a gene and its effect on disease susceptibility cannot be understood until the effect has been localized in the DNA sequence. Recently, polymorphisms incorporated in the HapMap Project have made linkage disequilibrium (LD) the most powerful tool for localization. The genetics of LD, the maps and databases that it provides, and their use for association mapping, as well as alternative methods for gene localization, are briefly described.