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Rare dominant genes with high penetrance can be identified by linkage without inbreeding, whereas rare recessive genes with high penetrance are most efficiently recognized by autozygosity mapping of homozygotes in pedigrees with preferential inbreeding. On the contrary, complex inheritance is characterized by common genes with low penetrance, for which family studies and inbreeding are inefficient. Here, we develop the Fisherian theory for diallelic cases and controls, show that it compares favorably with Bayesian estimates, and evaluate their currently low power for discriminating cases and controls in Crohn disease (CD). Significance is enhanced by inclusion of composite likelihood, but identification of causal loci is delayed by low recognition of gene function. Clearly, association mapping is not yet optimal, and so strenuous effort is justified to develop a more inclusive gene map and association tests more powerful than single markers and the current use of composite likelihood. Because of its relatively high heritability and the correspondingly large number of detected causal loci, CD presents an ideal test system to determine the power and flaws of competing methods of whole-genome case/control association analysis in publicly available data. Until such a test is exploited by competing statisticians, their Herculean efforts will be inconclusive, and the costly advances from increased sample size will be suboptimal and disappointing.

The Danish breast cancer data collected by Jacobsen (1946) have been reanalysed using morbid risks which incorporate mortality due to breast cancer. A dominant gene is favoured for familial breast cancer, supporting the conclusions of Williams & Anderson (1984) and later authors. Neglect of specific mortality does not greatly alter estimates of gene frequency and displacement, but the evidence for a major gene is inflated. No evidence for heterogeneity was found. Earlier claims of non-Mendelian transmission are in error since we have discovered that transmission probabilities are not correctly implemented in the computer program POINTER. Cases with bilateral breast cancer and males with breast cancer all belonged to families favouring a major gene. Of the cancer sites frequently reported to be associated with familial breast cancer, only ovarian cancer is significant in this material.

The pattern of inheritance of fasting blood glucose was examined in a Japanese cohort of 500 nuclear families living in Hawaii. A principal component of glucose was defined to improve the ranking of diabetics and individuals receiving treatment (medication and/or diet) for hyperglycemia, thereby allowing as well as possible for inability to determine untreated levels in patients. Results from path and segregation analysis show that family resemblance for glucose is low in this population. The additive variation can be explained by a cultural model of inheritance without introducing intergenerational differences, a maternal-paternal effect, or even genetic parameters. Heritability is approximately 0.125. Complex segregation analysis provides no convincing evidence for a major gene, with preliminary support based upon leptokurtic outliers in five families disappearing on further analysis by partial truncation. A claim by other workers of a major recessive gene for hyperglycemia may be due to their failure to allow for treatment, skewness, and multifactorial heritability. In future, the search for major loci acting on liability to hyperglycemia should use multiple determinations of fasting glucose or be addressed to more primary and repeatable variables than fasting blood glucose.

Consequences of three models of multifactorial inheritance are deduced for inbreeding effects and recurrence risks, and methods are developed to test goodness of fit. Applying the computer program DISQUAC to several bodies of data, we find that every one which fits a quasi-continuous modcl also fits a discontinuous one. Our results show that it is exceedingly difficult, and may be practically impossible, to infer the genetic basis of traits which do not give regular mendelian ratios. The only consolation is that predicted recurrence risks are esscntially the same for similar models. Thus the two quasi-continuous models of Falconer and Edwards, which assume cumulative gene action, seem in practice indistinguishable, while the genetic load model can be differentiated only if there is significant dominancc. Useful predictions for genetic counseling may be made from a well-fitting model even when the mode of inheritance is unclear. In particular, it is shown how to estimate the probability of affection in the next child after s sibs have been born, of whom r were affected, when there is no birth order effect.

In its expanded form, the fragile X triplet repeat at Xq27.3 gives rise to the most common form of inherited mental retardation, fragile X syndrome. This high population frequency persists despite strong selective pressure against mutation-bearing chromosomes. Males carrying the full mutation rarely reproduce and females heterozygous for the premutation allele are at risk of premature ovarian failure. Our diagnostic facility and previous research have provided a large databank of X chromosomes that have been tested for the FRAXA allele. Using this resource, we have conducted a detailed genetic association study of the FRAXA region to determine any cis-acting factors that predispose to expansion of the CGG triplet repeat. We have genotyped SNP variants across a 650-kb tract centered on FRAXA in a sample of 877 expanded and normal X chromosomes. These chromosomes were selected to be representative of the haplotypic diversity encountered in our population. We found expansion status to be strongly associated with a ∼50-kb region proximal to the fragile site. Subsequent detailed analyses of this region revealed no specific genetic determinants for the whole population. However, stratification of chromosomes by risk subgroups enabled us to identify a common SNP variant which cosegregates with the subset of D group haplotypes at highest risk of expansion (, p=0.00002). We have verified that this SNP acts as a marker of repeat expansion in three independent samples. Hum Mutat 28(12), 1216–1224, 2007. © 2007 Wiley-Liss, Inc.

Ambitious programs have recently been advocated or launched to create genomewide databases for meta-analysis of association between DNA markers and phenotypes of medical and/or social concern. A necessary but not sufficient condition for success in association mapping is that the data give accurate estimates of both genomic location and its standard error, which are provided for multifactorial phenotypes by composite likelihood. That class includes the Malecot model, which we here apply with an illustrative example. This preliminary analysis leads to five inferences: permutation of cases and controls provides a test of association free of autocorrelation; two hypotheses give similar estimates, but one is consistently more accurate; estimation of the false-discovery rate is extended to causal genes in a small proportion of regions; the minimal data for successful meta-analysis are inferred; and power is robust for all genomic factors except minor-allele frequency. An extension to meta-analysis is proposed. Other approaches to genome scanning and meta-analysis should, if possible, be similarly extended so that their operating characteristics can be compared.

Previous analyses have provided evidence for one or more loci affecting body weight in the H19-IGF2-INS-TH region on chromosome 11p15. To identify the location of a possible causal locus or loci we applied association analysis by composite likelihood to a large cohort under the Malecot model for body weight. A random sample of 2731 men in the UK were typed for eleven single nucleotide polymorphisms (SNPs) in IGF2, two SNPs in H19, one SNP in INS and one microsatellite marker in the TH genes. Using F tests appropriate to small marker sets, the superiority of regression over correlation was confirmed. All the evidence for association came from IGF2, with P= 0.007 for height-adjusted weight and P= 0.019 for weight additionally adjusted for smoking and alcohol drinking. Although the estimated point location for the suspected causal variant was close to IGF2 ApaI, the 95% confidence and support intervals covered most of IGF2 but none of the other loci. Identification of the causal SNP or SNPs within IGF2 will require typing of more variants in this region.

Two genetic maps with additive distances contribute information about recombination patterns, recombinogenic sequences, and discovery of genes affecting a particular phenotype. Recombination is measured in morgans ( w ) over a single generation in a linkage map but may cover thousands of generations in a linkage disequilibrium (LD) map measured in LD units (LDU). We used a subset of single nucleotide polymorphisms from the HapMap Project to create a genome-wide map in LDU. Recombination accounts for 96.8% of the LDU variance in chromosome arms and 92.4% in their deciles. However, deeper analysis shows that LDU/ w , an estimate of the effective bottleneck time ( t ), is significantly variable among chromosome arms because ( i ) the linkage map is approximated from the Haldane function, then adjusted toward the Kosambi function that is more accurate but still exaggerates w for all chromosomes, especially shorter ones; ( ii ) the nonpseudoautosomal region of the X chromosome is subject to hemizygous selection; and ( iii ) at resolution less than ≈40,000 markers per w , there are indeterminacies (holes) in the LD map reflecting intervals of very high recombination. Selection and stochastic variation in small regions must have effects, which remain to be investigated by comparisons among populations. These considerations suggest an optimal strategy to eliminate holes quickly, greatly enhance the resolution of sex-specific linkage maps, and maximize the gain in association mapping by using LD maps.

We have developed a simple yet powerful approach for disease gene association mapping by linkage disequilibrium (LD). This method is unique because it applies a model with evolutionary theory that incorporates a parameter for the location of the causal polymorphism. The method exploits LD maps, which assign a location in LD units (LDU) for each marker. This approach is based on single marker tests within a composite likelihood framework, which avoids the heavy Bonferroni correction through multiple testing. As a proof of principle, we tested an 890 kb region flanking the CYP2D6 gene associated with poor drug-metabolizing activity in order to refine the localization of a causal mutation. Previous LD mapping studies using single markers and haplotypes have identified a 390 kb significant region associated with the poor drug-metabolizing phenotype on chromosome 22. None of the 27 Single nucleotide polymorphisms was within the gene. Using a metric LDU map, the commonest functional polymorphism within the gene was located at 14.9 kb from its true location, surrounded within a 95% confidence interval of 172 kb. The kb map had a relative efficiency of 33% compared with the LDU map. Our findings indicate that the support interval and location error are smaller than any published results. Despite the low resolution and the strong LD in the region, our results provide evidence of the substantial utility of LDU maps for disease gene association mapping. These tests are robust to large numbers of markers and are applicable to haplotypes, diplotypes, whole-genome association or candidate region studies.

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 Wald’s 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.

Genetic epidemiology developed in the middle of the last century, focused on inherited causes of disease but with methods and results applicable to other traits and even forensics. Early success with linkage led to the localization of genes contributing to disease, and ultimately to the Human Genome Project. The discovery of millions of DNA markers has encouraged more efficient positional cloning by linkage disequilibrium (LD), using LD maps and haplotypes in ways that are rapidly evolving. This has led to large international programmes, some promising and others alarming, with laws about DNA patenting and ethical guidelines for responsible research still struggling to be born.

A linkage disequilibrium map is expressed in linkage disequilibrium (LD) units (LDU) discriminating blocks of conserved LD that have additive distances and locations monotonic with physical (kb) and genetic (cM) maps. There is remarkable agreement between LDU steps and sites of meiotic recombination in the one body of data informative for crossing over, and good agreement with another method that defines blocks without assigning an LD location to each marker. The map may be constructed from haplotypes or diplotypes, and efficiency estimated from the empirical variance of LD is substantially greater for the ρ metric based on evolutionary theory than for the absolute correlation r , and for the LD map compared with its physical counterpart. The empirical variance is nearly three times as great for the worst alternative ( r and kb map) as for the most efficient approach (ρ and LD map). According to the empirical variances, blocks are best defined by zero distance between included markers. Because block size is algorithm-dependent and highly variable, the number of markers required for positional cloning is minimized by uniform spacing on the LD map, which is estimated to have ≈1 LDU per locus, but with much variation among regions. No alternative representation of linkage disequilibrium (some of which are loosely called maps) has these properties, suggesting that LD maps are optimal for positional cloning of genes determining disease susceptibility.

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.

Comparison of different metrics, using three large samples of haplotypes from different populations, demonstrates that rho is the most efficient measure of association between pairs of single nucleotide polymorphisms (SNPs). Pairwise data can be modeled, using composite likelihood, to describe the decline in linkage disequilibrium with distance (the Malecot model). The evidence from more isolated populations (Finland, Sardinia) suggests that linkage disequilibrium extends to 427-893 kb but, even in samples representative of large heterogeneous populations, such as CEPH, the extent is 385 kb or greater. This suggests that isolated populations are not essential for linkage disequilibrium mapping of common diseases with SNPs. The in parameter of the Malecot model (recombination and time), evaluated at each SNP, indicates regions of the genome with extensive and less extensive disequilibrium (low and high values of in respectively). When plotted against the physical map, the regions with extensive and less extensive linkage disequilibrium may correspond to recombination cold and hot spots. This is discussed in relation to the Xq25 cytogenetic band and the HFE gene region.

The performance of some weakly parametric linkage tests in common use was compared on 200 replicates of oligogenic inheritance from Genetic Analysis Workshop 10. Each random sample for the quantitative trait was dichotomized at different thresholds and also selected through 2 affected sibs, generating 8 combinations of sample and variable. The variance component program SOLAR performed best with a continuous trait, even in selected samples, when the population mean was used. The sib-pair program SIBPAL2 was best in most other cases when the phenotype product, population mean, and empirical estimates of pair correlations were used. The BETA program that introduced phenotype products was slightly more powerful than maximum likelihood scores under the null hypothesis and approached but did not exceed SIBPAL2 under its optimal conditions. Type I errors generally exceeded expectations from a χ2 test, but were conservative with respect to bounds on lods. All methods can be improved by use of the population mean, empirical correlations, logistic representation for affection status, and correct lods for samples that favour the null hypothesis. It remains uncertain whether all information can be extracted by weakly parametric methods and whether correction for ascertainment bias demands a strongly parametric model. Performance on a standard set of simulated data is indispensable for recognising optimal methods.

FRAXE full mutations are rare and appear to be associated with mild mental retardation. As part of a screening survey of boys with learning difficulties to determine the frequency of full and premutations, we have collected data on the frequency of instability at FRAXE for about 4000 transmissions and the haplotype for over 7000 chromosomes. The distribution of FRAXE repeats was similar to other English populations but differed from two North American Caucasian series. Observed instability at FRAXE was rare but increased with increasing repeat number, and there were no expansions into the full mutation range, except in pedigrees ascertained through a full mutation. Haplotype analysis suggested division into five groups with each group having a characteristic distribution of FRAXE repeats. Fourteen of the 15 full mutations occurred on a single haplotype and this haplotype also had a significant excess of intermediate-sized alleles, suggesting that full mutations originate from large normal alleles. However, a related haplotype also had a significant excess of intermediates but we observed no full mutations on this haplotype, suggesting either loss or gain of stability determinants on it. We suggest that whilst triplet repeat size is a significant predisposing factor for expansion at FRAXE other genetic determinants are also likely to be important.

Meta-analysis is presented for published studies on linkage or allelic association that have in common only reported significance levels. Reporting is biassed, and nonsignificance is seldom quantified. Therefore meta-analysis cannot identify oligogenes within a candidate region nor establish their significance, but it defines candidate regions well. Applied to a database on atopy and asthma, candidate regions are identified on chromosomes 6, 5, 16, 11, 12, 13, 14, 7, 20, and 10, in rank order from strongest to weakest evidence. On the other hand, there is little support for chromosomes 9, 8, 18, 1, and 15 in the same rank order. The evidence from 156 publications is reviewed for each region. With reasonable type I and II errors several thousand affected sib pairs would be required to detect a locus accounting for 1/10 of the genetic effect on asthma. Identification of regions by a genome scan for linkage and allelic association requires international collaborative studies to reach the necessary sample size, using lod-based methods that specify a weakly parametric alternative hypothesis and can be combined over studies that differ in ascertainment, phenotypes, and markers. This has become the central problem in complex inheritance.Apresenta-se uma meta-análise de estudos publicados sobre associação alélica ou de ligação que têm em comum apenas os níveis de significância relatados. Os relatos são tendenciosos e a não-significância é raramente quantificada. Portanto, a meta-análise não pode identificar oligogenes dentro de uma região candidata nem estabelecer sua significância, mas define bem as regiões candidatas. Aplicando-se a um banco de dados sobre atopia e asma, as regiões candidatas são identificadas nos cromossomos 6, 5, 16, 11, 12, 13, 14, 7, 20 e 10, ordenados partindo-se das evidências mais fortes para as mais fracas. Por outro lado, há pouca evidência para os cromossomos 9, 8, 18, 1 e 15, na mesma ordem. As evidências obtidas em 156 publicações são revistas para cada região. Com erros tipo I e II aceitáveis, vários milhares de pares de irmãos afetados seriam necessários para detectar um loco responsável por 1/10 do efeito genético na asma. A identificação de regiões por uma avaliação geral do genoma visando a associação alélica e de ligação requer estudos colaborativos internacionais para atingir o tamanho necessário da amostra, usando métodos baseados em "lod" que especifiquem uma hipótese alternativa fracamente paramétrica e que possam ser combinados com relação a estudos que diferem em avaliação, fenótipos e marcadores. Este é o problema central em heranças complexas.

Every science begins in folklore and matures as it reacts against dogma and myth. Astronomy developed in the Neolithic, but it did not outgrow astrology until the sixteenth century. Chemistry discarded alchemy at about the same time. On the contrary, the short history of genetics has been concurrent with the pseudo-science of eugenics, which, at times, has been widely accepted and incorporated in population policy and directive genetic counselling, with rare opposition by geneticists. Societal pressures are likely to increase with the power of genetic technology, the fear it generates and the perception that population growth threatens human welfare. Without a pertinent ethical code, geneticists are vulnerable to both temptation and opprobrium. The intrusion of eugenics into genetic counselling has been a recent source of concern to societies and congresses of genetics. This review traces the causes of this concern and the manner of its expression in the absence of an international voice for genetics that could address ethical and other common interests.

Genetic epidemiological studies are useful for the knowledge of the association of markers and genes involved in diseases. In the present work, we studied the frequency of four adenomatous polyposis coli intragenic RFLP markers often used in risk evaluation in a population of 10 familial adenomatous polyposis patients from 10 unrelated Portuguese familial adenomatous polyposis families not sharing the same mutation, and in a population of 55 unrelated healthy Portuguese volunteers. We compared the frequency obtained to normal and affected populations and to results already reported in other populations. We observed allelic frequencies for the Portuguese population that agree with the published ones. The intragenic polymorphisms show strong gametic disequilibrium suggesting little recombination between them. We observed haplotype frequencies significantly different in patients and controls. The gametic disequilibrium may be due to a common founder for a proportion of apparently unrelated probands.

We present evidence of linkage between markers on chromosome 12 and asthma using the BETA program for nonparametric single- and multipoint linkage analysis. We have used quantitative scores as our phenotypic variables, combining data into indices for asthma and atopy and maximizing heritability. The largest single-locus LODs were achieved for asthma: D12S342 and asthma score (LOD 2.255), D12S324 and asthma affection (LOD 2.214), and D12S366 and wheeze (LOD 3.307). The region of interest identified using multipoint analysis, with a maximum LOD of 2.29, centers around D12S97 at location 173.5 cM with a standard error of 6.5 for the asthma score and close agreement for asthma affection and wheeze. Such evidence merits further investigation of this area in an attempt to define the region with greater precision with a view to identifying candidate genes. We hope that the methods presented will encourage researchers to use phenotypic information in a way that encourages meta-analysis.

Recombination acts on the genetic map, not on the physical map. On the other hand, the physical map is usually more accurate. Choice of the genetic or physical map for positional cloning by allelic association depends on the goodness of fit of data to each map under an established model. Huntington disease illustrates the usual case in which the greater reliability of physical data outweighs recombinational heterogeneity. Hemochromatosis represents an exceptional case in which unrecognized recombinational heterogeneity retarded positional cloning for a decade. The Malecot model performs well for major genes, but no approach assuming either equilibrium or disequilibrium has been validated for oligogenes contributing to common disease. In this case of greatest interest, the power of allelic association relative to linkage is less clear than for major genes.

Summary A LOD score ⩾3 is necessary but not sufficient to make a linkage test reliable, and this applies to complex inheritance as well as to major loci. Factors that affect this threshold are considered here. A LOD score as small as 2 is suggestive but is unreliable except as confirmation of either a significant linkage or a strong candidate locus. A threshold as great as 4 is unnecessarily conservative if multipoint tests are used sensibly. Marker density is not a major factor, and biases in the evaluation of LOD scores—especially inadequate allowance for estimation of nuisance parameters in multiple models—are paramount. Allelic association increases resolution for oligogenes within a candidate region and remains the only practical method to locate polygenes. The method sketched here combines multipoint linkage and allelic association to test efficiently for a regional candidate locus.

Recently a graphical study of linkage disequilibrium around the CAPN3 locus failed to refine the 1.3-Mb interval suggested by haplotype sharing. On the contrary, the Malecot model as implemented in the ALLASS program maps CAPN3 within 3 kb of its true location (23 kb from the locus midpoint), overcoming identified problems with small samples, interrelated sibships, and short duration.

A sample of 95 sib pairs affected with insulin-dependent diabetes and typed with their normal parents for 28 markers on chromosome 6 has been analyzed by several methods. When appropriate parameters are efficiently estimated, a parametric model is equivalent to the β model, which is superior to nonparametric alternatives both in single point tests (as found previously) and in multipoint tests. Theory is given for meta-analysis combined with allelic association, and problems that may be associated with errors of map location and/or marker typing are identified. Reducing by multipoint analysis the number of association tests in a dense map can give a 3-fold reduction in the critical lod, and therefore in the cost of positional cloning.

High-resolution maps integrated with the enhanced location data base software ( ldb+ ) give improved estimates of genetic parameters and reveal characteristics of cytogenetic bands. Chiasma interference is intermediate between Kosambi and Carter–Falconer levels, as in Drosophila and the mouse. The autosomal genetic map is 2832 and 4348 centimorgans in males and females, respectively. Telomeric T-bands are strikingly associated with male recombination and gene density. Position and centromeric heterochromatin have large effects, but nontelomeric R-bands are not significantly different from G-bands. Several possible reasons are discussed. These regularities validate the maps, despite their high resolution and inevitable local errors. No other approach has been demonstrated to integrate such a large number of loci, which are increasing at about 45% per year. The maps and the data and software from which they are constructed are available through the Internet ( http://cedar.genetics.soton.ac.uk/public_html ). Successive versions of this location data base may also be accessed on CD-ROM.

SUMMARY The first integrated map of chromosome 1 was published in 1992. We present an updated summary map of 371 loci constructed from a location database that includes physical and genetic data. The summary map subsumes a composite physical location, sex-specific genetic location, cytogenetic assignment, mouse homology, rank and references to physical maps. The genetic length is 208 cM for the male map, in close agreement with the chiasma map, and 371 cM for the female map. There is evidence for a high level of interference on chromosome 1. The location database comprising both data and analytical software is discussed in relation to alternative approaches and possible enhancements.

Sib pair tests for linkage to a quantitative trait or affection status are examined by simulation. A sibship of size s contributes only s-1 independent sib pairs but all s(s-1)/2 pairs are needed for an efficient test. Redundancy increases with sibship size. Using simulated data on the null hypothesis of no linkage, we have considered equal and unequal weights. Unequal weights lose power as measured by the equivalent number of observations, and goodness of fit to the theoretical distribution is degraded. The Fisher z(r) test with equally weighted pairs is more reliable than any t(r) test based on conjectured degrees of freedom, but significance levels must be established by simulation if the number of pairs is small or redundancy is large. An approach to parametric analysis through nuisance parameters is discussed.

After digression by a National Research Council committee, forensic use of DNA identification is returning to methods that do not violate population genetics and statistics. Polemic has been replaced by normal science as advances are made in molecular techniques and presentation of evidence. Rigorous quality control over the chain of custody and likelihood calculations still need to be implemented, and evidence extended on the structure of forensic populations and the operating characteristics of alternative tests.

Risks for breast cancer when there is a family history of the disease are usually calculated using data from segregation analyses which favour a single dominant gene with high penetrance. There are, however, at least three loci known to be associated with familial breast cancer (p53, BRCA1, and an as yet unpublished locus) and the frequencies and penetrances of these genes are not likely to be the same. We have attempted to address the problem of which genetic parameters should be used to calculate risks for different patterns of familial breast cancer. Data from 384 nuclear families ascertained through a proband selected for early onset breast cancer were subjected to complex segregation analysis, correcting for ascertainment bias resulting from selection for severe phenotype. Age of onset of breast cancer, incorporated as severity, provides additional information to the segregation model over and above that given by assigning liability classes on the basis of age at observation. The use of this additional parameter in the analysis is described. There is fair agreement between estimates from this sample and previous predictions from consecutive probands and consultands. The differences suggest more than one rare dominant gene for susceptibility to breast cancer, with different penetrances. Although refinements of segregation analysis will help to delineate these different genes, perfect resolution will require identification of the mutant alleles. Methods to estimate genetic parameters under genotype specific mortality need to be developed. Meanwhile, we suggest that high and low estimates of penetrance be used in risk estimation for genetic counselling, and as a guide to candidates for entry into clinical trials of screening and chemoprevention in breast cancer.

Traits related to atopy and asthma were defined in a random cohort of 131 families with three or more children. Correlation analysis provides no evidence of imprinting, maternal effect, or a major role of environment shared by sibs. Commingling analysis favours more than one distribution, the upper one being common for asthma and very common for atopy. Segregation analysis of rank-transformed variables provides only equivocal evidence of major genes against a polygenic background but suggests that such genes (if present) are individually common and not of large effect. Segregation analysis under a two-locus model gives consistent results with minimal distributional assumptions. To enter combined segregation analysis we favour a restricted model in which the major locus is additive on the liability scale and the pseudopolygenic modifier locus accounts for at least half the genetic variance. Total IgE and bronchial reactivity are proposed for meta-analysis of atopy and asthma respectively. Genetic analysis of complex inheritance is discussed and it is shown that allelic association with random loci is not a feasible approach.

Traditional models of the genetic transmission of human diseases have often assumed that the phenotype is a simple dichotomous trait, which is unrealistic for many psychiatric conditions, and may result in loss of valuable information. We describe a new model for complex phenotypes, implemented in the program COMDS, which subclassifies normal and affected individuals into polychotomies correlated with the underlying genetic liability to the disorder. The model is applied to 18 Scottish pedigrees ascertained for schizophrenia, in which auditory P300 latency had been measured as a possible correlate of the genetic predisposition to schizophrenia. The results suggest that there may be a major locus for schizophrenia, but that there are also other familial determinants, possibly a second modifier locus. In addition, the results indicate that auditory P300 latency may be a useful measure of the genetic predisposition to schizophrenia among asymptomatic relatives, although the relationship between P300 latency and the degree of genetic predisposition in clinical cases was not significant, presumably because other factors are operating on P300 latency. Because of the possible selection biases in this sample, there is a need to replicate these findings in systematically ascertained pedigrees.

Segregation analysis provides a genetic model of disease based upon morbid risks in age-specific classes, from which the model derives genotype-specific morbid risks. In the absence of disease-specific mortality each morbid risk is a cumulative incidence (age-specific penetrance). If disease-specific mortality reduces the number of affected in the older classes, the morbid risk is less than the corresponding penetrance. When counselling individuals with a family history of disease, their genetic risk is a function of penetrances, which can be calculated from morbid risks. We have applied this method to breast, ovarian and colorectal cancer.

Summary The AD1 locus on chromosome 21 (MIM 104300) maps to the β-amyloid precursor locus (APP) at approximately 27·7 Mb from pter (10·9 cM in males and 33·9 cM in females), flanked proximally by D21S8 and distally by D21S111, with D21S124 and D21S210 close but of uncertain order. AD1 accounts for 63±11 % of multiplex Alzheimer pedigrees for which lod scores have been reported. Since a much smaller proportion of pedigrees have mutations in the cDNA for β-amyloid (APP exons 16 and 17), it is likely that the AD1 locus spans controlling elements near those exons. There is no evidence for a second locus on chromosome 21. The remaining pedigrees may include sporadic cases as well as mutations at an AD2 locus on another chromosome.

Summary 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.

Starting from a broad definition of genetic epidemiology, current developments in association, segregation, and linkage analysis of complex inheritance are considered together with integration of genetic and physical maps and resolution of genetic heterogeneity. Mitochondrial inheritance, imprinting, uniparental disomy, pregressive amplification, and gonadal mosaicism are some of the novel mechanisms discussed, with speculation about the future of genetic epidemiology.

Summary 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.

This paper describes the Centre d'Etude du Polymorphisme Humain (CEPH) consortium linkage map of human chromosome 1. The map contains 101 loci defined by genotypes generated from CEPH family DNAs with 146 different contributions from 11 laboratories. A total of 58 loci are uniquely placed on the map with likelihood support of at least 1000:1. The map extends from loci in the terminal bands of both chromosome arms (locus D1Z2 in 1p36.3 and D1S68 in 1q44) and is anchored at the centromere by the D1Z5 alpha-satellite polymorphism. With the exception of a single locus, the remaining loci are arrayed on the fixed map in short intervals and their possible locations are indicated. Multipoint linkage analyses provided estimates that the male, female, and sex-averaged maps extend for 308, 478, and 390 cM, respectively. The sex-averaged map contains only four intervals greater than 15 cM, and the mean genetic distance between the 58 uniquely placed loci is 6.7 cM.

The HapMap Project has shifted genetic epidemiology of complex inheritance away from linkage into association mapping of genes affecting disease and response to therapy. Starting with a physical map produced by the Human Genome Project and recent investigation of structural polymorphisms in HapMap samples, population-specific linkage disequilibrium (LD) maps that accurately reflect the fine structure of blocks and steps have been created for use in association mapping, and by interpolation to increase the resolution of linkage maps. All this evidence can be integrated by meta-analysis if expressed as an estimated location and its standard error, a property apparently unique to composite likelihood, recently freed from autocorrelation by permutation of affection status. Methods that do not estimate a standard error are easier to apply, but may be misleading if a causal marker has not been typed. The month of June 2007 saw advances in genome-wide association scans (GWAS) for several diseases. Many questions remain to be answered if genetic epidemiology is to continue the significant contribution to medicine that its definition promises and its history illustrates.

SUMMARY To achieve consensus more exact definitions of genetical maps are required, of which standard, comprehensive and skeletal might be some. A standard genetic map gives distance from pter in centimorgans (cM), uses the international nomenclature for assigned loci, is sex-specific, and allows as well as possible for interference and typing errors. A standard physical map gives distance from pter in megabases (Mb). A standard map is called comprehensive if it aims to include all syntenic loci, and skeletal if it is limited to loci whose order is well supported. Loci with established order are called skeletal, and are used to define regional assignments of other loci. These principles are illustrated using the CEPH data for chromosome 10. Map lengths by multiple 2-point analysis under supported interference are in good agreement with other evidence, but multipoint mapping gives a substantial overestimate. There are currently 21 loci in the skeletal genetic map and 40 loci in the comprehensive genetic map. From these data, cytogenetic assignments, and partial genetic maps the physical location has been estimated for 85 loci. MEN2A is in a region close to the centromere in which male recombination per megabase is much reduced. Order of DNA markers in this densely mapped region has not been determined, and therefore the exact location of MEN2A is uncertain, although it is likely to lie between D10S34 and D10S30 and close to D10S11.

A haplotype block is a DNA sequence containing polymorphisms in strong linkage disequilibrium (LD) and with low haplotype diversity, separated from other blocks by steps of low LD with high haplotype diversity. Haplotype blocks may be as short as 2 kb or more than 150 kb, depending both on block definition and the spacing of LD cold spots, which tend to be shorter than blocks. Haplotype diversity measured by the effective number of haplotypes is said to be low if smaller than the number of polymorphisms defining the haplotype. To be useful in genetic analysis, the haplotype should be shorter than a typical block. Keywords: haplotype block; linkage disequilibrium; haplotype diversity; linkage disequilibrium map; selective sweep

Objective: A number of linkage disequilibrium (LD)-based methods have been developed to describe recombination and infer hotspots. We determine the correspondence between LDMAP and LDhat, and between LDMAP and LDhot by comparison with linkage maps and hotspots that have been verified by sperm typing. Methods: Regression and variance analyses were used to compare LDMAP and LDhat with linkage maps. The location and intensity of hotspots inferred by LDMAP and LDhot were compared with fifteen verified hotspots. Results: Despite different methodologies and assumptions, LDMAP, LDhat, and linkage maps are highly concordant. Closer inspection shows that LDMAP corresponds more closely with linkage maps across the genome and on sixteen chromosomes compared with LDhat. LDhot identified fourteen and ten of the verified hotspots using high and low density maps. In comparison, LDMAP identified all fifteen hotspots at high and low density. However, some significant discrepancies between sperm and LD-based recombination rates remain. Conclusions: Combining information from linkage and LDMAP to construct sex-specific high resolution linkage maps suggests that some of these discrepancies may be due to female recombination while others may relate to the age of hotspots. LDMAP based estimates between ∼68,000 and ∼112,000 hotspots in the genome with mean widths less than 4 kb.

We describe an association mapping approach that utilizes linkage disequilibrium (LD) maps in LD units (LDU). This method uses composite likelihood to combine information from all single marker tests, and applies a model with a parameter for the location of the causal polymorphism. Previous analyses of the poor drug metabolizer phenotype provided evidence of the substantial utility of LDU maps for disease gene association mapping. Using LDU locations for the 27 single nucleotide polymorphisms (SNPs) flanking the CYP2D6 gene on chromosome 22, the most common functional polymorphism within the gene was located at 15 kb from its true location. Here, we examine the performance of this mapping approach by exploiting the high-density LDU map constructed from the HapMap data. Expressing the locations of the 27 SNPs in LDU from the HapMap LDU map, analysis yielded an estimated location that is only 0.3 kb away from the CYP2D6 gene. This supports the use of the high marker density HapMap-derived LDU map for association mapping even though it is derived from a much smaller number of individuals compared to the CYP2D6 sample. We also examine the performance of 2-SNP haplotypes. Using the same modelling procedures and composite likelihood as for single SNPs, the haplotype data provided much poorer localization compared to single SNP analysis. Haplotypes generate more autocorrelation through multiple inclusions of the same SNPs, which could inflate significance in association studies. The results of the present study demonstrate the great potential of the genome HapMap LDU maps for high-resolution mapping of complex phenotypes.

The FRAXA trinucleotide repeat at Xq27.3 gives rise to fragile X syndrome when fully expanded, and both premature ovarian failure (POF) and fragile X tremor and ataxia syndrome (FXTAS) when in the premutation range. Reports of phenotypic effects extending into the intermediate repeat range are inconsistent but some studies suggest that these smaller expansions predispose to special educational needs (SEN). This study utilises the Avon Longitudinal Study of Parents and Children (ALSPAC) cohort to investigate cognitive and behavioural variables that might be associated with FRAXA intermediate alleles. The current study failed to find any strong evidence of association of FRAXA intermediate alleles with SEN, behavioural problems or cognitive difficulties. However, our findings illustrate some of the difficulties encountered in identifying individuals with SEN. The power to identify specific components of cognitive and behavioural difficulties was reduced due to elective drop-out, which is characteristic of longitudinal studies. Our findings demonstrate the non-random loss of participants from this cohort and highlight problems that may arise when such data are used in genetic association studies.

Genetic epidemiology deals with etiology, distribution, and control of disease in groups of relatives and with inherited causes of disease in populations. It took its first steps before its recognition as a discipline, and did not reach its present scope until the Human Genome Project succeeded. The intimate relationship between genetics and epidemiology was discussed by Neel and Schull (1954), just a year after Watson and Crick reported the DNA double helix, and 2 years before human cytogenetics and the Japan Society of Human Genetics were founded. It is convenient to divide the next half-century into three phases. The first of these (1956-1979) was before DNA polymorphisms were typed, and so the focus was on segregation and linkage of major genes, cytogenetics, population studies, and biochemical genetics. The next phase (1980-2001) progressively identified DNA polymorphisms and their application to complex inheritance. The last phase began with a reliable sequence of the human genome (2002), followed by exploration of genomic diversity. Linkage continues to be useful to study recombination and to map major genes, but association mapping gives much greater resolution and enables studies of complex inheritance. The generation now entering human genetics will have collaborative opportunities undreamed of a few years ago, without the independence that led to great advances during the past half-century.