Chromosome-wide distribution of haplotype blocks and the role of recombination hot spots.

Recent studies of human populations suggest that the genome consists of chromosome segments that are ancestrally conserved ('haplotype blocks'; refs. 1-3) and have discrete boundaries defined by recombination hot spots. Using publicly available genetic markers, we have constructed a first-generation haplotype map of chromosome 19. As expected for this marker density, approximately one-third of the chromosome is encompassed within haplotype blocks. Evolutionary modeling of the data indicates that recombination hot spots are not required to explain most of the observed blocks, providing that marker ascertainment and the observed marker spacing are considered. In contrast, several long blocks are inconsistent with our evolutionary models, and different mechanisms could explain their origins.

Heritability and genetic correlations of insulin resistance and component phenotypes in Asian Indian families using a multivariate analysis.

AIMS/HYPOTHESIS: Insulin resistance and related metabolic disturbances are more common among Asian Indians than European whites. Little is known about the heritability of insulin resistance traits in Asian Indians. Our objective was to estimate heritabilities and genetic correlations in Asian Indian families. METHODS: Phenotypic data were assembled for 181 UK Asian Indian probands with premature CHD, and their 1,454 first-, second- and third-degree relatives. We calculated (narrow-sense) heritabilities and genetic correlations for insulin resistance traits, and common environmental effects using all study participants and a multivariate model. The analysis was repeated in a subsample consisting of individuals not on drug therapy. RESULTS: Heritability estimates (SE) for individuals not on drug therapy were: BMI 0.31 (0.04), WHR 0.27 (0.04), systolic BP 0.29 (0.03), triacylglycerol 0.40 (0.04), HDL-cholesterol 0.53 (0.04), glucose 0.37 (0.03), HOMA of insulin resistance (HOMA-IR) 0.22 (0.04), and HbA(1c) 0.60 (0.04). We observed many significant genetic correlations between the traits, in particular between HOMA-IR and BMI. Heritability estimates were lower for all phenotypes when analysed among all participants. CONCLUSIONS/INTERPRETATION: Genetic factors contribute to a significant proportion of the total variance in insulin resistance and related metabolic disturbances in Asian Indian CHD families.

Evaluating DNA evidence in a genetically complex population.

In forensic genetics, the likelihood ratio (LR), measuring the value of DNA profile evidence, is computed from a database of allele frequencies. Here, we address the choice of database and adjustments for population structure and sample size in the context of Brazil. The Brazilian population underwent a complex process of colonization, migration and mating, which created an admixed genetic composition that makes it difficult to obtain an appropriate database for a given case. National databases are now available, as well as databases for many Brazilian states. However, those databases are not statistically random samples, and state boundaries may not accurately reflect the sub-structuring of genetic diversity. We compared the LR calculated using the relevant state-specific database with the statistics calculated when a national database and when international databases were used. We evaluated two methods of adjustment for population structure, due to Wright [13] and Balding and Nichols [14]. We also considered two adjustments for database sample size: the Balding size bias correction [15] and a minimum allele frequency [16]. Our results show that the use of a national database with the Balding and Nichols adjustment and θ = 0.002 generated lower LR values than did the state-specific database in more than 50% of the profiles simulated using the state-based allele frequencies, while θ = 0.01 produced lower LRs for more than 90% of the profiles. We conclude that the utilization of a national database for Brazilian cases can be justified in association with the appropriate adjustment for population structure.

Measuring gametic disequilibrium from multilocus data.

We describe a Bayesian approach to analyzing multilocus genotype or haplotype data to assess departures from gametic (linkage) equilibrium. Our approach employs a Markov chain Monte Carlo (MCMC) algorithm to approximate the posterior probability distributions of disequilibrium parameters. The distributions are computed exactly in some simple settings. Among other advantages, posterior distributions can be presented visually, which allows the uncertainties in parameter estimates to be readily assessed. In addition, background knowledge can be incorporated, where available, to improve the precision of inferences. The method is illustrated by application to previously published datasets; implications for multilocus forensic match probabilities and for simple association-based gene mapping are also discussed.

Genealogical inference from microsatellite data.

Ease and accuracy of typing, together with high levels of polymorphism and widespread distribution in the genome, make microsatellite (or short tandem repeat) loci an attractive potential source of information about both population histories and evolutionary processes. However, microsatellite data are difficult to interpret, in particular because of the frequency of back-mutations. Stochastic models for the underlying genetic processes can be specified, but in the past they have been too complicated for direct analysis. Recent developments in stochastic simulation methodology now allow direct inference about both historical events, such as genealogical coalescence times, and evolutionary parameters, such as mutation rates. A feature of the Markov chain Monte Carlo (MCMC) algorithm that we propose here is that the likelihood computations are simplified by treating the (unknown) ancestral allelic states as auxiliary parameters. We illustrate the algorithm by analyzing microsatellite samples simulated under the model. Our results suggest that a single microsatellite usually does not provide enough information for useful inferences, but that several completely linked microsatellites can be informative about some aspects of genealogical history and evolutionary processes. We also reanalyze data from a previously published human Y chromosome microsatellite study, finding evidence for an effective population size for human Y chromosomes in the low thousands and a recent time since their most recent common ancestor: the 95% interval runs from approximately 15, 000 to 130,000 years, with most likely values around 30,000 years.

Inferring coalescence times from DNA sequence data.

The paper is concerned with methods for the estimation of the coalescence time (time since the most recent common ancestor) of a sample of intraspecies DNA sequences. The methods take advantage of prior knowledge of population demography, in addition to the molecular data. While some theoretical results are presented, a central focus is on computational methods. These methods are easy to implement, and, since explicit formulae tend to be either unavailable or unilluminating, they are also more useful and more informative in most applications. Extensions are presented that allow for the effects of uncertainty in our knowledge of population size and mutation rates, for variability in population sizes, for regions of different mutation rate, and for inference concerning the coalescence time of the entire population. The methods are illustrated using recent data from the human Y chromosome.

Detecting gene conversion: primate visual pigment genes.

The effects of gene conversion can be detected in the DNA sequences of multigene families. We develop a permutation test of the significance of patterns of sequence mismatches, and apply it to the sequences of the red- and green-sensitive visual pigment genes of human and the diana monkey. Whereas conventional tests of the rate of sequence divergence are equivocal, the permutation test convincingly excludes divergence in the absence of gene conversion (p = 10(-6)).

DNA profile match probability calculation: how to allow for population stratification, relatedness, database selection and single bands.

In DNA profile analysis, uncertainty arises due to a number of factors such as sampling error, single bands and correlations within and between loci. One of the most important of these factors is kinship: criminal and innocent suspect may share one or more bands through identity by descent from a common ancestor. Ignoring this uncertainty is consistently unfair to innocent suspects. The effect is usually small, but may be important in some cases. The report of the US National Research Committee proposed a complicated, ad-hoc and overly-conservative method of dealing with some of these problems. We propose an alternative approach which addresses directly the effect of kinship. Whilst remaining conservative, it is simple, logically coherent and makes efficient use of the data.

Evaluating DNA profile evidence when the suspect is identified through a database search.

The paper is concerned with the strength of DNA evidence when a suspect is identified via a search through a database of the DNA profiles of known individuals. Consideration of the appropriate likelihood ratio shows that in this setting the DNA evidence is (slightly) stronger than when a suspect is identified by other means, subsequently profiled, and found to match. The recommendation of the 1992 report of the US National Research Council that DNA evidence that is used to identify the suspect should not be presented at trial thus seems unnecessarily conservative. The widely held view that DNA evidence is weaker when it results from a database search seems to be based on a rationale that leads to absurd conclusions in some examples. Moreover, this view is inconsistent with the principle, which enjoys substantial support, that evidential weight should be measured by likelihood ratios. The strength of DNA evidence is shown also to be slightly increased for other forms of search procedure. While the DNA evidence is stronger after a database search, the overall case against the suspect may not be, and the problems of incorporating the DNA with the non-DNA evidence can be particularly important in such cases.

When can a DNA profile be regarded as unique?

The probability that a defendant's DNA profile is unique in a population of untyped individuals is shown to be bounded below by one minus twice the sum of the match probabilities over the population. This bound assumes that the possibility of laboratory or handling error can be neglected, and applies only when there is no non-DNA evidence in favour of the defendant. There cannot be a completely general lower bound: if there is overwhelming non-DNA evidence that the defendant is not the source of the crime stain, then that is also overwhelming evidence of non-uniqueness. Application to k-locus short tandem repeat (STR) profiles is discussed, and illustrated with calculations based on the 6-STR-locus system used in current UK casework. However, because of the problem of the non-DNA evidence, there seems to be no satisfactory way for an expert witness to address the question of uniqueness in court.

Fine mapping of disease genes via haplotype clustering.

We propose an algorithm for analysing SNP-based population association studies, which is a development of that introduced by Molitor et al. [2003: Am J Hum Genet 73:1368-1384]. It uses clustering of haplotypes to overcome the major limitations of many current haplotype-based approaches. We define a between-haplotype score that is simple, yet appears to capture much of the information about evolutionary relatedness of the haplotypes in the vicinity of a (unobserved) putative causal locus. Haplotype clusters can then be defined via a putative ancestral haplotype and a cut-off distance. The number of an individual's two haplotypes that lie within the cluster predicts the individual's genotype at the causal locus. This predicted genotype can then be investigated for association with the phenotype of interest. We implement our approach within a Markov-chain Monte Carlo algorithm that, in effect, searches over locations and ancestral haplotypes to identify large, case-rich clusters. The algorithm successfully fine-maps a causal mutation in a test analysis using real data, and achieves almost 98% accuracy in predicting the genotype at the causal locus. A simulation study indicates that the new algorithm is substantially superior to alternative approaches, and it also allows us to identify situations in which multi-point approaches can substantially improve over single-SNP analyses. Our algorithm runs quickly and there is scope for extension to a wide range of disease models and genomic scales.

A likelihood ratio approach to family-based association studies with covariates.

We introduce a procedure for association based analysis of nuclear families that allows for dichotomous and more general measurements of phenotype and inclusion of covariate information. Standard generalized linear models are used to relate phenotype and its predictors. Our test procedure, based on the likelihood ratio, unifies the estimation of all parameters through the likelihood itself and yields maximum likelihood estimates of the genetic relative risk and interaction parameters. Our method has advantages in modelling the covariate and gene-covariate interaction terms over recently proposed conditional score tests that include covariate information via a two-stage modelling approach. We apply our method in a study of human systemic lupus erythematosus and the C-reactive protein that includes sex as a covariate.

Design and analysis of chromosome physical mapping experiments.

Mathematical and statistical aspects of constructing ordered-clone physical maps of chromosomes are reviewed. Three broad problems are addressed: analysis of fingerprint data to identify configurations of overlapping clones, prediction of the rate of progress of a mapping strategy and optimal design of pooling schemes for screening large clone libraries.

Significant genetic correlations among Caucasians at forensic DNA loci.

Although the effect of population differentiation on the forensic use of DNA profiles has been the subject of controversy for some years now, the debate has largely failed to focus on the genetical questions directly relevant to the forensic context. We re-analyse two published data sets and find that they convey much the same message for forensic inference, in contrast with the dramatically differing conclusions of the original authors. The analysis is likelihood-based and combines information across loci and across populations without assuming constant genetic differentiation. Our results suggest that the relevant genetic correlation coefficients are too large to be ignored in forensic work: although DNA profile evidence is typically very strong, the effect of genetic correlations can be important in some cases. Such correlations can, however, be accommodated in an appropriate assessment of evidential strength so that population genetic issues should not present a barrier to the efficient and fair use of DNA profile evidence.

Statistical analysis of DNA fingerprint data for ordered clone physical mapping of human chromosomes.

A statistical framework is proposed for analysing DNA fingerprint data from experiments aimed at constructing ordered clone physical maps of chromosomes. The fingerprint data consists of the lengths and hybridization states of restriction digest fragments and the paper develops a solution to the fundamental problem of deciding whether or not two randomly selected clones overlap. Overlap probabilities are calculated using Bayes' rule together with appropriate statistical descriptions of the chromosome and experimental procedure. The analysis is flexible, allowing a variety of assumptions to account for experimental errors and difficulties, such as unobserved fragments. The approach described here provides a basis for predicting the rate of progress of an experimental protocol and hence for comparing alternate protocols. It is readily generalized to related problems with a wide range of possible data. Results are presented for the clone mapping protocol currently being employed at Los Alamos National Laboratory on human chromosome 16 (Stallings et al., 1990, Proc. natl. Acad. Sci. U.S.A., 87, 6218-6222).

The design of pooling experiments for screening a clone map.

We consider nonadaptive pooling designs for unique-sequence screening of a 1530-clone map of Aspergillus nidulans. The map has the properties that the clones are, with possibly a few exceptions, ordered and no more than 2 of them cover any point on the genome. We propose two subdesigns of the Steiner system S(3, 5, 65), one with 65 pools and approximately 118 clones per pool, the other with 54 pools and about 142 clones per pool. Each design allows 1 or 2 positive clones to be detected, even in the presence of substantial experimental error rates. More efficient designs are possible if the overlap information in the map is exploited, if there is no constraint on the number of clones in a pool, and if no error tolerance is required. An information theory lower bound requires at least 12 pools to satisfy these minimal criteria, and an "interleaved binary" design can be constructed on 20 pools, with about 380 clones per pool. However, the designs with more pools have important properties of robustness to various possible errors and general applicability to a wider class of pooling experiments.

Effects of population structure on DNA fingerprint analysis in forensic science.

DNA fingerprints are used in forensic sciences to identify individuals. However, current analyses could underestimate the probability of two individuals sharing the same profile because the effect of population structure is not incorporated. An alternative analysis is proposed to take into account population stratification. The analysis uses studies of inbreeding in human populations to obtain an empirical upper bound on the magnitude of the effect.

Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient.

Many well-established statistical methods in genetics were developed in a climate of severe constraints on computational power. Recent advances in simulation methodology now bring modern, flexible statistical methods within the reach of scientists having access to a desktop workstation. We illustrate the potential advantages now available by considering the problem of assessing departures from Hardy-Weinberg (HW) equilibrium. Several hypothesis tests of HW have been established, as well as a variety of point estimation methods for the parameter which measures departures from HW under the inbreeding model. We propose a computational, Bayesian method for assessing departures from HW, which has a number of important advantages over existing approaches. The method incorporates the effects-of uncertainty about the nuisance parameters--the allele frequencies--as well as the boundary constraints on f (which are functions of the nuisance parameters). Results are naturally presented visually, exploiting the graphics capabilities of modern computer environments to allow straightforward interpretation. Perhaps most importantly, the method is founded on a flexible, likelihood-based modelling framework, which can incorporate the inbreeding model if appropriate, but also allows the assumptions of the model to he investigated and, if necessary, relaxed. Under appropriate conditions, information can be shared across loci and, possibly, across populations, leading to more precise estimation. The advantages of the method are illustrated by application both to simulated data and to data analysed by alternative methods in the recent literature.

A method for quantifying differentiation between populations at multi-allelic loci and its implications for investigating identity and paternity.

A method is proposed for allowing for the effects of population differentiation, and other factors, in forensic inference based on DNA profiles. Much current forensic practice ignores, for example, the effects of coancestry and inappropriate databases and is consequently systematically biased against defendants. Problems with the 'product rule' for forensic identification have been highlighted by several authors, but important aspects of the problems are not widely appreciated. This arises in part because the match probability has often been confused with the relative frequency of the profile. Further, the analogous problems in paternity cases have received little attention. The proposed method is derived under general assumptions about the underlying population genetic processes. Probabilities relevant to forensic inference are expressed in terms of a single parameter whose values can be chosen to reflect the specific circumstances. The method is currently used in some UK courts and has important advantages over the 'Ceiling Principle' method, which has been criticized on a number of grounds.