Multipoint linkage analysis with many multiallelic or dense diallelic markers: Markov chain-Monte Carlo provides practical approaches for genome scans on general pedigrees

Computations for genome scans need to adapt to the increasing use of dense diallelic markers as well as of full-chromosome multipoint linkage analysis with either diallelic or multiallelic markers. Whereas suitable exact-computation tools are available for use with small pedigrees, equivalent exact computation for larger pedigrees remains infeasible. Markov chain-Monte Carlo (MCMC)-based methods currently provide the only computationally practical option. To date, no systematic comparison of the performance of MCMC-based programs is available, nor have these programs been systematically evaluated for use with dense diallelic markers. Using simulated data, we evaluate the performance of two MCMC-based linkage-analysis programs--lm_markers from the MORGAN package and SimWalk2--under a variety of analysis conditions. Pedigrees consisted of 14, 52, or 98 individuals in 3, 5, or 6 generations, respectively, with increasing amounts of missing data in larger pedigrees. One hundred replicates of markers and trait data were simulated on a 100-cM chromosome, with up to 10 multiallelic and up to 200 diallelic markers used simultaneously for computation of multipoint LOD scores. Exact computation was available for comparison in most situations, and comparison with a perfectly informative marker or interprogram comparison was available in the remaining situations. Our results confirm the accuracy of both programs in multipoint analysis with multiallelic markers on pedigrees of varied sizes and missing-data patterns, but there are some computational differences. In contrast, for large numbers of dense diallelic markers, only the lm_markers program was able to provide accurate results within a computationally practical time. Thus, programs in the MORGAN package are the first available to provide a computationally practical option for accurate linkage analyses in genome scans with both large numbers of diallelic markers and large pedigrees.     

Calculation of multipoint likelihoods using flanking marker data: a simulation study

The calculation of multipoint likelihoods is computationally challenging, with the exact calculation of multipoint probabilities only possible on small pedigrees with many markers or large pedigrees with few markers. This paper explores the utility of calculating multipoint likelihoods using data on markers flanking a hypothesized position of the trait locus. The calculation of such likelihoods is often feasible, even on large pedigrees with missing data and complex structures. Performance characteristics of the flanking marker procedure are assessed through the calculation of multipoint heterogeneity LOD scores on data simulated for Genetic Analysis Workshop 14 (GAW14). Analysis is restricted to data on the Aipotu population on chromosomes 1, 3, and 4, where chromosomes 1 and 3 are known to contain disease loci. The flanking marker procedure performs well, even when missing data and genotyping errors are introduced.     

Parametric and nonparametric linkage analysis: a unified multipoint approach.

In complex disease studies, it is crucial to perform multipoint linkage analysis with many markers and to use robust nonparametric methods that take account of all pedigree information. Currently available methods fall short in both regards. In this paper, we describe how to extract complete multipoint inheritance information from general pedigrees of moderate size. This information is captured in the multipoint inheritance distribution, which provides a framework for a unified approach to both parametric and nonparametric methods of linkage analysis. Specifically, the approach includes the following: (1) Rapid exact computation of multipoint LOD scores involving dozens of highly polymorphic markers, even in the presence of loops and missing data. (2) Non-parametric linkage (NPL) analysis, a powerful new approach to pedigree analysis. We show that NPL is robust to uncertainty about mode of inheritance, is much more powerful than commonly used nonparametric methods, and loses little power relative to parametric linkage analysis. NPL thus appears to be the method of choice for pedigree studies of complex traits. (3) Information-content mapping, which measures the fraction of the total inheritance information extracted by the available marker data and points out the regions in which typing additional markers is most useful. (4) Maximum-likelihood reconstruction of many-marker haplotypes, even in pedigrees with missing data. We have implemented NPL analysis, LOD-score computation, information-content mapping, and haplotype reconstruction in a new computer package, GENEHUNTER. The package allows efficient multipoint analysis of pedigree data to be performed rapidly in a single user-friendly environment.     

Rapid multipoint linkage analysis of recessive traits in nuclear families, including homozygosity mapping.

Homozygosity mapping is a powerful strategy for mapping rare recessive traits in children of consanguineous marriages. Practical applications of this strategy are currently limited by the inability of conventional linkage analysis software to compute, in reasonable time, multipoint LOD scores for pedigrees with inbreeding loops. We have developed a new algorithm for rapid multipoint likelihood calculations in small pedigrees, including those with inbreeding loops. The running time of the algorithm grows, at most, linearly with the number of loci considered simultaneously. The running time is not sensitive to the presence of inbreeding loops, missing genotype information, and highly polymorphic loci. We have incorporated this algorithm into a software package, MAPMAKER/HOMOZ, that allows very rapid multipoint mapping of disease genes in nuclear families, including homozygosity mapping. Multipoint analysis with dozens of markers can be carried out in minutes on a personal workstation.     

A major lung cancer susceptibility locus maps to chromosome 6q23-25

Lung cancer is a major cause of death in the United States and other countries. The risk of lung cancer is greatly increased by cigarette smoking and by certain occupational exposures, but familial factors also clearly play a major role. To identify susceptibility genes for familial lung cancer, we conducted a genomewide linkage analysis of 52 extended pedigrees ascertained through probands with lung cancer who had several first-degree relatives with the same disease. Multipoint linkage analysis, under a simple autosomal dominant model, of all 52 families with three or more individuals affected by lung, throat, or laryngeal cancer, yielded a maximum heterogeneity LOD score (HLOD) of 2.79 at 155 cM on chromosome 6q (marker D6S2436). A subset of 38 pedigrees with four or more affected individuals yielded a multipoint HLOD of 3.47 at 155 cM. Analysis of a further subset of 23 multigenerational pedigrees with five or more affected individuals yielded a multipoint HLOD score of 4.26 at the same position. The 14 families with only three affected relatives yielded negative LOD scores in this region. A predivided samples test for heterogeneity comparing the LOD scores from the 23 multigenerational families with those from the remaining families was significant (P=.007). The 1-HLOD multipoint support interval from the multigenerational families extends from C6S1848 at 146 cM to 164 cM near D6S1035, overlapping a genomic region that is deleted in sporadic lung cancers as well as numerous other cancer types. Parametric linkage and variance-components analysis that incorporated effects of age and personal smoking also supported linkage in this region, but with somewhat diminished support. These results localize a major susceptibility locus influencing lung cancer risk to 6q23-25.     

Linkage of Paget Disease of Bone to a Novel Region on Human Chromosome 18q23

Paget disease of bone (PDB) is characterized by increased osteoclast activity and localized abnormal bone remodeling. PDB has a significant genetic component, with evidence of linkage to chromosomes 6p21.3 (PDB1) and 18q21-22 (PDB2) in some pedigrees. There is evidence of genetic heterogeneity, with other pedigrees showing negative linkage to these regions. TNFRSF11A, a gene that is essential for osteoclast formation and that encodes receptor activator of nuclear factor-kappa B (RANK), has been mapped to the PDB2 region. TNFRSF11A mutations that segregate in pedigrees with either familial expansile osteolysis or familial PDB have been identified; however, linkage studies and mutation screening have excluded the involvement of RANK in the majority of patients with PDB. We have excluded linkage, both to PDB1 and to PDB2, in a large multigenerational pedigree with multiple family members affected by PDB. We have conducted a genomewide scan of this pedigree, followed by fine mapping and multipoint analysis in regions of interest. The peak two-point LOD scores from the genomewide scan were 2.75, at D7S507, and 1.76, at D18S70. Multipoint and haplotype analysis of markers flanking D7S507 did not support linkage to this region. Haplotype analysis of markers flanking D18S70 demonstrated a haplotype segregating with PDB in a large subpedigree. This subpedigree had a significantly lower age at diagnosis than the rest of the pedigree (51.2+/-8.5 vs. 64.2+/-9.7 years; P=.0012). Linkage analysis of this subpedigree demonstrated a peak two-point LOD score of 4.23, at marker D18S1390 (straight theta=0), and a peak multipoint LOD score of 4.71, at marker D18S70. Our data are consistent with genetic heterogeneity within the pedigree and indicate that 18q23 harbors a novel susceptibility gene for PDB.     

Multipoint estimation of identity-by-descent probabilities at arbitrary positions among marker loci on general pedigrees

OBJECTIVES: To describe, implement, and test an efficient algorithm to obtain multipoint identity-by-descent (IBD) probabilities at arbitrary positions among marker loci for general pedigrees. Unlike existing programs, our algorithm can analyze data sets with large numbers of people and markers. The algorithm has been implemented in the SimWalk2 computer package. METHODS: Using a rigorous testing regimen containing five pedigrees of various sizes with realistic marker data, we compared several widely used IBD computation programs: Allegro, Aspex, GeneHunter, MapMaker/Sibs, Mendel, Sage, SimWalk2, and Solar. RESULTS: The testing revealed a few discrepancies, particularly on consanguineous pedigrees, but overall excellent results in the deterministic multipoint packages. SimWalk2 was also found to be in good agreement with the deterministic multipoint programs, usually matching to two decimal places the kinship coefficient that ranges from 0 to 1. However, the packages based on single-point IBD estimation, while consistent with each other, often showed poor results, disagreeing with the multipoint kinship results by as much as 0.5. CONCLUSIONS: Our testing has clearly shown that multipoint IBD estimation is much better than single-point estimation. In addition, our testing has validated our algorithm for estimating IBD probabilities at arbitrary positions on general pedigrees.     

Linkage of body mass index to chromosome 20 in Utah pedigrees

Several linkage studies have hinted at the existence of an obesity predisposition locus on chromosome 20, but none of these studies has produced conclusive results. Therefore, we analyzed 48 genetic markers on chromosome 20 for linkage to severe obesity (BMI> or =35) in 103 extended Utah pedigrees (1,711 individuals), all of which had strong aggregation of severe obesity. A simple dominant model produced a maximum multipoint heterogeneity LOD score of 3.5 at D20S438 (55.1 cM). Two additional analyses were performed. First, a one-gene, two-mutation model (with one dominant mutation and one recessive mutation) increased the LOD score to 4.2. Second, a two-locus model (with one locus dominant and one recessive) generated a multipoint LOD score of 4.9. We conclude that one or more severe obesity predisposing genes lie within an interval of approx. 10 cM on chromosome 20. This study generated significant LOD scores which confirm suggestive linkage reports from previous studies. In addition, our analyses suggest that the predisposing gene(s) is localized very near the chromosome 20 centromere.     

Genome-wide linkage analysis of systolic blood pressure: a comparison of two approaches to phenotype definition

Problem 1 of the Genetic Analysis Workshop 13(GAW13) contains longitudinal data of cardiovascular measurements from 330 pedigrees. The longitudinal data complicates the phenotype definition because multiple measurements are taken on each individual. To address this complication, we propose an approach that uses generalized estimating equations to obtain residuals for each time point for each person. The mean residual is then taken as the new phenotype with which to use in a variance components linkage analysis. We compare our phenotype definition approach to an approach that first reduces the multiple measurements to a single measurement and then models these summary statistics as regression terms in a variance components analysis. For each approach, multipoint linkage analysis was performed using the residuals and the SOLAR computer program. Our results show little difference between the methods based on the LOD scores.     

Evidence for a prostate cancer-susceptibility locus on chromosome 20

Recent studies suggest that hereditary prostate cancer is a complex disease involving multiple susceptibility genes and variable phenotypic expression. While conducting a genomewide search on 162 North American families with > or =3 members affected with prostate cancer (PRCA), we found evidence for linkage to chromosome 20q13 with two-point parametric LOD scores >1 at multiple sites, with the highest two-point LOD score of 2.69 for marker D20S196. The maximum multipoint NPL score for the entire data set was 3.02 (P=.002) at D20S887. On the basis of findings from previous reports, families were stratified by the presence (n=116) or absence (n=46) of male-to-male transmission, average age of diagnosis (<66 years, n=73; > or =66 years, n=89), and number of affected individuals (<5, n=101; > or =5, n=61) for further analysis. The strongest evidence of linkage was evident with the pedigrees having <5 family members affected with prostate cancer (multipoint NPL 3.22, P=.00079), a later average age of diagnosis (multipoint NPL 3.40, P=.0006), and no male-to-male transmission (multipoint NPL 3.94, P=.00007). The group of patients having all three of these characteristics (n=19) had a multipoint NPL score of 3.69 (P=.0001). These results demonstrate evidence for a PRCA susceptibility locus in a subset of families that is distinct from the groups more likely to be linked to previously identified loci.     

The genetics of reading disability in an often excluded sample: novel loci suggested for reading disability in rolandic epilepsy

Background

Reading disability (RD) is a common neurodevelopmental disorder with genetic basis established in families segregating “pure” dyslexia. RD commonly occurs in neurodevelopmental disorders including Rolandic Epilepsy (RE), a complex genetic disorder. We performed genomewide linkage analysis of RD in RE families, testing the hypotheses that RD in RE families is genetically heterogenenous to pure dyslexia, and shares genetic influences with other sub-phenotypes of RE.

Methods

We initially performed genome-wide linkage analysis using 1000 STR markers in 38 US families ascertained through a RE proband; most of these families were multiplex for RD. We analyzed the data by two-point and multipoint parametric LOD score methods. We then confirmed the linkage evidence in a second US dataset of 20 RE families. We also resequenced the SEMA3C gene at the 7q21 linkage locus in members of one multiplex RE/RD pedigree and the DISC1 gene in affected pedigrees at the 1q42 locus.

Results

In the discovery dataset there was suggestive evidence of linkage for RD to chromosome 7q21 (two-point LOD score 3.05, multipoint LOD 3.08) and at 1q42 (two-point LOD 2.87, multipoint LOD 3.03). Much of the linkage evidence at 7q21 derived from families of French-Canadian origin, whereas the linkage evidence at 1q42 was well distributed across all the families. There was little evidence for linkage at known dyslexia loci. Combining the discovery and confirmation datasets increased the evidence at 1q42 (two-point LOD = 3.49, multipoint HLOD = 4.70), but decreased evidence at 7q21 (two-point LOD = 2.28, multipoint HLOD  = 1.81), possibly because the replication sample did not have French Canadian representation.

Discussion

Reading disability in rolandic epilepsy has a genetic basis and may be influenced by loci at 1q42 and, in some populations, at 7q21; there is little evidence of a role for known DYX loci discovered in “pure” dyslexia pedigrees. 1q42 and 7q21 are candidate novel dyslexia loci.     

Localization of a gene for familial hemophagocytic lymphohistiocytosis at chromosome 9q21.3-22 by homozygosity mapping.

Familial hemophagocytic lymphohistiocytosis (FHL), also known as familial erythrophagocytic lymphohistiocytosis and familial histiocytic reticulosis, is a rare autosomal recessive disorder of early childhood characterized by excessive immune activation. Linkage of the disease gene to an approximately 7.8-cM region between markers D9S1867 and D9S1790 at 9q21.3-22 was identified by homozygosity mapping in four inbred FHL families of Pakistani descent with a combined maximum multipoint LOD score of 6.05. This is the first genetic locus to be described in FHL. However, homozygosity by descent across this interval could not be demonstrated in an additional affected kindred of Arab origin, whose maximum multipoint LOD score was -0.12. The combined sample revealed significant evidence for linkage to 9q markers (LOD score with heterogeneity, 5.00). Identification of the gene(s) involved in the pathogenesis of FHL will contribute to an understanding of the control of T-lymphocyte and macrophage activation, which is central to homeostasis in the immune system.     

Comparison of genome screens for two independent cohorts provides replication of suggestive linkage of bone mineral density to 3p21 and 1p36

Low bone mineral density (BMD) is a major risk factor for osteoporotic fracture. Studies of BMD in families and twins have shown that this trait is under strong genetic control. To identify regions of the genome that contain quantitative trait loci (QTL) for BMD, we performed independent genomewide screens, using two complementary study designs. We analyzed unselected nonidentical twin pairs (1,094 pedigrees) and highly selected, extremely discordant or concordant (EDAC) sib pairs (254 pedigrees). Nonparametric multipoint linkage (NPL) analyses were undertaken for lumbar spine and total-hip BMD in both cohorts and for whole-body BMD in the unselected twin pairs. The maximum evidence of linkage in the unselected twins (spine BMD, LOD 2.7) and the EDAC pedigrees (spine BMD, LOD 2.1) was observed at chromosome 3p21 (76 cM and 69 cM, respectively). These combined data indicate the presence, in this region, of a gene that regulates BMD. Furthermore, evidence of linkage in the twin cohort (whole-body BMD; LOD 2.4) at chromosome 1p36 (17 cM) supports previous findings of suggestive linkage to BMD in the region. Weaker evidence of linkage (LOD 1.0-2.3) in either cohort, but not both, indicates the locality of additional QTLs. These studies validate the use, in linkage analysis, of large cohorts of unselected twins phenotyped for multiple traits, and they highlight the importance of conducting genome scans in replicate populations as a prelude to positional cloning and gene discovery.     

Multilocus and interaction-based genome scan for alcoholism risk factors in Caucasian Americans: the COGA study

In this paper, we applied the nonparametric linkage regression approach to the Caucasian genome scan data from the Collaborative Study on the Genetics of Alcoholism to search for regions of the genome that exhibit evidence for linkage to putative alcoholism-predisposing genes. The multipoint single-locus model identified four regions of the genome with LOD scores greater than one. These regions were on 7p near D7S1790 (LOD = 1.31), two regions on 7q near D7S1870 (LOD = 1.15) and D7S1799 (LOD = 1.13) and 21q near D21S1440 and D21S1446 (LOD = 1.78). Jointly modeling these loci provided stronger evidence for linkage in each of these regions (LOD = 1.58 on 7q11, LOD = 1.61 on 11q23, and LOD = 1.95 on 21q22). The evidence for linkage tended to increase among pedigrees with earlier mean age of onset at 8q23 (p = 0.0016), 14q21 (p = 0.0079), and 18p12 (p = 0.0021) and with later mean age of onset at 4q35 (p = 0.0067) and 9p22 (p = 0.0008).     

A posterior probability of linkage-based re-analysis of schizophrenia data yields evidence of linkage to chromosomes 1 and 17

OBJECTIVE: Linkage analysis using 22 Canadian pedigrees identified a promising schizophrenia candidate region on 1q23 with a maximum 2-point HLOD under a recessive model of 5.8 [Brzustowicz et al. 2000]. In the current study, we revisited this data set using a Bayesian linkage analysis technique, namely the posterior probability of linkage (PPL). METHODS: The PPL has been developed as an alternative to traditional linkage analysis. It differs from both LOD scores and 'non-parametric' methods in that it directly measures the probability of linkage given the data, and incorporates prior genomic information. RESULTS: As expected, PPL results for 1q23 supported the previously observed linkage, with an estimated multipoint PPL of 99.7%. However, the PPL supported two further results: a second peak on chromosome 1 at 1p13 with a multipoint with PPL of 70% and a chromosome 17 marker (D17S784 at 17q25) with a multipoint PPL of 44%. CONCLUSIONS: The PPL-based analysis presented has the advantage over other likelihood-based linkage methods in that it avoids maximization and produces a less complex view of the strength of evidence for linkage.     

Towards fully automated genotyping: use of an X linked recessive spastic paraplegia family to test alternative analysis methods

Advances in dinucleotide-based genetic maps open possibilities for large scale genotyping at high resolution. The current rate-limiting steps in use of these dense maps is data interpretation (allele definition), data entry, and statistical calculations. We have recently reported automated allele identification methods. Here we show that a 10-cM framework map of the human X chromosome can be analyzed on two lanes of an automated sequencer per individual (10–12 loci per lane). We use this map and analysis strategy to generate allele data for an X-linked recessive spastic paraplegia family with a known PLP mutation. We analyzed 198 genotypes in a single gel and used the data to test three methods of data analysis: manual meiotic breakpoint mapping, automated concordance analysis, and whole chromosome multipoint linkage analysis. All methods pinpointed the correct location of the gene. We propose that multipoint exclusion mapping may permit valid inflation of LOD scores using the equation max LOD — (next best LOD).     

Genomewide Multipoint Linkage Analysis of Seven Extended Palauan Pedigrees with Schizophrenia, by a Markov-Chain Monte Carlo Method

Palauans are an isolated population in Micronesia with lifetime prevalence of schizophrenia (SCZD) of 2%, compared to the world rate of approximately 1%. The possible enrichment for SCZD genes, in conjunction with the potential for reduced etiological heterogeneity and the opportunity to ascertain statistically powerful extended pedigrees, makes Palauans a population of choice for the mapping of SCZD genes. We have used a Markov-chain Monte Carlo method to perform a genomewide multipoint analysis in seven extended pedigrees from Palau. Robust multipoint parametric and nonparametric linkage (NPL) analyses were performed under three nested diagnostic classifications-core, spectrum, and broad. We observed four regions of interest across the genome. Two of these regions-on chromosomes 2p13-14 (for which, under core diagnostic classification, NPL=6.5 and parametric LOD=4.8) and 13q12-22 (for which, under broad diagnostic classification, parametric LOD=3.6, and, under spectrum diagnostic classification, parametric LOD=3.5)-had evidence for linkage with genomewide significance, after correction for multiple testing; with the current pedigree resource and genotyping, these regions are estimated to be 4.3 cM and 19.75 cM in size, respectively. A third region, with intermediate evidence for linkage, was identified on chromosome 5q22-qter (for which, under broad diagnostic classification, parametric LOD=2.5). The fourth region of interest had only borderline suggestive evidence for linkage (on 3q24-28; for this region, under broad diagnostic classification, parametric LOD=2.0). All regions exhibited evidence for genetic heterogeneity. Our findings provide significant evidence for susceptibility loci on chromosomes 2p13-14 and 13q12-22 and support both a model of genetic heterogeneity and the utility of a broader set of diagnostic classifications in the population from Palau.     

Linkage disequilibrium across two different single-nucleotide polymorphism genome scans

Linkage disequilibrium (LD) content was calculated for the Genetic Analysis Workshop 14 Affymetrix and Illumina single-nucleotide polymorphism (SNP) genome scans of the Collaborative Study on the Genetics of Alcoholism samples. Pair-wise LD was measured as both D' and r2 on 505 pedigree founder individuals. The r2 estimates were then used to correct the multipoint identity by descent matrix (MIBD) calculation to account for LD and LOD scores on chromosomes 3 and 18 were calculated for COGA's ttdt3 electrophysiological trait using those MIBDs. Extensive LD was observed throughout both marker sets, and it was higher in Affymetrix's more dense SNP map. However, SNP density did not solely account for Affymetrix's higher LD. MIBD estimation procedures assume linkage equilibrium to construct genotypes of non-genotyped pedigree founder individuals, and dense SNP genotyping maps are likely to contain moderate to high LD between markers. LOD score plots calculated after correction for LD followed the same general pattern as uncorrected ones. Since in our study almost half of the pedigree founders were genotyped, it is possible that LD had a minor impact on the LOD scores. Caution should probably be taken when using high density SNP maps when many non-genotyped founders are present in the study pedigrees.     

SLEB3 in systemic lupus erythematosus (SLE) is strongly related to SLE families ascertained through neuropsychiatric manifestations

Seizures and psychosis are neuropsychiatric (NP) manifestations of a large number of systemic lupus erythematosus (SLE) patients. Since NP manifestations were part of the SLE phenotype for some, but not all SLE affecteds, we hypothesized that those SLE patient families with NP manifestations might be more genetically homogeneous at loci important to NP-related SLE, and hence have increased power to detect linkage. We identified 23 families of European-American (EA) origin and 20 families of African-American (AA) origin, in which at least one SLE patient in each family was diagnosed with the presence of NP manifestations. A total of 318 microsatellite markers at an average marker density of 11 cM were genotyped. Uncertainty of the genetic model led us to perform the initial genome scan by a multipoint non-parametric allele sharing linkage method. Once the evidence of linkage was suggestive, we then performed parametric model-based linkage by maximizing the relevant parameters to define a parsimonious genetic model. We found the maximum multipoint parametric LOD score was 5.19 and the non-parametric linkage score (Zlr) was 3.12 ( P=9x10(-4)) for EA NP pedigrees at 4p16, previously identified as SLEB3. The segregation behavior of this linked locus suggests a dominant mode of inheritance with an almost 100% homogeneous genetic effect in these pedigrees. The results demonstrated a significant increase of LOD score to detect SLEB3 when the families were further ascertained through NP, compared with the analysis of all EA SLE families together.     

Improving estimates of genetic maps: a maximum likelihood approach

As a result of previous large, multipoint linkage studies there is a substantial amount of existing marker data. Due to the increased sample size, genetic maps estimated from these data could be more accurate than publicly available maps. However, current methods for map estimation are restricted to data sets containing pedigrees with a small number of individuals, or cannot make full use of marker data that are observed at several loci on members of large, extended pedigrees. In this article, a maximum likelihood (ML) method for map estimation that can make full use of the marker data in a large, multipoint linkage study is described. The method is applied to replicate sets of simulated marker data involving seven linked loci, and pedigree structures based on the real multipoint linkage study of Abkevich et al. (2003, American Journal of Human Genetics 73, 1271-1281). The variance of the ML estimate is accurately estimated, and tests of both simple and composite null hypotheses are performed. An efficient procedure for combining map estimates over data sets is also suggested.