Two-locus disease models with two marker loci: the power of affected-sib-pair tests.

Recently, Schork et al. found that two-trait-locus, two-marker-locus (parametric) linkage analysis can provide substantially more linkage information than can standard one-trait-locus, one-marker-locus methods. However, because of the increased burden of computation, Schork et al. do not expect that their approach will be applied in an initial genome scan. Further, the specification of a suitable two-locus segregation model can be crucial. Affected-sibpair tests are computationally simple and do not require an explicit specification of the disease model. In the past, however, these tests mainly have been applied to data with a single marker locus. Here, we consider sib-pair tests that make it possible to analyze simultaneously two marker loci. The power of these tests is investigated for different (epistatic and heterogeneous) two-trait-locus models, each trait locus being linked to one of the marker loci. We compare these tests both with the test that is optimal for a certain model and with the strategy that analyzes each marker locus separately. The results indicate that a straightforward extension of the well-known mean test for two marker loci can be much more powerful than single-marker-locus analysis and that is power is only slightly inferior to the power of the optimal test.     

Two-locus linkage analysis of cutaneous malignant melanoma/dysplastic nevi.

Previous linkage analyses of 19 cutaneous malignant melanoma/dysplastic nevi (CMM/DN) kindreds showed significant evidence of linkage and heterogeneity to both chromosomes 1p and 9p. Five kindreds also showed evidence of linkage (Z>0.7) to both regions. To further examine these findings, we conducted two-trait-locus, two-marker-locus linkage analysis. We examined one homogeneity and one heterogeneity single-locus model (SL-Hom and SL-Het), and two-locus (2L) models: an epistatic model (Ep), in which CMM was treated as a genuine 2L disease, and a heterogeneity model (Het), in which CMM could result from disease alleles at either locus. Both loci were modeled as autosomal dominant. The LOD scores for CMM alone were highest using the SL-Het model (Z = 8.48, theta = .0). There was much stronger evidence of linkage to chromosome 9p than to 1p for CMM alone; the LOD scores were approximately two times greater on 9p than on 1p. The change in LOD scores from an evaluation of CMM alone to CMM/DN suggested that a chromosome 1p locus (or loci) contributed to both CMM and CMM/DN, whereas a 9p locus contributed more to CMM alone. For both 2L models, the LOD scores from 1p were greater for CMM/DN than for CMM alone (Ep: Z=4.63 vs. 3.83; Het: 4.94 vs. 3.80, respectively). In contrast, for 9p, the LOD scores were substantially lower with CMM/DN than with CMM alone (Ep: 4.64 vs. 7.06; Het: 5.38 vs. 7.99, respectively). After conditioning on linkage to the other locus, only the 9p locus consistently showed significant evidence for linkage to CMM alone. Thus, the application of 2L models may be useful to help unravel the complexities of familial melanoma.     

Confirmation of the HPCX prostate cancer predisposition locus in large Utah prostate cancer pedigrees

Several genetic predisposition loci for prostate cancer have been identified through linkage analysis, and it is now generally recognized that no single gene is responsible for more than a small proportion of prostate cancers. However, published confirmations of these loci have been few, and failures to confirm have been frequent. The genetic etiology of prostate cancer is clearly complex and includes significant genetic heterogeneity, phenocopies, and reduced penetrance. Powerful analyses that involve robust statistics and methods to reduce genetic heterogeneity are therefore necessary. We have performed linkage analysis on 143 Utah pedigrees for the previously published Xq27-28 (HPCX) prostate cancer susceptibility locus. We employed a robust multipoint statistic (TLOD) and a novel splitting algorithm to reduce intra-familial heterogeneity by iteratively removing the top generation from the large Utah pedigrees. In a dataset containing pedigrees having no more than five generations, we observed a multipoint TLOD of 2.74 (P=0.0002), which is statistically significant after correction for multiple testing. For both the full-structure pedigrees (up to seven generations) and the smaller sub-pedigrees, the linkage evidence was much reduced. This study thus represents the first significant confirmation of HPCX (Xq27-28) and argues for the continued utility of large pedigrees in linkage analyses for complex diseases.     

How to model a complex trait. 2. Analysis with two disease loci

Complex traits are often governed by more than one trait locus. The first step towards an adequate model for such diseases is a linkage analysis with two trait loci. Such an analysis can be expected to have higher power to detect linkage than a standard single-trait-locus linkage analysis. However, it is crucial to accurately specify the parameters of the two-locus model. Here, we recapitulate the general two-locus model with and without genomic imprinting. We relate heterogeneity, multiplicative, and additive two-locus models to biological or pathophysiological mechanisms, and give the corresponding averaged ("best-fitting") single-trait-locus models for each of the two loci. Furthermore, we derive the two-locus penetrances from the averaged single-locus models, under the assumption of one of the three model classes mentioned above. Using these formulae, if the best-fitting single-locus models are available, investigators may perform a two-trait-locus linkage analysis under a realistic model. This procedure will maximize the power to detect linkage for traits which are governed by two or more loci, and lead to more accurate estimates of the disease-locus positions.     

Identification of a locus for progressive familial intrahepatic cholestasis PFIC2 on chromosome 2q24.

Progressive familial intrahepatic cholestasis (PFIC; OMIM 211600) is the second most common familial cholestatic syndrome presenting in infancy. A locus has previously been mapped to chromosome 18q21-22 in the original Byler pedigree. This chromosomal region also harbors the locus for benign recurrent intrahepatic cholestasis (BRIC) a related phenotype. Linkage analysis in six consanguineous PFIC pedigrees from the Middle East has previously excluded linkage to chromosome 18q21-22, indicating the existence of locus heterogeneity within the PFIC phenotype. By use of homozygosity mapping and a genome scan in these pedigrees, a locus designated "PFIC2" has been mapped to chromosome 2q24. A maximum LOD score of 8.5 was obtained in the interval between marker loci D2S306 and D2S124, with all families linked.     

Linkage analysis of quantitative trait loci in the presence of heterogeneity

Variance component modeling for linkage analysis of quantitative traits is a powerful tool for detecting and locating genes affecting a trait of interest, but the presence of genetic heterogeneity will decrease the power of a linkage study and may even give biased estimates of the location of the quantitative trait loci. Many complex diseases are believed to be influenced by multiple genes and therefore genetic heterogeneity is likely to be present for many real applications of linkage analysis. We consider a mixture of multivariate normals to model locus heterogeneity by allowing only a proportion of the sampled pedigrees to segregate trait-influencing allele(s) at a specific locus. However, for mixtures of normals the classical asymptotic distribution theory of the maximum likelihood estimates does not hold, so tests of linkage and/or heterogeneity are evaluated using resampling methods. It is shown that allowing for genetic heterogeneity leads to an increase in power to detect linkage. This increase is more prominent when the genetic effect of the locus is small or when the percentage of pedigrees not segregating trait-influencing allele(s) at the locus is high.     

Genetic heterogeneity in benign familial neonatal convulsions: identification of a new locus on chromosome 8q.

The syndrome of benign familial neonatal convulsions (BFNC) is a rare autosomal dominant disorder characterized by unprovoked seizures in the first few weeks of life. One locus for BFNC has been mapped to chromosome 20 in several pedigrees, but we have excluded linkage to chromosome 20 in one large kindred. In order to identify this novel BFNC locus, dinucleotide repeat markers distributed throughout the genome were used to screen this family. Maximum pairwise LOD scores of 4.43 were obtained with markers D8S284 and D8S256 on chromosome 8q. Multipoint analysis placed the BFNC locus in the interval spanned by D8S198-D8S274. This study establishes the presence of a new BFNC locus and confirms genetic heterogeneity of this disorder.     

Evidence for linkage of migraine in Rolandic epilepsy to known 1q23 FHM2 and novel 17q22 genetic loci

Migraine headaches are a common comorbidity in Rolandic epilepsy (RE) and familial aggregation of migraine in RE families suggests a genetic basis not mediated by seizures. We performed a genome‐wide linkage analysis of the migraine phenotype in 38 families with RE to localize potential genetic contribution, with a follow‐up in an additional 21 families at linked loci. We used two‐point and multipoint LOD (logarithm of the odds) score methods for linkage, maximized over genetic models. We found evidence of linkage to migraine at chromosome 17q12‐22 [multipoint HLOD (heterogeneity LOD) 4.40, recessive, 99% penetrance], replicated in the second dataset (HLOD 2.61), and suggestive evidence at 1q23.1‐23.2, centering over the FHM2 locus (two‐point LOD 3.00 and MP HLOD 2.52). Sanger sequencing in 14 migraine‐affected individuals found no coding mutations in the FHM2 gene ATP1A2. There was no evidence of pleiotropy for migraine and either reading or speech disorder, or the electroencephalographic endophenotype of RE when the affected definition was redefined as those with migraine or the comorbid phenotype, and pedigrees were reanalyzed for linkage. In summary, we report a novel migraine susceptibility locus at 17q12‐22, and a second locus that may contribute to migraine in the general population at 1q23.1‐23.2. Comorbid migraine in RE appears genetically influenced, but we did not obtain evidence that the identified susceptibility loci are consistent with pleiotropic effects on other comorbidities in RE. Loci identified here should be fine‐mapped in individuals from RE families with migraine, and prioritized for analysis in other types of epilepsy‐associated migraine.     

Parametric and nonparametric multipoint linkage analysis with imprinting and two-locus-trait models: application to mite sensitization

We present two extensions to linkage analysis for genetically complex traits. The first extension allows investigators to perform parametric (LOD-score) analysis of traits caused by imprinted genes-that is, of traits showing a parent-of-origin effect. By specification of two heterozygote penetrance parameters, paternal and maternal origin of the mutation can be treated differently in terms of probability of expression of the trait. Therefore, a single-disease-locus-imprinting model includes four penetrances instead of only three. In the second extension, parametric and nonparametric linkage analysis with two trait loci is formulated for a multimarker setting, optionally taking imprinting into account. We have implemented both methods into the program GENEHUNTER. The new tools, GENEHUNTER-IMPRINTING and GENEHUNTER-TWOLOCUS, were applied to human family data for sensitization to mite allergens. The data set comprises pedigrees from England, Germany, Italy, and Portugal. With single-disease-locus-imprinting MOD-score analysis, we find several regions that show at least suggestive evidence for linkage. Most prominently, a maximum LOD score of 4.76 is obtained near D8S511, for the English population, when a model that implies complete maternal imprinting is used. Parametric two-trait-locus analysis yields a maximum LOD score of 6.09 for the German population, occurring exactly at D4S430 and D18S452. The heterogeneity model specified for analysis alludes to complete maternal imprinting at both disease loci. Altogether, our results suggest that the two novel formulations of linkage analysis provide valuable tools for genetic mapping of multifactorial traits.     

Predisposition locus for major depression at chromosome 12q22-12q23.2

Major depression disorder is a common psychiatric disease with a major economic impact on society. In many cases, no effective treatment is available. The etiology of major depression is complex, but it is clear that the disease is, to a large extent, determined genetically, especially among individuals with a familial history of major depression, presumably through the involvement of multiple predisposition genes in addition to an environmental component. As a first step toward identification of chromosomal loci contributing to genetic predisposition to major depression, we have conducted a genomewide scan by using 628 microsatellite markers on 1,890 individuals from 110 Utah pedigrees with a strong family history of major depression. We identified significant linkage to major depression in males at marker D12S1300 (multipoint heterogeneity LOD score 4.6; P=.00003 after adjustment for multiple testing). With additional markers, the linkage evidence became highly significant, with the multipoint heterogeneity LOD score at marker D12S1706 increasing to 6.1 (P=.0000007 after adjustment for multiple testing). This study confirms the presence of one or more genes involved in psychiatric diseases on the q arm of chromosome 12 and provides strong evidence for the existence of a sex-specific predisposition gene to major depression at 12q22-q23.2.     

Genomewide search in familial Paget disease of bone shows evidence of genetic heterogeneity with candidate loci on chromosomes 2q36, 10p13, and 5q35

Paget disease of bone (PDB) is a common disorder characterized by focal abnormalities of increased and disorganized bone turnover. Genetic factors are important in the pathogenesis of PDB, and previous studies have shown that the PDB-like bone dysplasia familial expansile osteolysis is caused by activating mutations in the TNFRSF11A gene that encodes receptor activator of nuclear factor kappa B (RANK); however, linkage studies, coupled with mutation screening, have excluded involvement of RANK in the vast majority of patients with PDB. To identify other candidate loci for PDB, we conducted a genomewide search in 319 individuals, from 62 kindreds with familial PDB, who were predominantly of British descent. The pattern of inheritance in the study group as a whole was consistent with autosomal dominant transmission of the disease. Parametric multipoint linkage analysis, under a model of heterogeneity, identified three chromosomal regions with LOD scores above the threshold for suggestive linkage. These were on chromosomes 2q36 (LOD score 2.7 at 218.24 cM), 5q35 (LOD score 3.0 at 189.63 cM), and 10p13 (LOD score 2.6 at 41.43 cM). For each of these loci, formal heterogeneity testing with HOMOG supported a model of linkage with heterogeneity, as opposed to no linkage or linkage with homogeneity. Two-point linkage analysis with a series of markers from the 5q35 region in another large kindred with autosomal dominant familial PDB also supported linkage to the candidate region with a maximum LOD score of 3.47 at D5S2034 (187.8 cM). These data indicate the presence of several susceptibility loci for PDB and identify a strong candidate locus for the disease, on chromosome 5q35.     

A second-generation genetic linkage map of the baboon (Papio hamadryas) genome

Construction of genetic linkage maps for nonhuman primate species provides information and tools that are useful for comparative analysis of chromosome structure and evolution and facilitates comparative analysis of meiotic recombination mechanisms. Most importantly, nonhuman primate genome linkage maps provide the means to conduct whole genome linkage screens for localization and identification of quantitative trait loci that influence phenotypic variation in primate models of common complex human diseases such as atherosclerosis, hypertension, and diabetes. In this study we improved a previously published baboon whole genome linkage map by adding more loci. New loci were added in chromosomal regions that did not have sufficient marker density in the initial map. Relatively low heterozygosity loci from the original map were replaced with higher heterozygosity loci. We report in detail on baboon chromosomes 5, 12, and 18 for which the linkage maps are now substantially improved due to addition of new informative markers.     

Construction of a genetic linkage map in man using restriction fragment length polymorphisms.

We describe a new basis for the construction of a genetic linkage map of the human genome. The basic principle of the mapping scheme is to develop, by recombinant DNA techniques, random single-copy DNA probes capable of detecting DNA sequence polymorphisms, when hybridized to restriction digests of an individual's DNA. Each of these probes will define a locus. Loci can be expanded or contracted to include more or less polymorphism by further application of recombinant DNA technology. Suitably polymorphic loci can be tested for linkage relationships in human pedigrees by established methods; and loci can be arranged into linkage groups to form a true genetic map of "DNA marker loci." Pedigrees in which inherited traits are known to be segregating can then be analyzed, making possible the mapping of the gene(s) responsible for the trait with respect to the DNA marker loci, without requiring direct access to a specified gene's DNA. For inherited diseases mapped in this way, linked DNA marker loci can be used predictively for genetic counseling.     

A genome-wide search for genes predisposing to manic-depression, assuming autosomal dominant inheritance.

Manic-depressive illness (MDI), also known as "bipolar affective disorder," is a common and devastating neuropsychiatric illness. Although pivotal biochemical alterations underlying the disease are unknown, results of family, twin, and adoption studies consistently implicate genetic transmission in the pathogenesis of MDI. In order to carry out linkage analysis, we ascertained eight moderately sized pedigrees containing multiple cases of the disease. For a four-allele marker mapping 5 cM from the disease gene, the pedigree sample has > 97% power to detect a dominant allele under genetic homogeneity and has > 73% power under 20% heterogeneity. To date, the eight pedigrees have been genotyped with 328 polymorphic DNA loci throughout the genome. When autosomal dominant inheritance was assumed, 273 DNA markers gave lod scores < -2.0 at recombination fraction (theta) = .0, 174 DNA loci produced lod scores < -2.0 at theta = .05, and 4 DNA marker loci yielded lod scores > 1 (chromosome 5--D5S39, D5S43, and D5S62; chromosome 11--D11S85). Of the markers giving lod scores > 1, only D5S62 continued to show evidence for linkage when the affected-pedigree-member method was used. The D5S62 locus maps to distal 5q, a region containing neurotransmitter-receptor genes for dopamine, norepinephrine, glutamate, and gamma-aminobutyric acid. Although additional work in this region may be warranted, our linkage results should be interpreted as preliminary data, as 68 unaffected individuals are not past the age of risk.     

DNA pooling strategy for saturation mapping in outbred crosses

We present a method to identify molecular markers linked to a genomic interval in outbred pedigrees. Using information from fully informative RFLP markers on a single linkage group containing a quantitative trait locus for wood specific gravity, we constructed four DNA pools from nonrecombinant progeny of a three-generation outbred pedigree. The four pools were screened to identify linked RAPD markers. The phase and zygosity of a linked RAPD marker could be determined directly from the array of RAPD bands present or absent in the four pools. Two hundred fifty-six primers were tested on the four DNA pools, revealing 61 putatively linked loci. Nine RAPD loci were linked to the genomic interval. The approach developed here could be generally applied to saturation mapping in outbred pedigrees where fully informative markers have previously been mapped.     

A comparison of different linkage statistics in small to moderate sized pedigrees with complex diseases

ABSTRACT: BACKGROUND: In the last years GWA studies have successfully identified common SNPs associated with complex diseases. However, most of the variants found this way account for only a small portion of the trait variance. This fact leads researchers to focus on rare-variant mapping with large scale sequencing, which can be facilitated by using linkage information. The question arises why linkage analysis often fails to identify genes when analyzing complex diseases. Using simulations we have investigated the power of parametric and nonparametric linkage statistics (KC-LOD, NPL, LOD and MOD scores), to detect the effect of genes responsible for complex diseases using different pedigree structures. RESULTS: As expected, a small number of pedigrees with less than three affected individuals has low power to map disease genes with modest effect. Interestingly, the power decreases when unaffected individuals are included in the analysis, irrespective of the true mode of inheritance. Furthermore, we found that the best performing statistic depends not only on the type of pedigrees but also on the true mode of inheritance. CONCLUSIONS: When applied in a sensible way linkage is an appropriate and robust technique to map genes for complex disease. Unlike association analysis, linkage analysis is not hampered by allelic heterogeneity. So, why does linkage analysis often fail with complex diseases? Evidently, when using an insufficient number of small pedigrees, one might miss a true genetic linkage when actually a real effect exists. Furthermore, we show that the test statistic has an important effect on the power to detect linkage as well. Therefore, a linkage analysis might fail if an inadequate test statistic is employed. We provide recommendations regarding the most favorable test statistics, in terms of power, for a given mode of inheritance and type of pedigrees under study, in order to reduce the probability to miss a true linkage.     

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.     

Pooled genome linkage scan of aggressive prostate cancer: results from the International Consortium for Prostate Cancer Genetics

While it is widely appreciated that prostate cancers vary substantially in their propensity to progress to a life-threatening stage, the molecular events responsible for this progression have not been identified. Understanding these molecular mechanisms could provide important prognostic information relevant to more effective clinical management of this heterogeneous cancer. Hence, through genetic linkage analyses, we examined the hypothesis that the tendency to develop aggressive prostate cancer may have an important genetic component. Starting with 1,233 familial prostate cancer families with genome scan data available from the International Consortium for Prostate Cancer Genetics, we selected those that had at least three members with the phenotype of clinically aggressive prostate cancer, as defined by either high tumor grade and/or stage, resulting in 166 pedigrees (13%). Genome-wide linkage data were then pooled to perform a combined linkage analysis for these families. Linkage signals reaching a suggestive level of significance were found on chromosomes 6p22.3 (LOD = 3.0), 11q14.1–14.3 (LOD = 2.4), and 20p11.21–q11.21 (LOD = 2.5). For chromosome 11, stronger evidence of linkage (LOD = 3.3) was observed among pedigrees with an average at diagnosis of 65 years or younger. Other chromosomes that showed evidence for heterogeneity in linkage across strata were chromosome 7, with the strongest linkage signal among pedigrees without male-to-male disease transmission (7q21.11, LOD = 4.1), and chromosome 21, with the strongest linkage signal among pedigrees that had African American ancestry (21q22.13–22.3; LOD = 3.2). Our findings suggest several regions that may contain genes which, when mutated, predispose men to develop a more aggressive prostate cancer phenotype. This provides a basis for attempts to identify these genes, with potential clinical utility for men with aggressive prostate cancer and their relatives. The names of all authors and their affiliations are listed in the Acknowledgements. The fact that Dr Schaid’s name is given here for purposes of correspondence should not be taken to imply that he played the sole leading part in writing this article. An erratum to this article can be found at     

An integrated genetic linkage map with 1,137 markers constructed from five F2 crosses of autoimmune disease-prone and -resistant inbred rat strains

The rat (Rattus norvegicus) is an important experimental model for many human diseases including arthritis, diabetes, and other autoimmune and chronic inflammatory diseases. The rat genetic linkage map, however, is less well developed than those of mouse and human. Integrated rat genetic linkage maps have been previously reported by Pravenec et al. (1996, Mamm. Genome 7: 117-127) (500 markers mapped in one cross), Bihoreau et al. (1997, Genome Res. 7: 434-440) (767 markers mapped in three crosses), Wei et al. (1998, Mamm. Genome 9: 1002-1007) (562 markers mapped in two crosses), Brown et al. (1998, Mamm. Genome 9: 521-530) (678 markers mapped in four crosses), and Nordquist et al. (1999, Rat Genome 5: 15-20) (330 markers mapped in two crosses). The densest linkage map combined with a radiation hybrid map, reported by Steen et al. (1999, Genome Res. 9: AP1-AP8), includes 4736 markers mapped in two crosses. Here, we present an integrated linkage map with 1137 markers. We have constructed this map by genotyping F2 progeny of five crosses: F344/NHsd x LEW/NHsd (673 markers), DA/Bkl x F344/NHsd (531 markers), BN/SsN x LEW/N (714 markers), DA/Bkl x BN/SsNHsd (194 markers), and DA/Bkl x ACI/SegHsd (245 markers). These inbred rat strains vary in susceptibility/resistance to multiple autoimmune diseases and are used extensively for many types of investigation. The integrated map includes 360 loci mapped in three or more crosses. The map contains 196 new SSLP markers developed by our group, as well as many SSLP markers developed by other groups. Two hundred forty genes are incorporated in the map. This integrated map should allow comparison of rat genetic maps from different groups and thereby facilitate genetic studies of rat autoimmune and related disease models.     

Utility and efficiency of linked marker genes for genetic counseling. III. Proportion of informative families under linkage disequilibrium.

A marker locus closely linked to a disease locus is often useful for genetic counseling provided that a counselee is heterozygous at both disease and marker loci. Furthermore, the linkage phase of these genes in the counselee must be known. When the linkage between the disease and marker loci is very close, one often finds linkage disequilibrium between the loci. To evaluate the effect of such nonrandom associations on the utility of linked marker genes for genetic counseling, the proportion of informative families is studied for X-linked recessive and autosomal dominant diseases. This proportion is higher for X-linked genes than for autosomal genes, if other factors are the same. In general, codominant markers are more useful than dominant markers. Also, under appropriate conditions, the proportion of informative families is higher when linkage disequilibrium is present. The results obtained in this paper are useful for evaluating the utility of polymorphic restriction endonuclease cleavage sites as markers in genetic counseling.