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A simulated annealing algorithm for maximum likelihood pedigree reconstruction.

The calculation of maximum likelihood pedigrees for related organisms using genotypic data is considered. The problem is formulated so that the domain of optimization is a permutation space. This is a feature shared by the travelling salesman problem, for which simulated annealing is known to be effective. Using this technique it is found that pedigrees can be reconstructed with minimal error using genotypic data of a quality currently realizable. In complex pedigrees accurate reconstruction can be done with no a priori age or sex information. For smaller numbers of individuals a method of efficiently enumerating all admissible pedigrees of nonzero likelihood is given.

Algorithms↗

Diminished support for linkage between manic depressive illness and X-chromosome markers in three Israeli pedigrees.

The hypothesis that chromosomal region Xq27-28 harbours a gene for manic-depression has been a focus of interest in human genetics. X-linked inheritance of manic depressive illness has been re-examined in 3 multigeneration Israeli kindreds. Extension and re-evaluation of pedigree data, including new individuals, diagnostic follow-up, and analysis with DNA markers, shows greatly diminished support for linkage to Xq28. The peak lod scores in two of the pedigrees have dropped several lod units to clearly negative values at the RCP-F8-G6PD gene cluster. On the other hand, positive lod scores (Zmax = 2.09) are sustained in another pedigree at the same map location. None of the pedigrees show linkage to more proximal markers, including the Xq27 locus DXS98. Our analysis underscores the uncertainties in studying complex disorders.

Adult↗

A common disease haplotype segregating in spinocerebellar ataxia 2 (SCA2) pedigrees of diverse ethnic origin.

The identification of a CAG trinucleotide repeat expansion, located within the coding sequence of the ataxin-2 gene, as the mutation underlying spinocerebellar ataxia 2 (SCA2) has facilitated direct investigation of pedigrees previously excluded from linkage analysis due to insufficient size or pedigree structure. We have previously described the identification of the ancestral disease haplotype segregating in the Cuban founder population used to assign the disease locus to chromosome 12q23-24.1. We now report evidence for the segregation of the identical core haplotype in pedigrees of diverse ethnic origin from India, Japan and England, established by the analysis of the loci D12S1672 and D12S1333 located 20kb proximal and 200 kb distal to the triplet repeat motif respectively. Interpretation of this data is suggestive that for these pedigrees at least, the mutation has arisen on a single ancestral or predisposing chromosome.

Alleles↗

Analytic power calculation for QTL linkage analysis of small pedigrees.

Power calculation for QTL linkage analysis can be performed via simple algebraic formulas for small pedigrees, but requires intensive computation for large pedigrees, in order to evaluate the expectation of the test statistic over all possible inheritance vectors at the test position. In this report, we show that the non-centrality parameter for an arbitrary pedigree can be approximated by the sum of the variances of the correlations between all pairs of relatives, each variance being weighted by a factor that is determined by the mean correlation of the pair. We show that this approximation is sufficiently accurate for practical purposes in small to moderately large pedigrees, and that large sibships are more efficient than other family structures under a range of genetic models.

Analysis of Variance↗

QTL analysis in arbitrary pedigrees with incomplete marker information.

Mapping quantitative trait loci (QTL) in arbitrary outbred pedigrees is complicated by the combinatorial possibilities of allele flow relationships and of the founder allelic configurations. Exact methods are only available for rather short and simple pedigrees. Stochastic simulation using Markov chain Monte Carlo (MCMC) integration offers more flexibility. MCMC methods are less natural in a frequentist than in a Bayesian context, which we therefore adopt. Among the MCMC algorithms for updating marker locus genotypes, we implement the descent-graph algorithm. It can be used to update marker locus allele flow relationships and can handle arbitrarily complex pedigrees and missing marker information. Compared with updating marker genotypic information, updating QTL parameters, such as position, effects, and the allele flow relationships is relatively easy with MCMC. We treat the effect of each diploid combination of founder alleles as a random variable and only estimate the variance of these effects, ie, we model diploid genotypic effects instead of the usual partition in additive and dominance effects. This is a variant of the random model approach. The number of QTL alleles is generally unknown. In the Bayesian context, the number of QTL present on a linkage group can be treated as variable. Computer simulations suggest that the algorithm can indeed handle complex pedigrees and detect two QTL on a linkage group, but that the number of individuals in a single extended family is limited to about 50 to 100 individuals.

Chromosome Mapping↗

Homozygous missense mutation in fibulin-5 in an Iranian autosomal recessive cutis laxa pedigree and associated haplotype.

Cutis laxa is a rare group of inherited and acquired disorders characterized by loose and redundant skin with reduced elasticity. Mutations in the elastin coding gene have been shown to cause autosomal dominant cutis laxa in three families. A homozygous mutation in the fibulin-5 coding gene was discovered in a Turkish pedigree showing recessive inheritance, and a different mutation in this gene was found in the heterozygous state in a sporadic case of the disease. Here, we report the third case of a mutation in the fibulin-5 coding gene in a recessive Iranian cutis laxa pedigree. The mutation is the same as previously reported in the Turkish pedigree, further confirming that it is causative of disease. A haplotype consisting of seven intragenic sequence variations common to both pedigrees is described for the mutation-carrying fibulin-5 allele.

Adolescent↗

A genome screen of 13 bipolar affective disorder pedigrees provides evidence for susceptibility loci on chromosome 3 as well as chromosomes 9, 13 and 19.

Bipolar affective disorder is a severe mood disorder that afflicts approximately 1% of the population worldwide. Twin and adoption studies have indicated that genetic factors contribute to the disorder and while many chromosomal regions have been implicated, no susceptibility genes have been identified. We undertook a combined analysis of 10 cM genome screen data from a single large bipolar affective disorder pedigree, for which we have previously reported linkage to chromosome 13q14 (Badenhop et al, 2001) and 12 pedigrees independently screened using the same 400 microsatellite markers. This 13-pedigree cohort consisted of 231 individuals, including 69 affected members. Two-point LOD score analysis was carried out under heterogeneity for three diagnostic and four genetic models. Non-parametric multipoint analysis was carried out on regions of interest. Two-point heterogeneity LOD scores (HLODs) greater than 1.5 were obtained for 11 markers across the genome, with HLODs greater than 2.0 obtained for four of these markers. The strongest evidence for linkage was at 3q25-26 with a genome-wide maximum score of 2.49 at D3S1279. Six markers across a 50 cM region at 3q25-26 gave HLODs greater than 1.5, with three of these markers producing scores greater than 2.0. Multipoint analysis indicated a 20 cM peak between markers D3S1569 and D3S1614 with a maximum NPL of 2.8 (P= 0.004). Three other chromosomal regions yielded evidence for linkage: 9q31-q33, 13q14 and 19q12-q13. The regions on chromosomes 3q and 13q have previously been implicated in other bipolar and schizophrenia studies. In addition, several individual pedigrees gave LOD scores greater than 1.5 for previously reported bipolar susceptibility loci on chromosomes 18p11, 18q12, 22q11 and 8p22-23.

Bipolar Disorder↗

A genome screen of 13 bipolar affective disorder pedigrees provides evidence for susceptibility loci on chromosome 3 as well as chromosomes 9, 13 and 19.

Bipolar affective disorder is a severe mood disorder that afflicts approximately 1% of the population worldwide. Twin and adoption studies have indicated that genetic factors contribute to the disorder and while many chromosomal regions have been implicated, no susceptibility genes have been identified. We undertook a combined analysis of 10 cM genome screen data from a single large bipolar affective disorder pedigree, for which we have previously reported linkage to chromosome 13q14 (Badenhop et al, 2001) and 12 pedigrees independently screened using the same 400 microsatellite markers. This 13 pedigree cohort consisted of 231 individuals, including 69 affected members. Two-point LOD score analysis was carried out under heterogeneity for three diagnostic and four genetic models. Non-parametric multipoint analysis was carried out on regions of interest. Two-point heterogeneity LOD scores (HLODs) greater than 1.5 were obtained for 11 markers across the genome, with HLODs greater than 2.0 obtained for four of these markers. The strongest evidence for linkage was at 3q25-26 with a genome-wide maximum score of 2.49 at D3S1279. Six markers across a 50 cM region at 3q25-26 gave HLODs greater than 1.5, with three of these markers producing scores greater than 2.0. Multipoint analysis indicated a 20 cM peak between markers D3S1569 and D3S1614 with a maximum NPL of 2.8 (P = 0.004). Three other chromosomal regions yielded evidence for linkage: 9q31-q33, 13q14 and 19q12-q13. The regions on chromosomes 3q and 13q have previously been implicated in other bipolar and schizophrenia studies. In addition, several individual pedigrees gave LOD scores greater than 1.5 for previously reported bipolar susceptibility loci on chromosomes 18p11, 18q12, 22q11 and 8p22-23.

Bipolar Disorder↗

Linkage of a bipolar disorder susceptibility locus to human chromosome 13q32 in a new pedigree series.

Bipolar (BP) disorder or manic depressive illness is a major psychiatric disorder for which numerous family, twin and adoption studies support a substantial genetic contribution. Recently, we reported the results of a genome-wide search for BP disorder susceptibility loci in 20 pedigrees. Suggestive evidence for linkage was found in this study at three markers on 13q, representing possibly two peaks separated by 18 cM. We have now collected a second set of 32 pedigrees segregating BP disorder and have tested for evidence of linkage to markers on human chromosome 13q. In this sample, we have replicated the linkage result in 13q32 at D13S154 (lod=2.29), the more proximal of the two original peaks. When all 52 pedigrees were combined, the multipoint maximum lod score peaked approximately 7 cM proximal to D13S154 (lod=3.40), with a second peak occurring between D13S225 and D13S796 (lod=2.58). There have been several other reports of significant linkage to both BP disorder and schizophrenia in this region of chromosome 13. These pedigrees provide additional evidence for at least one locus for BP disorder in 13q32, and are consistent with other reports of a possible genetic overlap between these disorders.

Bipolar Disorder↗

Genetic dissection of human stature in a large sample of multiplex pedigrees.

Recently, we reported a whole genome scan on a sample of 630 Caucasian subjects from 53 human pedigrees. Several genomic regions were suggested to be linked to height. In an attempt to confirm the identified genomic regions, as well as to identify new genomic regions linked to height, we conducted a whole genome linkage study on an extended sample of 1,816 subjects from 79 pedigrees, which includes the 53 pedigrees containing the original 630 subjects from our previous whole genome study and an additional 128 new subjects, and 26 further pedigrees containing 1,058 subjects. Several regions achieved suggestive linkage signals, such as 9q22.32 [MLS (multipoint LOD score) = 2.74], 9q34.3 [MLS = 2.66], Xq24 [two-point LOD score = 2.64 at the marker DXS8067], and 7p14.2 [MLS = 2.05]. The importance of the above regions is supported either by other whole genome studies or by candidate genes within these regions relevant to linear growth or pathogenesis of short stature. In addition, this study has tentatively confirmed the Xq24 region's linkage to height, as this region was also detected in the previous whole genome study. To date, our study has achieved the largest sample size in the field of genetic linkage studies of human height. Together with the findings of other studies, the current study has further delineated the genetic basis of human stature.

Adult↗

No evidence for significant linkage between bipolar affective disorder and chromosome 18 pericentromeric markers in a large series of multiplex extended pedigrees.

Bipolar affective disorder (BP) is a major neuropsychiatric disorder with high heritability and complex inheritance. Previously reported linkage between BP and DNA markers in the pericentromeric region of chromosome 18, with a parent-of-origin effect (linkage was present in pedigrees with paternal transmission and absent in pedigrees with exclusive maternal inheritance), has been a focus of interest in human genetics. We reexamined the evidence in one of the largest samples reported to date (1,013 genotyped individuals in 53 unilineal multiplex pedigrees), using 10 highly polymorphic markers and a range of parametric and nonparametric analyses. There was no evidence for significant linkage between BP and chromosome 18 pericentromeric markers in the sample as a whole, nor was there evidence for significant parent-of-origin effect (pedigrees with paternal transmission were not differentially linked to the implicated chromosomal region). Two-point LOD scores and single-locus sib-pair results gave some support for suggestive linkage, but this was not substantiated by multilocus analysis, and the results were further tempered by multiple test effects. We conclude that there is no compelling evidence for linkage between BP and chromosome 18 pericentromeric markers in this sample.

Adolescent↗

Prostate cancer susceptibility locus HPC1 in Utah high-risk pedigrees.

A prostate cancer susceptibility locus ( HPC1 ) at 1q24-25 has been identified. Subsequent analysis showed that the majority of the evidence for localization was provided by families with relatively young (<65 years) average age at diagnosis. We examined evidence for linkage to this region in a set of 41 extended multi-case prostate cancer pedigrees containing 440 prostate cancer cases. Genotyping of five short tandem repeat markers in the region was performed on DNA from 1724 individuals, including 284 prostate cancer cases. In comparison with the families reported in the initial localization, the Utah pedigrees are generally much larger (average of 10.7 versus 5.1 cases) and have an older average age at diagnosis (69 versus 65 years). Two- and three-point linkage analyses were conducted using a previously reported model and provided replication for HPC1 (two-point: LOD = 1.73, P = 0.005 at D1S196; three-point: LOD = 2.06, P = 0.002 for the interval D1S196-D1S416 ). The youngest quartile (by median age at diagnosis) yielded a maximum LOD of 2.82, P = 0. 0003 (at D1S215-D1S222 ), compared with a maximum LOD of 0.73, P = 0. 07 for the oldest quartile pedigrees at the same locus. Further analysis with an age-dependent model, specifying higher sporadic rates for older cases, suggests that the linkage evidence may be lower than expected given the power of the resource due to a high sporadic rate in the large Utah pedigrees.

Aged↗

Enumeration and simulation of marriage node graphs on zero-loop pedigrees.

We present a method that for the marriage node graph of a zero-loop pedigree will enumerate all possible pedigrees that share the same underlying tree structure. The enumeration method leads naturally to a scheme for simulating from a uniform distribution on such pedigrees. This is extended to simulating pedigrees for which the underlying marriage node graph is a tree of any particular size.

Female↗

Monte Carlo estimation of variance component models for large complex pedigrees.

Variance component models are widely used in animal and plant breeding. In human genetics, they can be used to identify, among other traits associated with the definition of disease, those that have a significant genetic component in their aetiology. In addition, they can be used in genetic counselling. Most of the methods currently proposed for estimating variance component models often involve repeated inversion of large matrices, resulting in intensive computations, large storage requirements, and numerical instability. Consequently, these methods are restricted to data on nuclear families, to small pedigrees, or to designed pedigrees of simple form. In this paper, the authors propose a method for estimating variance component models for large complex pedigrees using jointly the EM algorithm and the Gibbs sampler. The method can handle variance component models with multiple variance components, without the need for repeated inversion of large matrices even on large complex pedigrees. The method is conceptually simple, numerically stable, and easy to implement.

Algorithms↗

The aunt and uncle effect: an empirical evaluation of the confounding influence of full sibs of parents on pedigree reconstruction.

This study used simulations and a known two-generation pedigree of chinook salmon (Oncorhynchus tshawytscha) to evaluate the effect of full sibs of parents on pedigree reconstruction. Parentage analysis was conducted on 100 parent pair-offspring relationships from pedigrees with unrelated (simulation) and related (chinook salmon) candidate parents. Parentage assignment success for the chinook salmon was lower than in the simulated populations. For example, the six most variable loci (mean H(E) = 0.87) provided a mean of 97% unambiguous assignments in the simulated population and 67% unambiguous assignments for the chinook salmon. Estimates of the pairwise relatedness coefficient ((xy)) for most nonexcluded false parents and true parents of chinook salmon offspring exceeded 0.50. These results support the conclusion that closely related candidate parents decrease the power of genetic markers for pedigree reconstruction based on exclusion. Ambiguous parentage may be resolved using single parent- and parent pair-offspring likelihood analysis, however, these methods should be used with caution and they are not replacements for using more loci when many candidate parents are full sibs.

Animals↗

A pedigree series for mapping disease genes in bipolar affective disorder: sampling, assessment, and analytic considerations.

A series of 57 extended pedigrees with high density of bipolar affective disorder is described. Ascertainment and diagnostic procedures are documented and simulation studies to assess statistical power are carried out. The pedigrees, obtained in the US and Israel, are comprised of 1508 adult individuals with best estimate consensus diagnoses (12-71 relatives per pedigree), 490 of whom (including 401 sib pairs) meet criteria for a conservative disease definition (bipolar disorder or recurrent major depression). Cell lines have been established on 1324 of these individuals. Statistical power to detect linkage with lod score analysis, assuming autosomal dominant transmission and highly polymorphic DNA markers, is nearly 100% for alpha (proportion of linked families) = 30%, and 75% for alpha = 20%. This is the largest bipolar pedigree series reported to date; its unique features make it amenable to various gene detection techniques.

Bipolar Disorder↗

Unusual pedigree patterns in seven families with spinal muscular atrophy; further evidence for the allelic model hypothesis.

Clinical and genetic findings are presented in 18 patients, from 7 pedigrees with different types of spinal muscular atrophy (SMA). The SMA diagnosis was based on EMG and muscle biopsy findings. All 7 pedigrees show an unusual genetic pattern, not consistent with simple autosomal recessive inheritance. Furthermore, in 6 of the 7 pedigrees different types of SMA were present within each pedigree. Our findings can be explained by an extension of a multiple alleles hypothesis originally described by Becker in 1964.

Alleles↗

An algorithm for Monte Carlo estimation of genotype probabilities on complex pedigrees.

Exact probability and likelihood computation on complex pedigrees is often infeasible, since exact methods are too computationally intensive even with today's computing technology. A statistical tool, Markov chain Monte Carlo (MCMC), is increasingly being explored as a technique for estimating probabilities of genotypic configurations on pedigrees conditional on phenotypic data. However, this conditional probability distribution on a complex pedigree is, in general, multimodal, and multimodality is one of the major difficulties in MCMC exploration of a probability surface. In this paper, a new member of the MCMC Metropolis-Hastings class of algorithms is proposed; the heated-Metropolis algorithm. The algorithm achieves passage through low probability states to other local modes of the probability distribution, and so provides much improved estimates of probabilities of interest. The example considered is the estimation of the probabilities of carrier genotype for the founders of a complex pedigree in which a very rare lethal recessive trait is segregating.

Algorithms↗