A score test for linkage analysis of ordinal traits based on IBD sharing

Statistical methods for linkage analysis are well established for both binary and quantitative traits. However, numerous diseases including cancer and psychiatric disorders are rated on discrete ordinal scales. To analyze pedigree data with ordinal traits, we recently proposed a latent variable model which has higher power to detect linkage using ordinal traits than methods using the dichotomized traits. The challenge with the latent variable model is that the likelihood is usually very complicated, and as a result, the computation of the likelihood ratio statistic is too intensive for large pedigrees. In this paper, we derive a computationally efficient score statistic based on the identity-by-decent sharing information between relatives. Using simulation studies, we examined the asymptotic distribution of the test statistic and the power of our proposed test under various levels of heritability. We compared the computing time as well as power of the score test with the likelihood ratio test. We then applied our method for the Collaborative Study on the Genetics of Alcoholism and performed a genome scan to map susceptibility genes for alcohol dependence. We found a strong linkage signal on chromosome 4.     

Potential bias in NMR relaxation data introduced by peak intensity analysis and curve fitting methods

We present an evaluation of the accuracy and precision of relaxation rates calculated using a variety of methods, applied to data sets obtained for several very different protein systems. We show that common methods of data evaluation, such as the determination of peak heights and peak volumes, may be subject to bias, giving incorrect values for quantities such as R₁ and R₂. For example, one common method of peak-height determination, using a search routine to obtain the peak-height maximum in successive spectra, may be a source of significant systematic error in the relaxation rate. The alternative use of peak volumes or of a fixed coordinate position for the peak height in successive spectra gives more accurate results, particularly in cases where the signal/noise is low, but these methods have inherent problems of their own. For example, volumes are difficult to quantitate for overlapped peaks. We show that with any method of sampling the peak intensity, the choice of a 2- or 3-parameter equation to fit the exponential relaxation decay curves can dramatically affect both the accuracy and precision of the calculated relaxation rates. In general, a 2-parameter fit of relaxation decay curves is preferable. However, for very low intensity peaks a 3 parameter fit may be more appropriate.     

Estimating effective population size from linkage disequilibrium: severe bias in small samples

Effective population size (N _e) is a central concept in evolutionary biology and conservation genetics. It predicts rates of loss of neutral genetic variation, fixation of deleterious and favourable alleles, and the increase of inbreeding experienced by a population. A method exists for the estimation of N _e from the observed linkage disequilibrium between unlinked loci in a population sample. While an increasing number of studies have applied this method in natural and managed populations, its reliability has not yet been evaluated. We developed a computer program to calculate this estimator of N _e using the most widely used linkage disequilibrium algorithm and used simulations to show that this estimator is strongly biased when the sample size is small (<‰100) and below the true N _e. This is probably due to the linkage disequilibrium generated by the sampling process itself and the inadequate correction for this phenomenon in the method. Results suggest that N _e estimates derived using this method should be regarded with caution in many cases. To improve the method’s reliability and usefulness we propose a way to determine whether a given sample size exceeds the population N _e and can therefore be used for the computation of an unbiased estimate.     

A bias correction for estimates of effective population size based on linkage disequilibrium at unlinked gene loci*

Analysis of linkage disequilibrium (=mean squared correlation of allele frequencies at different gene loci) provides a means of estimating effective population size (N _e) from a single sample, but this method has seen much less use than the temporal method (which requires at least two samples). It is shown that for realistic numbers of loci and alleles, the linkage disequilibrium method can provide precision comparable to that of the temporal method. However, computer simulations show that estimates of N _e based on for unlinked, diallelic gene loci are sharply biased downwards ( in some cases) if sample size (S) is less than true N _e. The bias is shown to arise from inaccuracies in published formula for when S and/or N _e are small. Empirically derived modifications to for two mating systems (random mating and lifetime monogamy) effectively eliminate the bias (residual bias in % in most cases). The modified method also performs well in estimating N _e in non-ideal populations with skewed sex ratio or non-random variance in reproductive success. Recent population declines are not likely to seriously affect , but if N has recently increased from a bottleneck can be biased downwards for a few generations. These results should facilitate application of the disequilibrium method for estimating contemporary N _e in natural populations. However, a comprehensive assessment of performance of with highly polymorphic markers such as microsatellites is needed.The US Governmentȁ9s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Inherent bias toward the null hypothesis in conventional multipoint nonparametric linkage analysis

Traditional nonparametric "multipoint" statistical procedures have been developed for assigning allele-sharing values at a locus of interest to pairs of relatives for linkage studies. These procedures attempt to accommodate a lack of informativity, nongenotyped loci, missing data, and related issues concerning the genetic markers used in a linkage study. However, such procedures often cannot overcome these phenomena in compelling ways and, as a result, assign relevant relative pairs allele-sharing values that are "expected" for those pairs. The practice of assigning expected allele-sharing values to relative pairs in the face of a lack of explicit allele-transmission information can bias traditional nonparametric linkage test statistics toward the null hypothesis of no locus effect. This bias is due to the use of expected values, rather than to a lack of information about actual allele sharing at relevant marker loci. The bias will vary from study to study on the basis of the DNA markers, sample size, relative-pair types, and pedigree structures used, but it can be extremely pronounced and could contribute to a lack of consistent success in the application of traditional nonparametric linkage analyses to complex human traits and diseases. There are several potential ways to overcome this problem, but their foundations deserve greater research. We expose many of the issues concerning allele sharing with data from a large affected-sibling-pair study investigating the genetic basis of autism.     

Prediction of IBD based on population history for fine gene mapping

A novel multiple regression method (RM) is developed to predict identity-by-descent probabilities at a locus L (IBD_L), among individuals without pedigree, given information on surrounding markers and population history. These IBD_L probabilities are a function of the increase in linkage disequilibrium (LD) generated by drift in a homogeneous population over generations. Three parameters are sufficient to describe population history: effective population size (Ne), number of generations since foundation (T), and marker allele frequencies among founders (p). IBD_L are used in a simulation study to map a quantitative trait locus (QTL) via variance component estimation. RM is compared to a coalescent method (CM) in terms of power and robustness of QTL detection. Differences between RM and CM are small but significant. For example, RM is more powerful than CM in dioecious populations, but not in monoecious populations. Moreover, RM is more robust than CM when marker phases are unknown or when there is complete LD among founders or Ne is wrong, and less robust when p is wrong. CM utilises all marker haplotype information, whereas RM utilises information contained in each individual marker and all possible marker pairs but not in higher order interactions. RM consists of a family of models encompassing four different population structures, and two ways of using marker information, which contrasts with the single model that must cater for all possible evolutionary scenarios in CM.     

The estimates of effective population size based on linkage disequilibrium are virtually unaffected by natural selection

The effective population size (N_e) is a key parameter to quantify the magnitude of genetic drift and inbreeding, with important implications in human evolution. The increasing availability of high-density genetic markers allows the estimation of historical changes in N_e across time using measures of genome diversity or linkage disequilibrium between markers. Directional selection is expected to reduce diversity and N_e, and this reduction is modulated by the heterogeneity of the genome in terms of recombination rate. Here we investigate by computer simulations the consequences of selection (both positive and negative) and recombination rate heterogeneity in the estimation of historical N_e. We also investigate the relationship between diversity parameters and N_e across the different regions of the genome using human marker data. We show that the estimates of historical N_e obtained from linkage disequilibrium between markers (N_eLD) are virtually unaffected by selection. In contrast, those estimates obtained by coalescence mutation-recombination-based methods can be strongly affected by it, which could have important consequences for the estimation of human demography. The simulation results are supported by the analysis of human data. The estimates of N_eLD obtained for particular genomic regions do not correlate, or they do it very weakly, with recombination rate, nucleotide diversity, proportion of polymorphic sites, background selection statistic, minor allele frequency of SNPs, loss of function and missense variants and gene density. This suggests that N_eLD measures mainly reflect demographic changes in population size across generations.     

Control of population stratification by correlation-selected principal components

In genome-wide association studies, population stratification is recognized as producing inflated type I error due to the inflation of test statistics. Principal component-based methods applied to genotypes provide information about population structure, and have been widely used to control for stratification. Here we explore the precise relationship between genotype principal components and inflation of association test statistics, thereby drawing a connection between principal component-based stratification control and the alternative approach of genomic control. Our results provide an inherent justification for the use of principal components, but call into question the popular practice of selecting principal components based on significance of eigenvalues alone. We propose a new approach, called EigenCorr, which selects principal components based on both their eigenvalues and their correlation with the (disease) phenotype. Our approach tends to select fewer principal components for stratification control than does testing of eigenvalues alone, providing substantial computational savings and improvements in power. Analyses of simulated and real data demonstrate the usefulness of the proposed approach.     

Genome-wide linkage analysis of population variation in high-density lipoprotein cholesterol

Lower plasma levels of high-density lipoprotein cholesterol (HDL-C) are associated with the metabolic syndrome (insulin resistance, obesity, hypertension) and higher cardiovascular risk. Recent association studies have suggested rare alleles responsible for very low HDL-C levels. However, for individual cardiovascular risk factors, the majority of population-attributable deaths are associated with average rather than extreme levels. Therefore, genetic factors that determine the population variation of HDL-C are particularly relevant. We undertook genome-wide and fine mapping to identify linkage to HDL-C in healthy adult nuclear families from the Victorian Family Heart Study. In 274 adult sibling pairs (average age 24 years, average plasma HDL-C 1.4 mmol/l), genome-wide mapping revealed suggestive evidence for linkage on chromosome 4 (Z score=3.5, 170 cM) and nominal evidence for linkage on chromosomes 1 (Z=2.1, 176 cM) and 6 (Z=2.6, 29 cM). Using genotypes and phenotypes from 932 subjects (233 of the sibling pairs and their parents), finer mapping of the locus on chromosome 4 strengthened our findings with a peak probability (Z score=3.9) at 169 cM. Our linkage data suggest that chromosome 4q32.3 is linked with normal population variation in HDL-C. This region coincides with previous reports of linkage to apolipoprotein AII (a major component of HDL) and encompasses the gene encoding the carboxypeptidase E, relevant to the metabolic syndrome and HDL-C. These findings are relevant for further understanding of the genetic determinants of cardiovascular risk at a population level.     

The IBD2 locus shows linkage heterogeneity between ulcerative colitis and Crohn disease

The IBD2 locus on chromosome 12 has been linked to both Crohn disease (CD) and ulcerative colitis (UC) but has not been detected in some CD-dominated data sets. In the present study, we genotyped 581 relative pairs with inflammatory bowel disease (252 from CD-only families, 138 from UC-only families, and 191 from mixed families containing cases of both CD and UC), using 12 markers spanning the IBD2 locus. A GENEHUNTER-PLUS multipoint LOD score of 3.91 was detected for pairs from UC-only families, compared with 1.66 for CD-only and 1.29 for mixed families. The difference between the LOD scores for UC and CD was significant in two different tests for heterogeneity (P=.0057 for one test and P=.0375 for the other). IBD2 thus appears to make a major contribution to UC susceptibility but to have only a relatively minor effect with regard to CD, for which there may be substantially more locus heterogeneity.     

Novel measures of linkage disequilibrium that correct the bias due to population structure and relatedness

Among the several linkage disequilibrium measures known to capture different features of the non-independence between alleles at different loci, the most commonly used for diallelic loci is the r(2) measure. In the present study, we tackled the problem of the bias of r(2) estimate, which results from the sample structure and/or the relatedness between genotyped individuals. We derived two novel linkage disequilibrium measures for diallelic loci that are both extensions of the usual r(2) measure. The first one, r(S)(2), uses the population structure matrix, which consists of information about the origins of each individual and the admixture proportions of each individual genome. The second one, r(V)(2), includes the kinship matrix into the calculation. These two corrections can be applied together in order to correct for both biases and are defined either on phased or unphased genotypes.We proved that these novel measures are linked to the power of association tests under the mixed linear model including structure and kinship corrections. We validated them on simulated data and applied them to real data sets collected on Vitis vinifera plants. Our results clearly showed the usefulness of the two corrected r(2) measures, which actually captured 'true' linkage disequilibrium unlike the usual r(2) measure.     

Towards linkage analysis with markers in linkage disequilibrium by graphical modelling

We review recent developments of MCMC integration methods for computations on graphical models for two applications in statistical genetics: modelling allelic association and pedigree based linkage analysis. We discuss and illustrate estimation of graphical models from haploid and diploid genotypes, and the importance of MCMC updating schemes beyond what is strictly necessary for irreducibility. We then outline an approach combining these methods to compute linkage statistics when alleles at the marker loci are in linkage disequilibrium. Other extensions suitable for analysis of SNP genotype data in pedigrees are also discussed and programs that implement these methods, and which are available from the author's web site, are described. We conclude with a discussion of how this still experimental approach might be further developed.     

The island syndrome and population dynamics of introduced rats

The island syndrome predicts directional changes in the morphology and demography of insular vertebrates, due to changes in trophic complexity and migration rates caused by island size and isolation. However, the high rate of human-mediated species introductions to some islands also increases trophic complexity, and this will reduce the perceived insularity on any such island. We test four hypotheses on the role of increased trophic complexity on the island syndrome, using introduced black rats (Rattus rattus) on two isolated coral atolls in the Mozambique Channel. Europa Island has remained relatively pristine and insular, with few species introductions, whereas Juan de Nova Island has had many species introductions, including predators and competitors of rats, anthropogenically increasing its trophic complexity. In the most insular environments, the island syndrome is expected to generate increases in body size and densities of rodents but decreases in the rates of reproduction and population cycling. Morphology and reproduction were compared using linear regression and canonical discriminant analysis, while density and population cycling were compared using spatially explicit capture–recapture analysis. Results were compared to other insular black rat populations in the Mozambique Channel and were consistent with predictions from the island syndrome. The manifestation of an island syndrome in rodents depends upon the trophic composition of a community, and may not relate to island size alone when many species additions, such as invasions, have occurred. The differing patterns of rodent population dynamics on each island provide information for future rodent eradication operations.     

Ordered stratification to reduce heterogeneity in linkage to diabetes-related quantitative traits

Phenotypic heterogeneity complicates detection of genomic loci predisposing to type 2 diabetes, potentially obscuring or unmasking specific loci. We conducted ordered-subsets linkage analyses (OSAs) for diabetes-related quantitative traits (fasting insulin and glucose, hemoglobin A1c (HbA1c), and 28-year-time-averaged fasting plasma glucose (FPG)) from 330 families of the Framingham Offspring Study. We calculated mean BMI, waist circumference (WC), and a diabetes "age-of-onset score" for each family. We constructed subsets by adding one family at a time in increasing (lean family to obese) or decreasing (obese to lean) adiposity order, or increasing or decreasing propensity to develop diabetes at a younger age, with the OSA LOD reported as the maximum LOD observed in any subset. Permutation P values tested the hypothesis that phenotypic ordering showed stronger linkage than random ordering. On chromosome 1, ordering by increasing family mean WC increased linkage to time-averaged FPG at 256 cM from LOD = 2.4 to 3.5 (permuted P = 0.02) and to HbA1c at 180 cM from LOD = 2.0 to 3.3 (P = 0.01). On chromosome 19, ordering by decreasing WC increased linkage to fasting insulin at 68 cM from LOD = 2.7 to 4.6 (P = 0.002), and ordering by decreasing propensity to develop diabetes at a young age increased linkage to fasting insulin at 73 cM from LOD = 2.7 to 4.0 (P = 0.046). We conclude that chromosomes 1 and 19 could harbor adiposity-interacting diabetes susceptibility genes. Such interactions might also influence trait-locus associations and may be useful to consider in diabetes genome-wide association studies.     

The role of solitary population waves in efficient suppression of adventive weeds by introduced phytophagous insects

Successful introduction and application of phytophagous insects to control invading weeds is a complex systemic process based on formation of solitary population waves (SPW) of phytophages. Consequently, each stage from selection to release of the biological control agent should pursue the objective of the wave formation. When selecting a biological control agent one should choose species among phylogenetically young “juvenile taxa,” which are capable of forming a solitary population wave upon introduction. The initial phytophage population increase, preceding the wave emergence, requires special conditions, in particular a high density of the weed in the release areas. The SPW restores the natural succession previously arrested by the weed, allowing the native plants to overgrow the weed completely.     

The quantitative trait linkage disequilibrium test: a more powerful alternative to the quantitative transmission disequilibrium test for use in the absence of population stratification

Linkage analysis based on identity-by-descent allele-sharing can be used to identify a chromosomal region harboring a quantitative trait locus (QTL), but lacks the resolution required for gene identification. Consequently, linkage disequilibrium (association) analysis is often employed for fine-mapping. Variance-components based combined linkage and association analysis for quantitative traits in sib pairs, in which association is modeled as a mean effect and linkage is modeled in the covariance structure has been extended to general pedigrees (quantitative transmission disequilibrium test, QTDT). The QTDT approach accommodates data not only from parents and siblings, but also from all available relatives. QTDT is also robust to population stratification. However, when population stratification is absent, it is possible to utilize even more information, namely the additional information contained in the founder genotypes. In this paper, we introduce a simple modification of the allelic transmission scoring method used in the QTDT that results in a more powerful test of linkage disequilibrium, but is only applicable in the absence of population stratification. This test, the quantitative trait linkage disequilibrium (QTLD) test, has been incorporated into a new procedure in the statistical genetics computer package SOLAR. We apply this procedure in a linkage/association analysis of an electrophysiological measurement previously shown to be related to alcoholism. We also demonstrate by simulation the increase in power obtained with the QTLD test, relative to the QTDT, when a true association exists between a marker and a QTL.     

Genetic characterization and founder effect analysis of recently introduced Salers cattle breed population

Salers are a native French breed used for beef and dairy production that has expanded to all the continents. The Salers breed was introduced to the north of Spain in 1985 with only 15 individuals from France and has successfully increased to over 20 000 animals. Although over time new animals have been imported from France for breeding, it is possible that the limiting number of founder animals could have resulted in a reduction of the genetic diversity found in Spanish Salers. Thus, the purpose of the present study has been to characterize the genetic diversity of Salers breed in Spain and evaluate a possible founder effect due to reduced number of the first reproducers. A total of 403 individuals from 12 Salers herds were analyzed using 12 microsatellite markers and compared with phylogenetically and geographically close related Blonde d’Aquitaine, Limousin and Charolais French breeds but also other 16 European breeds. Microsatellites in Salers were polymorphic, with a mean allelic richness of 5.129 and an expected heterozygosity of 0.621 across loci (0.576 to 0.736 among all breeds). Average observed heterozygosity was 0.618. All the loci fit the Hardy–Weinberg (HW) equilibrium except TGLA227 locus due to a significant deficit of heterozygotes in only one of the herds, probably attributable to a sampling effect. When all loci were combined, Salers inbreeding coefficient did not differ statistically from 0 (F_IS=0.005), indicating not significant excess or deficit of heterozygotes (P=0.309). Based in allelic distribution, Salers revealed a frequency of 0.488 in BM2113-131 and 0.064 in BM2113-143 diagnostic alleles, which are specific to the African zebu. These zebu alleles are also found in some French breeds, supported by STR data previously postulated hypothesis of a migration route through Mediterranean route by which North African cattle may have left a genetic signature in southern Europe. Phylogenetic tree and population structure analyses could unambiguously differentiate Salers cattle from the other populations and 10% of the total genetic variability could be attributed to differences among breeds (mean R_ST=0.105; P<0.01). Mutation-drift equilibrium tests (sign test and Wilcoxon’s sign rank test) were in correspondence to the absence of founder effect when Bonferroni was applied. Gene diversity previously reported in French Salers was comparable with the observed in our population. Thus, high genetic diversity in Spanish Salers highlights the resources of this population, which looks toward future breeding and selection programs.