Comparative performance of Bayesian and AIC-based measures of phylogenetic model uncertainty

Reversible-jump Markov chain Monte Carlo (RJ-MCMC) is a technique for simultaneously evaluating multiple related (but not necessarily nested) statistical models that has recently been applied to the problem of phylogenetic model selection. Here we use a simulation approach to assess the performance of this method and compare it to Akaike weights, a measure of model uncertainty that is based on the Akaike information criterion. Under conditions where the assumptions of the candidate models matched the generating conditions, both Bayesian and AIC-based methods perform well. The 95% credible interval contained the generating model close to 95% of the time. However, the size of the credible interval differed with the Bayesian credible set containing approximately 25% to 50% fewer models than an AIC-based credible interval. The posterior probability was a better indicator of the correct model than the Akaike weight when all assumptions were met but both measures performed similarly when some model assumptions were violated. Models in the Bayesian posterior distribution were also more similar to the generating model in their number of parameters and were less biased in their complexity. In contrast, Akaike-weighted models were more distant from the generating model and biased towards slightly greater complexity. The AIC-based credible interval appeared to be more robust to the violation of the rate homogeneity assumption. Both AIC and Bayesian approaches suggest that substantial uncertainty can accompany the choice of model for phylogenetic analyses, suggesting that alternative candidate models should be examined in analysis of phylogenetic data. [AIC; Akaike weights; Bayesian phylogenetics; model averaging; model selection; model uncertainty; posterior probability; reversible jump.].     

Detecting Marker-Qtl Linkage and Estimating Qtl Gene Effect and Map Location Using a Saturated Genetic Map

A simulation study was carried out on a backcross population in order to determine the effect of marker spacing, gene effect and population size on the power of marker-quantitative trait loci (QTL) linkage experiments and on the standard error of maximum likelihood estimates (MLE) of QTL gene effect and map location. Power of detecting a QTL was virtually the same for a marker spacing of 10 cM as for an infinite number of markers and was only slightly decreased for marker spacing of 20 or even 50 cM. The advantage of using interval mapping as compared to single-marker analysis was slight. ``Resolving power' of a marker-QTL linkage experiment was defined as the 95% confidence interval for the QTL map location that would be obtained when scoring an infinite number of markers. It was found that reducing marker spacing below the resolving power did not add appreciably to narrowing the confidence interval. Thus, the 95% confidence interval with infinite markers sets the useful marker spacing for estimating QTL map location for a given population size and estimated gene effect.     

A comparative genome approach to marker ordering

MOTIVATION: Genome maps are fundamental to the study of an organism and essential in the process of genome sequencing which in turn provides the ultimate map of the genome. The increased number of genomes being sequenced offers new opportunities for the mapping of closely related organisms. We propose here an algorithmic formalization of a genome comparison approach to marker ordering. RESULTS: In order to integrate a comparative mapping approach in the algorithmic process of map construction and selection, we propose to extend the usual statistical model describing the experimental data, here radiation hybrids (RH) data, in a statistical framework that models additionally the evolutionary relationships between a proposed map and a reference map: an existing map of the corresponding orthologous genes or markers in a closely related organism. This has concretely the effect of exploiting, in the process of map selection, the information of marker adjacencies in the related genome when the information provided by the experimental data is not conclusive for the purpose of ordering. In order to compute efficiently the map, we proceed to a reduction of the maximum likelihood estimation to the Traveling Salesman Problem. Experiments on simulated RH datasets as well as on a real RH dataset from the canine RH project show that maps produced using the likelihood defined by the new model are significantly better than maps built using the traditional RH model. AVAILABILITY: The comparative mapping approach is available in the last version of de Givry,S. et al. [(2004) Bioinformatics, 21, 1703-1704, www.inra.fr/mia/T/CarthaGene], a free (the LKH part is free for academic use only) mapping software in C++, including LKH (Helsgaun,K. (2000) Eur. J. Oper. Res., 126, 106-130, www.dat.ruc.dk/keld/research/LKH) for maximum likelihood computation.     

Three-point appraisal of genetic linkage maps

This paper develops a simple diagnostic for the investigation of uncertainty within genetic linkage maps using a Bayesian procedure. The method requires only the genotyping data and the proposed genetic map, and calculates the posterior probability for the possible orders of any set of three markers, accounting for the presence of genotyping error (mistyping) and for missing genotype data. The method uses a Bayesian approach to give insight into conflicts between the order in the proposed map and the genotype scores. The method can also be used to assess the accuracy of a genetic map at different genomic scales and to assess alternative potential marker orders. Simulation and two case studies were used to illustrate the method. In the first case study, the diagnostic revealed conflicts in map ordering for short inter-marker distances that were resolved at a distance of 8–12?cM, except for a set of markers at the end of the linkage group. In the second case study, the ordering did not resolve as distances increase, which could be attributed to regions of the map where many individuals were untyped.     

Construction of bovine whole-genome radiation hybrid and linkage maps using high-throughput genotyping

High-density whole-genome maps are essential for ordering genes or markers and aid in the assembly of genome sequence. To increase the density of markers on the bovine radiation hybrid map, and hence contribute to the assembly of the bovine genome sequence, an Illumina BeadStation was used to simultaneously type large numbers of markers on the Roslin-Cambridge 3000 rad bovine-hamster whole-genome radiation hybrid panel (WGRH3000). In five multiplex reactions, 6738 sequence tagged site (STS) markers were successfully typed on the WGRH3000 panel DNA. These STSs harboured SNPs that were developed as a result of the bovine genome sequencing initiative. Typically, the most time consuming and expensive part of creating high-density radiation hybrid (RH) maps is genotyping the markers on the RH panel with conventional approaches. Using the method described in this article, we have developed a high-density whole-genome RH map with 4690 loci and a linkage map with 2701 loci, with direct comparison to the bovine whole-genome sequence assembly (Btau_2.0) in a fraction of the time it would have taken with conventional typing and genotyping methods.     

Multilocus Analysis for Gene-Centromere Mapping Using First Polar Bodies and Secondary Oocytes

Polar body and oocyte typing is a new technique for gene-centromere mapping and for generating female linkage maps. A maximum likelihood approach is presented for ordering multiple markers relative to the centromere and for estimating recombination frequencies between markers and between the centromere and marker loci. Three marker-centromere orders are possible for each pair of markers: two orders when the centromere flanks the two markers and one order when the centromere is flanked by the two markers. For each possible order, the likelihood was expressed as a function of recombination frequencies for two adjacent intervals. LOD score for recombination frequency between markers or between the centromere and a marker locus was derived based on the likelihood for each gene-centromere order. The methods developed herein provide a general solution to the problem of multilocus genecentromere mapping that involves all theoretical crossover possibilities, including four-strand double crossovers.     

A 12 000-rad whole-genome radiation hybrid panel in sheep: application to the study of the ovine chromosome 18 region containing a QTL for scrapie susceptibility

Whole-genome radiation hybrid (RH) panels have been constructed for several species, including cattle. RH panels have proven to be an extremely powerful tool to construct high-density maps, which is an essential step in the identification of genes controlling important traits, and they can be used to establish high-resolution comparative maps. Although bovine RH panels can be used with ovine markers to construct sheep RH maps based on bovine genome organization, only some (c. 50%) of the markers available in sheep can be successfully mapped in the bovine genome. So, with the development of genomics and genome sequencing projects, there is a need for a high-resolution RH panel in sheep to map ovine markers. Consequently, we have constructed a 12 000-rad ovine whole-genome RH panel. Two hundred and eight hybrid clones were produced, of which 90 were selected based on their retention frequency. The final panel had an average marker retention frequency of 31.8%. The resolution of this 12 000-rad panel (SheepRH) was estimated by constructing an RH framework map for a 23-Mb region of sheep chromosome 18 (OAR18) that contains a QTL for scrapie susceptibility.     

Two statistical tests for meiotic breakpoint analysis.

Meiotic breakpoint analysis (BPA), a statistical method for ordering genetic markers, is increasing in importance as a method for building genetic maps of human chromosomes. Although BPA does not provide estimates of genetic distances between markers, it efficiently locates new markers on already defined dense maps, when likelihood analysis becomes cumbersome or the sample size is small. However, until now no assessments of statistical significance have been available for evaluating the possibility that the results of a BPA were produced by chance. In this paper, we propose two statistical tests to determine whether the size of a sample and its genetic information content are sufficient to distinguish between "no linkage" and "linkage" of a marker mapped by BPA to a certain region. Both tests are exact and should be conducted after a BPA has assigned the marker to an interval on the map. Applications of the new tests are demonstrated by three examples: (1) a synthetic data set, (2) a data set of five markers on human chromosome 8p, and (3) a data set of four markers on human chromosome 17q.     

Simultaneous maximum likelihood estimation of linkage and linkage phases in outcrossing species

With the advent of new molecular marker technologies, it is now feasible to initiate genome projects for outcrossing plant species, which have not received much attention in genetic research, despite their great agricultural and environmental value. Because outcrossing species typically have heterogeneous genomes, data structure for molecular markers representing an entire genome is complex: some markers may have more alleles than others, some markers are codominant whereas others are dominant, and some markers are heterozygous in one parent but fixed in the other parent whereas the opposite can be true for other markers. A major difficulty in analyzing these different types of marker at the same time arises from uncertainty about parental linkage phases over markers. In this paper, we present a general maximum-likelihood-based algorithm for simultaneously estimating linkage and linkage phases for a mixed set of different marker types containing fully informative markers (segregating 1:1:1:1) and partially informative markers (or missing markers, segregating 1:2:1, 3:1, and 1:1) in a full-sib family derived from two outbred parent plants. The characterization of linkage phases is based on the posterior probability distribution of the assignment of alternative alleles at given markers to two homologous chromosomes of each parent, conditional on the observed phenotypes of the markers. Two- and multi-point analyses are performed to estimate the recombination fraction and determine the most likely linkage phase between different types of markers. A numerical example is presented to demonstrate the statistical properties of the model for characterizing the linkage phase between markers.     

An updated ‘Essex’ by ‘Forrest’ linkage map and first composite interval map of QTL underlying six soybean traits

DNA marker maps based on single populations are the basis for gene, loci and genomic analyses. Individual maps can be integrated to produce composite maps with higher marker densities if shared marker orders are consistent. However, estimates of marker order in composite maps must include sets of markers that were not polymorphic in multiple populations. Often some of the pooled markers were not codominant, or were not correctly scored. The soybean composite map was composed of data from five separate populations based on northern US germplasm but does not yet include ‘Essex’ by ‘Forrest’ recombinant inbred line (RIL) population (E × F) or any southern US soybean cultivars. The objectives were, to update the E × F map with codominant markers, to compare marker orders among this map, the Forrest physical map and the composite soybean map and to compare QTL identified by composite interval maps to the earlier interval maps. Two hundred and thirty seven markers were used to construct the core of the E × F map. The majority of marker orders were consistent between the maps. However, 19 putative marker inversions were detected on 12 of 20 linkage groups (LG). Eleven marker distance compressions were also found. The number of inverted markers ranged from 1 to 2 per LG. Thus, marker order inversions may be common in southern compared to northern US germplasm. A total of 61 QTL among 37 measures of six traits were detected by composite interval maps, interval maps and single point analysis. Seventeen of the QTL found in composite intervals had previously been detected among the 29 QTL found in simple interval maps. The genomic locations of the known QTL were more closely delimited. A genome sequencing project to compare Southern and Northern US soybean cultivars would catalog and delimit inverted regions and the associated QTL. Gene introgression in cultivar development programs would be accelerated.Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

A bovine whole-genome radiation hybrid panel and outline map

A 3000-rad radiation hybrid panel was constructed for cattle and used to build outline RH maps for all 29 autosomes and the X and Y chromosomes. These outline maps contain about 1200 markers, most of which are anonymous microsatellite loci. Comparisons between the RH chromosome maps, other published RH maps, and linkage maps allow regions of chromosomes that are poorly mapped or that have sparse marker coverage to be identified. In some cases, mapping ambiguities can be resolved. The RH maps presented here are the starting point for mapping additional loci, in particular genes and ESTs that will allow detailed comparative maps between cattle and other species to be constructed. Radiation hybrid cell panels allow high-density genetic maps to be constructed, with the advantage over linkage mapping that markers do not need to be polymorphic. A large quantity of DNA has been prepared from the cells forming the RH panel reported here and is publicly available for mapping large numbers of loci.     

A radiation hybrid map of bovine chromosome 24 and comparative mapping with human chromosome 18

We present herein a bovine chromosome 24 (BTA24) radiation hybrid (RH) map using 40 markers scored on a panel of 90 RHs. Of these markers, 29 loci were ordered with odds of at least 1000:1 in a framework map. An average retention frequency of 17.4% was observed, with relatively higher frequencies near the centromere. The length of the comprehensive map was 640 centiray5000 (cR5000) with an average marker interval of approximately 17.3 cR5000. The observed locus order is generally consistent with currently published bovine linkage and physical maps. Nineteen markers were either Type I loci or closely associated with expressed sequences and thus could be used to compare the BTA24 RH map with human mapping information. All genes located on BTA24 were located on human chromosome 18, and previously reported regions of conserved synteny were extended. The comparative data revealed the presence of at least six conserved regions between these chromosomes.     

A 4,103 marker integrated physical and comparative map of the horse genome

A comprehensive second-generation whole genome radiation hybrid (RH II), cytogenetic and comparative map of the horse genome (2n = 64) has been developed using the 5000rad horse x hamster radiation hybrid panel and fluorescence in situ hybridization (FISH). The map contains 4,103 markers (3,816 RH; 1,144 FISH) assigned to all 31 pairs of autosomes and the X chromosome. The RH maps of individual chromosomes are anchored and oriented using 857 cytogenetic markers. The overall resolution of the map is one marker per 775 kilobase pairs (kb), which represents a more than five-fold improvement over the first-generation map. The RH II incorporates 920 markers shared jointly with the two recently reported meiotic maps. Consequently the two maps were aligned with the RH II maps of individual autosomes and the X chromosome. Additionally, a comparative map of the horse genome was generated by connecting 1,904 loci on the horse map with genome sequences available for eight diverse vertebrates to highlight regions of evolutionarily conserved syntenies, linkages, and chromosomal breakpoints. The integrated map thus obtained presents the most comprehensive information on the physical and comparative organization of the equine genome and will assist future assemblies of whole genome BAC fingerprint maps and the genome sequence. It will also serve as a tool to identify genes governing health, disease and performance traits in horses and assist us in understanding the evolution of the equine genome in relation to other species.     

Efficient multipoint mapping: making use of dominant repulsion-phase markers

The paper is devoted to the problem of multipoint gene ordering with a particular focus on "dominance" complication that acts differently in conditions of coupling-phase and repulsion-phase markers. To solve the problem we split the dataset into two complementary subsets each containing shared codominant markers and dominant markers in the coupling-phase only. Multilocus ordering in the proposed algorithm is based on pairwise recombination frequencies and using the well-known travelling salesman problem (TSP) formalization. To obtain accurate results, we developed a multiphase algorithm that includes synchronized-marker ordering of two subsets assisted by re-sampling-based map verification, combining the resulting maps into an integrated map followed by verification of the integrated map. A new synchronized Evolution-Strategy discrete optimization algorithm was developed here for the proposed multilocus ordering approach in which common codominant markers facilitate stabilization of the marker order of the two complementary maps. High performance of the employed algorithm allows systematic treatment for the problem of verification of the obtained multilocus orders, based on computing-intensive bootstrap and jackknife technologies for detection and removing unreliable marker scores. The efficiency of the proposed algorithm was demonstrated on simulated and real data.Communicated by J.W. Snape     

A Bayesian hierarchical approach to account for left-censored and missing radiation doses prone to classical measurement error when analyzing lung cancer mortality due to γ-ray exposure in the French cohort of uranium miners

Epidemiological data on cohorts of occupationally exposed uranium miners are currently used to assess health risks associated with chronic exposure to low doses of ionizing radiation. Nevertheless, exposure uncertainty is ubiquitous and questions the validity of statistical inference in these cohorts. This paper highlights the flexibility and relevance of the Bayesian hierarchical approach to account for both missing and left-censored (i.e. only known to be lower than a fixed detection limit) radiation doses that are prone to measurement error, when estimating radiation-related risks. Up to the authors’ knowledge, this is the first time these three sources of uncertainty are dealt with simultaneously in radiation epidemiology. To illustrate the issue, this paper focuses on the specific problem of accounting for these three sources of uncertainty when estimating the association between occupational exposure to low levels of γ-radiation and lung cancer mortality in the post-55 sub-cohort of French uranium miners. The impact of these three sources of dose uncertainty is of marginal importance when estimating the risk of death by lung cancer among French uranium miners. The corrected excess hazard ratio (EHR) is 0.81 per 100 mSv (95% credible interval: [0.28; 1.75]). Interestingly, even if the 95% credible interval of the corrected EHR is wider than the uncorrected one, a statistically significant positive association remains between γ-ray exposure and the risk of death by lung cancer, after accounting for dose uncertainty. Sensitivity analyses show that the results obtained are robust to different assumptions. Because of its flexible and modular nature, the Bayesian hierarchical models proposed in this work could be easily extended to account for high proportions of missing and left-censored dose values or exposure data, prone to more complex patterns of measurement error.

     

Second-generation integrated genetic linkage/radiation hybrid maps of the domestic cat (Felis catus)

We report construction of second-generation integrated genetic linkage and radiation hybrid (RH) maps in the domestic cat (Felis catus) that exhibit a high level of marker concordance and provide near-full genome coverage. A total of 864 markers, including 585 coding loci (type I markers) and 279 polymorphic microsatellite loci (type II markers), are now mapped in the cat genome. We generated the genetic linkage map utilizing a multigeneration interspecies backcross pedigree between the domestic cat and the Asian leopard cat (Prionailurus bengalensis). Eighty-one type I markers were integrated with 247 type II markers from a first-generation map to generate a map of 328 loci (320 autosomal and 8 X-linked) distributed in 47 linkage groups, with an average intermarker spacing of 8 cM. Genome coverage spans approximately 2,650 cM, allowing an estimate for the genetic length of the sex-averaged map as 3,300 cM. The 834-locus second-generation domestic cat RH map was generated from the incorporation of 579 type I and 255 type II loci. Type I markers were added using targeted selection to cover either genomic regions underrepresented in the first-generation map or to refine breakpoints in human/feline synteny. The integrated linkage and RH maps reveal approximately 110 conserved segments ordered between the human and feline genomes, and provide extensive anchored reference marker homologues that connect to the more gene dense human and mouse sequence maps, suitable for positional cloning applications.     

A high-resolution 15,000(rad) radiation hybrid panel for the domestic cat

The current genetic and recombination maps of the cat have fewer than 3,000 markers and a resolution limit greater than 1 Mb. To complement the first-generation domestic cat maps, support higher resolution mapping studies, and aid genome assembly in specific areas as well as in the whole genome, a 15,000(Rad) radiation hybrid (RH) panel for the domestic cat was generated. Fibroblasts from the female Abyssinian cat that was used to generate the cat genomic sequence were fused to a Chinese hamster cell line (A23), producing 150 hybrid lines. The clones were initially characterized using 39 short tandem repeats (STRs) and 1,536 SNP markers. The utility of whole-genome amplification in preserving and extending RH panel DNA was also tested using 10 STR markers; no significant difference in retention was observed. The resolution of the 15,000(Rad) RH panel was established by constructing framework maps across 10 different 1-Mb regions on different feline chromosomes. In these regions, 2-point analysis was used to estimate RH distances, which compared favorably with the estimation of physical distances. The study demonstrates that the 15,000(Rad) RH panel constitutes a powerful tool for constructing high-resolution maps, having an average resolution of 40.1 kb per marker across the ten 1-Mb regions. In addition, the RH panel will complement existing genomic resources for the domestic cat, aid in the accurate re-assemblies of the forthcoming cat genomic sequence, and support cross-species genomic comparisons.     

Bayesian fine-scale mapping of disease loci, by hidden Markov models

We present a new multilocus method for the fine-scale mapping of genes contributing to human diseases. The method is designed for use with multiple biallelic markers-in particular, single-nucleotide polymorphisms for which high-density genetic maps will soon be available. We model disease-marker association in a candidate region via a hidden Markov process and allow for correlation between linked marker loci. Using Markov-chain-Monte Carlo simulation methods, we obtain posterior distributions of model parameter estimates including disease-gene location and the age of the disease-predisposing mutation. In addition, we allow for heterogeneity in recombination rates, across the candidate region, to account for recombination hot and cold spots. We also obtain, for the ancestral marker haplotype, a posterior distribution that is unique to our method and that, unlike maximum-likelihood estimation, can properly account for uncertainty. We apply the method to data for cystic fibrosis and Huntington disease, for which mutations in disease genes have already been identified. The new method performs well compared with existing multi-locus mapping methods.     

Preliminary radiation hybrid map for river buffalo chromosome 6 and comparison to bovine chromosome 3

We present the first radiation hybrid (RH) map of river buffalo (Bubalus bubalis) chromosome 6 (BBU6) developed with a recently constructed river buffalo whole-genome RH panel (BBURH(5000)). The preliminary map contains 33 cattle-derived markers, including 12 microsatellites, 19 coding genes and two ESTs, distributed across two linkage groups. Retention frequencies for markers ranged from 14.4% to 40.0%. Most of the marker orders within the linkage groups on BBU6 were consistent with the cattle genome sequence and RH maps. This preliminary RH map is the starting point for comparing gene order between river buffalo and cattle, presenting an opportunity for the examination of micro-rearrangements of these chromosomes. Also, resources for positional candidate cloning in river buffalo are enhanced.     

A physical map of the bovine genome

Background

Cattle are important agriculturally and relevant as a model organism. Previously described genetic and radiation hybrid (RH) maps of the bovine genome have been used to identify genomic regions and genes affecting specific traits. Application of these maps to identify influential genetic polymorphisms will be enhanced by integration with each other and with bacterial artificial chromosome (BAC) libraries. The BAC libraries and clone maps are essential for the hybrid clone-by-clone/whole-genome shotgun sequencing approach taken by the bovine genome sequencing project.

Results

A bovine BAC map was constructed with HindIII restriction digest fragments of 290,797 BAC clones from animals of three different breeds. Comparative mapping of 422,522 BAC end sequences assisted with BAC map ordering and assembly. Genotypes and pedigree from two genetic maps and marker scores from three whole-genome RH panels were consolidated on a 17,254-marker composite map. Sequence similarity allowed integrating the BAC and composite maps with the bovine draft assembly (Btau3.1), establishing a comprehensive resource describing the bovine genome. Agreement between the marker and BAC maps and the draft assembly is high, although discrepancies exist. The composite and BAC maps are more similar than either is to the draft assembly.

Conclusion

Further refinement of the maps and greater integration into the genome assembly process may contribute to a high quality assembly. The maps provide resources to associate phenotypic variation with underlying genomic variation, and are crucial resources for understanding the biology underpinning this important ruminant species so closely associated with humans.