Bayesian joint mapping of quantitative trait loci for Gaussian and categorical characters in line crosses

Methodology for joint mapping of quantitative trait loci (QTL) affecting continuous and binary characters in experimental crosses is presented. The procedure consists of a Bayesian Gaussian-threshold model implemented via Markov chain Monte Carlo, which bypasses bottlenecks due to high-dimensional integrals required in maximum likelihood approaches. The method handles multiple binary traits and multiple QTL. Modeling of ordered categorical traits is discussed as well. Features of the method are illustrated using simulated datasets representing a backcross design, and the data are analyzed using mixed-trait and single-trait models. The mixed-trait analysis provides greater detection power of a QTL than a single-trait analysis when the QTL affects two or more traits. The number of QTL inferred in the mixed-trait analysis does not pertain to a specific trait, but the roles of each QTL on specific traits can be assessed from estimates of its effects. The impacts of varying incidence level and sample size on the mixed-trait QTL mapping analysis are investigated as well.     

Bayesian methods for expression-based integration of various types of genomics data

We propose methods to integrate data across several genomic platforms using a hierarchical Bayesian analysis framework that incorporates the biological relationships among the platforms to identify genes whose expression is related to clinical outcomes in cancer. This integrated approach combines information across all platforms, leading to increased statistical power in finding these predictive genes, and further provides mechanistic information about the manner in which the gene affects the outcome. We demonstrate the advantages of the shrinkage estimation used by this approach through a simulation, and finally, we apply our method to a Glioblastoma Multiforme dataset and identify several genes potentially associated with the patients’ survival. We find 12 positive prognostic markers associated with nine genes and 13 negative prognostic markers associated with nine genes.     

Expansion of the rare Eucalyptus risdonii under climate change through hybridization with a closely related species despite hybrid inferiority

Background and AimsHybridization is increasingly recognized as an integral part of the dynamics of species range expansion and contraction. Thus, it is important to understand the reproductive barriers between co-occurring species. Extending previous studies that argued that the rare Eucalyptus risdonii was expanding into the range of the surrounding E. amygdalina by both seed and pollen dispersal, we here investigate the long-term fitness of both species and their hybrids and whether expansion is continuing.MethodsWe assessed the survival of phenotypes representing a continuum between the two pure species in a natural hybrid swarm after 29 years, along with seedling recruitment. The performance of pure species as well as of artificial and natural hybrids was also assessed over 28 years in a common garden trial.Key ResultsIn the hybrid zone, E. amygdalina adults showed greater mortality than E. risdonii, and the current seedling cohort is still dominated by E. risdonii phenotypes. Morphologically intermediate individuals appeared to be the least fit. Similar results were observed after growing artificial first-generation and natural hybrids alongside pure species families in a common garden trial. Here, the survival, reproduction, health and growth of the intermediate hybrids were significantly less than those of either pure species, consistent with hybrid inferiority, although this did not manifest until later reproductive ages. Among the variable progeny of natural intermediate hybrids, the most E. risdonii-like phenotypes were the most fit.ConclusionsThis study contributes to the increasing number of reports of hybrid inferiority in Eucalyptus, suggesting that post-zygotic barriers contribute to the maintenance of species integrity even between closely related species. However, with fitness rapidly recovered following backcrossing, it is argued that hybridization can still be an important evolutionary process, in the present case appearing to contribute to the range expansion of the rare E. risdonii in response to climate change.     

A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. I. Methodology

A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameter estimators were marginal posterior means computed using a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage, and the parameters (allele frequency, QTL substitution effect, recombination rate, polygenic and residual variances). Several MCMC algorithms were derived for computing Bayesian tests of linkage, which consisted of the marginal posterior probability of linkage and the marginal likelihood of the QTL variance associated with the marker.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. I. Prior knowledge

Summary Prior information on gene effects at individual quantitative trait loci (QTL) and on recombination rates between marker loci and QTL is derived. The prior distribution of QTL gene effects is assumed to be exponential with major effects less likely than minor ones. The prior probability of linkage between a marker and another single locus is a function of the number and length of chromosomes, and of the map function relating recombination rate to genetic distance among loci. The prior probability of linkage between a marker locus and a quantitative trait depends additionally on the number of detectable QTL, which may be determined from total additive genetic variance and minimum detectable QTL effect. The use of this prior information should improve linkage tests and estimates of QTL effects.     

Molecular and morphological evidence of hybridization between newts Triturus vulgaris and T. montandoni (Caudata: Salamandridae) in Slovakia

Natural hybridization and introgression is recorded between the newt species Triturus vulgaris and T. montandoni in Slovakia. To confirm a hybrid status of two putative hybrids, morphological and Randomly Amplified Polymorphic DNA (RAPD) markers specific for T. vulgaris and T. montandoni were used. The individuals found in Zbojská (Veporské vrchy Mts, Slovakia; analyzed morphologically and genetically) and Zubrohlava (Oravská kotlina basin, Slovakia; analyzed only morphologically) possessed markers of both species. Segregation of RAPD markers together with a model-based Bayesian analysis revealed that the specimen from Zbojská belonged to later generation hybrids.     

Elevated substitution rate estimates from ancient DNA: model violation and bias of Bayesian methods

The increasing ability to extract and sequence DNA from noncontemporaneous tissue offers biologists the opportunity to analyse ancient DNA (aDNA) together with modern DNA (mDNA) to address the taxonomy of extinct species, evolutionary origins, historical phylogeography and biogeography. Perhaps more exciting are recent developments in coalescence-based Bayesian inference that offer the potential to use temporal information from aDNA and mDNA for the estimation of substitution rates and divergence dates as an alternative to fossil and geological calibration. This comes at a time of growing interest in the possibility of time dependency for molecular rate estimates. In this study, we provide a critical assessment of Bayesian Markov chain Monte Carlo (MCMC) analysis for the estimation of substitution rate using simulated samples of aDNA and mDNA. We conclude that the current models and priors employed in Bayesian MCMC analysis of heterochronous mtDNA are susceptible to an upward bias in the estimation of substitution rates because of model misspecification when the data come from populations with less than simple demographic histories, including sudden short-lived population bottlenecks or pronounced population structure. However, when model misspecification is only mild, then the 95% highest posterior density intervals provide adequate frequentist coverage of the true rates.     

A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. II. A simulation study

A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameters were estimated by marginal posterior means computed with a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), the event of linkage or nonlinkage, and the parameters (allele frequencies, QTL substitution effect, recombination rate, polygenic and residual variances). The analysis was evaluated empirically via application to simulated granddaughter designs consisting of 2000 sons, 20 related sires and their ancestors. Results obtained in this study and preliminary work on multiple linked markers and multiple QTLs support the usefulness of the Bayesian method for the statistical mapping of QTLs.     

Efficiency of population structures for mapping of Mendelian and imprinted quantitative trait loci in outbred pigs using variance component methods

In a simulation study different designs for a pure line pig population were compared for efficiency of mapping QTL using the variance component method. Phenotypes affected by a Mendelian QTL, a paternally expressed QTL, a maternally expressed QTL or by a QTL without an effect were simulated. In all alternative designs 960 progeny were phenotyped. Given the limited number of animals there is an optimum between the number of families and the family size. Estimation of Mendelian and parentally expressed QTL is more efficient in a design with large family sizes. Too small a number of sires should be avoided to minimize chances of sires to be non-segregating. When a large number of families is used, the number of haplotypes increases which reduces the accuracy of estimating the QTL effect and thereby reduces the power to show a significant QTL and to correctly position the QTL. Dense maps allow for smaller family size due to exploitation of LD-information. Given the different possible modes of inheritance of the QTL using 8 to16 boars, two litters per dam was optimal with respect to determining significance and correct location of the QTL for a data set consisting of 960 progeny. The variance component method combining linkage disequilibrium and linkage analysis seems to be an appropriate choice to analyze data sets which vary in marker density and which contain complex family structures.     

A set of highly discriminating microsatellite loci for the Galápagos marine iguana Amblyrhynchus cristatus

We describe here the cloning of 12 (7 dinucleotide, 1 trinucleotide and 4 tetranucleotide) microsatellite loci for the Galápagos marine iguana Amblyrhynchus cristatus. When tested for individuals from five different island populations on the Galápagos archipelago, high genetic diversities (9–20 alleles per locus) and heterozygosities (0.200–0.944) were observed. All loci showed no obvious deviations from Hardy–Weinberg equilibrium. The new set of microsatellite loci was able to assign individuals reliably to their island of origin, thus being able to discriminate between residents and migrants between islands.     

Isolation and characterization of microsatellite loci for parentage assessment in captive populations of roseate spoonbill (Ajaia ajaja)

Six microsatellite loci were isolated and characterized to assess genetic diversity and determine parentage in three captive roseate spoonbill (Ajaia ajaja) populations. Analysis of 61 individuals from three zoological parks and one wild population at five polymorphic loci revealed an average of six alleles per locus and expected heterozygosities from 59% to 81% (average 70%). Since spoonbills do not exhibit obvious sexual dimorphism, Aaju4, which exhibited ZW‐specific alleles, was exceptionally useful for sex identification. These loci will be valuable tools for investigating genetic diversity and documenting patterns of parentage in captive roseate spoonbill populations.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. II. Combining prior knowledge with experimental evidence

Summary A Bayesian method was developed for identifying genetic markers linked to quantitative trait loci (QTL) by analyzing data from daughter or granddaughter designs and single markers or marker pairs. Traditional methods may yield unrealistic results because linkage tests depend on number of markers and QTL gene effects associated with selected markers are overestimated. The Bayesian or posterior probability of linkage combines information from a daughter or granddaughter design with the prior probability of linkage between a marker locus and a QTL. If the posterior probability exceeds a certain quantity, linkage is declared. Upon linkage acceptance, Bayesian estimates of marker-QTL recombination rate and QTL gene effects and frequencies are obtained. The Bayesian estimates of QTL gene effects account for different amounts of information by shrinking information from data toward the mean or mode of a prior exponential distribution of gene effects. Computation of the Bayesian analysis is feasible. Exact results are given for biallelic QTL, and extensions to multiallelic QTL are suggested.     

Bayesian analyses of admixture in wild and domestic cats (Felis silvestris) using linked microsatellite loci

Methods recently developed to infer population structure and admixture mostly use individual genotypes described by unlinked neutral markers. However, Hardy-Weinberg and linkage disequilibria among independent markers decline rapidly with admixture time, and the admixture signals could be lost in a few generations. In this study, we aimed to describe genetic admixture in 182 European wild and domestic cats (Felis silvestris), which hybridize sporadically in Italy and extensively in Hungary. Cats were genotyped at 27 microsatellites, including 21 linked loci mapping on five distinct feline linkage groups. Genotypes were analysed with structure 2.1, a Bayesian procedure designed to model admixture linkage disequilibrium, which promises to assess efficiently older admixture events using tightly linked markers. Results showed that domestic and wild cats sampled in Italy were split into two distinct clusters with average proportions of membership Q > 0.90, congruent with prior morphological identifications. In contrast, free-living cats sampled in Hungary were assigned partly to the domestic and the wild cat clusters, with Q < 0.50. Admixture analyses of individual genotypes identified, respectively, 5/61 (8%), and 16-20/65 (25-31%) hybrids among the Italian wildcats and Hungarian free-living cats. Similar results were obtained in the past using unlinked loci, although the new linked markers identified additional admixed wildcats in Italy. Linkage analyses confirm that hybridization is limited in Italian, but widespread in Hungarian wildcats, a population that is threatened by cross-breeding with free-ranging domestic cats. The total panel of 27 loci performed better than the linked loci alone in the identification of domestic and known hybrid cats, suggesting that a large number of linked plus unlinked markers can improve the results of admixture analyses. Inferred recombination events led to identify the population of origin of chromosomal segments, suggesting that admixture mapping experiments can be designed also in wild populations.     

Population structure and landscape genetics of two endangered frog species of genus Odorrana: different scenarios on two islands

Isolation by distance and landscape connectivity are fundamental factors underlying speciation and evolution. To understand how landscapes affect gene flow and shape population structures, island species provide intrinsic study objects. We investigated the effects of landscapes on the population structure of the endangered frog species, Odorrana ishikawae and O. splendida, which each inhabit an island in southwest Japan. This was done by examining population structure, gene flow and demographic history of each species by analyzing 12 microsatellite loci and exploring causal environmental factors through ecological niche modeling (ENM) and the cost-distance approach. Our results revealed that the limited gene flow and multiple-population structure in O. splendida and the single-population structure in O. ishikawae were maintained after divergence of the species through ancient vicariance between islands. We found that genetic distance correlated with geographic distance between populations of both species. Our landscape genetic analysis revealed that the connectivity of suitable habitats influences gene flow and leads to the formation of specific population structures. In particular, different degrees of topographical complexity between islands are the major determining factor for shaping contrasting population structures of two species. In conclusion, our results illustrate the diversification mechanism of organisms through the interaction with space and environment. Our results also present an ENM approach for identifying the key factors affecting demographic history and population structures of target species, especially endangered species.     

Efficiency of markers and methods for detecting hybrids and introgression in stocked populations

Detection of hybridization and introgression in wild populations that have been supplemented by hatchery fish is necessary during development of conservation and management strategies. Initially, allozyme data and more recently highly polymorphic microsatellite markers have been used to obtain this information. We used both markers to assess the effectiveness of four assignment methods (Structure, NewHybrids, Baps and GeneClass) to detect hatchery introgression in wild stocked populations. Simulations of hybrid genotypes from real parental data revealed that the number and type of markers used with Structure, NewHybrids and Baps can identify as admixed most first and second generation hybrids as well as first generation backcrosses. In wild populations, introgression rates estimated from different markers and methods were correlated. However, slight disagreements were observed at both population and individual levels. Overall, the fully Bayesian (Structure, NewHybrids and Baps) performed better than partially Bayesian (GeneClass) assignment tests. In wild collections, Baps analyses were limited because of the lack of a native baseline. In all cases, the efficiency of methods was reduced as introgression increased.     

Patterns of genetic diversity and candidate genes for ecological divergence in a homoploid hybrid sunflower, Helianthus anomalus

Natural hybridization accompanied by a shift in niche preference by hybrid genotypes can lead to hybrid speciation. Natural selection may cause the fixation of advantageous alleles in the ecologically diverged hybrids, and the loci experiencing selection should exhibit a reduction in allelic diversity relative to neutral loci. Here, we analyzed patterns of genetic diversity at 59 microsatellite loci associated with expressed sequence tags (ESTs) in a homoploid hybrid sunflower species, Helianthus anomalus. We used two indices, ln RV and ln RH, to compare variation and heterozygosity (respectively) at each locus between the hybrid species and its two parental species, H. annuus and H. petiolaris. Mean values of ln RV and ln RH were significantly lower than zero, which implies that H. anomalus experienced a population bottleneck during its recent evolutionary history. After correcting for the apparent bottleneck, we found six loci with a significant reduction in variation or with heterozygosity in the hybrid species, compared to one or both of the parental species. These loci should be viewed as a ranked list of candidate loci, pending further sequencing and functional analyses. Sequence data were generated for two of the candidate loci, but population genetics tests failed to detect deviations from neutral evolution at either locus. Nonetheless, a greater than eight-fold excess of nonsynonymous substitutions was found near a putative N-myristoylation motif at the second locus (HT998), and likelihood-based models indicated that the protein has been under selection in H. anomalus in the past and, perhaps, in one or both parental species. Finally, our data suggest that selective sweeps may have united populations of H. anomalus isolated by a mountain range, indicating that even low gene-flow species may be held together by the spread of advantageous alleles.     

The transmission dynamic of different hepatitis B-infected individuals with the effect of hospitalization

We propose an epidemic model for the transmission of hepatitis B virus along with the classification of different infection phases and hospitalized class. We formulate the model and discuss its basic mathematical properties, e.g. existence, positivity, and biological feasibility. Exploiting the next generation matrix approach, we find the basic reproductive number of the model. We perform sensitivity analysis to illustrate the effect of various parameters on the transmission of the disease. We investigate stability of the equilibria of the model in terms of the basic reproduction number. Conditions for the stability of the proposed model are obtained using various approaches. Finally, we perform the numerical simulations to discuss sensitivity analysis and to support our analytical work.     

不同发展情景下青海省土地利用布局及生物多样性变化模拟

人类活动导致土地利用格局的剧烈变迁是全球生物多样性丧失的重要原因之一。为满足青海省生物多样性保护和社会经济发展对土地利用的需求, 本研究依据土地利用类型/干扰强度与生物多样性的关系, 制定了基线、美丽青海、智慧青海、和谐青海4种情景的设计方案, 并基于GeoSOS-FLUS模型和FLUS-Biodiversity模型分别模拟至2030年、2050年时, 4种情景下青海省土地利用布局及其原生群落平均物种多度(Mean Species Abundance, MSA)的空间格局演变。结果表明, 青海省大部分土地利用类型在现有格局的基础上均发生较大变化。其中, 基线情景(按原有发展趋势)中湿地、森林、草地的面积均有所下降, 导致生物多样性恢复速度缓慢。基于自然保护和经济发展的不同权衡, 美丽青海、智慧青海、和谐青海3种情景则对未来土地利用布局的优化效果较好, 大量中、高强度利用的草地恢复为湿地、原生林及低强度利用的草地, 部分常规农田转换为优质农田, 建设用地面积减少, 生物多样性因而得以较大提高。未来各情景下的青海省MSA值都能实现目标值, 生物多样性完整性相对于2020年都有所增加。