A method for computing identity by descent probabilities and quantitative trait loci mapping with dominant (AFLP) markers

Amplified fragment length polymorphisms (AFLPs) are a widely used marker system: the technique is very cost-effective, easy and rapid, and reproducibly generates hundreds of markers. Unfortunately, AFLP alleles are typically scored as the presence or absence of a band and, thus, heterozygous and dominant homozygous genotypes cannot be distinguished. This results in a significant loss of information, especially as regards mapping of quantitative trait loci (QTLs). We present a Monte Carlo Markov Chain method that allows us to compute the identity by descent probabilities (IBD) in a general pedigree whose individuals have been typed for dominant markers. The method allows us to include the information provided by the fluorescent band intensities of the markers, the rationale being that homozygous individuals have on average higher band intensities than heterozygous individuals, as well as information from linked markers in each individual and its relatives. Once IBD probabilities are obtained, they can be combined into the QTL mapping strategy of choice. We illustrate the method with two simulated populations: an outbred population consisting of full sib families, and an F2 cross between inbred lines. Two marker spacings were considered, 5 or 20 cM, in the outbred population. There was almost no difference, for the practical purpose of QTL estimation, between AFLPs and biallelic codominant markers when the band density is taken into account, especially at the 5 cM spacing. The performance of AFLPs every 5 cM was also comparable to that of highly polymorphic markers (microsatellites) spaced every 20 cM. In economic terms, QTL mapping with a dense map of AFLPs is clearly better than microsatellite QTL mapping and little is lost in terms of accuracy of position. Nevertheless, at low marker densities, AFLPs or other biallelic markers result in very inaccurate estimates of QTL position.     

A new strategy for estimating recombination fractions between dominant markers from an F2 population

Although most high-density linkage maps have been constructed from codominant markers such as single-nucleotide polymorphisms (SNPs) and microsatellites due to their high linkage information, dominant markers can be expected to be even more significant as proteomic technique becomes widely applicable to generate protein polymorphism data from large samples. However, for dominant markers, two possible linkage phases between a pair of markers complicate the estimation of recombination fractions between markers and consequently the construction of linkage maps. The low linkage information of the repulsion phase and high linkage information of coupling phase have led geneticists to construct two separate but related linkage maps. To circumvent this problem, we proposed a new method for estimating the recombination fraction between markers, which greatly improves the accuracy of estimation through distinction between the coupling phase and the repulsion phase of the linked loci. The results obtained from both real and simulated F2 dominant marker data indicate that the recombination fractions estimated by the new method contain a large amount of linkage information for constructing a complete linkage map. In addition, the new method is also applicable to data with mixed types of markers (dominant and codominant) with unknown linkage phase.     

Maximum likelihood techniques for the mapping and analysis of quantitative trait loci with the aid of genetic markers

A method is presented to estimate the biometric parameters of a quantitative trait locus linked to a genetic marker when both loci are segregating in the F-2 generation of a cross between two inbred lines. The method, which assumes underlying normal distributions, is a combination of maximum likelihood and moments methods and uses the statistics of the genetic marker genotype samples for the quantitative trait to estimate the recombination frequency between the two loci and the means and variances of the genotypes of the quantitative trait locus. With this method, the genetic parameters of a locus affecting plant height linked to an electrophoretic marker for esterase were accurately estimated from a sample of 1596 F-2 progeny of a cross between two species of Lycopersicon (tomato). Linkage distance between the two loci was 38 map units and the effect of the quantitative trait locus was 1.6 phenotypic standard deviation units. Accurate estimates of the genetic parameters and linkage distance for populations of 2000 individuals simulated with a segregating codominant locus with an effect of 1.63 standard deviations linked to a genetic marker with .2 recombination were also derived by this method. The method is not effective in distinguishing between complete and partial linkage in samples of only 500 individuals or for quantitative loci with effects less than a phenotypic standard deviation. The method is more effective for codominant than for dominant loci.     

基于分离亚群体QTL定位的模拟研究

在数量性状QTL的精细定位中, 通过数量性状目标QTL的近等基因系可构建分离群体。在目标QTL效应较大的情况下, 数量性状表型值可反映目标QTL的基因型。若目标QTL附近的标记密度大时, 大样本才能定位该QTL。但是, 这增加了试验费用。为节约试验经费, 若只利用QTL纯合隐性基因型植株的分子标记信息, 也可比较准确地定位该QTL。利用极大似然法, 分别推导出F2、BC、DH以及RIL群体中重组率及其标准误的估计公式。Monte Carlo模拟研究表明, 基于定位群体中全部数据或隐性纯合基因型数据所获得的重组率估计值是一致的, 且在相同样本容量条件下, 二者精度相当。     

应用贝叶斯理论推断DNA分子标记基因型

引入贝叶斯理论用以从DNA分子标记的表现型（电泳谱带）推断其基因型（DNA来源）。结果表明,根据标记座位独立贫富而确定的遗传信息不完全标记的基因型概率,与根据邻近的遗传信息完全标记的基因型和有关重组率算得的相应贝叶斯概率,通常都有很大的差异,所以在进行数量性状基因定位和标记辅助选择等工作前前,应当计算每一个体基因组上所有遗传信息不完全座位的有关基因型的贝叶斯概率,文中列出计算未知基因型的贝叶斯概率的详细过程,也讨论了贝叶斯概率的若干推广应用。     

Mapping quantitative trait loci using molecular marker linkage maps

Summary High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F₁ testcross (F₁TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F₂, and F₃ progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F₂ progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.     

Construction of a genetic linkage map in tetraploid species using molecular markers

This article presents methodology for the construction of a linkage map in an autotetraploid species, using either codominant or dominant molecular markers scored on two parents and their full-sib progeny. The steps of the analysis are as follows: identification of parental genotypes from the parental and offspring phenotypes; testing for independent segregation of markers; partition of markers into linkage groups using cluster analysis; maximum-likelihood estimation of the phase, recombination frequency, and LOD score for all pairs of markers in the same linkage group using the EM algorithm; ordering the markers and estimating distances between them; and reconstructing their linkage phases. The information from different marker configurations about the recombination frequency is examined and found to vary considerably, depending on the number of different alleles, the number of alleles shared by the parents, and the phase of the markers. The methods are applied to a simulated data set and to a small set of SSR and AFLP markers scored in a full-sib population of tetraploid potato.     

Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines

Dominant phenotype of a genetic marker provides incomplete information about the marker genotype of an individual. A consequence of using this incomplete information for mapping quantitative trait loci (QTL) is that the inference of the genotype of a putative QTL flanked by a marker with dominant phenotype will depend on the genotype or phenotype of the next marker. This dependence can be extended further until a marker genotype is fully observed. A general algorithm is derived to calculate the probability distribution of the genotype of a putative QTL at a given genomic position, conditional on all observed marker phenotypes in the region with dominant and missing marker information for an individual. The algorithm is implemented for various populations stemming from two inbred lines in the context of mapping QTL. Simulation results show that if only a proportion of markers contain missing or dominant phenotypes, QTL mapping can be almost as efficient as if there were no missing information in the data. The efficiency of the analysis, however, may decrease substantially when a very large proportion of markers contain missing or dominant phenotypes and a genetic map has to be reconstructed first on the same data as well. So it is important to combine dominant markers with codominant markers in a QTL mapping study. This revised version was published online in July 2006 with corrections to the Cover Date.     

Recombination in bacteriophage T1 in the presence of host restriction.

When unmodified phage T1 infects restricting host cells at high multiplicities of infection, there is an increase in recombination frequency in all regions of the T1 map compared to the level of recombination in standard crosses when short distances are examined. The enhancement of recombination frequency is not uniform for all regions but is greatest for markers near the center of the map and not so great for markers near the ends. Crosses between markers at the extremities of the map show that there is no increase in recombination frequency under restriction conditions. An examination of phage T1 heterozygotes suggests that an increase of ends created by the process of P1 restriction increases recombination. When T1 crosses are done in the absence of host restriction, recombination defects in the host have no effect on phage recombination and we conclude that phage T1 codes for its own recombination genes. Host recombination functions are also dispensable for the recombination occurring during infection of restricting host cells by unmodified phage at high multiplicities of infection.     

A Genetic Map of Quantitative Trait Loci for Body Weight in the Mouse

The genetic basis of body weight in the mouse was investigated by measuring frequency changes of microsatellite marker alleles in lines divergently selected for body weight from a base population of a cross between two inbred strains. In several regions of the genome, sharp peaks of frequency change at linked markers were detected, which suggested the presence of single genes of moderate effect, although in several other regions, significant frequency changes occurred over large portions of chromosomes. A method based on maximum likelihood was used to infer effects and map positions of quantitative trait loci (QTLs) based on genotype frequencies at one or more marker loci. Eleven QTLs with effects in the range 0.17-0.28 phenotypic standard deviations were detected; but under an additive model, these did not fully account for the observed selection response. Tests for the presence of more than one QTL in regions where there were large changes of marker allele frequency were mostly inconclusive.     

Mapping quantitative trait loci by genotyping haploid tissues.

Mapping strategies based on a half- or full-sib family design have been developed to map quantitative trait loci (QTL) for outcrossing species. However, these strategies are dependent on controlled crosses where marker-allelic frequency and linkage disequilibrium between the marker and QTL may limit their application. In this article, a maximum-likelihood method is developed to map QTL segregating in an open-pollinated progeny population using dominant markers derived from haploid tissues from single meiotic events. Results from the haploid-based mapping strategy are not influenced by the allelic frequencies of markers and their linkage disequilibria with QTL, because the probabilities of QTL genotypes conditional on marker genotypes of haploid tissues are independent of these population parameters. Parameter estimation and hypothesis testing are implemented via expectation/conditional maximization algorithm. Parameters estimated include the additive effect, the dominant effect, the population mean, the chromosomal location of the QTL in the interval, and the residual variance within the QTL genotypes, plus two population parameters, outcrossing rate and QTL-allelic frequency. Simulation experiments show that the accuracy and power of parameter estimates are affected by the magnitude of QTL effects, heritability levels of a trait, and sample sizes used. The application and limitation of the method are discussed.     

Criteria to optimize designs for detection and estimation of linkage between marker loci from segregating populations containing several families

Summary Construction of a genome map of highly polymorphic markers has become possible in the past decade. Establishing a complete marker map is an enormous task. Therefore, designs to map molecular markers should be optimal. Designs to detect and estimate linkage between markers from segregating populations were studied. Two measures of design quality were used. The expectation of the maximum lod score indicates the possibility of designs to detect linkage. The accuracy of estimating recombination rate was measured as the probability that the true recombination rate is in a specified internal given the estimate. Accurate approximate methods were developed for rapid evaluation of designs. Seven family types (e.g., double backcross) can be distinguished that describe all families in a segregating population. The family type influences the expected maximum lod score and the accuracy of estimation. The frequency of favorable family types increased with increasing marker polymorphism. At a true recombination rate of 0.20,27 observations on offspring when five alleles were segregating, and 55 observations on offspring when two alleles were segregating, were necessary to obtain an expected maximum lod score of 3. The probability that the true recombination rate was between 0.15 and 0.25, given an estimate of 0.20, was about 0.85 for a design with 40 families with ten offspring and two alleles segregating and for a design with ten families with ten offspring and six alleles segregating. For smaller designs, accuracies were less, approximate evaluation of accuracy was not justified and, on average, true recombination rates were much greater than estimated given a specified value for the estimated recombination rate.     

A simple note on how to save money in linkage analysis

Genetic linkage maps are often based on maximum-likelihood estimates of recombination fractions which are converted into map units by mapping functions. This paper presents a cost analysis of linkage analysis for a segregating F₂␣population with codominant or dominant molecular markers and a qualitative monogenic dominant–recessive trait. For illustration, a disease-resistance trait is considered, where the susceptible allele is recessive. Three sub-populations of the F₂ can be used for linkage analysis [susceptible (= recessive) individuals, resistant (= dominant) individuals, complete F₂]. While it is well-known that recessive individuals are more informative than dominant individuals, it is not obvious a priori, which of the three sub-populations should be preferred, when costs of phenotyping and genotyping are taken into consideration. A comparative economic analysis of alternative procedures of linkage detection based on these three sub-populations does exhibit a clear economic superiority of the sub-population of susceptible (= recessive) individuals, when costs of genotyping are high. This cost-effectiveness is due to the higher information content of this sub-population compared to the sub-population of dominant (= resistant) individuals and also compared to the complete F₂. Our final conclusion/recommendation is as follows: If the cost to genotype an individual is sufficiently large compared with the cost to phenotype an individual, then linkage analysis and genetic mapping should be only based on susceptible (= recessive) individuals. Conversely, if the cost of phenotyping exceeds that for genotyping, it may be preferable to genotype all plants. The exact conditions under which a strategy is preferable are described in the paper.     

Genotype‐specific SNP map based on whole chromosome 3B sequence information from wheat cultivars Arina and Forno

Agronomically important traits are frequently controlled by rare, genotype‐specific alleles. Such genes can only be mapped in a population derived from the donor genotype. This requires the development of a specific genetic map, which is difficult in wheat because of the low level of polymorphism among elite cultivars. The absence of sufficient polymorphism, the complexity of the hexaploid wheat genome as well as the lack of complete sequence information make the construction of genetic maps with a high density of reproducible and polymorphic markers challenging. We developed a genotype‐specific genetic map of chromosome 3B from winter wheat cultivars Arina and Forno. Chromosome 3B was isolated from the two cultivars and then sequenced to 10‐fold coverage. This resulted in a single‐nucleotide polymorphisms (SNP) database of the complete chromosome. Based on proposed synteny with the Brachypodium model genome and gene annotation, sequences close to coding regions were used for the development of 70 SNP‐based markers. They were mapped on a Arina × Forno Recombinant Inbred Lines population and found to be spread over the complete chromosome 3B. While overall synteny was well maintained, numerous exceptions and inversions of syntenic gene order were identified. Additionally, we found that the majority of recombination events occurred in distal parts of chromosome 3B, particularly in hot‐spot regions. Compared with the earlier map based on SSR and RFLP markers, the number of markers increased fourfold. The approach presented here allows fast development of genotype‐specific polymorphic markers that can be used for mapping and marker‐assisted selection.     

Detection and parameter estimation for quantitative trait loci using regression models and multiple markers

A strategy of multi-step minimal conditional regression analysis has been developed to determine the existence of statistical testing and parameter estimation for a quantitative trait locus (QTL) that are unaffected by linked QTLs. The estimation of marker-QTL recombination frequency needs to consider only three cases: 1) the chromosome has only one QTL, 2) one side of the target QTL has one or more QTLs, and 3) either side of the target QTL has one or more QTLs. Analytical formula was derived to estimate marker-QTL recombination frequency for each of the three cases. The formula involves two flanking markers for case 1), two flanking markers plus a conditional marker for case 2), and two flanking markers plus two conditional markers for case 3). Each QTL variance and effect, and the total QTL variance were also estimated using analytical formulae. Simulation data show that the formulae for estimating marker-QTL recombination frequency could be a useful statistical tool for fine QTL mapping. With 1 000 observations, a QTL could be mapped to a narrow chromosome region of 1.5 cM if no linked QTL is present, and to a 2.8 cM chromosome region if either side of the target QTL has at least one linked QTL.     

Detection of closely linked multiple quantitative trait loci using a genetic algorithm

The existence of a quantitative trait locus (QTL) is usually tested using the likelihood of the quantitative trait on the basis of phenotypic character data plus the recombination fraction between QTL and flanking markers. When doing this, the likelihood is calculated for all possible locations on the linkage map. When multiple QTL are suspected close by, it is impractical to calculate the likelihood for all possible combinations of numbers and locations of QTL. Here, we propose a genetic algorithm (GA) for the heuristic solution of this problem. GA can globally search the optimum by improving the "genotype" with alterations called "recombination" and "mutation." The "genotype" of our GA is the number and location of QTL. The "fitness" is a function based on the likelihood plus Akaike's information criterion (AIC), which helps avoid false-positive QTL. A simulation study comparing the new method with existing QTL mapping packages shows the advantage of the new GA. The GA reliably distinguishes multiple QTL located in a single marker interval.     

The Effects of Selection on Linkage Analysis for Quantitative Traits

The effects of within-sample selection on the outcome of analyses detecting linkage between genetic markers and quantitative traits were studied. It was found that selection by truncation for the trait of interest significantly reduces the differences between marker genotype means thus reducing the power to detect linked quantitative trait loci (QTL). The size of this reduction is a function of proportion selected, the magnitude of the QTL effect, recombination rate between the marker locus and the QTL, and the allele frequency of the QTL. Proportion selected was the most influential of these factors on bias, e.g., for an allele substitution effect of one standard deviation unit, selecting the top 80%, 50% or 20% of the population required 2, 6 or 24 times the number of progeny, respectively, to offset the loss of power caused by this selection. The effect on power was approximately linear with respect to the size of gene effect, almost invariant to recombination rate, and a complex function of QTL allele frequency. It was concluded that experimental samples from animal populations which have been subjected to even minor amounts of selection will be inefficient in yielding information on linkage between markers and loci influencing the quantitative trait under selection.     

Molecular Tagging and Mapping of Quantitative Trait Loci for Lint Percentage and Morphological Marker Genes in Upland Cotton

Using 219 F2 Individuals developed by crossing the genetic standard line TM-1 and the multiple dominant marker line T586 In Gossyplum hirsutum L., a genetic linkage map with 19 linkage groups was constructed based on simple sequence repeat （SSR） markers. Compared with our tetraploid backboned molecular genetic map from a （TM-1xHal 7124）xTM-1 BC1 population, 17 of the 19 I｜nkage groups were combined and anchored to 12 chromosomes （sub-genomes）. Of these groups, four morphological marker genes In T586 had been mapped Into the molecular linkage map. Meanwhile, three quantitative trait loci for lint percentage were tagged and mapped separately on the A03 linkage group and chromosome 6.     

Effectiveness of bulking procedures in measuring population-pairwise similarity with dominant and co-dominant genetic markers

Two bulking procedures (bulking individuals before and after genotyping) are commonly applied in similarity based studies of genetic distance at the population or higher level, but their effectiveness is largely unknown. In this study, expected population-pairwise similarity for both bulking procedures is derived with dominant and co-dominant diallelic markers. Numerical examples for the derived formulae are given with up to ten individuals randomly selected from each population. The procedure of bulking individuals after genotyping with either marker system is generally more informative than the procedure of bulking individuals before genotyping, because the former incorporates the information from marker alleles of intermediate frequency. Both procedures are effective with 5–10 individuals selected randomly from either population, but the procedure of bulking before genotyping requires a genotyping effort several-fold less than the procedure of bulking after genotyping. For either bulking procedure, a co-dominant marker system is generally more informative than a dominant marker system. Received: 20 October 1999 / Accepted: 11 November 1999     

Linkage analysis in unconventional mating designs in line crosses

Linkage estimation and genetic map construction with genotyped DNA markers in plants preferentially employ a few maximally informative early-generation or recombinant-inbred mating designs. Fitting their recombination models to unconventional designs adapted to cultivar development (series of backcrossing, selfing, haploid-doubling, random-intercrossing, and sib-mating steps) distorts single- and multipoint linkage estimates even with dense marker coverage. Two methods are provided for correct linkage estimation in unconventional designs: fitting a correct multigeneration model, or correcting the estimates produced by fitting a one-generation model with any conventional software. These methods also support calculation of multilocus genotype frequencies and QTL-genotype distributions and are available in software.