Accuracy of marker-assisted selection with single markers and marker haplotypes in cattle

A key question for the implementation of marker-assisted selection (MAS) using markers in linkage disequilibrium with quantitative trait loci (QTLs) is how many markers surrounding each QTL should be used to ensure the marker or marker haplotypes are in sufficient linkage disequilibrium (LD) with the QTL. In this paper we compare the accuracy of MAS using either single markers or marker haplotypes in an Angus cattle data set consisting of 9323 genome-wide single nucleotide polymorphisms (SNPs) genotyped in 379 Angus cattle. The extent of LD in the data set was such that the average marker-marker r2 was 0.2 at 200 kb. The accuracy of MAS increased as the number of markers in the haplotype surrounding the QTL increased, although only when the number of markers in the haplotype was 4 or greater did the accuracy exceed that achieved when the SNP in the highest LD with the QTL was used. A large number of phenotypic records (>1000) were required to accurately estimate the effects of the haplotypes.     

A comparison between methods for linkage disequilibrium fine mapping of quantitative trait loci

We present a maximum likelihood method for mapping quantitative trait loci that uses linkage disequilibrium information from single and multiple markers. We made paired comparisons between analyses using a single marker, two markers and six markers. We also compared the method to single marker regression analysis under several scenarios using simulated data. In general, our method outperformed regression (smaller mean square error and confidence intervals of location estimate) for quantitative trait loci with dominance effects. In addition, the method provides estimates of the frequency and additive and dominance effects of the quantitative trait locus.     

Mapping Quantitative Trait Loci in Crosses between Outbred Lines Using Least Squares

The use of genetic maps based upon molecular markers has allowed the dissection of some of the factors underlying quantitative variation in crosses between inbred lines. For many species crossing inbred lines is not a practical proposition, although crosses between genetically very different outbred lines are possible. Here we develop a least squares method for the analysis of crosses between outbred lines which simultaneously uses information from multiple linked markers. The method is suitable for crosses where the lines may be segregating at marker loci but can be assumed to be fixed for alternative alleles at the major quantitative trait loci (QTLs) affecting the traits under analysis (e.g., crosses between divergent selection lines or breeds with different selection histories). The simultaneous use of multiple markers from a linkage group increases the sensitivity of the test statistic, and thus the power for the detection of QTLs, compared to the use of single markers or markers flanking an interval. The gain is greater for more closely spaced markers and for markers of lower information content. Use of multiple markers can also remove the bias in the estimated position and effect of a QTL which may result when different markers in a linkage group vary in their heterozygosity in the F(1) (and thus in their information content) and are considered only singly or a pair at a time. The method is relatively simple to apply so that more complex models can be fitted than is currently possible by maximum likelihood. Thus fixed effects and effects of background genotype can be fitted simultaneously with the exploration of a single linkage group which will increase the power to detect QTLs by reducing the residual variance. More complex models with several QTLs in the same linkage group and two-locus interactions between QTLs can similarly be examined. Thus least squares provides a powerful tool to extend the range of crosses from which QTLs can be dissected whilst at the same time allowing flexible and realistic models to be explored.     

Long-term impacts of genome-enabled selection

The objective was to evaluate the effects of directional selection based on estimated genomic breeding values (GEBVs) for a quantitative trait. Selection affects GEBV prediction accuracy as well as genetic architecture via changes in allelic frequencies and linkage disequilibrium (LD), and the resulting changes are different from those in the absence of selection. How marker density affects long-term GEBV accuracy and selection response needs to be understood as well. Simulations were used to characterize the impact of selection based on GEBVs over generations. Single-nucleotide polymorphism (SNP) marker effects were estimated with the Bayesian Lasso method in the base generation, and these estimates were used to calculate the GEBVs in subsequent generations. GEBV accuracy decreased over generations of selection, and it was lower than under random selection, where a decay took place as well. In the long term, selection response tended to reach a plateau, but, at higher marker density, both the magnitude and duration of the response were larger. Selection changed quantitative trait loci (QTL) allele frequencies and generated new but unfavorable LD for prediction. Family effects had a considerable contribution to GEBV accuracy in early generations of selection.     

Genetic resolution and verification of quantitative trait loci for flowering and plant height with recombinant inbred lines of maize.

Recombinant inbred (RI) lines offer several advantages for detecting quantitative trait loci (QTLs), including increased precision of trait measurements, power for detection of additive effects, and resolution of linked QTLs. This study was conducted to detect and characterize QTLs in maize for flowering and plant height and to compare QTL detection in an early (F2:3) generation of the same population. One hundred and eighty-six RIs from a cross between inbred lines Mo17 and H99 were evaluated in a replicated field experiment and analyzed at 101 loci detected by restriction fragment length polymorphisms. QTLs were identified by single-factor analysis of variance. A total of 59 QTLs were detected for plant height, ear height, top height, anthesis, silk emergence, and anthesis to silk interval. Individual QTLs explained 2.2-15.4% of trait variation, and multiple models including all QTLs detected for a trait explained up to 52.5% of the phenotypic variation. Comparison of QTLs detected with 150 F2:3 lines from the same population indicated that 16 (70%) of the 23 F2:3 QTLs were also observed in the F6:7 generation. Parental effects were consistent across generations. At 14 of the 16 QTLs detected in both generations, genetic effects were smaller in the F6:7. Also, some QTLs detected in the F2:3 were resolved into multiple linked QTLs in the F6:7, indicating the additional power of RI populations for mapping, with important implications for marker-assisted selection as well as map-based cloning of QTLs. Key words : Zea mays, RFLP, plant breeding, genetics, recombination.     

The effect of using approximate gametic variance covariance matrices on marker assisted selection by BLUP

Under additive inheritance, the Henderson mixed model equations (HMME) provide an efficient approach to obtaining genetic evaluations by marker assisted best linear unbiased prediction (MABLUP) given pedigree relationships, trait and marker data. For large pedigrees with many missing markers, however, it is not feasible to calculate the exact gametic variance covariance matrix required to construct HMME. The objective of this study was to investigate the consequences of using approximate gametic variance covariance matrices on response to selection by MABLUP. Two methods were used to generate approximate variance covariance matrices. The first method (Method A) completely discards the marker information for individuals with an unknown linkage phase between two flanking markers. The second method (Method B) makes use of the marker information at only the most polymorphic marker locus for individuals with an unknown linkage phase. Data sets were simulated with and without missing marker data for flanking markers with 2, 4, 6, 8 or 12 alleles. Several missing marker data patterns were considered. The genetic variability explained by marked quantitative trait loci (MQTL) was modeled with one or two MQTL of equal effect. Response to selection by MABLUP using Method A or Method B were compared with that obtained by MABLUP using the exact genetic variance covariance matrix, which was estimated using 15 000 samples from the conditional distribution of genotypic values given the observed marker data. For the simulated conditions, the superiority of MABLUP over BLUP based only on pedigree relationships and trait data varied between 0.1% and 13.5% for Method A, between 1.7% and 23.8% for Method B, and between 7.6% and 28.9% for the exact method. The relative performance of the methods under investigation was not affected by the number of MQTL in the model.     

Estimating linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations.

Positional cloning of gene(s) underlying a complex trait requires a high-resolution linkage map between the trait locus and genetic marker loci. Recent research has shown that this may be achieved through appropriately modeling and screening linkage disequilibrium between the candidate marker locus and the major trait locus. A quantitative genetics model was developed in the present study to estimate the coefficient of linkage disequilibrium between a polymorphic genetic marker locus and a locus underlying a quantitative trait as well as the relevant genetic parameters using the sample from randomly mating populations. Asymptotic covariances of the maximum-likelihood estimates of the parameters were formulated. Convergence of the EM-based statistical algorithm for calculating the maximum-likelihood estimates was confirmed and its utility to analyze practical data was exploited by use of extensive Monte-Carlo simulations. Appropriateness of calculating the asymptotic covariance matrix in the present model was investigated for three different approaches. Numerical analyses based on simulation data indicated that accurate estimation of the genetic parameters may be achieved if a sample size of 500 is used and if segregation at the trait locus explains not less than a quarter of phenotypic variation of the trait, but the study reveals difficulties in predicting the asymptotic variances of these maximum-likelihood estimates. A comparison was made between the statistical powers of the maximum-likelihood analysis and the previously proposed regression analysis for detecting the disequilibrium.     

Quantitative trait loci for spawning date and body weight in rainbow trout: testing for conserved effects across ancestrally duplicated chromosomes

We incorporated 69 microsatellite loci into an existing data set of 132 markers to test for quantitative trait loci (QTLs) affecting spawning date and body weight in a backcross between two outbred strains of rainbow trout (Oncorhynchus mykiss). Twenty-six linkage groups were identified and synteny of duplicated microsatellite markers was used to confirm 13 homeologous chromosome pairs. Gene-centromere data were used to localize the centromeres for 13 linkage groups whose orientations were previously unknown. We applied a combination of interval mapping and single marker analysis to the segregating maternal and paternal alleles at 201 microsatellite loci. Four spawning date QTLs with suggestive evidence for an additional two QTLs were detected in female trout spawning at 3 and 4 years of age. Similarly we detected three QTLs for body weight in females at 2 years of age plus four suggestive QTLs for this trait. We found marginal evidence that three pairs of ancestral homeologues contained detectable QTLs for the same trait. In one of the three pairs of homeologues, the duplicated QTL regions mapped to the same relative chromosomal location, while the exact localization of the QTL position in one of the other pairs was difficult to infer since it was based on data from a male-derived map. The existing data were unable to refute a hypothesis that duplicated functional genes will be maintained within the telomeric regions of salmonids due to preferential male-mediated crossing over in this region. Two of the four spawning date QTLs were detected on linkage groups with unknown homeologous relationships. QTLs with possible pleiotropic effects on both spawning date and body size were localized to two linkage groups.     

A model for marker-assisted selection among single crosses with multiple genetic markers

 Trait means of marker genotypes are often inconsistent across experiments, thereby hindering the use of regression techniques in marker-assisted selection. Best linear unbiased prediction based on trait and marker data (TM-BLUP) does not require prior information on the mean effects associated with specific marker genotypes and, consequently, may be useful in applied breeding programs. The objective of this paper is to present a flanking-marker, TM-BLUP model that is applicable to interpopulation single crosses that characterize maize (Zea mays L.) breeding programs. The performance of a single cross is modeled as the sum of testcross additive and dominance effects at unmarked quantitative trait loci (QTL) and at marked QTL (MQTL). The TM-BLUP model requires information on the recombination frequencies between flanking markers and the MQTL and on MQTL variances. A tabular method is presented for calculating the conditional probability that MQTL alleles in two inbreds are identical by descent given the observed marker genotypes (G ^k _obs) at the kth MQTL. Information on identity by descent of MQTL alleles can then be used to calculate the conditional covariance of MQTL effects between single crosses given G ^k _obs. The inverse of the covariance matrix for dominance effects at unmarked QTL and MQTL can be written directly from the inverse of the covariance matrices of the corresponding testcross additive effects. In practice, the computations required in TM-BLUP may be prohibitive. The computational requirements may be reduced with simplified TM-BLUP models wherein dominance effects at MQTL are excluded, only the single crosses that have been tested are included, or information is pooled across several MQTL. Received: 22 June 1997 / Accepted: 25 February 1998     

Genetic evaluation by best linear unbiased prediction using marker and trait information in a multibreed population.

Genetic evaluation by best linear unbiased prediction (BLUP) requires modeling genetic means, variances, and covariances. This paper presents theory to model means, variances, and covariances in a multibreed population, given marker and breed information, in the presence of gametic disequilibrium between the marker locus (ML) and linked quantitative trait locus (MQTL). Theory and algorithms are presented to construct the matrix of conditional covariances between relatives (Gv) for the MQTL effects in a multibreed population and to obtain the inverse of Gv efficiently. Theory presented here accounts for heterogeneity of variances among pure breeds and for segregation variances between pure breeds. A numerical example was used to illustrate how the theory and algorithms can be used for genetic evaluation by BLUP using marker and trait information in a multibreed population.     

Locus-specific heritability estimation via the bootstrap in linkage scans for quantitative trait loci

BACKGROUND/AIMS: In genome-wide linkage analysis of quantitative trait loci (QTL), locus-specific heritability estimates are biased when the original data are used to both localize linkage and estimate effects, due to maximization of the LOD score over the genome. Positive bias is increased by adoption of stringent significance levels to control genome-wide type I error. We propose multi-locus bootstrap resampling estimators for bias reduction in the situation in which linkage peaks at more than one QTL are of interest. METHODS: Bootstrap estimates were based on repeated sample splitting in the original dataset. We conducted simulation studies in nuclear families with 0 to 5 QTLs and applied the methods in a genome-wide analysis of a blood pressure phenotype in extended pedigrees from the Framingham Heart Study (FHS). RESULTS: Compared to na?ve estimates in the original simulation samples, bootstrap estimates had reduced bias and smaller mean squared error. In the FHS pedigrees, the bootstrap yielded heritability estimates as much as 70% smaller than in the original sample. CONCLUSIONS: Because effect estimates obtained in an initial study are typically inflated relative to those expected in an independent replication study, successful replication will be more likely when sample size requirements are based on bias-reduced estimates.     

Modeling linkage disequilibrium between a polymorphic marker locus and a locus affecting complex dichotomous traits in natural populations

Linkage disequilibrium is an important topic in evolutionary and population genetics. An issue yet to be settled is the theory required to extend the linkage disequilibrium analysis to complex traits. In this study, we present theoretical analysis and methods for detecting or estimating linkage disequilibrium (LD) between a polymorphic marker locus and any one of the loci affecting a complex dichotomous trait on the basis of samples randomly or selectively collected from natural populations. Statistical properties of these methods were investigated and their powers were compared analytically or by use of Monte Carlo simulations. The results show that the disequilibrium may be detected with a power of 80% by using phenotypic records and marker genotype when both the trait and marker variants are common (30%) and the LD is relatively high (40-100% of the theoretical maximum). The maximum-likelihood approach provides accurate estimates of the model parameters as well as detection of linkage disequilibrium. The likelihood method is preferred for its higher power and reliability in parameter estimation. The approaches developed in this article are also compared to those for analyzing a continuously distributed quantitative trait. It is shown that a larger sample size is required for the dichotomous trait model to obtain the same level of power in detecting linkage disequilibrium as the continuous trait analysis. Potential use of these estimates in mapping the trait locus is also discussed.     

Genetic mapping of local adaptation along the altitudinal gradient in <Emphasis Type="Italic">Abies sachalinensis</Emphasis>

Understanding the genetic bases of local adaptation in dominant conifer species is critical in predicting the impacts of rapid climate change on forest ecosystems. However, the genetic basis of adaptation is not yet fully understood due to the huge and complex genomes of conifers and the unavailability to date of suitable crossing material. In this study, we constructed a linkage map for Abies sachalinensis (2n = 24) and investigated quantitative trait loci (QTLs) associated with local adaptation along an altitudinal gradient. A segregating population of 239 seedlings was produced from a cross between two F₁ hybrids (high-altitude × low-altitude genotypes). QTL mapping of phenological and growth traits was performed using a pseudo-testcross strategy with linkage maps based on 1251 single-nucleotide polymorphism (SNP) and three simple sequence repeat (SSR) markers. Two maps consisting of 12 linkage groups with an average marker interval of ca. 3 cM were constructed for each parent. The total lengths of the maps were 1861 and 1949 cM. A permutation test identified four significant QTLs and 11 additional suggestive QTLs, with high logarithm of odds (LOD) scores (> 3.0). This is the first highly saturated linkage map produced for Abies taxa. Our results suggest that spring bud phenology is controlled by several QTLs with moderate effects. The use of the mapping population created by crossing two hybrids (high × low altitude genotypes) and numerous SNP markers enabled us to investigate the genetic basis of adaptive traits in conifer species.     

METHODS FOR DETECTION AND ESTIMATION OF LINKAGE BETWEEN A MARKER LOCUS AND QUANTITATIVE TRAIT LOCI Ⅰ. USING F_2 FAMILY SUBPOPULATION

Several methods heve been proposed over the years to detect linkage between a marker gene and a quantitative trait locus (QTL). Use of isozymes and restriction fragment length polymorphisms (RFLPs) as genetic markers has encouraged the development of new methods to detect linkage. In the paper authors present three methods to detect linkage and two methods to measure recombination frequency (r). The three methods that detect linkage are fit for the test of one or several QTLs of quantitative trait considered as long as the net gene effect vaIue of all loci belonging to a linkage cluster is greater significantly than zero, irrespective of their linkage relationship among the several QTLs.     

Linear models for joint association and linkage QTL mapping

Background

Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure.

Results

We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders'' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided.

Conclusion

The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.     

The Contribution of Quantitative Trait Loci and Neutral Marker Loci to the Genetic Variances and Covariances among Quantitative Traits in Random Mating Populations

Using Cockerham's approach of orthogonal scales, we develop genetic models for the effect of an arbitrary number of multiallelic quantitative trait loci (QTLs) or neutral marker loci (NMLs) upon any number of quantitative traits. These models allow the unbiased estimation of the contributions of a set of marker loci to the additive and dominance variances and covariances among traits in a random mating population. The method has been applied to an analysis of allozyme and quantitative data from the European oyster. The contribution of a set of marker loci may either be real, when the markers are actually QTLs, or apparent, when they are NMLs that are in linkage disequilibrium with hidden QTLs. Our results show that the additive and dominance variances contributed by a set of NMLs are always minimum estimates of the corresponding variances contributed by the associated QTLs. In contrast, the apparent contribution of the NMLs to the additive and dominance covariances between two traits may be larger than, equal to or lower than the actual contributions of the QTLs. We also derive an expression for the expected variance explained by the correlation between a quantitative trait and multilocus heterozygosity. This correlation explains only a part of the genetic variance contributed by the markers, i.e., in general, a combination of additive and dominance variances and, thus, provides only very limited information relative to the method supplied here.     

Use of Multiple Genetic Markers in Prediction of Breeding Values

Genotypes at a marker locus give information on transmission of genes from parents to offspring and that information can be used in predicting the individuals' additive genetic value at a linked quantitative trait locus (MQTL). In this paper a recursive method is presented to build the gametic relationship matrix for an autosomal MQTL which requires knowledge on recombination rate between the marker locus and the MQTL linked to it. A method is also presented to obtain the inverse of the gametic relationship matrix. This information can be used in a mixed linear model for simultaneous evaluation of fixed effects, gametic effects at the MQTL and additive genetic effects due to quantitative trait loci unlinked to the marker locus (polygenes). An equivalent model can be written at the animal level using the numerator relationship matrix for the MQTL and a method for obtaining the inverse of this matrix is presented. Information on several unlinked marker loci, each of them linked to a different locus affecting the trait of interest, can be used by including an effect for each MQTL. The number of equations per animal in this case is 2m + 1 where m is the number of MQTL. A method is presented to reduce the number of equations per animal to one by combining information on all MQTL and polygenes into one numerator relationship matrix. It is illustrated how the method can accommodate individuals with partial or no marker information. Numerical examples are given to illustrate the methods presented. Opportunities to use the presented model in constructing genetic maps are discussed.     

Quantitative trait loci for growing degree days to flowering and photoperiod response in Sunflower (Helianthus annuus L.)

The number of days from seedling emergence to flowering (DTF) is a major consideration in sunflower breeding programs. This is a complex trait determined by the genotype, environmental conditions and interactions. Photoperiod and temperature have major effects on DTF and could be important sources of genotype× environment interaction. The objectives of this study were to locate quantitative trait loci (QTLs) associated with growing degree days (GDD) to flowering and photoperiod (PP) response in an elite sunflower population. Two hundred and thirty five F₂-generation plants and their F_2:3 and F_2:4 progenies of a single-cross population of two divergent inbred lines were evaluated in six environments (locations, years and sowing dates) with photoperiods known to elicit a PP response between the inbred lines. Detection of QTLs was facilitated with a genetic linkage map of 205 RFLP loci and composite interval mapping. The 205 restriction fragment length polymorphism (RFLP) loci covered 1380 cM and were arranged in 17 linkage groups, which is the haploid number of chromosomes in this species. The average interval size was 5.9 cM. Six QTLs in linkage groups A, B, F, I, J and L were associated with GDD to flowering and accounted for 76% of the genotypic variation in the mean environment. QTLs in linkage groups A and B accounted for 72% of the genetic variation. QTL×environment (QTL×E) interactions were highly significant for linkage groups A, B, F and J (P<0.01). QTLs in linkage groups A and B were highly dependent on PP. Also, QTL mapping of the ratio of the GDD required by a progeny to flower at a PP of 12.1 and 15.0 h, defined as the photoperiod response (PPR), suggested that alleles at QTLs in linkage groups A and B were responsive to PP. QTLs in linkage groups F and J showed QTL×E interaction but the LOD values were not associated with PP. QTL×E interactions for additive effects were highly significant (P<0.01) for linkage groups A, B and F. QTL×E interactions for QTLs with dominant effects were significant (P<0.01) for linkage groups A, B and J. The dominant effect of QTLs in linkage group B increased in environments with a longer PP. The knowledge of how these QTLs influence the GDD for flowering and how they interact with the environment will facilitate marker- assisted selection and backcross conversion of photoperiod-sensitive germplasm. Received: 7 February 2000 / Accepted: 13 June 2000     

3FunMap: full-sib family functional mapping of dynamic traits

MOTIVATION: Functional mapping that embeds the developmental mechanisms of complex traits shows great power to study the dynamic pattern of genetic effects triggered by individual quantitative trait loci (QTLs). A full-sib family, produced by crossing two heterozygous parents, is characteristic of uncertainties about cross-type at a locus and linkage phase between different loci. Integrating functional mapping into a full-sib family requires a model selection procedure capable of addressing these uncertainties. 3FunMap, written in VC++ 6.0, provides a flexible and extensible platform to perform full-sib functional mapping of dynamic traits. Functions in the package encompass linkage phase determination, marker map construction and the pattern identification of QTL segregation, dynamic tests of QTL effects, permutation tests and numerical simulation. We demonstrate the features of 3FunMap through real data analysis and computer simulation. AVAILABILITY: http://statgen.psu.edu/software.     

Quantitative trait loci for partial resistance to crown rust, Puccinia coronata, in cultivated oat, Avena sativa L.

To facilitate the detection of quantitative trait loci (QTLs) for partial resistance to oat crown rust, Puccinia coronata f. sp. avenae Eriks., a genetic map was generated in a population of 158 F(6)-derived oat recombinant inbred lines from a cross of a partial resistance line MN841801-1 by a susceptible cultivar selection 'Noble-2'. The map, developed using 230 marker loci, mostly restriction fragment length polymorphism and amplified fragment length polymorphism markers, spanned 1,509 cM (Haldane) arranged into 30 linkage groups of 2-18 markers each. Four consistently detected major QTLs for partial rust resistance, Prq1a, Prq1b, Prq2, and Prq7, and three minor QTLs, Prq3, Prq5, and Prq6, were found in tests involving three field and two greenhouse environments. In addition, two major QTLs for flowering time, Ftq1 and Ftq7, and five weaker QTLs, Ftq2, Ftq3, Ftq4, Ftq5, and Ftq6, were revealed. Overlapping of the map segments of Ftq1 and Prq1 and of Ftq7 and Prq7 suggested either linkage between the flowering time QTLs and resistance QTLs or a pleiotropic effect of the Ftq QTLs on rust resistance. Relatively low heritability estimates (0.30) obtained for partial resistance to crown rust in the field indicate a potential value for marker-assisted selection.