More on the efficiency of marker-assisted selection

 Computer simulations were used to study the efficiency of marker-assisted selection (MAS) based on an index combining the phenotypic value and the molecular score of individuals. The molecular score is computed from the effects attributed to markers by multiple regression of phenotype on marker genotype. The results show that in the first generation the ratio RE of the expected efficiency of MAS over the expected efficiency of purely phenotypic selection generally increases when considering: (1) larger population sizes, (2) lower heritability values of the trait, and (3) a higher type-I error risk of the regression. This is consistent with previously published results. However, at low heritabilities our results point out that response to MAS is more variable than response to phenotypic selection. Hence, when the difference of genetic gains is considered instead of their ratio, RE, the heritability values corresponding to maximal advantage of using MAS rather than phenotypic selection are still low, but higher than predicted based on RE. The study over several successive generations of the rate of fixation of QTLs shows that the higher efficiency of MAS on QTLs with large effects in early generations is balanced by a higher rate of fixation of unfavourable alleles at QTLs with small effects in later generations. This explains why MAS may become less efficient than phenotypic selection in the long term. MAS efficiency therefore depends on the genetic determinism of the trait. Finally, we investigate a modified MAS method involving an alternation of selection on markers with and without phenotypic evaluation. Our results indicate that such a selection method could at low cost, provide an important increase in the genetic gain per unit of time in practical breeding programs. Received: 11 July 1997 / Accepted: 4 August 1997     

性状遗传力与QTL方差对标记辅助选择效果的影响

在采用动物模型标记辅助最佳线性无偏预测方法对个体育种值进行估计的基础上,模拟了在一个闭锁群体内连续对单个性状选择10个世代的情形,并系统地比较了性状遗传力和QTL方差对标记辅助选择所获得的遗传进展、QTL增效基因频率和群体近交系数变化的影响。结果表明：在对高遗传力和QTL方差较小的性状实施标记辅助选择时,可望获得更大的遗传进展;遗传力越高,QTL方差越大,则QTL增效基因频率的上升速度越快;遗传力较高时,群体近交系数上升的速度较为缓慢,而QTL方差对群体近交系数上升速度的影响则不甚明显。结合前人关于标记辅助选择相对效率的研究结果,可以认为：当选择性状的遗传力和QTL方差为中等水平时,标记辅助选择可望获得理想的效果。     

A method for marker-assisted selection based on QTLs with epistatic effects

A method for marker-assisted selection (MAS) based on quantitative trait loci (QTLs) with epistatic effects is proposed. The efficiency of such method is investigated by simulations under a wide range of situations. In the presence of epistasis, MAS generally yields longer persistence response than that based exclusively on additive or additive and dominance. Neglecting epistasis could result in considerable loss in response, and more pronounced at later generations. In addition to population size and trait heritability, genetic variance configurations play an important role in determining both the short- and long-term efficiencies of MAS. MAS using breeding values not only achieves higher response, but also tends to have smaller standard error than other methods in most cases. Errors in QTL detection cause distinct reductions in responses to MAS in most cases. It is thus concluded that verifications of putative QTL and its magnitude of effect and accurate map chromosome location are imperative to realize the potentials of MAS.     

Biased estimators of quantitative trait locus heritability and location in interval mapping

In many empirical studies, it has been observed that genome scans yield biased estimates of heritability, as well as genetic effects. It is widely accepted that quantitative trait locus (QTL) mapping is a model selection procedure, and that the overestimation of genetic effects is the result of using the same data for model selection as estimation of parameters. There are two key steps in QTL modeling, each of which biases the estimation of genetic effects. First, test procedures are employed to select the regions of the genome for which there is significant evidence for the presence of QTL. Second, and most important for this demonstration, estimates of the genetic effects are reported only at the locations for which the evidence is maximal. We demonstrate that even when we know there is just one QTL present (ignoring the testing bias), and we use interval mapping to estimate its location and effect, the estimator of the effect will be biased. As evidence, we present results of simulations investigating the relative importance of the two sources of bias and the dependence of bias of heritability estimators on the true QTL heritability, sample size, and the length of the investigated part of the genome. Moreover, we present results of simulations demonstrating the skewness of the distribution of estimators of QTL locations and the resulting bias in estimation of location. We use computer simulations to investigate the dependence of this bias on the true QTL location, heritability, and the sample size.     

The accuracy of a heritability estimator using molecular information

The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.     

Detecting genetic variation in developmental instability by artificial selection on fluctuating asymmetry

Abstract Fluctuating asymmetry (FA) is frequently used as a measure of developmental instability (DI). Assuming a genetic basis to DI, many have argued that FA may be a good indicator of genetic quality to potential mates and to human managers of populations. Unfortunately FA is a poor indicator of DI, making it very difficult to verify this assertion. A recent review of the literature suggests that previous studies of the inheritance of FA and DI using half‐sib covariances and parent–offspring regression have been unable to put meaningful limits on the heritability of FA and DI because of the extremely low power of the experiments performed. In this study, we consider the power of artificial selection on FA as an alternative approach to studying the inheritance of FA and DI. Using simulations, we investigate the efficacy of selection for both increased and decreased FA for detecting genetic variation. We find that selection for increased FA has much more power to detect the presence of genetic variation than does selection for decreased FA. These results hold when realistic sample sizes are employed. Artificial selection for increased FA is currently the most powerful approach for the detection of genetic variation in DI.     

Marker-assisted selection in segregating generations of self-fertilizing crops

Computer simulations were used to study the efficiency of MAS for breeding self-fertilizing crops, based on a general model including additive, dominance and epistasis. It was shown that MAS not only gave larger genetic responses but also dramatically increased the frequencies of superior genotypes as compared with phenotypic selection. However, the advantages of MAS over phenotypic selection were considerably reduced when conducting selection in later generations. A modified method combining MAS in early generations with phenotypic selection in later generations was thus proposed from an efficiency standpoint. We also proposed a potential index to measure the probability of an individual showing superior genotypes under selfing. It was apparent that more superior genotypes could be derived from selection by using the potential index than by using other methods. The implications of these findings for plant breeding are discussed.Communicated by H.C. Becker     

Within-family marker-assisted selection for aquaculture species

A within-family marker-assisted selection scheme was designed for typical aquaculture breeding schemes, where most traits are recorded on sibs of the candidates. Here, sibs of candidates were tested for the trait and genotyped to establish genetic marker effects on the trait. BLUP breeding values were calculated, including information of the markers (MAS) or not (NONMAS). These breeding values were identical for all family members in the NONMAS schemes, but differed between family members in the MAS schemes, making within-family selection possible. MAS had up to twice the total genetic gain of the corresponding NONMAS scheme. MAS was somewhat less effective when heritability increased from 0.06 to 0.12 or when the frequency of the positive allele was < 0.5. The relative efficiency of MAS was higher for schemes with more candidates, because of larger fullsib family sizes. MAS was also more efficient when male:female mating ratio changed from 1:1 to 1:5 or when the QTL explained more of the total genetic variation. Four instead of two markers linked to the QTL increased genetic gain somewhat. There was no significant difference in polygenic genetic gain between MAS and NONMAS for most schemes. The rates of inbreeding were lower for MAS than NON-MAS schemes, because fewer full-sibs were selected by MAS.     

Accuracy of marker-assisted selection with auxiliary traits

Genetic information on molecular markers is increasingly being used in plant and animal improvement programmes particularly as indirect means to improve a metric trait by selection either on an individual basis or on the basis of an index incorporating such information. This paper examines the utility of an index of selection that not only combines phenotypic and molecular information on the trait under improvement but also combines similar information on one or more auxiliary traits. The accuracy of such a selection procedure has been theoretically studied for sufficiently large populations so that the effects of detected quantitative trait loci can be perfectly estimated. The theory is illustrated numerically by considering one auxiliary trait. It is shown that the use of an auxiliary trait improves the selection accuracy; and, hence, the relative efficiency of index selection compared to individual selection which is based on the same intensity of selection. This is particularly so for higher magnitudes of residual genetic correlation and environmental correlation having opposite signs, lower values of the proportion of genetic variation in the main trait associated with the markers, negligible proportion of genetic variation in the auxiliary trait associated with the markers, and lower values of the heritability of the main trait but higher values of the heritability of the auxiliary trait.     

A general framework for marker-assisted selection

Early simulation studies have showed that the inclusion of epistatic components (especially the additive-by-additive effects) into marker-assisted selection (MAS) can improve selection efficiency for a short-term breeding program. In this study I extend Lande and Thompson's theory to incorporate both additive and non-additive effects into MAS with reference to the mass selection case. Four different indices are analytically examined in terms of the type of genetic components involved in the marker scores: phenotype-, general combining ability (GCA)-, and GCA and reciprocal effects-based marker scores. The phenotype-based marker index is applicable to any population of non-random mating, while the other three indices are applicable to the synthetic population derived from diallel crosses. All these indices may have higher selection efficiencies than the index with solely additive effects-associated markers as long as the detectable transient non-additive effects are present. The improvement in selection efficiency depends on the magnitude of non-additive variances and the proportion of them explained by markers. The index with the phenotype-based marker scores operates on the whole of the additive and non-additive effects, and has the largest selection efficiency. The indices with the GCA-based marker scores operate only on additive and additive-by-additive genetic variation and have relatively small selection efficiencies. Inclusion of the markers from organelle genomes can also increase selection efficiency, depending upon the proportion of the total genetic variation attributable to organelle genomes and the proportion of them explained by organelle genomic markers. Sharing of markers among different marker scores does not facilitate the improvement of selection efficiency.     

Accounting for linkage disequilibrium in genome scans for selection without individual genotypes: The local score approach

Detecting genomic footprints of selection is an important step in the understanding of evolution. Accounting for linkage disequilibrium in genome scans increases detection power, but haplotype‐based methods require individual genotypes and are not applicable on pool‐sequenced samples. We propose to take advantage of the local score approach to account for linkage disequilibrium in genome scans for selection, cumulating (possibly small) signals from single markers over a genomic segment, to clearly pinpoint a selection signal. Using computer simulations, we demonstrate that this approach detects selection with higher power than several state‐of‐the‐art single‐marker, windowing or haplotype‐based approaches. We illustrate this on two benchmark data sets including individual genotypes, for which we obtain similar results with the local score and one haplotype‐based approach. Finally, we apply the local score approach to Pool‐Seq data obtained from a divergent selection experiment on behaviour in quail and obtain precise and biologically coherent selection signals: while competing methods fail to highlight any clear selection signature, our method detects several regions involving genes known to act on social responsiveness or autistic traits. Although we focus here on the detection of positive selection from multiple population data, the local score approach is general and can be applied to other genome scans for selection or other genomewide analyses such as GWAS.     

Genomic selection for marker-assisted improvement in line crosses

Efficiency of genomic selection with low-cost genotyping in a composite line from a cross between inbred lines was evaluated for a trait with heritability 0.10 or 0.25 using a low-density marker map. With genomic selection, selection was on the sum of estimates of effects of all marker intervals across the genome, fitted either as fixed (fixed GS) or random (random GS) effects. Reponses to selection over 10 generations, starting from the F₂, were compared with standard BLUP selection. Estimates of variance for each interval were assumed independent and equal. Both GS strategies outperformed BLUP selection, especially in initial generations. Random GS outperformed fixed GS in early generations and performed slightly better than fixed GS in later generations. Random GS gave higher genetic gain when the number of marker intervals was greater (180 or 10 cM intervals), whereas fixed GS gave higher genetic gain when the number of marker intervals was low (90 or 20 cM). Including interactions between generation and marker scores in the model resulted in lower genetic gains than models without interactions. When phenotypes were available only in the F₂ for GS, treating marker scores as fixed effects led to considerably lower genetic gain than random GS. Benefits of GS over standard BLUP were lower with high heritability. Genomic selection resulted in greater response than MAS based on only significant marker intervals (standard MAS) by increasing the frequency of QTL with both large and small effects. The efficiency of genomic selection over standard MAS depends on stringency of the threshold used for QTL detection. In conclusion, genomic selection can be effective in composite lines using a sparse marker map.     

Marker-assisted selection to increase effective population size by reducing Mendelian segregation variance

Using both the genetic drift and inbreeding approaches, we derive more general equations for effective size (N(e)) of a diploid species under random mating. These equations show explicitly that inbreeding or genetic drift comes from two sources, the variation in the number of offspring from each parent and the variation in contribution between these parents' own paternally and maternally derived genes to their offspring. The first source can be easily and effectively controlled by choosing an equal number of offspring from each family, while the second can be manipulated by using information on genetic markers to reduce the variance due to Mendelian segregation. Marker-assisted selection (MAS) methods to increase N(e) for the whole genome with single or multiple marker loci per chromosome, different numbers of males, and females are developed and implemented in stochastic simulations. The analytical and simulation results show that, although in principle N(e) can be increased indefinitely, the efficiency of MAS is restricted in practice by the amount of marker information, the genome size, and the number of marker-genotyped offspring per family. The assumptions made in developing the theory and methods and the applications of MAS in conservation are discussed.     

A Population Genetics Model of Marker-Assisted Selection

A deterministic two-loci model was developed to predict genetic response to marker-assisted selection (MAS) in one generation and in multiple generations. Formulas were derived to relate linkage disequilibrium in a population to the proportion of additive genetic variance used by MAS, and in turn to an extra improvement in genetic response over phenotypic selection. Predictions of the response were compared to those predicted by using an infinite-loci model and the factors affecting efficiency of MAS were examined. Theoretical analyses of the present study revealed the nonlinearity between the selection intensity and genetic response in MAS. In addition to the heritability of the trait and the proportion of the marker-associated genetic variance, the frequencies of the selectively favorable alleles at the two loci, one marker and one quantitative trait locus, were found to play an important role in determining both the short- and long-term efficiencies of MAS. The evolution of linkage disequilibrium and thus the genetic response over several generations were predicted theoretically and examined by simulation. MAS dissipated the disequilibrium more quickly than drift alone. In some cases studied, the rate of dissipation was as large as that to be expected in the circumstance where the true recombination fraction was increased by three times and selection was absent.     

Marker-assisted selection in autogamous RIL populations: a simulation study

 Molecular markers may enable plant breeders to select indirectly for genes affecting quantitative traits by selecting for molecular markers closely linked to these genes (marker-assisted selection, MAS). We have assessed the effectiveness of MAS compared to phenotypic selection. Key variables in this assessment were: trait heritability, selection intensity, genetic architecture and uncertainty in QTL mapping. Simulation studies showed that the application of MAS in autogamous crops, with the objective of obtaining transgressive genotypes, can improve selection results when compared to conventional selection procedures. Marker-assisted selection appears particularly promising when dominant alleles at quantitative trait loci are present and linked in coupling phase. Uncertainty in estimated QTL map positions reduces the benefits of marker-assisted selection, but this reduction remains limited in most cases. Received: 5 September 1997 / Accepted: 6 October 1997     

Resampling methods to reduce the selection bias in genetic effect estimation in genome-wide scans

Using the simulated data of Problem 2 for Genetic Analysis Workshop 14 (GAW14), we investigated the ability of three bootstrap-based resampling estimators (a shrinkage, an out-of-sample, and a weighted estimator) to reduce the selection bias for genetic effect estimation in genome-wide linkage scans. For the given marker density in the preliminary genome scans (7 cM for microsatellite and 3 cM for SNP), we found that the two sets of markers produce comparable results in terms of power to detect linkage, localization accuracy, and magnitude of test statistic at the peak location. At the locations detected in the scan, application of the three bootstrap-based estimators substantially reduced the upward selection bias in genetic effect estimation for both true and false positives. The relative effectiveness of the estimators depended on the true genetic effect size and the inherent power to detect it. The shrinkage estimator is recommended when the power to detect the disease locus is low. Otherwise, the weighted estimator is recommended.     

QTL×环境互作对标记辅助选择响应的影响

基因型×环境互作是植物数量性状的普通属性和遗传育种改良的关注重点.采用Monte Carlo模拟方法研究了基因型×环境互作对标记辅助选择(Marker-assisted selection,简称MAS)响应的影响,揭示了育种上利用QTL(Quantitafivetrait locus,简称QTL)应当同时考虑其环境互作效应.存在基因型×环境互作下,MAS比普通表型选择更有效.特别以选育广适应性的品种为目标,MAS的优越性更明显.基于单个环境QTLs的MAS,QTL×环境互作效应通常降低了一般选择响应,一般选择响应累积量的降低程度与改良性状的QTL×环境互作效应大小相关.基于多个环境QTLs的MAS,不但产生较高的一般选择响应,而且获得的一般选择响应不受其QTL×环境互作效应大小的影响.但在某一特定环境下获得的总体选择响应仅与改良性状的总遗传率大小有关,普通遗传率和基因型与环境互作遗传率的相对变化对其影响很小.还比较研究了单地和穿梭选择对MAS遗传响应的影响.植物育种者应谨慎将某一环境的QTL信息用于实施另一环境的育种研究.     

Evaluation of genome-wide selection efficiency in maize nested association mapping populations

In comparison to conventional marker-assisted selection (MAS), which utilizes only a subset of genetic markers associated with a trait to predict breeding values (BVs), genome-wide selection (GWS) improves prediction accuracies by incorporating all markers into a model simultaneously. This strategy avoids risks of missing quantitative trait loci (QTL) with small effects. Here, we evaluated the accuracy of prediction for three corn flowering traits days to silking, days to anthesis, and anthesis-silking interval with GWS based on cross-validation experiments using a large data set of 25 nested association mapping populations in maize (Zea mays). We found that GWS via ridge regression-best linear unbiased prediction (RR-BLUP) gave significantly higher predictions compared to MAS utilizing composite interval mapping (CIM). The CIM method may be selected over multiple linear regression to decrease over-estimations of the efficiency of GWS over a MAS strategy. The RR-BLUP method was the preferred method for estimating marker effects in GWS with prediction accuracies comparable to or greater than BayesA and BayesB. The accuracy with RR-BLUP increased with training sample proportion, marker density, and heritability until it reached a plateau. In general, gains in accuracy with RR-BLUP over CIM increased with decreases of these factors. Compared to training sample proportion, the accuracy of prediction with RR-BLUP was relatively insensitive to marker density.     

Marker-Based Estimation of Heritability in Immortal Populations

Heritability is a central parameter in quantitative genetics, from both an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within- and between-genotype variability. This approach estimates broad-sense heritability and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker-based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human genetics but are rarely reported for plant traits. A major obstacle is that current methodology and software assume a single phenotypic value per genotype, hence requiring genotypic means. An alternative that we propose here is to use mixed models at the individual plant or plot level. Using statistical arguments, simulations, and real data we investigate the feasibility of both approaches and how these affect genomic prediction with the best linear unbiased predictor and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at the individual plant or plot level produced more realistic estimates, and for simulated traits standard errors were up to 13 times smaller. Genomic prediction was also improved by using these mixed models, with up to a 49% increase in accuracy. For genome-wide association studies on simulated traits, the use of individual plant data gave almost no increase in power. The new methodology is applicable to any complex trait where multiple replicates of individual genotypes can be scored. This includes important agronomic crops, as well as bacteria and fungi.     

Genomics and genome-wide association studies: an integrative approach to expression QTL mapping

Expression QTL mapping by integrating genome-wide gene expression and genotype data is a promising approach to identifying functional genetic variation, but is hampered by the large number of multiple comparisons inherent in such studies. A novel approach to addressing multiple testing problems in genome-wide family-based association studies is screening candidate markers using heritability or conditional power. We apply these methods in settings in which microarray gene expression data are used as phenotypes, screening for SNPs near the expressed genes. We perform association analyses for phenotypes using a univariate approach. We also perform simulations on trios with large numbers of causal SNPs to determine the optimal number of markers to use in a screen. We demonstrate that our family-based screening approach performs well in the analysis of integrative genomic datasets and that screening using either heritability or conditional power produces similar, though not identical, results.