Journal of Heredity Advance Access originally published online on September 18, 2006
Journal of Heredity 2006 97(5):473-482; doi:10.1093/jhered/esl028
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A Method for Identification of the Expression Mode and Mapping of QTL Underlying Embryo-Specific Characters
From the Jiangsu Provincial Key Laboratory of Crop Genetics and Physiology, Yangzhou University, Yangzhou 225009, China
Address correspondence to Dr C. Xu, Department of Agronomy, Yangzhou University, Yangzhou 225009, China, or e-mail: qtls{at}yzu.edu.cn.
Embryos of crop seeds are one of the major sources of the plant protein and lipid for human nutrition. The genetic expression for embryo-specific characters in crop seeds can be controlled exclusively by the embryo or the maternal genotypes and sometimes by both simultaneously. However, current methods for mapping quantitative trait loci (QTLs) underlying characters of maternal plants have not been effective in dealing with the QTL analysis of embryo characters. On the basis of the expression feature of embryo, a statistical method was proposed for the identification of expression mode and mapping of QTL controlling embryo traits. The maximum likelihood method implemented via the expectation maximization algorithm was used to estimate parameters of a putative embryo-specific QTL. The QTL expression mode was identified by the likelihood ratio test statistic. Statistical power and other properties of the proposed method were investigated under a variety of scenarios through simulation studies. The results showed that the mapping method neglecting the effects of embryo genotype or maternal effects could neither identify the expression mode of QTL nor estimate its genetic effects accurately, whereas the proposed method could effectively map the embryo-specific QTL of various expression modes.
Embryo-specific characters refer to those characters that are determined by the physical and chemical properties of the seed embryo, such as the oil content in soybeans and rapes as well as the embryo size in maize and rice. The inheritance of the embryo characters has been widely investigated by geneticists for the crucial role of seed embryos of crops in providing plant protein and dietary lipid for humans (Gupta et al. 2004; Goffman et al. 2005; Hajduch et al. 2006). Genetically, there are several unique properties of these traits, distinguishing them from the usual agronomic traits. First, as a result of fertilization, the embryo symbolizes the beginning of the next generation. Second, each single seed is genetically independent. As a result, the segregation of embryo genotypes is based on the seeds from one heterozygous plant, rather than on the plants. Finally, because seeds are formed and developed on the maternal plant which plays a pivotal role in the development phase of embryo and endosperm, the genetic expression for embryo-specific characters in crop seeds can be controlled exclusively by the embryo or the maternal genotypes and sometimes by both simultaneously (Zhu and Weir 1994). All these unique properties should be given sufficient consideration in the practical analysis. With the recent successful cloning and functional validation of several sporophytic maternal-effect genes affecting the expression of embryo characters (Colombo et al. 1997; Kinoshita et al. 1999; Yadegari et al. 2000; Garcia et al. 2005; Ohto et al. 2005), biologists are now full of enthusiasm for identifying the maternal effect in higher plants and unraveling the genetic mechanisms underlying those phenomena.
Based on the expression features of the seed characters, Foolad and Jones (1992) and Zhu and Weir (1994) proposed a series of statistical methods allowing for partitioning of the total phenotypic variation into various genetic components. Zhu and Weir (1994) further implemented the linear mixture model theory to detect all the potential genetic effects that affect seed characters. The applications of these methods have confirmed an important fact that many traits of oil plant seeds are influenced both by maternal and embryo genotypes (Wu et al. 2005; Zhang et al. 2004a). This discovery provided valuable information on illustrating the genetic mechanism underlying the expression of embryo-specific characters and to the genetic improvement of those traits in plant breeding. However, the traditional methods have been proceeded by treating all the genetic contributions to the phenotypic variance as an integrated whole, which thus failed to provide further information like the position and the specific effects of each possible quantitative trait loci (QTLs) (Hu and Xu 2005). With the advent of the molecular markers, numerous statistical methods for QTL mapping have been proposed, such as the interval mapping method proposed by Lander and Botstein (1989), the composite interval mapping method by Jansen and Stam (1994) and Zeng (1994), the multiple interval mapping method by Kao (2004), and the recently popular Bayesian mapping method (Satagopan et al. 1996; Wang et al. 2005). These methods offer an effective way to locate the genetic effects on the corresponding position of the genome, and they have already been successfully applied to many plant species (Frary et al. 2000; Li et al. 2003a, 2003b). But most of them are not suitable for the analysis of the embryo-specific traits, as they postulate that the studied characters are exclusively controlled by the genes carried by an individual itself. The assumption is obviously incorrect in the context of embryo trait analysis. In this paper, a novel statistical method that incorporates the unique properties of embryo-specific characters is proposed, which is able to scan a genome for the QTL regulating embryo traits and to identify the expression pattern of each detected QTL. The statistical properties of the method are investigated through simulations under various scenarios.
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Methods |
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Statistical models for embryo traits
Suppose there is a segregating QTL controlling an embryo trait with 2 alternative alleles, Q and q, for any segregation population, the genetic constitution of QTL from the maternal plant can be defined as p1QQ + p2Qq + p3qq, where p1, p2, and p3 denote the probabilities of 3 possible QTL genotypes in segregation population. The embryo genotypes of autogamous progeny are all QQ in plant of genotype QQ and which are all qq in plant of genotype qq; for plant of homozygote Qq, the embryo genotypes are segregated as 1/4QQ + 1/2Qq + 1/4qq. Therefore, taking both the direct effect and maternal effect into account, there will be 5 possible maternal offspring QTL genotypes for each QTL controlling endosperm traits, that is, QQ(QQ), Qq(QQ), Qq(Qq), Qq(qq), and qq(qq). The genotypic value components of the joint genotypes are then defined according to Foolad and Jones (1992), as shown in Table 1.
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Let Yij be the phenotypic value of the jth embryo on the ith plant in the segregation population, which can be described by the following linear model:
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e2), where e2 stands for residual variance.
Let Xij = (1 X1ij X2ij X3ij X4ij) and b = (b0 b1 b2 b3 b4)T. Then the model can be expressed in matrix notation as
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N(Xijb, e2).
Maximum likelihood estimation of QTL effects
Define plij (l = 1,2,...,5) as the conditional probabilities of 5 possible QTL genotypes for the jth embryo on the ith plant from the segregation population, which is inferred from the molecular marker genotypes derived from the maternal plants in this study (Xu et al. 2003). The distribution of Yij is thus a mixture distribution with the probability density of
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(·) denotes the probability density function of normal distribution and Hl stands for the vector of genetic effects under the lth genotype, which can be assigned as the lth row of the matrix 
The joint log-likelihood for ni independent observations from k plants now is
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e2 in formula (4) can be obtained using the expectation maximization (EM) algorithm (Dempster et al. 1977), which may proceed as follows.
First, calculate the expectation of the complete-data log-likelihood function conditional on the current parameter values 
(t–1) and the data Y = {Yij} as
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e2, we have
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Likelihood ratio test for the genetic expression pattern of embryo QTL
The presence of QTL can be tested through the following null hypotheses. H0: b1 = b2 = b3 = b4 = 0, that is, no QTL was detected at the tested point versus alternative hypothesis—H1: at least one of the parameters above is not equal to zero. The log-likelihood values under the null hypothesis and alternative hypothesis, denoted as L0 and L1, respectively, are calculated by plugging the MLEs of parameters in model (1) into formula (4). The likelihood ratio test statistics for testing hypotheses is given by
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The presence of maternal effect can be tested on the basis of the following hypotheses. H2: b1 = b2 = 0, that is, there are no maternal effects. Denote the log-likelihood value under this hypothesis by L2. The likelihood ratio test statistic is therefore given by
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The hypothesis about the embryo effects of QTL is tested using H3: b3 = b4 = 0. Denote corresponding maximum log-likelihood function as L3. The likelihood ratio test statistic is therefore given by
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In the practical data analysis, we usually first scan the entire genome for QTL using Equation (10). With the achieved likelihood profile of QTL, both the presence and the position of QTL can be estimated. The presence of the corresponding maternal effect and the embryo effect of a QTL can further be investigated using Equations (11) and (12).
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Simulation Studies |
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The applicability of the proposed method was demonstrated by analyzing 3 simulation experiments, 2 for a single chromosome (designs I and II), and 1 for an entire genome with 12 chromosome (design III). All designs used the widely used F2 as the mapping population. In designs I and II, a chromosome of length 100 cM covered by 11 evenly spaced markers was simulated. A single QTL affecting an embryo trait was hypothesized to be located at position 55 cM on the chromosome. In design I, the effects of the QTL were assigned based on 3 different schemes, each representing a specific expression mode. Scheme 1, full-effect mode, that is, embryo trait affected both by QTL genotype of embryo and maternal plant; genetic effects of the QTL were set at a = 3, d = 1, a' = 1, and d' = 3. Scheme 2, maternal-effect mode, that is, only the maternal QTL genotype influence the involved character with the following effects: a = 3, d = 1, a' = 0, d' = 0. Scheme 3, embryo-effect mode, that is, the QTL only has embryo genotypic effect with the following effects: a = 0, d = 0, a' = 1, and d' = 3. Experimental factors considered in this design include 1) the proportion of phenotypic variance contributed by both the maternal and embryo effects of an individual QTL, which was simulated at 2 levels: 5% and 10%; (2) number of plants in the segregation population, which was set at 3 levels: 100, 200, and 500; (3) number of embryos collected per plant, which was simulated at 2 levels: 5 and 20. The total number of treatment combinations was therefore 2 x 3 x 2 = 12. The overall mean of the embryo trait was simulated at 20. Each treatment combination of the simulation experiments was replicated 100 times. All simulation data were analyzed under 3 methods implementing full model, maternal model (b3 = b4 = 0), and embryo model (b1 = b2 = 0), respectively.
In design II, we analyzed other 2 sets of treatments to examine the performance of our method under different genetic parameters. In treatment 1, the genetic effects of the QTL were a = 3, d = 0, a' = 1, and d' = 0, which was designed as a purely additive model. In treatment 2, the genetic effects of the QTL were a = 0, d = 1, a' = 0, and d' = 3, which thus was purely dominant. In this design, QTL heritability was simulated at 10%, sample size of the population was simulated at 200, and the number of embryos was 20.
In design III, a genome consisting of 12 chromosomes was simulated. The number of markers per chromosome and the marker positions were generated randomly. The simulated linkage map information is listed in Table 2. We simulated 5 QTLs distributed along 4 of the 12 chromosomes. Their positions and hypothesized effects are shown in Table 3. The proportion of phenotypic variance contributed by an individual QTL ranged from 4.19% to 18.82%. The overall phenotypic variance explained by all 5 QTLs, the population size, and the number of embryos per plant are set at 50%, 200, and 20, respectively.
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The quick method developed by Piepho (2001) was adopted to declare statistical significance for QTL detection, which can determine the empirical critical value at chromosome-wide or genome-wide level. The principal statistical properties to be investigated in this study include 1) empirical statistical power, calculated by counting the number of replicates that have a significant test statistic or QTL is detected and 2) precision and accuracy of estimates for QTL location and effects, which are measured by means and standard deviations (SDs) of estimates from significant samples, respectively.
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Results |
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Tables 4–6 give the means and SDs of the QTL effects and locations' estimates as well as the empirical powers for 3 schemes under design I. From these tables, we see the following. 1) Higher QTL heritability and larger sample sizes tend to produce more accurate and precise estimates, whereas lower heritability, especially with smaller sample sizes, produce less accurate estimates with large estimation errors, which is in accordance with our general expectations. For example, when the QTL heritability is 5%, number of plants is 50, and only 5 embryos were collected, we did not get satisfactory results. But the power was almost perfect when the heritability was set at 10%, number of plants was 200, and the number of embryos per plant was 20. 2) Different genetic expression patterns may also affect the QTL detection efficiency. It was found that the QTL can be detected more easily when the maternal effect have a larger proportion in the total variation of the embryo phenotype. For instance, when 100 F2 plants and 5 embryos for each plant are collected and the QTL heritability is 5%, the statistical powers of 3 methods for 3 schemes are 77%, 74%, and 75% (scheme 1); 81%, 81%, and 80% (scheme 2); and 27%, 18%, and 18% (scheme 3), respectively. 3) The full model method (I) proposed here can estimate all the genetic effects accurately under various genetic expression patterns of QTL. The maternal genetic effect model (II) and the embryo genetic effect model (III) produce similar statistical power, which, however, can only produce accurate estimates under specific simulation scheme. For example, when 500 plants and 20 embryos are simulated and the QTL heritability is set at 10%, in the simulation scheme 1 only method I can estimate all genetic effects with high accuracy, where the estimates of genetic parameters from method II and method III are severely biased. When the embryo trait is exclusively influenced by the maternal QTL genotype (scheme 2), both method I and method II can produce satisfactory estimates, where the estimates from method III are significantly biased. For the third scheme, except method II, the other 2 methods can estimate all genetic effects with high accuracy. Table 7 shows the result under design II. All parameters can be quite reliably estimated, indicating that our method can be implemented successfully regardless of the gene mode.
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The mean estimates and SDs of locations and effects of 5 QTLs and corresponding statistical powers in the third design are listed in Table 8. From the table, we see that only 2 QTLs, qtl3 and qtl5, have powers less than 100% (both are 98%), whereas all other QTLs have powers of 100%. This is predictable because the heritabilities of the 2 QTLs are relatively low. Both the effect and position estimates of these QTLs are reasonably close to the true value. The estimated locations of qtl1 and qtl2 are found slightly biased toward the center of the chromosome. This behavior may be explained by the fact that 2 QTLs were located in the close region of the same chromosome. It is understandable that the overall performance on the genome is not as ideal as previously observed from the single chromosome because including multiple QTLs could incur additional variation on each locus.
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Discussion |
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Analogous to the endosperm trait, the genetic expression of embryo-specific characters is regulated by both the maternal genotype and the embryo genotype (Foolad and Jones 1992; Zhu and Weir 1994). However, the current QTL mapping methods took merely the genetic effects of one generation into account, which is incapable of testing whether the embryo characters were influenced exclusively by the genotypes of maternal plant, by that of embryo, or by both simultaneously (Lander and Botstein 1989; Jansen and Stam 1994; Zeng 1994; Kao 2004; Wang et al. 2005). If a trait is regulated by multiple genetic systems jointly, ignoring any possible system will cause systematic bias (Hu and Xu 2005; Wu et al. 2005). For this reason, traditional QTL mapping methods for common agronomic traits may not be appropriate for application to embryo-specific traits (Dong et al. 2003; Al-Chaarani et al. 2005). Cui et al. (2004, 2006) and Zhang et al. (2004b) have recently derived a statistical method and framework to understand the genetics underlying maternal–offspring interactions, which provided an efficient way to study maternal inheritance. It is known that the genetic material of offspring is derived and inherited from maternal plant and undergoes Mendelian transmission. Hence, it is reasonable to assume that both maternal and offspring QTLs are controlled by one unique genetic system. In such a system, the QTL could express exclusively in maternal plant or in embryo, exhibiting distinct temporal and spatial expression patterns. The QTL underlying embryo traits can thus be categorized into 3 groups according to their expression patterns: 1) maternal-expressed QTLs, which are expressed exclusively in maternal tissue and usually functions by affecting the maternal metabolize such as the photosynthetic intensity and the transportation velocity of nutrient; 2) offspring-expressed QTLs, the type that are merely expressed in embryo tissue, such as the genes that encode enzymes responsible for regulating the transformation speed of carbohydrate from transportable stage to storage stage; 3) constitutive-expressed QTLs, which are expressed both in maternal and offspring tissues, including the genes involved in respiration pathway. However, no method has been applied to handle this type of QTL, and this work is the first attempt.
In this paper, we have developed a new method for mapping of QTL controlling embryo-specific traits. The proposed model incorporated both the maternal and embryo effects of the QTL. All the genetic effects were estimated by maximum likelihood method via the EM algorithm. The expression mode was further identified based on the likelihood ratio test between the full model and a restricted one. Our model differs from those of Cui et al. (2004, 2006) in several essential ways. First, because the F2 population was used in this study, both additive and dominant effects can be estimated separately, whereas only a confounding effect can be estimated in the backcross design of Cui et al. Second, although the studies of Cui et al. mainly focus on the problem associated with the intergenomic epistasis, our research are more interested in exploring the expression behavior of each locus in 2 sets of genomes. Probably, the greatest difference between the 2 methods lies in the way how to model multiple genomes. In the studies of Cui et al., 2 genomes were actually treated independently, where the gene interactions between different genomes were modeled in a similar way with the ones within genome. In this study, however, we incorporated both the maternal and embryo genomes by extending the ordinal QTL effects of single genome to 4 components. As a result, 2 genomes can be scanned simultaneously, with all the effects being estimated at the same time. We think that such a model is closer to biological reality because the linkage maps of the maternal and embryo genomes are highly correlated, if not identical.
The results of the complex simulation studies further show that our proposal based on the integrated scan is sensible. The method has been found to provide accurate estimates of the QTL effects and locations at different genetic parameters and expression modes. Robust results were also obtained at the genome level. It is interesting to find that, under the same heritability and sample size, the maternal-expressed QTLs tend to be detected more easily than others, whereas the embryo-expressed QTLs have the least power to be detected. A similar tendency was also observed in the precision and the accuracy of the estimates of the genetic parameters. The phenomenon can be explained by the fact that marker information is derived purely from the maternal genome in this study. Under this design, it is apparent that the maternal QTL genotype can be inferred more effectively. And when the maternal effects contribute a larger proportion in the total phenotypic variation, the QTL can be more easily detected with the genetic effects being estimated more precisely. Therefore, the detection power of our method may further be improved by employing the 2-stage hierarchical design method for endosperm traits as proposed by Wu et al. (2002), in which genetic information was derived from both the maternal and embryo genomes.
Although our method appears to work well over a range of simulated conditions, we do not claim that the present model is an optimal one. Except to further incorporate the marker genotypes of the embryo as discussed above, many other improvements can be made. The method developed herein is based on a selfing progeny design. This leads to some extent of dependence between the maternal and the offspring gene effects because 2 genomes share the same genotypes when the maternal genotype is homozygous. Therefore, a reasonable sample size is required here to achieve a satisfactory result. Obviously, reducing the existing genotypic dependence can increase the information content included and thus make the method more powerful and precise. One possible solution is to choose more sophisticated mating designs such as the North Carolina III (NCIII) Design and the Triple Test Cross (TTC), where the genotypes at 2 generations are better diversified. It is worth noting that incorporating the marker information from both generations also has an effect of decreasing the genotypic dependence, which thus can be served as an alternative strategy. Finally, it is also important to extend the present framework to accommodate bulked segregation data. For some crops such as rice and maize, measuring the embryo trait individually could be problematic due to the relatively small embryos. The embryo trait values of these crops are usually measured by bulking several seeds from one plant together. Under this extension, however, the information loss caused by the bulked data can even incur a total failure of the present model. We therefore need to combine this idea with other strategies like adopting more informative experimental designs. Further work should be devoted to investigate many other behaviors of the extended model. By incorporating these extensions, our model will be more powerful and more tractable in real applications.
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Acknowledgments |
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The authors are grateful to the Associate Editor Reid G. Palmer and 3 anonymous reviewers for their constructive comments and suggestions that significantly improved the presentation of the manuscript. This work was supported by the National Basic Research Program of China (grant no. 2006CB101700), the National Natural Science Foundation of China (grant no. 30370758), and Program for New Century Excellent Talents in University, Ministry of Education of China to C.X.
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Footnotes |
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Corresponding Editor: Reid Palmer
Received March 21, 2006
Accepted July 11, 2006
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References |
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