A Novel Method For Mapping QTL Controlling Seed Traits

Crop 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 seed traits in crop seeds can be controlled exclusively by the embryo or the maternal genotypes and sometimes by both simultaneously. Statistical methods designed specifically for mapping QTL controlling endosperm trait have been proposed by several researchers in recent years, but these methods all ignored the influence of the maternal genome upon the development of seed. On the basis of the expression feature of seed, a new statistical method was proposed for the identification of expression mode and mapping of QTL controlling embryo and endosperm traits. The maximum likelihood method implemented via the expectation maximization algorithm was used to estimate parameters of a putative QTL. The algorithm may be summarized in the following steps: (1) Calculate the conditional probabilities of the QTL genotypes by using the molecular marker information derived from the segregation population; (2) Calculate the posterior probabilities by combining the conditional probabilities above and the phenotypic values of the seed trait; (3) Calculate the expectations of missing values, and then solve formulae to get the estimates of all genetic parameters, which are then used to update the initial values, and here ends the first iteration; (4) Repeat steps 2 and 3 until convergence. Estimates at convergence are the MLE of the parameters.Since seed traits can be influenced by the maternal and the offspring genomes simultaneously, the genetic effects from the seed and its maternal genomes should be modeled as a form of joint maternal-offspring genotype. Two design strategies are adopted for genotyping of molecular makers. Strategy 1, conditional probabilities are inferred by the marker genotypes derived from maternal tissues merely. Strategy 2, marker genotypes derived from the embryo and its sporophyte are used jointly for calculation of conditional probabilities. Given that the endosperm and the embryo have different ploidy levels and are formed through different inheritance mechanisms, endosperm and embryo traits are modeled separately. Extensive simulations were performed to investigate the statistical properties of proposed approach.Factors considered in the simulations include: QTL heritability, number of plants in the segregation population and number of endosperms collected per plant. Each treatment combination of the simulation experiments was repeated 100 times. The principal statistical properties to be investigated include empirical statistical power, precision and accuracy of estimates for QTL location and effects. Two simulation strategies are summarized as follows.Strategy 1: marker genotypes derived purely from the maternal genome. In this strategy, molecular marker genotypes through maternal genome and phenotypic observation for quantitative seed traits are required. Considering genetic difference between endosperm and embryo, we proposed two specific genetic models for them.The total 36 treatment combinations of experimental factors are adopted to investigate the performance of this method in mapping endosperm traits. The results show that (1) Only 5 out of the 36 treatments have powers less than 100% while all other treatments in the simulation studies have perfect statistical power, suggesting that the new model is highly powerful in detecting the QTL controlling endosperm traits. Even though in the setting when the number of endosperm is 10 and only 100 F2 plants, the proposed method still has power of 100% in detecting the QTL whose heritability is only 5%. (2) The method definitely shows high precision and accuracy in estimating QTL position and effects in most schemes; As shown in the results, with the intermediately dense markers of 10cM, 200 F2 plants and 20 endosperms per plant, the new method provides accurate estimates of both the QTL effects and locations with high statistical power, regardless of the levels of QTL heritability.The statistical properties of this method in mapping embryo traits were further investigated via the simulation of 12 treatments. The genetic effects of the QTL were assigned based on 3 different schemes, each representing a specific expression pattern including: Scheme 1, embryo trait affected by both QTL genotype of embryo and that of its maternal plant; Scheme 2, only the maternal QTL genotype influences the involved character; and Scheme 3, only embryo genotypic effects exist. All simulation data were analyzed under full model (method I), maternal model (method II) and embryo model (method III), respectively. The results show that: (1) method I has higher statistical power than the other two methods. Given F2 500 plants and 20 embryos per plant, under the first scheme, only method I can properly estimate all the genetic parameters of QTL, but estimates from methods II and III are significantly biased. Under the second scheme, estimates from both methods I and III are close to true values, but the results from method II are biased. Under the third scheme, both methods I and II can properly estimate all genetic effects while estimates from method III are biased. (2) Simulation studies also suggest that the statistical power detecting QTL is influenced by the QTL expression pattern as well as the heritability and the sample size. The QTL can be detected easily especially when the maternal effects have larger contribution to the phenotypic value. Given 100 F2 plants and 5 embryos per plant, the detection powers of the 3 methods are 77%, 74% and 75% under scheme 1; 81%, 81% and 80% under scheme 2; 27%, 18% and 18% under scheme 3, respectively.Strategy 2: marker genotypes derived from both maternal and offspring genomes. In strategy 1, the conditional probabilities of the joint maternal-offspring QTL genotypes for each individual in the population are inferred from QTL genotype of maternal plant rather than from seed genome. Therefore, the conditional probabilities for all QTL genotype of the seed are largely dependent on that of its maternal plant. So we further propose strategy 2 which uses the molecular makers derived from both maternal and offspring genomes to infer the probabilities of the joint maternal-offspring genotypes of the underlying QTL. This strategy is more complicated than the previous one in that it needs genotype of the embryo in addition to the genotypes of the maternal sporophyte and phenotypic value of seed traits. The statistical properties of this strategy were investigated via the simulation of 12 treatments for embryo traits and endosperm traits. The results show: (1) this strategy is more powerful due to the use of the additional molecular markers from embryo genomes. For endosperm and embryo traits, there are 1 and 2 treatments, respectively, have power less than 100% when only the maternal marker is involved. However, when the embryo was also genotyped, all treatments in the simulation studies have perfect statistical power. (2) Parameter estimates from this strategy have smaller standard deviations than those from strategy 1, suggesting that using the molecular markers from embryo and its maternal tissue can decrease the correlation between the calculated conditional probabilities of the genotypes for the two generations. Because of the unavoidable correlation between offspring and its maternal genotypes and the fact that the two endosperm heterozygous genotypes always shared equivalent conditional probabilities, we suggest that a reasonably large population should be used for the proper estimation of the endosperm dominant effects.