Mixed linear model approach for mapping quantitative trait loci underlying crop seed traits

Abstract The crop seed is a complex organ that may be composed of the diploid embryo, the triploid endosperm and the diploid maternal tissues. According to the genetic features of seed characters, two genetic models for mapping quantitative trait loci (QTLs) of crop seed traits are proposed, with inclusion of maternal effects, embryo or endosperm effects of QTL, environmental effects and QTL-by-environment (QE) interactions. The mapping population can be generated either from double back-cross of immortalized F2 (IF2) to the two parents, from random-cross of IF2 or from selfing of IF2 population. Candidate marker intervals potentially harboring QTLs are first selected through one-dimensional scanning across the whole genome. The selected candidate marker intervals are then included in the model as cofactors to control background genetic effects on the putative QTL(s). Finally, a QTL full model is constructed and model selection is conducted to eliminate false positive QTLs. The genetic main effects of QTLs, QE interaction effects and the corresponding P-values are computed by Markov chain Monte Carlo algorithm for Gaussian mixed linear model via Gibbs sampling. Monte Carlo simulations were performed to investigate the reliability and efficiency of the proposed method. The simulation results showed that the proposed method had higher power to accurately detect simulated QTLs and properly estimated effect of these QTLs. To demonstrate the usefulness, the proposed method was used to identify the QTLs underlying fiber percentage in an upland cotton IF2 population. A computer software, QTLNetwork-Seed, was developed for QTL analysis of seed traits. Introduction Given the importance of cereal grain seeds as the staple food and nutrition resources for humans and animals, and raw materials for food industry, understanding the genetic architecture underlying the development of crop seed traits becomes increasingly demanding in crop breeding program (Benner et al., 1989; Mazur et al., 1999; van der Meer et al., 2001). Seed development starts at double fertilization of the embryo sac in which two sperm cells fuse with a female gametophyte, the egg and central cell, respectively, giving rise to the diploid (2n) embryo and the triploid (3n) endosperm. One sperm cell fuses with the egg cell to produce a zygote and then divide asymmetrically to form embryo and its suspensor, respectively. The other sperm cell merges with the central cell to form a triploid endosperm nucleus that possibly develops into endosperm in most flowering plants such as rice and wheat through two steps: a coenocytic stage followed by a cellularized and differentiated stage (Olsen, 1998; Sundaresan, 2005). Although the diploid embryo and the triploid endosperm are enclosed in the maternal integument that is a part of seed, development of seed depends on the allocation of nutrient and other physiological active substances from the mother plant. Proper development of a seed trait requires coordinated communications among the involved components, embryo, endosperm and maternal plant. Thus, in order to thoroughly understand how seed traits are genetically determined, it is provident to consider the integrity of these components in the genetic models (Bazzaz, 2001). It is well evidenced that additive and/or epistatic maternal effects, embryo effects, endosperm effects and gene–environment interaction effects are involved in the genetic development and evolution of crop seed (Zhang et al., 1999; Shi et al., 2000; Cui et al., 2004; Cui and Wu, 2005a,2005b Cui et al., 2006). A considerable body of genetic models and statistical methods have been developed and applied to the analysis of real data. On the basis of genetic features of seed characters, Mo (1995) advocated a statistical genetic model that focuses on partitioning the phenotypic variance of the endosperm traits into various genetic and environmental factors. Zhu and Weir (1994) further proposed the mixed linear model approach to analyze the maternal, embryo, endosperm and cytoplasm effects, and their interactions with environment underlying seed traits collected from a diallel cross experiment. The above approaches can only dissect the genetic variation of seed traits into several cumulative components, but fail to provide detailed information at the individual gene level such as the positions and effects of quantitative trait loci (QTLs) as all the genes controlling the seed traits were analyzed as a whole. Advancements in molecular markers and statistical methods enable us to partition the total genetic variation into the effects of individual QTLs, based on co-segregation between molecular markers and the putative QTL (Lander and Botstein, 1989; Zeng, 1994). A number of researchers applied traditional diploid genetic model to map QTLs underlying endosperm traits (Sourdille et al., 1996; Parker et al., 1998; Araki et al., 1999; Sene et al., 2001; Tan et al., 2001), until tailored QTL mapping methods were developed for seed traits. Genetically, endosperm represents the next generation developed in maternal plants, with a more complex segregation patterns and genetic mechanism than diploid tissues. For example, a biallelic locus (Q-q) has four possible genotypes, namely, QQQ, QQq, Qqq and qqq, and three kinds of endosperm genetic effects can be involved, namely additive effect (a), the first dominance effect (d1) and the second dominance effect (d2). Bases on such genetic basis, Kao (2004) proposed a statistical method using multiple-interval mapping that took triploid nature of endosperm into account. It can estimate all three kinds of endosperm effect. However, one more important feature ignored in this method and others is that endosperm is a tissue developed in its maternal plant, implying that its phenotypes may be affected not only by its own triploid endosperm genotypes, but also by the diploid maternal genotypes via supplies of nutrition and other physiological active substances. This point of view has been supported by several studies on model species such as Arabidopsis and maize (Letchworth and Lambert, 1998; Garcia et al., 2005; Ohto et al., 2005). To take maternal effects into account, it is theoretically desirable to integrate both maternal genome and offspring genome into one model. Hu and Xu (2005) proposed a mapping method to characterize genetic effects of maternal genome on offspring traits that incorporates both the quantitative genetic model for diploid maternal traits and that for triploid endosperm traits into a unified QTL mapping framework. Wen and Wu (2007) further proposed a method of interval mapping of endosperm traits based on a two-stage hierarchical design that considers both the endosperm effects and the maternal effects. In addition, Cui and Wu (2005a) and Cui et al. (2006) proposed an epistasis model for mapping endosperm QTLs in a double backcross population. The above approaches do not include genetic effects o (...truncated)