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Genetics, Vol. 177, 669-672, September 2007, Copyright © 2007
doi:10.1534/genetics.107.074302
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Jiangsu Provincial Key Laboratory of Crop Genetics and Physiology, Key Laboratory of Plant Functional Genomics of Ministry of Education, Yangzhou University, Yangzhou 225009, China
1 Corresponding author: Department of Plant Genetics and Breeding, Yangzhou University, Yangzhou 225009, China.
E-mail: qtls{at}yzu.edu.cn
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ABSTRACT |
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 TOP ABSTRACT ACKNOWLEDGEMENTSLITERATURE CITED |
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In this note, we explore a class of mating schemes derived through reciprocal crosses, in which each type of nuclear genotype is obtained under two cytoplasmic backgrounds. The statistical model for a genomewide scan of loci involving cytonuclear epistasis is constructed and analyzed via modifying the existing model for testing genotype x environment (G x E) interactions. Simulation studies are performed to verify the feasibility of the proposed methods and to compare the efficiencies of various mating schemes.
The experimental design for the dissection of the cytoplasmic factors is illustrated in Figure 1. The design starts with a pair of crosses that reverse the sexes of two parental lines carrying the different cytoplasms. The reciprocal F1 families derived are therefore identically heterozygous but have alternative cytoplasms, which are inherited through only the female lineage. On the basis of the F1 hybrids, five mapping populations with bulked cytoplasmic background can then be created, i.e., double haploid (DH), two backcrosses (BC1 and BC2), F2, and recombinant inbred lines (RIL). Each population contains different combinations of nuclear genotypes and cytoplasms (hereafter cytonuclear genotypes). In this way, the quantitative variations of cytoplasmsic effects and their interactions with nuclei are fully or partially introduced. For instance, in the F2 population there are six cytonuclear genotypes, allowing a complete dissection of all the effect components.
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 | (1) |
) individual in a mapping population; 
is the overall mean of the population; c is the cytoplasmic effect; a and d are the additive and dominance effects of QTL, respectively; and 
and 
are the additive x cytoplasm and dominance x cytoplasm interactions, respectively. 
is an indicator variable, denoting 
for P1 cytoplasm and 
for P2 cytoplasm. 
and 
are the indicator variables describing different QTL genotypes and are defined in Table 1. 
and 
are corresponding variables for marker l, assuming t markers are selected for controlling residual genetic variation. The definitions are the same with and 
and 
are partial regression coefficients of 
on 
and 
denotes the residual error with a 
distribution. The above model is treated as a mixture model with components representing each cytonuclear genotype. The maximum-likelihood estimation of the parameters in composite-interval mapping is based on the ECM algorithm (MENG and RUBIN 1993). The detailed likelihood analysis and numerical implementation of the ECM iteration can be found in ZENG (1994) and JIANG and ZENG (1995).
Given model (1), a series of null hypotheses can be constructed and tested by constraining relevant parameters to specific values. The presence of QTL, cytoplasmic effect, and cytonuclear epistasis effects are tested against the null hypotheses 
respectively. The log-likelihood values under these null hypotheses are calculated in a similar way within the full model and denoted as 
The likelihood-ratio statistics for each test are thus given by 
respectively, where 
denotes the log-likelihood value under the model (1). Our strategy is therefore different from the one addressing QTL x environment interaction in JIANG and ZENG (1995), where different environments were regarded as different trait states and the existence of QTL x environment interaction was tested against the reduced model that constrains the parameters in different states to be equivalent.
The applicability of the proposed method was further demonstrated by a series of simulation experiments. A genome consisting of 12 chromosomes was simulated for the reciprocal F2 population. The linkage map was generated randomly (supplemental Table 1 at http://www.genetics.org/supplemental/). We simulated five QTL distributed along four chromosomes under different inheritance scenarios, e.g., no additive x cytoplasm interaction ( = 0), no dominance x cytoplasm interaction ( = 0), or no dominance effect (d = 0). A sample of 200 individuals was assumed to be collected from the mapping population (MP4) and we performed 200 replicates for each analysis. The quick method developed by PIEPHO (2001) was adopted to declare statistical significance for QTL detection. The principal statistical properties to be investigated include the empirical statistical power, precision, and accuracy of estimates for QTL location and effects. The true values and summary estimates of the parameters for this experiment are given in Table 2. In general, our method provides a fairly accurate estimate of QTL positions and effects with reasonable precision, based on which different scenarios of cytonuclear interactions can be easily identified. As we expected, the loci with higher heritabilities can be detected with greater power and tend to produce more accurate and precise estimates. To compare the mapping efficiencies of different mating schemes, we also simulated a single chromosome of 100 cM for the DH, combined BC, F2, and RIL populations. The chromosome is covered by 11 equidistant markers and a putative QTL is assumed to locate at position 55 cM. The methodology for the F2 population can be readily used to analyze the data from DH and RIL populations by modifying the effect components in the model. The mapping results (supplemental Tables 2–5 at http://www.genetics.org/supplemental/) suggest that the DH population tends to produce higher power than the others, although it is noninformative in inferring the dominance effect and the dominance x cytoplasm interaction.
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It is worth mentioning that in the typical reciprocal crosses another important source of genetic variation is genetic imprinting, which is an epigenetic regulation mechanism through which gene expression depends completely or partially upon parental origin (BARLOW 1995; REIK and WALTER 2001). The F1 hybrids in our design differ not only in the alternative cytoplasms but also in the parent-of-origin effects on the nuclear alleles. Therefore, the effects of genetic imprinting will be confounded with cytoplasmic factors if only F1 populations are studied. CUI (2007) recently proposed a method that models the genetic imprinting effects as a probability measure with which one can test the degree of imprinting. But the imprinting effect should not cause any problem in our study since no variation between reciprocal heterozygotes is included in the bulked mapping populations that are derived from reciprocal F1.
The method developed should be very useful in detecting the genetic architecture of hybrid fitness. The inheritance mechanism of hybrid inferiority and heterosis has long been a contentious issue. A large amount of research has been conducted, focusing on the epistasis among nuclear genes (YU et al. 1997; LI et al. 2001; ALLEN 2005; MALMBERG et al. 2005). However, relatively few studies have explored the role of these nonnuclear effects on the hybrid performance. Increasing evidence from cytoplasmic substitution lines and cell fusion lines has indicated that hybrid weakness is often related to the interactions between the nuclear genome and the chloroplast and mitochondrial genomes, and these interactions could play an important role in the origin and isolation of species (LEVIN 2003; RHODE and CRUZAN 2005). Our method will give a clearer picture of the contributions of cytoplasmic factors, especially cytonuclear effects, to hybrid fitness. Moreover, the proposed design and method can be easily incorporated into the existing methods for detecting nuclear epistatic QTL (CARLBORG et al. 2000; KAO and ZENG 2002; YI et al. 2003, 2005). Significant discoveries can be expected on the basis of this more comprehensive model.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTACKNOWLEDGEMENTSLITERATURE CITED |
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LITERATURE CITED |
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TOPABSTRACTACKNOWLEDGEMENTSLITERATURE CITED |
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Communicating editor: J. B. WALSH
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