It has long been recognized that epistasis or interactions between non-allelic genes plays an important role in the genetic control and evolution of quantitative traits. However, the detection of epistasis and estimation of epistatic effects are difficult due to the complexity of epistatic patterns, insufficient sample size of mapping populations and lack of efficient statistical methods. Under the assumption of additivity of QTL effects on the phenotype of a trait in interest, the additive effect of a QTL can be completely absorbed by the flanking marker variables, and the epistatic effect between two QTL can be completely absorbed by the four marker-pair multiplication variables between the two pairs of flanking markers. Based on this property, we proposed an inclusive composite interval mapping (ICIM) by simultaneously considering marker variables and marker-pair multiplications in a linear model. Stepwise regression was applied to identify the most significant markers and marker-pair multiplications. Then a two-dimensional scanning (or interval mapping) was conducted to identify QTL with significant digenic epistasis using adjusted phenotypic values based on the best multiple regression model. The adjusted values retain the information of QTL on the two current mapping intervals but exclude the influence of QTL on other intervals and chromosomes. Epistatic QTL can be identified by ICIM, no matter whether the two interacting QTL have any additive effects. Simulated populations and one barley doubled haploids (DH) population were used to demonstrate the efficiency of ICIM in mapping both additive QTL and digenic interactions.

Missing marker and segregation distortion are commonly encountered in actual quantitative trait locus (QTL) mapping populations. Our objective in this study was to investigate the impact of the two factors on QTL mapping through computer simulations. Results indicate that detection power decreases with increasing levels of missing markers, and the false discovery rate increases. Missing markers have greater effects on smaller effect QTL and smaller size populations. The effect of missing markers can be quantified by a population with a reduced size similar to the marker missing rate. As for segregation distortion, if the distorted marker is not closely linked with any QTL, it will not have significant impact on QTL mapping; otherwise, the impact of the distortion will depend on the degree of dominance of QTL, frequencies of the three marker types, the linkage distance between the distorted marker and QTL, and the mapping population size. Sometimes, the distortion can result in a higher genetic variance than that of non-distortion, and therefore benefits the detection of linked QTL. A formula of the ratio of genetic variance explained by QTL under distortion and non-distortion was given in this study, so as to easily determine whether the segregation distortion marker (SDM) increases or decreases the QTL detection power. The effect of SDM decreases rapidly as its linkage relationship with QTL becomes looser. In general, distorted markers will not have a great effect on the position and effect estimations of QTL, and their effects can be ignored in large-size mapping populations.

F 2 populations are commonly used in genetic studies of animals and plants. For simplicity, most quantitative trait locus or loci (QTL) mapping methods have been developed on the basis of populations having two distinct genotypes at each polymorphic marker or gene locus. In this study, we demonstrate that dominance can cause the interactions between markers and propose an inclusive linear model that includes marker variables and marker interactions so as to completely control both additive and dominance effects of QTL. The proposed linear model is the theoretical basis for inclusive compositeinterval QTL mapping (ICIM) for F 2 populations, which consists of two steps: first, the best regression model is selected by stepwise regression, which approximately identifies markers and marker interactions explaining both additive and dominance variations; second, the interval mapping approach is applied to the phenotypic values adjusted by the regression model selected in the first step. Due to the limited mapping population size, the large number of variables, and multicollinearity between variables, coefficients in the inclusive linear model cannot be accurately determined in the first step. Interval mapping is necessary in the second step to fine tune the QTL to their true positions. The efficiency of including marker interactions in mapping additive and dominance QTL was demonstrated by extensive simulations using three QTL distribution models with two population sizes and an actual rice F 2 population.

Nanostructured tungsten carbides on ultrahigh-surface-area carbon (>3000 m2/g), a kind of novel carbon material with uniform pore distribution, have been prepared by carbothermal reduction, carbothermal hydrogen reduction, and metal-promoted carbothermal hydrogen reduction under mild conditions. The resulting carbides have been characterized by X-ray diffraction, transmission electron microscopy, temperature-programmed reduction−mass spectroscopy, and N2 physico-sorption. The adsorption properties of thiophene on nanostructured tungsten carbides on ultrahigh-surface-area carbon were also investigated in a fixed-bed reactor. The results show that nanostructured W2C particles of about 10 nm on ultrahigh-surface-area carbon material can be synthesized by carbothermal reduction and carbothermal hydrogen reduction at 850 °C. Nanostructured W2C has also been obtained by metal Ni-promoted carbothermal hydrogen reduction even at 650 °C. The results also show that carbothermal hydrogen reduction can form tungsten carbides under relatively mild conditions compared to carbothermal reduction, and addition of Ni further decreases formation temperatures of tungsten carbides. Tungsten carbides formation involves the sequence WO3 → WO x (0 < x < 3) → W → W2C → WC. The results on adsorption show that W2C/HSAC has superior properties for removal of sulfur-containing compounds in fuel oil and the adsorption properties can be recovered after H2 reduction at 800 °C. The adsorption capacity of the samples on thiophene is in the following order:  W2C/HSAC > W/HSAC > WC/HSAC ≫ HSAC. Nanostructured W2C/HSAC may be of great potential in ultra-deep removal of sulfur-containing compounds in fuel oil.