Estimation of genetic parameters and their sampling variances for quantitative traits in the type 2 modified augmented design

The type 2 modified augmented design(MAD2) is an efficient unreplicated experimental design used for evaluating large numbers of lines in plant breeding and for assessing genetic variation in a population. Statistical methods and data adjustment for soil heterogeneity have been previously described for this design. In the absence of replicated test genotypes in MAD2, their total variance cannot be partitioned into genetic and error components as required to estimate heritability and genetic correlation of quantitative traits, the two conventional genetic parameters used for breeding selection. We propose a method of estimating the error variance of unreplicated genotypes that uses replicated controls, and then of estimating the genetic parameters. Using the Delta method, we also derived formulas for estimating the sampling variances of the genetic parameters.Computer simulations indicated that the proposed method for estimating genetic parameters and their sampling variances was feasible and the reliability of the estimates was positively associated with the level of heritability of the trait. A case study of estimating the genetic parameters of three quantitative traits, iodine value, oil content, and linolenic acid content, in a biparental recombinant inbred line population of flax with 243 individuals, was conducted using our statistical models. A joint analysis of data over multiple years and sites was suggested for genetic parameter estimation. A pipeline module using SAS and Perl was developed to facilitate data analysis and appended to the previously developed MAD data analysis pipeline(http://probes.pw.usda.gov/bioinformatics_ tools/MADPipeline/index.html).

The Genetic Variances for the Phytic Acid and Inorganic Phosphorus Contents of Elite Inbred Lines in Tropical Maize

The study aimed to determine the genetic variances of phytic acid （myo-inositol 1,2,3,4,5,6 hexakis-dihydrogen phosphate） （PA） and inorganic phosphorus contents （InP） in grains of tropical maize （Zea mays L.）. The understanding of genetic variances in PA and InP in tropical maize would be useful for breeding management in tropical region. A total of 16 Ki inbred lines and 26 new inbred lines of tropical maize were planted in Completely Randomized Design （CRD） on the dry season 2008 at lnseechandrastitya Institute for Crops Research and Development, Thailand. The results showed that genotypic differences were highly significant （P 〈 0.01） for InP in both sources of germplasm, but genotype effect only was found significant in new inbred lines for PA content. The values for broad sense heritability （h2b） was generally lower on PA in maize grains compared with InP both in Ki and new inbred lines [h^2b of PA： 2.42 （Ki）, 14.18 （commercial hybrid extracted）; h^2b of InP： 32 （Ki） and 29.53 （commercial hybrid extracted）].

Genetic Diversity and Relationship of Weedy Rice in Taizhou City, Jiangsu Province, China

Microsatellite markers and morphological characteristics were used to explore the genetic diversity and possible origin of weedy rice in Taizhou City, Jiangsu Province, China. Fifty-two weedy rice (Oryza sativa L.) accessions were compared with two wild rice, four hybrid rice and five cultivars using 22 simple sequence repeat (SSR) primer pairs. A total of 107 fragments were amplified, averaging 5.6 alleles per primer pair. The polymorphic index content (PIC) values ranged from 0.3077 to 0.7951, averaging at 0.5870. The average genetic distance of all samples ranged from 0.02 to 0.46 with an average of 0.262. The genetic distance among Taizhou weedy rice ranged from 0.03 to 0.44 with an average of 0.224. Cluster analysis showed that all the weedy rice accessions from Taizhou City were indica, and could be subdivided into different genotypes. The majority (86%) of weedy rice was most closely related to hybrid rice. The Taizhou weedy rice accessions were morphologically similar, but still could be delineated into indica or japonica group by some morphological traits. It is suggested that the levels of genetic and morphological diversities of weedy rice in Taizhou City are low and these weedy rice plants originated from the segregating progenies of hybrid rice that had naturally introgressed with cultivated rice.

GENETIC MODELS AND ANALYSIS METHODS FOR SEX-LINKED AND MATERNAL GENE EFFECTS

Genetic models are proposed for analyzing sex-linked and maternal effects as well as autosomal gene effects.For the model with no genotype×environment interaction,the total genetic effect is partitioned into direct additive （A）,direct dominance （D）,sexlinked （L）,maternal additive （Am） and maternal dominance （Dm） genetic components.For the model including genotype×environment interaction （GE）,GE can also be partitioned into components of direct additive by environment interaction （AE）,direct dominance by environment interaction （DE）,sex-linked by environment interaction （LE）,maternal additive by environment interaction （AmE ）,and maternal dominance by environment interaction （DmE）.Linear functions of genetic components are listed for parent,F1,and F2.A set of parents,their reciprocal F1’s and F2’s is applicable for efficient analysis.Variance and covariance components can be well mated by MINQUE（O/l） with the jackknife procedure.The t-test conducted by the jackknife procedure is applicable for detecting significance of variation.Adjusted Unbiased Prediction （AUP） method is suggested for predicting genetic effects.

Developmental Genetic Analysis of Brown Rice Weight Under Different Environmental Conditions in indica Rice

Analysis of genetic main effects and genotype x environment (GE) interaction effects for brown rice weight (BRW) at four different filling stages in indica lice (Oryza sativa L.) was conducted for two-year experimental data by using developmental genetic models and corresponding statistical approaches for quantitative traits of seeds in cereal crops. It was indicated that the genetic main effects and their GE interaction effects of triploid endosperm, cytoplasmic and diploid maternal plant genes were important for BRW at different filling stages of rice, especially for endosperm or maternal additive main effects and their additive interaction effects. Because of the higher additive effects and additive interaction effects for BRW at different filling stages, the better improving effects for this trait could be expected by selection in rice breeding. The results of conditional genetic variance components showed that the new expression of quantitative genes in endosperm and maternal plant for BRW was mostly found at all different filling stages of rice. The gene expression, however, was most active at the early filling stages especially for the first (1-7 d) and the second filling stages (8-14 d after flowering). The phenomena that some genes were spasmodically expressible among filling stages of rice were detected for some genetic effects especially for net cytoplasmic main effects or its interaction effects and net dominance main effects. Predicted genetic effects at different filling stages of rice showed that some parents such as V20 and Zuo 5 were better than others for improving the BRW.

Hybrid Vigour and Genetic Control of Some Quantitative Traits of Tomato (<i>Solanum lycopersicum</i>L.)

Parental lines, F1 generation of domesticated tomato (Solanum lycopersicum L.) and Lycopersicon pimpinellifolium L. were evaluated at Department of Crop Science, University of Nigeria, Nsukka for improvement in their quantitative traits. The experiment was laid out in a randomized complete block design with three replications. Data were collected on the quantitative traits and fruit yield. Better Parent Heterosis (BPH), genetic variances, gene effects and heritability of the traits were estimated for the hybrids. BPH result showed that the Wild × Petomech cross had the highest positive BPH of 358.36% in fruit yield. The highest negative BPH of -95.59% was recorded for the hybrid, Wild × Grosso in average fruit weight while the hybrid, Insulata × Grosso had the lowest negative BPH of -16.27% in average fruit weight. Additive gene action and additive × additive gene action (aa) were significantly in control of three crosses, W × P, W × In and W × G in fruit yield. Additive variance was higher than dominance variance in fruit yield for all the hybrids with wild as one of its parents. Again, hybrids with wild as one of its parent as, W × G, W × In, and W × P had the highest narrow sense heritability in fruit yield (59.15%, 51.69%, 59.88%, respectively). High level of epistasis controlled some of the quantitative traits and hybridization evidenced by the result was effective in developing new tomato cultivars with positive heterotic effects in fruit yield.

Intra-population genetic variance for grain iron and zinc contents and agronomic traits in pearl millet

Crop biofortification is a sustainable approach for fighting micronutrient malnutrition in the world. The estimation of variance components in genetically broad-based populations provides information about their genetic architecture, allowing the design of an appropriate biofortification breeding method for cross-pollinated crops such as pearl millet. The objective of this study was to estimate intra-population genetic variance using self(S1) and half-sib(HS) progenies in two populations, AIMP92901 and ICMR312. Field trials were evaluated in two contrasting seasons(2009 rainy and 2010 summer; otherwise called environments) in Alfisols at ICRISAT, Patancheru. Analyses of variance showed highly significant variation for S1 s and HS progenies, reflecting high within-population genetic variation for both micronutrients and other key traits. However, the HS showed narrow ranges and lower genetic variances than the S1 for all of the traits. The micronutrients were highly positively correlated in S1(r = 0.77 to 0.86; P < 0.01) and HS(r = 0.74 to 0.77; P < 0.01)progenies of both populations, implying concurrent genetic improvement for both micronutrients. The genetic variance component was different among populations for Fe and Zn contents across environments, with AIMP92901 showing a greater proportion of dominance and ICMR312 greater additive variance for these micronutrients. The estimates of variance(additive and dominance) were specific for each population, given their dependence on the additive and dominance effects of the segregating loci, which also differ among populations. The possible causes for such differences were discussed. The results showed that the expression of these micronutrients in pearl millet shows largely additive variance, so that breeding high-iron hybrids will require incorporation of these micronutrient traits into both parental lines.

Modeling and Adaptive Self-Tuning MVC Control of PAM Manipulator Using Online Observer Optimized with Modified Genetic Algorithm

In this paper, the application of modified genetic algorithms (MGA) in the optimization of the ARX Model-based observer of the Pneumatic Artificial Muscle (PAM) manipulator is investigated. The new MGA algorithm is proposed from the genetic algorithm with important additional strategies, and consequently yields a faster convergence and a more accurate search. Firstly, MGA-based identification method is used to identify the parameters of the nonlinear PAM manipulator described by an ARX model in the presence of white noise and this result will be validated by MGA and compared with the simple genetic algorithm (GA) and LMS (Least mean-squares) method. Secondly, the intrinsic features of the hysteresis as well as other nonlinear disturbances existing intuitively in the PAM system are estimated online by a Modified Recursive Least Square (MRLS) method in identification experiment. Finally, a highly efficient self-tuning control algorithm Minimum Variance Control (MVC) is taken for tracking the joint angle position trajectory of this PAM manipulator. Experiment results are included to demonstrate the excellent performance of the MGA algorithm in the NARX model-based MVC control system of the PAM system. These results can be applied to model, identify and control other highly nonlinear systems as well.

Genetic Parameters Evaluation of Main Reproductive Traits for the New Yorkshire Dam Line with High Prolificacy

The genetic parameters of main reproductive traits for the new Yorkshire line with high prolificacy were evaluated by multiple animal model DFREML The re- suits showed that the heritability evaluates of the total number of born （TNB）, alive number of born （ANB）, litter weigh at birth （LWB） and litter weight at age of 21 days were 0.10, 0.15, 0.09 and 0.14, respectively. The genetic correlations between these traits, for example, the correlations between TNB/ANB, NB/LWB, TNB/LW21, ANB/LWB, ANB/LW21 and LWB/LW21 were 0.87, 0.74, 0.43, 0.69, 0.59 and 0.51, respectively.

WOMBAT—A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML)

WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http：//agbu. une.edu.au/-kmeyer/wombat.html

Genetic analysis of fruit shape traits at different maturation stages in sponge gourd

The fruit shape is important quantitative trait closely related to the fruit quality. However, the genetic model of fruit shapes has not been proposed. Therefore, in the present study, analysis of genetic effects for fruit shape traits （fruit length and fruit perimeter） in sponge gourd was conducted by employing a developmental genetic model including fruit direct effects and maternal effects. Analysis approaches of unconditional and conditional variances were applied to evaluate the genetic behavior of fruit shape traits at economical and physiological maturation times. The results of variance analysis indicated that fruit length and fruit perimeter were simultaneously affected by fruit direct genetic effects and maternal effects. Fruit direct genetic effects were relatively more important for fruit shape traits at whole developmental period. The gene expression was most active at the economical maturation stage （1-12 d after flowering） for two shape traits, and the activation of gene was mostly due to direct dominance effects at physiological maturation stage （13-60 datter flowering）. The coefficients due to different genetic effects, as well as the phenotypic correlation coefficients, varied significantly between fruit shape traits themselves at various maturation stages. The results showed that it was relatively easy to improve fruit shape traits for industrial purpose by carefully selecting the parents at economical maturation stage instead of that at physiological maturation stage.

Studies on the Developmental Genetics of Tiller Number in Three-line Indica Hybrid Rice

Following NCI design, the developmental genetic behavior of tiller number (TN) in three-line indica hybrid rice was studied using additive-dominance developmental genetic models and the corresponding statistical methods. The results showed that dominance effects were predominant for TN. The expression of those additive effects were affected by environment and genotype interaction, but the expression of dominance effects were not affected. Heterosis was the strongest in the middle developmental periods of TN. Additive effects and dominance effects were selectively expressed throughout in the entire tillering developmental stage. Analysis of genetic correlation between TN at different stages and the productive panicles indicated that a close correlation appeared earlier in the populations with higher heterosis than in those with less heterosis. Utilization of heterosis at the middle tillering stage might enhance the final biomass but reduce the percentage of productive panicles.

Exceptionally high genetic variance of the doubled haploid(DH)population of poplar

Doubled haploid(DH)plants have been widely used for breeding and biological research in crops.Pop ulus spp.have been used as model woody plant species for biological research.However,the induction of DH poplar plants is onerous,and limited biological or breeding work has been carried out on DH individuals or populations.In this study,we provide an effective protocol for poplar haploid induction based on an anther culture method.A total of 96 whole DH plant lines were obtained using an F1hybrid of Populus simonii×P.nigra as a donor tree.The phenotypes of the DH population showed exceptionally high variance when compared to those of half-sib progeny of the donor tree.Each DH line displayed distinct features compared to those of the other DH lines or the donor tree.Additionally,some excellent homozygous lines have the potential to be model plants in genetic and breeding studies.

Estimation of the Genetic Parameters on Reproduction Performances of the China Yorkshire Line SⅡ_1

[Objective] This study was to investigate the genetic parameters on reproduction performances of China Yorkshire line SII,. [Method] Using China Yorkshire line SII, as experimental animal, its genetic parameters on reproduction performance, such as total number of born （TNB）, the alive number of born （ANB）, the litter weight of born （LWB） and the litter weight at age of 21 days （/W21 ） , were estimated by using the DFREML method of multi-traits animal model. [Result] The heritability estimates of TNB, ANB, LWB and LW21 were 0.11,0.19, 0.14 and 0.05, respectively; and the genetic correlations between the traits as TNB/ANB, TNB/LWB, TNB/LW21, ANB/LWB, ANB/LW21, LWB/LW21 were 0.91, 0.76, 0.65, 0.85, 0.59 and 0.38, respectively. [ Conclusion] Main genetic parameters of reproduction traits in China Yorkshire line all, have all reached or even exceeded the requirements of breeding.

Developmental Analysis of Genetic Behavior of Brown Rice Width in indica-japonica Hybrids

The developmental genetic behaviors of brown rice width （BRW） have been studied in indica-japonica hybrid rice （Oryza sativa L.）, in which seven indica male sterile lines and five japonica restorer lines were applied, by using the developmental genetic models and corresponding statistical approaches for quantitative traits of triploid in cereal crops. The BRW of indica-japonica hybrid rice was co-determined by gene expression of tdploid endosperm, cytoplasm, diploid maternal plant and their genotype × environmental interaction effects. Unconditional analysis showed that the endosperm additive and matemal additive effects were predominant for the development of BRW from early- to late-stage of the grain development, but the endosperm dominant effect together with matemal effect and cytoplasmic effect became the major factor determing the BRW at the ripening stage. Moreover, conditional analysis found that there were new onset and offset of gene expression at different developmental stages of BRW in indica-japonica hybrid rice. Maternal and cytoplasm general heritabilities and their interaction heritabilities were more important compared to other components of heritability for BRW at all the five developmental stages.

Genetic Algorithm-Based Approaches for Optimizing S-Boxes

Multi-objective genetic algorithm is much suitable for solving multi-objective optimization problems. By use of Genetic algorithm, the optimization of S-boxes is explored in this paper. Results of the experiments show that, with heuristic mutation strategy, the algorithm has high searching efficiency and fast convergence speed. Meanwhile, we also have take the avalanche probability of S-boxes into account, besides nonlinearity and difference uniformity. Under this method, an effective genetic algorithm for 6×6 S-boxes is provided and a number of S-boxes with good cryptographic capability can be obtained.

Longitudinal genetic analysis of growth-related traits in red swamp crayfish Procambarus clarkii (Girard)

The red swamp crayfish,Procambarus clarkii,is an economically important species especially in China.Their exoskeleton places serious constraints on growth and culture management.Their growth is achieved through intermittent molting/ecdysis.The longitudinal genetic dynamics for growth-related traits at different ecdysial points in P.clarkii has been unclear to date.In this study,conditional genetic analysis was carried out for growth-related traits(body weight,body length,chela length,and cephalothorax length)based upon a mixed genetic model with conditional additive,dominance,and genotype by environment effects in P.clarkii.A complete diallel cross was made among three geographic populations of P.clarkii for the genetic mating design.Results of the conditional genetic analysis showed that from 4 th molt to 9 th molt the conditional additive variations were increased significantly whereas the conditional non-additive genetic variations(dominance and genotype by environment interaction)were decreased significantly for these growth-related traits.This indicated that lots of new expression of additive effect genes for body weight,body length,chela length,and cephalothorax length occurred during ontogeny,and environment played a signifi cant role in the expression of genes affecting these growth-related traits.Growth of the four traits was mainly affected by non-additive genetic effects in early developmental stage(prior to 4 th molt).The cumulative conditional additive variation for the growth-related traits from 4 th molt to 9 th molt accounted for a large majority of the total conditional additive variations from 2 nd molt to 9 th molt,indicating that this period was very important for the growth of this species.Using the conditional analysis method,dynamics of growth-related traits during an important ontogenetic phase of red swamp crayfish was uncovered.Our results provide valuable insights into refining production of this species.

Genetic Analysis of Leucine Content in Indica-Japonica Hybrid Rice (Oryza sativa L.)

Genetic control of leucine content in indica-japonica hybrid rice (Oryza sativa L.) was studied in 35 crosses of F1 and F2 generations, which were derived from crossing 7 male sterile indica rice lines with 5 restorer japonica rice lines along with their parents. Two genetic models and their corresponding statistical methods for quantitative traits of triploid seeds in cereal crops were used for the analysis. The first was the unconditional genetic model, which refers to the analysis of cumulative measurements (from flowering to a specific time) along the developmental stages, while the second was the conditional genetic model, which relates to analysis from one developmental stage to another stage (t - 1→t). The results showed that leucine content of indica-japonica hybrid rice was controlled by the expression of triploid endosperm effect (endosperm additive effect and endosperm dominant effect), cytoplasm effect, diploid maternal plant effect (maternal additive effect and maternal dominant effect) and their environmental interaction effects. Of these effects, endosperm dominant effect and maternal dominant effect were more important at the earlier stages, while endosperm additive effect and maternal additive effect were more important at the later stages of rice grain development under both unconditional and conditional genetic analyses. Due to the high heritabilities, which came from endosperm, maternal and cytoplasm effects for leucine content at different developmental stages, selection for leucine content of indica-japonica hybrid rice would be more efficient at early generations in breeding programs.

Decomposition Method of Genetic Correlation Coefficient Based on NC Ⅱ Mating Design

There are different degrees of correlation between crop traits. The phenotypic correlation is decomposed into genetic and environmental correlation in quantitative genetics. In this paper,according to stochastic model of variance and covariance analysis,we calculate different genetic components,bring up a decomposition method of genetic correlation coefficient based on NC II mating design,and use examples to show analytic steps and interpret results.

Estimated Genetic Variance Explained by Single Nucleotide Polymorphisms of Different Minor Allele Frequencies for Carcass Traits in Japanese Black Cattle

Japanese Black cattle are a beef breed and well known to excel in carcass quality, but the details of genetic architectures for carcass traits in beef breeds including this breed are still poorly understood. The objective of this study was to estimate the degree of additive genetic variance explained by single nucleotide polymorphism (SNP) marker groups with different levels of minor allele frequency (MAF) for marbling score and carcass weight in Japanese Black cattle. Phenotypic data on 872 fattened steers with the genotype information about 40,000 autosomal SNPs were analyzed using two different statistical models: one considering only SNPs selected based on MAF (model 1) and the other also considering all remaining SNPs as the different term (model 2). All available SNPs were classified into 10 groups based on their MAFs. For both traits, the estimated proportions of additive genetic variance explained by SNPs selected based on their MAFs using model 1 were always higher than the estimated ones using model 2. For carcass weight, relatively high values of the proportion of the additive genetic variance were estimated when using SNPs with MAFs which were in the ranges of 0.20 to 0.25 and 0.25 to 0.30, which may be partly due to the three previously-reported quantitative trait loci candidate regions. The results could have provided some information on the genetic architecture for the carcass traits in Japanese Black cattle, although its validity may be limited, mainly due to the sample size and the use of simpler statistical models in this study.