Genetic Dissection of Grain Size Traits Through Genome-Wide Association Study Based on Genic Markers in Rice

Grain size plays a significant role in rice,starting from affecting yield to consumer preference,which is the driving force for deep investigation and improvement of grain size characters.Quantitative inheritance makes these traits complex to breed on account of several alleles contributing to the complete trait expression.We employed genome-wide association study in an association panel of 88 rice genotypes using 142 new candidate gene based SSR(cgSSR)markers,derived from yield-related candidate genes,with the efficient mixed-model association coupled mixed linear model for dissecting complete genetic control of grain size traits.A total of 10 significant associations were identified for four grain size-related characters(grain weight,grain length,grain width,and length-width ratio).Among the identified associations,seven marker trait associations explain more than 10%of the phenotypic variation,indicating major putative QTLs for respective traits.The allelic variations at genes OsBC1L4,SHO1 and OsD2 showed association between 1000-grain weight and grain width,1000-grain weight and grain length,and grain width and length-width ratio,respectively.The cgSSR markers,associated with corresponding traits,can be utilized for direct allelic selection,while other significantly associated cgSSRs may be utilized for allelic accumulation in the breeding programs or grain size improvement.The new cgSSR markers associated with grain size related characters have a significant impact on practical plant breeding to increase the number of causative alleles for these traits through marker aided rice breeding programs.

On Concomitants of Record Values from Generalized Farlie-Gumbel-Morgenstem Distribution

In this paper, we derive the distributions of concomitants of record values from generalized Farlie-Gumbel-Morgenstern family of bivariate distributions. We derive the single and the product moments of the concomitants for the general case. The results are then applied to the ease of the two-parameter exponential marginal distributions. Using concomitants of record values we derive the best linear unbiased estimators of parameters of the marginal distributions. Moreover, two methods for obtaining predictors of concomitants of record values are presented. Finally, a numerical illustration is performed to highlight the theoretical results obtained.

Family Selection as a Strategy for Stem Borer (Eldana Saccharina Lepidoptera: Pyralidae) Resistance Breeding in South Africa

Eldana saccharina is the most damaging stem borer of sugarcane in South Africa causing US$90 million losses of revenue annually. The breeding strategy at the South African Sugarcane Research Institute is based on evaluating parents for breeding values using progeny data derived from family plots and selecting parents with high breeding values for crossing. Family selection entails selecting whole populations of progenies based on family mean. The objective of this study was to evaluate the contribution of family selection to eldana resistance breeding. Data were collected from stage 1 (seedlings stage) trials. In each plot, stalks were examined for eldana entry and exit holes and stalks with borings were counted. The number of bored stalks was expressed as a percent of total stalks and subjected to analysis of variance. The family broad sense heritabilities ranged from 0.51 - 0.56 compared with 0.17 for Individual Genotype Selection (IGS). Predicted family selection gains ranged from 20% to 69% compared with 18% for IGS indicating the value of family selection. Female parental effects F-values (1.63 - 2.01) were significant (P = 0.0017 - 0.0041) compared with non-significant male F-values (1.33 - 1.41) and (P = 0.088 - 0.1464) suggesting maternal effects. Crossing parents with higher resistance such as 96M0058 × 94M0017, 87M0965 × 98G1166 and 97M0653 × 94M0017 produced significantly (P < 0.05) fewer bored stalks compared with those showing lower resistance (96H0590 × 95H0167, 94F2694 × 86F3326 and 76L1295 × 91L1492) suggesting additive genetic effects and that recurrent selection will be an effective breeding method.

Checking for normality in linear mixed models

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

Dynamic stress–strength reliability estimation of system with survivalsignature

In this paper, we proposed a dynamic stress–strength model for coherent system. It is supposedthat the system consists of n components with initial random strength and each component issubjected to random stresses. The stresses, applied repeatedly at random cycle times, will causethe degradation of strength. In addition, the number of cycles in an interval is assumed to followa Poisson distribution. In the case of the strength and stress random variables following exponential distributions, the expression for the reliability of the proposed dynamic stress–strengthmodel is derived based on survival signature. The reliability is estimated by using the best linearunbiased estimation (BLUE). Considering the Type-II censored failure times, the best linear unbiased predictors (BLUP) for the unobserved coherent system failure times are developed basedon the observed failure times. Monte Carlo simulations are performed to compare the BLUE ofparameters with different values and compute the BLUP. A real data set is also analysed for anillustration of the findings.