Analysis of cytoplasmic and maternal effects I. A genetic model for diploid plant seeds and animals

A genetic model for modified diallel crosses is proposed for estimating variance and covariance components of cytoplasmic, maternal additive and dominance effects, as well as direct additive and dominance effects. Monte Carlo simulations were conducted to compare the efficiencies of minimum norm quadratic unbiased estimation (MINQUE) methods. For both balanced and unbalanced mating designs, MINQUE (0/1), which has 0 for all the prior covariances and 1 for all the prior variances, has similar efficiency to MINQUE(), which has parameter values for the prior values. Unbiased estimates of variance and covariance components and their sampling variances could be obtained with MINQUE(0/1) and jackknifing. A t-test following jackknifing is applicable to test hypotheses for zero variance and covariance components. The genetic model is robust for estimating variance and covariance components under several situations of no specific effects. A MINQUE(0/1) procedure is suggested for unbiased estimation of covariance components between two traits with equal design matrices. Methods of unbiased prediction for random genetic effects are discussed. A linear unbiased prediction (LUP) method is shown to be efficient for the genetic model. An example is given for a demonstration of estimating variance and covariance components and predicting genetic effects.     

A comparison of four experimental designs for the estimation of heritability

Summary The partial diallel cross, the complete diallel cross, and the designs known as North Carolina Experiments 1 and 2 are compared for their usefulness in estimating heritability. It is first shown that reliable values for the sampling mean and variance of heritability estimates are obtained from approximate expressions based on the moments of the chi-square distribution. These expressions are then applied to determine the optimum experimental designs for a range of situations.The main basis for discrimination is the amount of information per unit, defined as i = 1/(N var( ²)), where ² is the estimate of the heritability h ² and N is the number of units in the experiment, either individuals or families.The two parameters considered were the heritability of individuals and the heritability of full-sib families, and for each of these the partial diallel cross was the most preferred, followed in decreasing order of preference by design NC2, the complete diallel, and design NC1.It is first shown that there is no optimum number of parents for a partial diallel cross or male parents for designs NC1 and NC2. The number of crosses per parent for a partial diallel or dams per sire for designs NC2 and NC2 should generally be six or less. Any expansion should be in the direction of using more parents in the case of the partial diallel, or more male parents in the case of designs NC1 and NC2. For the two heritability parameters considered in this study it is inefficient to increase the number of replicates beyond two.     

On the finite sample distribution of the likelihood ratio statistic for testing heterogeneity in meta-analysis

In meta-analysis, hypothesis testing is one of the commonly used approaches for assessing whether heterogeneity exists in effects between studies. The literature concluded that the Q-statistic is clearly the best choice and criticized the performance of the likelihood ratio test in terms of the type I error control and power. However, all the criticism for the likelihood ratio test is based on the use of a mixture of two chi-square distributions with 0 and 1 degrees of freedom, which is justified only asymptotically. In this study, we develop a novel method to derive the finite sample distribution of the likelihood ratio test and restricted likelihood ratio test statistics for testing the zero variance component in the random effects model for meta-analysis. We also extend this result to the heterogeneity test when metaregression is applied. A numerical study shows that the proposed statistics have superior performance to the Q-statistic, especially when the number of studies collected for meta-analysis is small to moderate.     

On the sampling variance of intraclass correlations and genetic correlations.

Widely used standard expressions for the sampling variance of intraclass correlations and genetic correlation coefficients were reviewed for small and large sample sizes. For the sampling variance of the intraclass correlation, it was shown by simulation that the commonly used expression, derived using a first-order Taylor series performs better than alternative expressions found in the literature, when the between-sire degrees of freedom were small. The expressions for the sampling variance of the genetic correlation are significantly biased for small sample sizes, in particular when the population values, or their estimates, are close to zero. It was shown, both analytically and by simulation, that this is because the estimate of the sampling variance becomes very large in these cases due to very small values of the denominator of the expressions. It was concluded, therefore, that for small samples, estimates of the heritabilities and genetic correlations should not be used in the expressions for the sampling variance of the genetic correlation. It was shown analytically that in cases where the population values of the heritabilities are known, using the estimated heritabilities rather than their true values to estimate the genetic correlation results in a lower sampling variance for the genetic correlation. Therefore, for large samples, estimates of heritabilities, and not their true values, should be used.     

Comparison of REML and Gibbs sampling estimates of multi-trait genetic parameters in Scots pine

Multi-trait (co)variance estimation is an important topic in plant and animal breeding. In this study we compare estimates obtained with restricted maximum likelihood (REML) and Bayesian Gibbs sampling of simulated data and of three traits (diameter, height and branch angle) from a 26-year-old partial diallel progeny test of Scots pine (Pinus sylvestris L.). Based on the results from the simulated data we can conclude that the REML estimates are accurate but the mode of posterior distributions from the Gibbs sampling can be overestimated depending on the level of the heritability. The mean and median of the posteriors were considerably higher than the expected values of the heritabilities. The confidence intervals calculated with the delta method were biased downwardly. The highest probablity density (HPD) interval provides a better interval estimate, but could be slightly biased at the lower level. Similar differences between REML and Gibbs sampling estimates were found for the Scots pine data. We conclude that further simulation studies are needed in order to evaluate the effect of different priors on (co)variance components in the genetic individual model.     

Monitoring vegetation change caused by trampling: a study in the Cairngorms,Scotland

Summary

A study was made in the Cairngorms, Scotland to make recommendations for a monitoring scheme capable of detecting changes in the vegetation caused by recreational pressure following the development of a funicular railway. Four methods were used in field trials to assess percentage cover of plant species and gravel, rock and bare ground, where appropriate, in two vegetation types (open and closed). The methods used were visual estimates in 50 × 40 cm quadrats (Q), the mean of visual estimates in twenty 10 × 10 cm sub-quadrats of the 50 × 40 cm quadrats (Q₂₀), a modified point intercept method (RL) and photography. Variances between observers and between-quadrats were estimated for the different methods. The sampling design for detecting change was based on a model of variance, constructed from field trial data.

Between-observer and between-quadrat variances were related to mean percentage cover and approximated to a binomial distribution. The between-quadrat variance was larger than observer variance. The Q₂₀ method achieved appreciably better precision than the other methods. Analysis of half of the 10 × 10 cmsub-quadrats (1/2Q₂₀) selected in a checker board design achieved a relative efficiency of 78% compared with the Q₂₀. This result suggests that comparable precision to the Q₂₀ method could be achieved by choosing about 14 sub-quadrats in a larger quadrat, thus saving some time. Variation between quadrats also suggested that the Q₂₀ method was the one of choice for maximising precision. The precision of the photographic method was based on fewer data points, so is less accurate than other estimates.

Minimum sample sizes were estimated for detecting a 10% relative change of a species in open vegetation with 30% cover (i.e. a change from 30% to <27 or to >33% cover). With a 10 % Type II error rate and 5 % Type I error rate the minimum sample sizes were 47 quadrats for Q, 18 for Q ₂₀, 43 for RL, and 23 for the means of ten 10 × 10 cm sub-quadrats in open vegetation.

The most time-efficient field recording appeared to be the use of Q despite the required sample size being 2.6 times higher than that of Q₂₀. The far lower time requirement per quadrat, however, compensated for the higher numbers. The number of quadrats would depend on the specified change in percentage cover and on the statistical significance level used. For example, to detect a 10% absolute change in cover (i.e. from 30% to either <20 % or >40 % cover) at 95 % probability the net effective recording time is estimated at 5 h per vegetation type while to detect a 5 % change at 99 % probability would require c. 25 h. Larger samples may be required for other species or for species with a low initial cover.     

Approximate Confidence Intervals for Contrasts in the Balanced Three Factor Mixed Model

When conducting a statistical analysis of data from a designed experiment, an investigator is often interested in confidence intervals for contrasts of the fixed effects. If the analysis involves a mixed linear model, exact confidence intervals for contrasts of the fixed effects are not always available. In such cases, confidence intervals with approximate coverage probabilities must be used. As will be shown, this problem may be generalized to that of constructing a confidence interval for the parameter μ, where X is a normal random variable with mean μ and variance ∑ a_qθ_q, where a₁…,a_Q are known constants, U_q = n_qS/θ_q is a chi-squared random variable with n_q degrees of freedom, for each q = 1,…, Q, and X,U₁,…, U_Q are mutually independent. In this paper, we consider the case where Q = 3 and a₃ ≤0.     

THE GENETIC BASIS OF SEXUAL ISOLATION BETWEEN DROSOPHILA MELANOGASTER AND D. SIMULANS

The genetic analysis of sexual isolation between the closely-related species Drosophila melanogaster and Drosophila simulans involved two experiments with no-choice tests. The efficiency of sexual isolation was measured by the frequency of courtship initiation and interspecific mating. We first surveyed the variation in sexual isolation between D. melanogaster strains and D. simulans strains of different geographic origin. Then, to investigate variation in sexual isolation within strains, we made F₁ diallel sets of reciprocal crosses within strains of D. melanogaster and D. simulans. The F₁ diallel progeny of one sex were paired with the opposite sex of the other species. The first experiment showed significant differences in the frequency of interspecific mating between geographic strains. There were more matings between D. simulans females and D. melanogaster males than between D. melanogaster females and D. simulans males. The second experiment uncovered that the male genotypes in the D. melanogaster diallel significantly differed in interspecific mating frequency, but not in courtship initiation frequency. The female genotypes in the D. simulans diallel were not significantly different in courtship initiation and interspecific mating frequency. Genetic analysis reveals that in D. melanogaster males sexual isolation was not affected by either maternal cytoplasmic effects, sex-linked effects, or epistatic interaction. The main genetic components were directional dominance and overdominance. The F₁ males achieved more matings with D. simulans females than the inbred males. The genetic architecture of sexual isolation in D. melanogaster males argues for a history of weak or no selection for lower interspecific mating propensity. The behavioral causes of variation in sexual isolation between the two species are discussed.     

Generalization of the QST framework in hierarchically structured populations: Impacts of inbreeding and dominance

Q_ST is a differentiation parameter based on the decomposition of the genetic variance of a trait. In the case of additive inheritance and absence of selection, it is analogous to the genic differentiation measured on individual loci, F_ST. Thus, Q_ST?F_ST comparison is used to infer selection: selective divergence when Q_ST > F_ST, or convergence when Q_ST < F_ST. The definition of Q‐statistics was extended to two‐level hierarchical population structures with Hardy–Weinberg equilibrium. Here, we generalize the Q‐statistics framework to any hierarchical population structure. First, we developed the analytical definition of hierarchical Q‐statistics for populations not at Hardy–Weinberg equilibrium. We show that the Q‐statistics values obtained with the Hardy–Weinberg definition are lower than their corresponding F‐statistics when F_IS > 0 (higher when F_IS < 0). Then, we used an island model simulation approach to investigate the impact of inbreeding and dominance on the Q_ST?F_ST framework in a hierarchical population structure. We show that, while differentiation at the lower hierarchical level (Q_SR) is a monotonic function of migration, differentiation at the upper level (Q_RT) is not. In the case of additive inheritance, we show that inbreeding inflates the variance of Q_RT, which can increase the frequency of Q_RT > F_RT cases. We also show that dominance drastically reduces Q‐statistics below F‐statistics for any level of the hierarchy. Therefore, high values of Q‐statistics are good indicators of selection, but low values are not in the case of dominance.     

Multivariate statistical analysis of grain yield and agronomic characters in Durum wheat

Summary Correlation, stepwise multiple regression and factor analyses were conducted on grain yield and a number of agronomic characters in the parental, F ₁ and F ₂ families originating from a 10 X 10 diallel cross in durum wheat. For the F ₁ diallel, the correlation analysis indicated that the number of spikes and kernels per plant and 1,000 kernel weight had the highest correlations with grain yield; for the F ₂ diallel, the number of spikes and kernels per meter, 1000 kernel weight and plant height showed most striking correlations with same.Stepwise multiple regression analysis indicated that, for the F ₁ diallel, number of kernels per plant, 1000 kernel weight and days to maturity were the most potent predictor variables for grain yield, accounting for 78% of its variability. For the F ₂ diallel, the number of kernels and number of spikes per meter, 1000 kernel weight and number of kernels per spike were the most potent predictors for grain yield, accounting for 91 % of its variability. Five common factors were extracted which explained 98.8% and 98.1% of the total variance in the F ₁ and F ₂ diallel, respectively. However, the importance of each of the five factors and the characters which loaded highly on each of them differed from generation to generation.Contribution No. 323 from Plant Science Department, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada.     

Analysis of genetic effects of major genes and polygenes on quantitative traits I. Genetic model for diploid plants and animals

A genetic model was proposed to simultaneously investigate genetic effects of both polygenes and several single genes for quantitative traits of diploid plants and animals. Mixed linear model approaches were employed for statistical analysis. Based on two mating designs, a full diallel cross and a modified diallel cross including F₂, Monte Carlo simulations were conducted to evaluate the unbiasedness and efficiency of the estimation of generalized least squares (GLS) and ordinary least squares (OLS) for fixed effects and of minimum norm quadratic unbiased estimation (MINQUE) and Henderson III for variance components. Estimates of MINQUE (1) were unbiased and efficient in both reduced and full genetic models. Henderson III could have a large bias when used to analyze the full genetic model. Simulation results also showed that GLS and OLS were good methods to estimate fixed effects in the genetic models. Data on Drosophila melanogaster from Gilbert were used as a worked example to demonstrate the parameter estimation. Received: 11 November 2000 / Accepted: 2 May 2001     

Some Theoretical Aspects of Analysis in Half Diallel

The analysis of F₁ and F₂ half diallel has been discussed as compared to full diallel without reciprocal effects given by MATHER and JINKS (1971). In practice, mostly the half diallel (one-way) crosses are prepared and erroreously analysed using the least square estimates of full diallel without reciprocal effects. The H₁ and H₂, however, appeared to be over estimated when full diallel without reciprocal effects estimates were used in place of those of half diallel. Least square estimates were also obtained assuming heterogeneity of error components between parents and F₁/F₂ families.     

Sequence of the mouse Q4 class I gene and characterization of the gene product

The Q4 class I gene has been shown to participate in gene conversion events within the mouse major histocompatibility complex. Its complete genomic nucleotide sequence has been determined. The 5 half of Q4 resembles H-2 genes more strongly than other Q genes. Its 3 end, in contrast, is Q-like and contains a translational stop signal in exon 5 which predicts a polypeptide with an incomplete membrane spanning segment. The presence of two inverted B1 repeats suggests that part of the Q4 gene may be mobile within the genome. Gene transfer experiments have shown that the Q4 gene encodes a ²-microglobulin associated polypeptide of M_r 41 000. A similar protein was found in activated mouse spleen cells. The Q4 polypeptide was found to be secreted both by spleen cells and by transfected fibroblasts and was not detectable on the cell surface. Antibody binding and two-dimensional gel electrophoresis indicate that the Q4 molecule is identical to a mouse class I polypeptide, Qb-1, which has been previously described.     

SEED SET AND SEED MASS IN IPOMOPSIS AGGREGATA: VARIANCE PARTITIONING AND INFERENCES ABOUT POSTPOLLINATION SELECTION

Events that follow pollination, such as pollen-tube growth and seed maturation, comprise an important phase of angiosperm reproduction. Differential success during this “postpollination” phase may represent phenotypic selection, including sexual selection, or interaction between parents caused, for example, by their genetic similarity. By providing a detailed partitioning of variance in success, diallel crossing designs offer great potential to determine which processes are occurring and their relative magnitudes. We performed three partial diallels with the montane herb Ipomopsis aggregata, using a large sample of parental plants (69 total). Embedded in the designs were crossing-distance treatments of 1 m, 10 m, and 100 m, reflecting a range of parental genetic similarity. We partitioned phenotypic variance in seed set per fruit into six components using restricted maximum-likelihood (REML) analysis. For one diallel, we also partitioned variance in seed mass into five components, and estimated two components of covariance between seed set and mass. Variance caused by maternal effects (V_mat) comprised 12%–35% of total variance in seed set and 62% of variance in seed mass, and there was a significant negative environmental covariance between seed set and seed mass. Parental interaction made no detectable contribution to phenotypic variance in either of our measures of postpollination success, although crossing distance did contribute slightly but significantly to fit of the model in some cases. Finally, there was no detectable paternal variance (V_pat) in seed set or seed mass. These results are in keeping with reports from other studies of natural plant populations. The finding of little or no paternal variance in particular suggests little scope for postpollination sexual selection through the male function of cosexual plants such as I. aggregata.     

Genetic analysis of agronomic characters in chickpea. II. Estimates of genetic variances from line × tester mating designs

Summary Thirty line x tester experiments involving diverse chickpea (Cicer arietinum L.) germplasm were conducted over 8 years and three locations to determine the nature of the genetic variance for grain yield and related characters, and the effects of generation and environment on these genetic parameters. Days-to-flowering, 100-seed mass, and seeds per pod were predominantly under the control of additive genetic variance, while both additive and non-additive genetic components of variance were important for days-to-maturity, plant height, primary and secondary branches, pods per plant, and seed yield. The F₁ and F₂ generations were found equally useful in estimating the genetic variances for different characters because the generation did not significantly interact with genetic parameters in the majority of cases. Sites or seasons, on the other hand, showed significant interaction with genetic components of variances; additive variance showed a larger interaction with environments than non-additive variance. This indicated the importance of more than one site and/ or season for unbiased estimation of the genetic components of variance. The results were compared with previous findings from diallel analyses.ICRISAT Journal Article No. 1200     

Side-chain entropy and packing in proteins.

What role does side-chain packing play in protein stability and structure? To address this question, we compare a lattice model with side chains (SCM) to a linear lattice model without side chains (LCM). Self-avoiding configurations are enumerated in 2 and 3 dimensions exhaustively for short chains and by Monte Carlo sampling for chains up to 50 main-chain monomers long. This comparison shows that (1) side-chain degrees of freedom increase the entropy of open conformations, but side-chain steric exclusion decreases the entropy of compact conformations, thus producing a substantial entropy that opposes folding; (2) there is a side-chain “freezing” or ordering, i.e., a sharp decrease in entropy, near maximum compactness; and (3) the different types of contacts among side chains (s) and main-chain elements (m) have different frequencies, and the frequencies have different dependencies on compactness. mm contacts contribute significantly only at high densities, suggesting that main-chain hydrogen bonding in proteins may be promoted by compactness. The distributions of mm, ms, and ss contacts in compact SCM configurations are similar to the distributions in protein structures in the Brookhaven Protein Data Bank. We propose that packing in proteins is more like the packing of nuts and bolts in a jar than like the pairwise matching of jigsaw puzzle pieces.     

Testing for Homogeneity in Meta‐Analysis I. The One‐Parameter Case: Standardized Mean Difference

Summary Meta‐analysis seeks to combine the results of several experiments in order to improve the accuracy of decisions. It is common to use a test for homogeneity to determine if the results of the several experiments are sufficiently similar to warrant their combination into an overall result. Cochran’s Q statistic is frequently used for this homogeneity test. It is often assumed that Q follows a chi‐square distribution under the null hypothesis of homogeneity, but it has long been known that this asymptotic distribution for Q is not accurate for moderate sample sizes. Here, we present an expansion for the mean of Q under the null hypothesis that is valid when the effect and the weight for each study depend on a single parameter, but for which neither normality nor independence of the effect and weight estimators is needed. This expansion represents an order O(1/n) correction to the usual chi‐square moment in the one‐parameter case. We apply the result to the homogeneity test for meta‐analyses in which the effects are measured by the standardized mean difference (Cohen’s d‐statistic). In this situation, we recommend approximating the null distribution of Q by a chi‐square distribution with fractional degrees of freedom that are estimated from the data using our expansion for the mean of Q. The resulting homogeneity test is substantially more accurate than the currently used test. We provide a program available at the Paper Information link at the Biometrics website http://www.biometrics.tibs.org for making the necessary calculations.     

Genetic analysis of phytic acid content in pearl millet

Summary The genetics of phytic acid content in pearl millet (Pennisettum typhoides (Burm) S & H) was studied using a 12 parent diallel. The analysis of variance of diallel progenies exhibited significant genotypic differences. Different analyses, i.e., combining ability analysis, analysis of variance of diallel tables and genetic component analysis, showed that both additive and non additive gene effects were significant. It is suggested that a population improvement is possible by breeding for low phytic acid cultivars of pearl millet.     

中亚热带赤皮青冈天然种群表型多样性分析

赤皮青冈(Quercus gilva)是我国中亚热带地区极具经济价值的珍贵用材树种。为揭示其表型多样性与变异规律以及影响表型变异的关键地理气候因子，该研究以14个赤皮青冈天然种群115个单株为材料，对其15个树体和叶片性状进行测量，并采用巢式方差分析、表型分化系数分析、多样性指数分析、相关性分析、主成分分析以及聚类分析等方法，探究赤皮青冈的表型变异规律及其与地理气候因子的相关性。结果表明：(1)赤皮青冈表型多样性水平较高，15个表型性状的变异系数和Shannon-Wiener指数平均值分别为35.070%和1.998,14个种群的变异系数在14.94%(洞口)～35.56%(龙山)之间、Shannon-Wiener指数在1.127(松阳)～1.980(常宁)之间。(2)15个表型性状在种群间和种群内均存在极显著差异(P<0.01),种群平均表型分化系数为41.491%,表型变异主要来源于种群内。(3)相关性分析发现，赤皮青冈部分性状间存在显著或极显著相关性，表型性状与地理因子间相关性不明显，降水是影响赤皮青冈表型性状的主要气候因子。(4)主成分分析发现，基于11个表型可提炼出4个...     

Genetic polymorphisms ofQ region genes from wild-derived mice: Implications forQ region evolution

Both serological and DNA sequence analyses were performed to determine the extent of genetic polymorphism inQ region genes. A panel of Qa-2-specific monoclonal antibodies (mAbs) was tested on 35 wildderived and inbred mouse strains. Members of this reagent panel recognize multiple and distinct epitopes on the Qa-2-bearing molecule(s). Although quantitative variations in Qa-2 levels were observed, no structural polymorphisms were detected. All strains were either entirely positive or entirely negative with the complete set of reagents. Moreover, cell surface Qa-2 expression was not significantly affected by differences in age or sex of the mouse or cell cycle status. To confirm this apparent lack of genetic polymorphism, the polymerase chain reaction (PCR) technique was used to amplify a portion of the 3 end of theQ region genes,Q4 toQ9, from several independent wild-derived strains of mice. Sequence analysis of the amplified material revealed very little evidence of nucleotide divergence. All strains tested had aQ even DNA sequence identical to that ofQ6/Q8 in the B10 strain. Likewise, all tested strains had aQ odd DNA sequence identical toQ7/Q9 in the B10 strain. Two strains showed additionalQ even sequences, while all strains tested possessed additionalQ odd sequences. The observed lack of polymorphism suggests that theQ genes have evolved in a different manner fromH-2K andH-2D. Moreover, duplications of these genes appear to have arisen prior to nucleotide sequence divergence.The nucleotide sequence data reported in this paper have been submitted to the GenBank nucleotide sequence database and have been assigned the accession numbers M30896-30902.