Analysis of asymmetries in the African fruit bats Eidolon helvum and Rousettus egyptiacus (Mammalia: Megachiroptera) from the islands of the Gulf of Guinea. I. Variance and size components of bilateral variation

A set of cranial characters was examined in the fruit bats Rousettus egyptiacus and Eidolon helvum to compare trends and relative importance of major components of bilateral morphometric variation, and their relationship with character size. Using two‐way, sides‐by‐individuals ANOVA , four components of variation were estimated for each bilateral variable: individual variation (I), directional asymmetry (DA), non‐directional asymmetry (NDA) and measurement error (E). Both species exhibit similar major trends of variation in asymmetry across characters, as shown by principal component analysis, using variance components as variables. Degree of interspecific congruence among characters was confirmed by a two‐way ANOVA with species and variance components as fixed factors. Congruence of asymmetry patterns between species suggests that the concept of population asymmetry parameter (PAP) could be extended to higher hierarchies. PAPs above the species level may result from common mechanisms or similar developmental constraints acting on species’ buffering capacities and morphological integration processes.     

Standard errors of heritabilities for forage breeding nurseries

Estimators for standard errors of heritability for two typical and complex forage breeding models are illustrated with estimates of variance and covariance components from least-squares and restricted maximum likelihood methods. The first experiment (Model 1) is a factorial design (two grazing management factors) with two layers of split plots (populations and grazing periods) and with plants within populations nested beneath the first split. The second model is for a sites pooling of randomized complete block experiments, with plants nested inside plots and with a split in time. One definition of heritability was applied to the plant habit character for both models in a red clover germplasm. Heritability estimates were statistically the same for the two methods for both models.     

内蒙古锡林郭勒高原大针茅种群分株构件数量性状的地理变异研究

采用单因素方差分析、变异组分分析和分形几何学的原理和方法,对内蒙古锡林郭勒盟不同气候条件下的三个大针茅种群分株构件数量性状进行了研究,并结合它们所在生境特点对所得结果进行了分析。结果显示：（1）整个生长季内,不同种群大针茅营养枝高度的生长模式不同;营养枝高度和生殖枝高度在种群间差异显著,且多数变异存在于种群之间;（2）在不同生长期内,大针茅种群地上部干重与植株高度之间存在显著的分形关系;在无强度干扰的情况下,大针茅种群营养枝分形维数的大小与大针茅营养枝地上部干重的累积程度是一致的;但在长期严重干旱条件下,分形维数值表现为快速增加;（3）整个生长季内,同一生境条件下大针茅种群营养枝地上部干重与植株高度之间也存在显著的分形关系,且不同样地间分形维数值差异显著。不同生境条件下大针茅种群分株构件数量性状的差异是对所在生境长期适应、自然选择的结果。     

The PX-EM algorithm for fast stable fitting of Henderson's mixed model

This paper presents procedures for implementing the PX-EM algorithm of Liu, Rubin and Wu to compute REML estimates of variance covariance components in Henderson''s linear mixed models. The class of models considered encompasses several correlated random factors having the same vector length e.g., as in random regression models for longitudinal data analysis and in sire-maternal grandsire models for genetic evaluation. Numerical examples are presented to illustrate the procedures. Much better results in terms of convergence characteristics (number of iterations and time required for convergence) are obtained for PX-EM relative to the basic EM algorithm in the random regression.     

Mid-Po River zooplankton

The temporal crustacean-zooplankton variation in the mid-Po River (Italy) was analyzed from November 1974 through November 1982. Samples were collected at three stations at monthly intervals.Separate taxon-by-taxon multiple regression analyses (MLTRG) were carried out with zooplankton taxa as the criterion variable and river depth, river discharge and water temperature as the predictor variables. Moina brachiata and Eucyclops serrulatus were correlated with water temperature, Cyclops vicinus inversely correlated with temperature, Eudiaptomus padanus, C. vicinus and Daphniidae with river discharge; Copepodites inversely correlated with river depth.MLTRG showed that water temperature and river discharge account for about 15% of total zooplankton variation.Factorial analysis of variance (ANOVA) was carried out on residuals calculated from MLTRG. Among-years and among-months variation were significant for all the examined taxa. Significant years × months interactions indicated that seasonal variations were also different in different years.ANOVA stressed that there were still unexplained significant residuals in years and months variations.Weekly and daily samples collected in Summer 1979 were submitted to MLTRG and ANOVA as above. Among-week variations were significant for all the examined taxa, whereas among-days were significant for Daphiidae and M. brachiata (Cladocera), and not significant for any of the other taxa. Caution is recommended in interpreting the results of river zooplankton studies. Differences between species responses warn us not to pool species into larger taxa. Temporal variation changes from year to year, so long-time series are necessary to clarify the most important trends of river zooplankton.     

Parent-of-origin effects cause genetic variation in pig performance traits

In order to assess the relative importance of genomic imprinting for the genetic variation of traits economically relevant for pork production, a data set containing 21 209 records from Large White pigs was analysed. A total of 33 traits for growth, carcass composition and meat quality were investigated. All traits were recorded between 1997 and 2006 at a test station in Switzerland and the pedigree included 15 747 ancestors. A model with two genetic effects for each animal was applied: the first corresponds to a paternal and the second to a maternal expression pattern of imprinted genes. The imprinting variance was estimated as the sum of both corresponding genetic variances per animal minus twice the covariance. The null hypothesis of no imprinting was tested by a restricted maximum likelihood ratio test with two degrees of freedom. Genomic imprinting significantly contributed to the genetic variance of 19 traits. The proportion of the total additive genetic variance that could be attributed to genomic imprinting was of the order between 5% and 19%.     

ESTIMATING HIERARCHICAL F-STATISTICS

This paper presents an analysis of variance (ANOVA) approach by which estimation of F-statistics can be made from data with an arbitrary s-level hierarchical population structure. Assuming a complete random-effect model, a general ANOVA procedure is developed to estimate F-statistics as ratios of different variance components for all levels of population subdivision in the hierarchy. A generalized relationship among F-statistics is also derived to extend the well-known relationship originally found by Sewall Wright. Although not entirely free from the bias particular to small number of subdivisions at each hierarchy and extreme gene frequencies, the ANOVA estimators of F-statistics consider sampling effects at each level of hierarchy, thus removing the bias incurred in the other estimators that are commonly based on direct substitution of unknown gene frequencies by their sample estimates. Therefore, the ANOVA estimation procedure presented here may become increasingly useful in analyzing complex population structure because of increasing use of the estimated hierarchical F-statistics to infer genetic and demographic structures of natural populations within and among species.     

Scales of association: hierarchical linear models and the measurement of ecological systems

A fundamental challenge to understanding patterns in ecological systems lies in employing methods that can analyse, test and draw inference from measured associations between variables across scales. Hierarchical linear models (HLM) use advanced estimation algorithms to measure regression relationships and variance–covariance parameters in hierarchically structured data. Although hierarchical models have occasionally been used in the analysis of ecological data, their full potential to describe scales of association, diagnose variance explained, and to partition uncertainty has not been employed. In this paper we argue that the use of the HLM framework can enable significantly improved inference about ecological processes across levels of organization. After briefly describing the principals behind HLM, we give two examples that demonstrate a protocol for building hierarchical models and answering questions about the relationships between variables at multiple scales. The first example employs maximum likelihood methods to construct a two-level linear model predicting herbivore damage to a perennial plant at the individual- and patch-scale; the second example uses Bayesian estimation techniques to develop a three-level logistic model of plant flowering probability across individual plants, microsites and populations. HLM model development and diagnostics illustrate the importance of incorporating scale when modelling associations in ecological systems and offer a sophisticated yet accessible method for studies of populations, communities and ecosystems. We suggest that a greater coupling of hierarchical study designs and hierarchical analysis will yield significant insights on how ecological processes operate across scales.     

MIXED MODEL APPROACHES FOR ESTIMATING GENETIC VARIANCES AND COVARIANCES

The limitations of methods for analysis of variance(ANOVA)in estimating genetic variances are discussed. Among the three methods(maximum likelihood ML, restricted maximum likelihood REML, and minimum norm quadratic unbiased estimation MINQUE)for mixed linear models, MINQUE method is presented with formulae for estimating variance components and covariances components and for predicting genetic effects. Several genetic models, which cannot be appropriately analyzed by ANOVA methods, are introduced in forms of mixed linear models. Genetic models with independent random effects can be analyzed by MINQUE(1)method whieh is a MINQUE method with all prior values setting 1. MINQUE(1)method can give unbiased estimation for variance components and covariance components, and linear unbiased prediction (LUP) for genetic effects. There are more complicate genetic models for plant seeds which involve correlated random effects. MINQUE(0/1)method, which is a MINQUE method with all prior covariances setting 0 and all prior variances setting 1, is suitable for estimating variance and covariance components in these models. Mixed model approaches have advantage over ANOVA methods for the capacity of analyzing unbalanced data and complicated models. Some problems about estimation and hypothesis test by MINQUE method are discussed.     

Estimation of Covariance Matrices in Unbalanced Random and Mixed Multivariate Models

Three HENDERSON'S Methods of estimating the variance components are generalized from one to p variables using a compact matrix notation. These results are obtained using a generalized Kronecker product of matrices, generalized trace of order p and a generalized quadratic form.     

The Effect of Categorization on a Simple Analysis of Variance Model

Many statistical procedures assume a continuous model in spite of the fact that observations are necessarily discrete. Here we consider a simple ANOVA model—one factor with fixed effects—and assess the effect of categorisation by simulating sizes and calculating asymptotic relative efficiencies. Even for severe categorisation the effects are small.     

Developments from analysis of variance through to generalized linear models and beyond

The collaborations between statisticians and biologists during the 100 years since AAB was founded have led to a very impressive list of statistical techniques, whose use now goes well beyond agriculture and biology. One example is the maximum likelihood methodology for probit analysis, arising from the collaboration between Sir Ronald Fisher and Chester Bliss. Others include analysis of variance, design of experiments, generalized linear models and the residual, or restricted, maximum likelihood (REML) algorithm for fitting unbalanced linear mixed models.     

The genetics of phenotypic plasticity I. Heritability

Methods for estimating the genetic component of phenotypic plasticity are presented. In the general case of clonal replicates or full-sibs raised in several environments, the heritability of plasticity can be measured as the ratio of the genotype-environment interaction variance to the total phenotypic variance. In the special case of only two environments plasticity also can be measured as the difference among environments in genotype or family means. In that case, the heritability of plasticity can be measured as either a ratio of variance components or as the slope of a parent-offspring regression. The general measure suffers because no least-square standard errors have been developed, although they can be calculated by maximum-likelihood or bootstrapping techniques. For the other two methods least-square standard errors can be calculated but require very large experiments for statistical significance to be achieved. The heritability measures are compared using data on plasticity of thorax size in response to temperature in Drosophila melanogaster. The heritability estimates are all in close agreement. Models of the evolution of phenotypic plasticity have treated it as a trait in its own right and as a cross-environment genetic correlation. Although the first approach is the one used here, neither one is preferred.     

Phenotypic plasticity for life history traits in Drosophila melanogaster. II. Epigenetic mechanisms and the scaling of variances

Abstract We manipulated developmental time and dry weight at eclosion in 15 genotypes of Drosophila melanogaster by growing the larvae in 9 environments defined by 3 yeast concentrations at 3 temperatures. We observed how the genetic and various environmental components of phenotypic variation scaled with the mean values of the traits. Temperature, yeast, within-environmental factors and genotype influenced the genotypic and environmental standard deviations of the two traits in patterns that point to very different modes of physiological and developmental action of these factors. Since different factors affected the environmental and genetic components of the phenotypic variation either in parallel or inversely, we conclude that environmental heterogeneity may have small or large effects on evolutionary rates depending on which factors cause the heterogeneity. The analysis also suggests that the scaling of variances with the mean is not as trivial as is often assumed when coefficients of variation are computed to “standardize” variation.     

用R法估计方差组分的原理、方法和应用

综述了R法估计方差组分的原理、方法和应用,目的是使该方法能够得到合理应用。R法是通过计算全数据集对亚数据集随机效应的回归因子（R）来估计方差组分的。利用一种基于一个变换矩阵的多变量迭代算法,结合先决条件的共扼梯度法求解混合模型方程组使R法的计算效率大为改善。R法的主要优点是计算成本低,同时可以得到方差组分估值的抽样误差和近似置信区间。其缺点是对于同样的数据,R法较其他方法的抽样误差大,而且在小样本中估计值往往有偏。做为一种可选方法,R法可以应用到大数据集的方差组分估计中,同时应进一步研究其理论特性,拓宽其应用范围。Abstract: Theory, method and application of Method R on estimation of (co)variance components were reviewed in order to make the method be reasonably used. Estimation requires R values,which are regressions of predicted random effects that are calculated using complete dataset on predicted random effects that are calculated using random subsets of the same data. By using multivariate iteration algorithm based on a transformation matrix,and combining with the preconditioned conjugate gradient to solve the mixed model equations, the computation efficiency of Method R is much improved. Method R is computationally inexpensive,and the sampling errors and approximate credible intervals of estimates can be obtained. Disadvantages of Method R include a larger sampling variance than other methods for the same data,and biased estimates in small datasets. As an alternative method, Method R can be used in larger datasets. It is necessary to study its theoretical properties and broaden its application range further.     

The Design and Analysis of Twin Animal Experiments

The experimental design used in twin studies on veal calves at the University of Guelph during the years 1965–1968 combined split trials with uniformity trials on each treatment. Each replicate consisted of four twin pairs. Both members of one pair selected at random were put on treatment 1, both members of another pair were put on treatment 2, and the remaining two pairs were “split” with one twin from each pair randomly assigned to each treatment. There were a number of replicates of this basic design over the course of the experiment. The objective of this paper is: (i) to determine the feasibility of an overall analysis of the given design, (ii) to determine an accurate method for assessing treatment effects, and (iii) to find an efficient method for detecting the presence of treatment Xpair interaction.     

A New Algorithm for Explicit Determination of Variance Component Estimations in Mixed Models and Mixed Classifications of Balanced ANOVA

This paper deals with the balanced case of the analysis of variance. The use of a classification function leads to an easy determination of all possible sources of variation of any mixed classification. For mixed models a new method is derived, which allows to represent explicit the ANOVA-estimations of the variance components respectively the estimation of the mean sum of squares of the fixed effects for all sources of variation. Thereby the corresponding F-quotients and the approximate confidence intervals of variance components are received in a simple way.     

The effect of epistasis on the excess of the additive and nonadditive variances after population bottlenecks

The effect of population bottlenecks on the components of the genetic variance generated by two neutral independent epistatic loci has been studied theoretically (VA, additive; VD, dominant; VAA, additive x additive; VAD, additive x dominant; VDD; dominant x dominant components of variance). Nonoverdominance and overdominance models were considered, covering all possible types of marginal gene action at the single locus level. The variance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of allele frequencies and effects at each locus and the corresponding epistatic value. An excess of VA after bottlenecks can be assigned to two sources: (1) the spatiotemporal changes in the marginal average effects of gene substitution alpha(i), which are equal to zero only for additive gene action within and between loci; and (2) the covariance between alpha2(i) and the heterozygosity at the loci involved, which is generated by dominance, with or without epistasis. Numerical examples were analyzed, indicating that an increase in VA after bottlenecks will only occur if its ancestral value is minimal or very small. For the nonoverdominance model with weak reinforcing epistasis, that increase has been detected only for extreme frequencies of the negative allele at one or both loci. With strong epistasis, however, this result can be extended to a broad range of intermediate frequencies. With no epistasis, the same qualitative results were found, indicating that dominance can be considered as the primary cause of an increase in VA following bottlenecks. In parallel, the derived total nonadditive variance exceeded its ancestral value (V(NA) = V(D) + V(AA) + V(AD) + V(DD)) for a range of combinations of allele frequencies covering those for an excess of VA and for very large frequencies of the negative allele at both loci. For the overdominance model, an increase in V(A) and V(NA) was respectively observed for equilibrium (intermediate) frequencies at one or both loci or for extreme frequencies at both loci. For all models, the magnitude of the change of V(A) and V(NA) was inversely related to N and t. At low levels of inbreeding, the between-line variance was not affected by the type of gene action. For the models considered, the results indicate that it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived V(A) over its ancestral value.