A Multivariate Analysis of Hybridization when Covariance Matrices are Unequal

Numerous occurrences of natural hybridization have been known in many groups of animals. It has a bearing on growth, nomenclature, speciation, genetics and wildlife management. It is well recognised that demonstration of intermediacy based on several characters makes the identification of hybrids more certain than that based on just a single character, and that differences among the hybrids and the parental populations should be analysed for variations due to the additive genetic (A) and the non-additive genetic (NA) factors separately. In the present paper (i) it is pointed out that sometimes the assumption that covariance matrices of the hybrids and the parental populations are equal, may not be valid, and (ii) a multivariate method of testing hypotheses analysing differences between the hybrids and the parents, qualified by the A and the NA factors, when covariance matrices are not equal, is submitted.     

Use of the score test as a goodness-of-fit measure of the covariance structure in genetic analysis of longitudinal data

Model selection is an essential issue in longitudinal data analysis since many different models have been proposed to fit the covariance structure. The likelihood criterion is commonly used and allows to compare the fit of alternative models. Its value does not reflect, however, the potential improvement that can still be reached in fitting the data unless a reference model with the actual covariance structure is available. The score test approach does not require the knowledge of a reference model, and the score statistic has a meaningful interpretation in itself as a goodness-of-fit measure. The aim of this paper was to show how the score statistic may be separated into the genetic and environmental parts, which is difficult with the likelihood criterion, and how it can be used to check parametric assumptions made on variance and correlation parameters. Selection of models for genetic analysis was applied to a dairy cattle example for milk production.     

Discriminant functions for linear comparisons of means when covariance matrices are unequal

Situations exist, as in the biological example of discriminant analysis for natural hybridization, cited in the text, where (a) not all populations have equal variances, and (b) comparisions based on single degrees of freedom must be planned. This paper presents a statistical methodology of estimating discriminant functions for linear comparisons among k(<2) multivariate normal populations, and of testing their significance, when these populations have unequal covariance matrices.     

A Concise Formula to Compute General Orthogonal Contrast Coefficients

A proof is given of a general formula conjectured by ABT to calculate the values of orthogonal polynomials for the case of nonequidistant levels and unequal numbers of observations. Also, a general derivation of the contrast coefficients is given on the basis of the conditions of orthogonality only. The practicality of the formulae with regard to applications in analysis of variance and regression analysis is stressed.     

Foundations of spatial ecology: the reification of patches through quantitative description of patterns and pattern repetition

Insect populations tend to be patchy, and the nature of the patches is a critical component of ecology. Predator-prey interactions, coexistence of competing species, survival of rare species as habitat is destroyed, and damage to crops are just a few examples of spatially-dependent ecological processes. For want of tractable quantitative approaches, understanding of spatial ecology has lagged far behind recognition of its importance. We assert that a quantitative foundation of a spatial ecology involves the reification of patches as objects of study. We introduce two new measures of patch dynamics: total covariance for comparing degrees of patchiness between populations, and quantile variance for quantifying the constancy of dispersion patterns through time. These new measures, in combination with the long-established spatial covariance from geostatistics, comprise a rudimentary toolbox for reification of patches and empirical field studies in spatial ecology.     

数据处理方法不确定性对CO2通量组分估算的影响

基于中国陆地生态系统通量观测研究网络(ChinaFLUX)4个站点(2个森林站和2个草地站)的涡度相关通量观测资料,分析了CO₂通量数据处理过程中异常值剔除参数设置、夜间摩擦风速(u^*)临界值(u^*_c)确定及数据插补模型选择对CO₂通量组分估算的影响.结果表明： 3种数据处理方法均对净生态系统碳交换量(NEE)年总量估算有显著影响,其中u^*_c确定是影响NEE估算的重要因子;异常值剔除、u^*_c确定及数据插补模型选择导致NEE年总量估算偏差分别为0.62～21.31 g C·m^-2·a^-1(0.84%～65.31%)、4.06～30.28 g C·m^-2·a^-1(3.76%～21.58%)和0.69～27.73 g C·m^-2·a^-1(0.23%～55.62%),草地生态系统NEE估算对数据处理方法参数设置更敏感;数据处理方法不确定性引起的总生态系统碳交换量和生态系统呼吸年总量估算相对偏差分别为3.88%～11.41%和6.45%～24.91%.     

医学实验中常见设计类型的辨析及统计方法的合理选用

目的帮助医学研究工作者提高对常见统计应用识别能力,提高对统计学的正确利用率。方法：明确阐述秒种常见医学实验设计类型的异同点和应用场合,揭示常见统计应用错误的实质和危害性。结果：给出不适合用ｔ检验取代方差分析的充足理由和正确运用统计学的基本要领。结论：要提高实际工作者的统计学应用水平。需要经常对其进行统计培养,积极引导与统计学工作者开展科研协作。     

The effect of using approximate gametic variance covariance matrices on marker assisted selection by BLUP

Under additive inheritance, the Henderson mixed model equations (HMME) provide an efficient approach to obtaining genetic evaluations by marker assisted best linear unbiased prediction (MABLUP) given pedigree relationships, trait and marker data. For large pedigrees with many missing markers, however, it is not feasible to calculate the exact gametic variance covariance matrix required to construct HMME. The objective of this study was to investigate the consequences of using approximate gametic variance covariance matrices on response to selection by MABLUP. Two methods were used to generate approximate variance covariance matrices. The first method (Method A) completely discards the marker information for individuals with an unknown linkage phase between two flanking markers. The second method (Method B) makes use of the marker information at only the most polymorphic marker locus for individuals with an unknown linkage phase. Data sets were simulated with and without missing marker data for flanking markers with 2, 4, 6, 8 or 12 alleles. Several missing marker data patterns were considered. The genetic variability explained by marked quantitative trait loci (MQTL) was modeled with one or two MQTL of equal effect. Response to selection by MABLUP using Method A or Method B were compared with that obtained by MABLUP using the exact genetic variance covariance matrix, which was estimated using 15 000 samples from the conditional distribution of genotypic values given the observed marker data. For the simulated conditions, the superiority of MABLUP over BLUP based only on pedigree relationships and trait data varied between 0.1% and 13.5% for Method A, between 1.7% and 23.8% for Method B, and between 7.6% and 28.9% for the exact method. The relative performance of the methods under investigation was not affected by the number of MQTL in the model.     

Covariance Analysis of Chlorophyll Distribution in the Sundays River Estuary,Eastern Cape

Summary

An analysis of covariance performed on chlorophyll a distribution data from the Sundays River estuary identified five persistent water masses with significantly different chlorophyll a contents. These corresponded to different hydrodynamic regions within the estuary. The relationship between salinity and chlorophyll a was used to identify a transition zone between the low-salinity upper estuary and the brackish riverine inflow. Chlorophyll a concentrations ranged from <6 μg 1^?1 near the mouth to >100 μg 1^?1 in the middle and upper reaches. High variance of chlorophyll a data in this region was the result of temporal chlorophyll a fluctuations in two time scales. The first related to the daily ebb/tide and the second to the lunar spring/neap tidal cycle. Unlike its importance in larger and deeper estuaries, light played only a minor role in the horizontal distribution of chlorophyll a. The presence of a chlorophyll a maximum in the turbid low salinity region is explained in terms of the relatively constant photic depth/mixed depth ratio along the estuary and the high residence time of water in this region.     

Rank Covariance Methods for the Analysis of Survival Data

A procedure for comparing survival times between several groups of patients through rank analysis of covariance was introduced by WOOLSON and LACHENBRUCH (1983). It is a modification of Quade' rank analysis of covariance procedure (1967) and can be used for the analysis of right-censored data. In this paper, two additional modifications of Quade' original test statistic are proposed and compared to the original modification introduced by Woolson and Lachenbruch. These statistics are compared to one another and to the score test from Cox' proportional hazards model by way of a limited Monte Carlo study. One of the statistics, Q_R2, is recommended for general use for the rank analysis of covariance of right-censored survivorship data.