三参数增长模型拟合:以季风常绿阔叶林中两个优势乔木种群为例

Logistic、Mitscherlich、Gompertz方程是一类三参数饱和增长曲线模型,广泛地应用于许多学科领域．本文基于logistic方程饱和值K估计的三点法、四点法,推导出Mitscherlich、Gompertz方程K值的三点法、四点法估计公式,并以南亚热带季风常绿阔叶林中两种优势乔木厚壳桂、黄果厚壳桂种群为例,先用三点法或四点法估计出K值,再通过线性回归与非线性回归相结合的方法,可获得三个增长模型中三个参数的最优无偏估计．实例研究表明,两个优势种群增长数据均符合三个增长模型,但更符合增长曲线呈S形的logistic、Gompertz方程,且以logistic方程最适合于观察;黄果厚壳桂种群增长快于厚壳桂种群．     

Structured latent growth curves for twin data.

We describe methods to fit structured latent growth curves to data from MZ and DZ twins. The well-known Gompertz, logistic and exponential curves may be written as a function of three components - asymptote, initial value, and rate of change. These components are allowed to vary and covary within individuals in a structured latent growth model. Such models are highly economical, requiring a small number of parameters to describe covariation across many occasions of measurement. We extend these methods to analyse longitudinal data from MZ and DZ twins and focus on the estimation of genetic and environmental variation and covariation in each of the asymptote, initial and rate of growth factors. For illustration, the models are fitted to longitudinal Bayley Infant Mental Development Scale data published by McArdle (1986). In these data, all three components of growth appear strongly familial with the majority of variance associated with the shared environment; differences between the models were not great. Occasion-specific residual factors not associated with the curve components account for approximately 40% of variance of which a significant proportion is additive genetic. Though the growth curve model fit less well than some others, they make restrictive, falsifiable predictions about the mean, variance and twin covariance of other (not yet measured) occasions of measurement.     

Evaluation and interpretation of results for three cross-over designs

In cross-over designs, individual sequences of treatments are applied to the animals. Within such designs it is possible that every treatment could modify the effect of the subsequent treatment applied to the same animal. We compared three cross-over designs each with three treatments, three periods, and two blocks. This comparison was done with respect to the variance of the estimations of the effects and its biases caused by the interactions between the treatment and the carry over effect of the foregoing treatment. Moreover, different methods of estimating variance components and calculating the degrees of freedom were compared by means of simulation. If the animal variance component is small, then the bias of the REML estimator of the variance components is greater than one of the widespread ANOVA-estimator called 'TYPE3'. But nevertheless, the mean squared error of this estimation is smaller in the case of REML in comparison to ANOVA. Therefore, the REML method should be preferred. For calculating the degrees of freedom, the Kenward-Roger method should be used. After applying this method, the true significance level is almost equal to its required value, but if the Satterthwaite method is used, the true significance level will be too high. If the interaction (treatment × carry over) is ignored in the model although it exists, the standard error of the treatment effect estimation is too great, and, therefore, the true significance level is too small. The methods which have been evaluated are available in the SAS-procedure MIXED (<citeref rid="b9">SAS Institute, 1999a</citeref>). To assist the investigation of cross-over designs by using this software, we developed programs for data management and data analysis. These programs are available from the first author.     

滇南人工种子繁殖灯台树林木生长状况研究

以不同环境条件下人工灯台树林木50cm处直径、株高、枝下高、分台数、分枝数和冠幅的实测数据为基础,用方差分析、多重比较分析和均值比较等方法研究了灯台树的生长状况。结果表明,灯台树幼林植株长势具有随年均温、最冷月温和相对湿度递增,但随海拔高度递减,呈现良好的长势。     

A test of quantitative genetic theory using Drosophila- effects of inbreeding and rate of inbreeding on heritabilities and variance components

Inbreeding is expected to decrease the heritability within populations. However, results from empirical studies are inconclusive. In this study, we investigated the effects of three breeding treatments (fast and slow rate of inbreeding - inbred to the same absolute level - and a control) on heritability, phenotypic, genetic and environmental variances of sternopleural bristle number in Drosophila melanogaster. Heritability, and phenotypic, genetic and environmental variances were estimated in 10 replicate lines within each of the three treatments. Standard least squares regression models and Bayesian methods were used to analyse the data. Heritability and additive genetic variance within lines were higher in the control compared with both inbreeding treatments. Heritabilities and additive genetic variances within lines were higher in slow compared with fast inbred lines, indicating that slow inbred lines retain more evolutionary potential despite the same expected absolute level of inbreeding. The between line variance was larger with inbreeding and more than twice as large in the fast than in the slow inbred lines. The different pattern of redistribution of genetic variance within and between lines in the two inbred treatments cannot be explained invoking the standard model based on selective neutrality and additive gene action. Environmental variances were higher with inbreeding, and more so with fast inbreeding, indicating that inbreeding and the rate of inbreeding affect environmental sensitivity. The phenotypic variance decreased with inbreeding, but was not affected by the rate of inbreeding. No inbreeding depression for mean sternopleural bristle number was observed in this study. Considerable variance between lines in additive genetic variance within lines was observed, illustrating between line variation in evolutionary potential.     

Quantifying the Length and Variance of the Eukaryotic Cell Cycle Phases by a Stochastic Model and Dual Nucleoside Pulse Labelling

A fundamental property of cell populations is their growth rate as well as the time needed for cell division and its variance. The eukaryotic cell cycle progresses in an ordered sequence through the phases and and is regulated by environmental cues and by intracellular checkpoints. Reflecting this regulatory complexity, the length of each phase varies considerably in different kinds of cells but also among genetically and morphologically indistinguishable cells. This article addresses the question of how to describe and quantify the mean and variance of the cell cycle phase lengths. A phase-resolved cell cycle model is introduced assuming that phase completion times are distributed as delayed exponential functions, capturing the observations that each realization of a cycle phase is variable in length and requires a minimal time. In this model, the total cell cycle length is distributed as a delayed hypoexponential function that closely reproduces empirical distributions. Analytic solutions are derived for the proportions of cells in each cycle phase in a population growing under balanced growth and under specific non-stationary conditions. These solutions are then adapted to describe conventional cell cycle kinetic assays based on pulse labelling with nucleoside analogs. The model fits well to data obtained with two distinct proliferating cell lines labelled with a single bromodeoxiuridine pulse. However, whereas mean lengths are precisely estimated for all phases, the respective variances remain uncertain. To overcome this limitation, a redesigned experimental protocol is derived and validated in silico. The novelty is the timing of two consecutive pulses with distinct nucleosides that enables accurate and precise estimation of both the mean and the variance of the length of all phases. The proposed methodology to quantify the phase length distributions gives results potentially equivalent to those obtained with modern phase-specific biosensor-based fluorescent imaging.     

DNA synthesis studies in pre-meiotic mouse oogenesis

DNA fiber autoradiography was used in mouse oogenesis to test Callan's hypothesis that a longer S phase results from a reduction in the number of active initiation sites. The data indicated that the premeiotic increase in the duration of S phase in mouse oogenesis was characterized by a rapid initial rate of chain growth and a larger replicon size when compared with replicating DNA of somatic mouse cells. These findings were at variance with those in mouse spermatogenesis and also did not support the Callan hypothesis of activation site repression.     

Quantifying the impact of fixed effects modeling of clusters in multiple imputation for cluster randomized trials

In cluster randomized trials (CRTs), identifiable clusters rather than individuals are randomized to study groups. Resulting data often consist of a small number of clusters with correlated observations within a treatment group. Missing data often present a problem in the analysis of such trials, and multiple imputation (MI) has been used to create complete data sets, enabling subsequent analysis with well-established analysis methods for CRTs. We discuss strategies for accounting for clustering when multiply imputing a missing continuous outcome, focusing on estimation of the variance of group means as used in an adjusted t-test or ANOVA. These analysis procedures are congenial to (can be derived from) a mixed effects imputation model; however, this imputation procedure is not yet available in commercial statistical software. An alternative approach that is readily available and has been used in recent studies is to include fixed effects for cluster, but the impact of using this convenient method has not been studied. We show that under this imputation model the MI variance estimator is positively biased and that smaller intraclass correlations (ICCs) lead to larger overestimation of the MI variance. Analytical expressions for the bias of the variance estimator are derived in the case of data missing completely at random, and cases in which data are missing at random are illustrated through simulation. Finally, various imputation methods are applied to data from the Detroit Middle School Asthma Project, a recent school-based CRT, and differences in inference are compared.     

Population differentiation in G matrix structure due to natural selection in Rana temporaria

The additive genetic variance-covariance matrix (G) is a concept central to discussions about evolutionary change over time in a suite of traits. However, at the moment we do not know how fast G itself changes as a consequence of selection or how sensitive it is to environmental influences. We investigated possible evolutionary divergence and environmental influences on G using data from a factorial common-garden experiment where common frog (Rana temporaria) tadpoles from two divergent populations were exposed to three different environmental treatments. G-matrices were estimated using an animal model approach applied to data from a NCII breeding design. Matrix comparisons using both Flury and multivariate analysis of variance methods revealed significant differences in G matrices both between populations and between treatments within populations, the former being generally larger than the latter. Comparison of levels of population differentiation in trait means using Q(ST) indices with that observed in microsatellite markers (F(ST)) revealed that the former values generally exceeded the neutral expectation set by F(ST). Hence, the results suggest that intraspecific divergence in G matrix structure has occurred mainly due to natural selection.     

Introduction of a boost of Legionella pneumophila into a stagnant-water model by heat treatment

An environmentally representative stagnant-water model was developed to monitor the growth dynamics of Legionella pneumophila. This model was evaluated for three distinct water treatments: untreated tap water, heat-treated tap water, and heat-treated tap water supplemented with Pseudomonas putida, a known biofilm-forming bacterium. Bringing heat-treated tap water after subsequent cooling into contact with a densely formed untreated biofilm was found to promote the number of L. pneumophila by 4 log units within the biofilm, while the use of untreated water only sustained the L. pneumophila levels. Subsequent colonization of the water phase by L. pneumophila was noticed in the heat-treated stagnant-water models, with concentrations as high as 1 x 10(10) mip gene copies L(-1) stagnant water. Denaturing gradient gel electrophoresis in combination with clustering analysis of the prokaryotic community in the water phase and in the biofilm phase suggests that the different water treatments induced different communities. Moreover, boosts of L. pneumophila arising from heat treatment of water were accompanied by shifts to a more diverse eukaryotic community. Stimulated growth of L. pneumophila after heating of the water may explain the rapid recolonization of L. pneumophila in water systems. These results highlight the need for additional or alternative measures to heat treatment of water in order to prevent or abate potential outbreaks of L. pneumophila.     

Improved Horvitz–Thompson Estimation of Model Parameters from Two-phase Stratified Samples: Applications in Epidemiology

The case-cohort study involves two-phase samplings: simple random sampling from an infinite superpopulation at phase one and stratified random sampling from a finite cohort at phase two. Standard analyses of case-cohort data involve solution of inverse probability weighted (IPW) estimating equations, with weights determined by the known phase two sampling fractions. The variance of parameter estimates in (semi)parametric models, including the Cox model, is the sum of two terms: (i) the model-based variance of the usual estimates that would be calculated if full data were available for the entire cohort; and (ii) the design-based variance from IPW estimation of the unknown cohort total of the efficient influence function (IF) contributions. This second variance component may be reduced by adjusting the sampling weights, either by calibration to known cohort totals of auxiliary variables correlated with the IF contributions or by their estimation using these same auxiliary variables. Both adjustment methods are implemented in the R survey package. We derive the limit laws of coefficients estimated using adjusted weights. The asymptotic results suggest practical methods for construction of auxiliary variables that are evaluated by simulation of case-cohort samples from the National Wilms Tumor Study and by log-linear modeling of case-cohort data from the Atherosclerosis Risk in Communities Study. Although not semiparametric efficient, estimators based on adjusted weights may come close to achieving full efficiency within the class of augmented IPW estimators.     

Comparison of different treatments of rare species in canonical correspondence analysis

运用吕梁山南段植物群落及其环境调查数据,比较研究不同稀有种处理(剔除稀有种、稀有种不做处理与降低稀有种权重3种方法处理)对典范对应分析(CCA)排序结果的影响,并用Spearman秩相关系数检验对应排序轴的相关性。结果表明3种方法的分析效果基本一致,但它们对环境因子的解释趋势有差异。基于环境数据、物种数据和样方数据的排序轴相关分析结果显示:未处理稀有种的CCA与降低稀有种权重的CCA吻合度高于剔除稀有种的CCA与降低稀有种权重的CCA的吻合度,未处理稀有种的CCA与降低稀有种权重的CCA的前4轴呈极显著的一一对应关系;剔除稀有种的CCA和降低稀有种权重的CCA仅在基于环境数据和样方数据分析时前3轴呈极显著的一一对应关系,而在基于物种数据的相关分析时前4轴的对应相关性不显著。从物种-环境关系的解释量上来看,降低稀有种权重的CCA最优,剔除稀有种的CCA和未处理稀有种的CCA次之。结合对应排序轴的相关性分析和物种-环境关系累计解释量来看,这3种稀有种处理方法在准确地揭示物种与环境关系时的顺序依次为:降低稀有种权重>对稀有种不做处理>剔除稀有种。     

Colonyzer: automated quantification of micro-organism growth characteristics on solid agar

Background  

High-throughput screens comparing growth rates of arrays of distinct micro-organism cultures on solid agar are useful, rapid methods of quantifying genetic interactions. Growth rate is an informative phenotype which can be estimated by measuring cell densities at one or more times after inoculation. Precise estimates can be made by inoculating cultures onto agar and capturing cell density frequently by plate-scanning or photography, especially throughout the exponential growth phase, and summarising growth with a simple dynamic model (e.g. the logistic growth model). In order to parametrize such a model, a robust image analysis tool capable of capturing a wide range of cell densities from plate photographs is required.     

Insights from the clustering of microarray data associated with the heart disease

Heart failure (HF) is the major of cause of mortality and morbidity in the developed world. Gene expression profiles of animal model of heart failure have been used in number of studies to understand human cardiac disease. In this study, statistical methods of analysing microarray data on cardiac tissues from dogs with pacing induced HF were used to identify differentially expressed genes between normal and two abnormal tissues. The unsupervised techniques principal component analysis (PCA) and cluster analysis were explored to distinguish between three different groups of 12 arrays and to separate the genes which are up regulated in different conditions among 23912 genes in heart failure canines'' microarray data. It was found that out of 23912 genes, 1802 genes were differentially expressed in the three groups at 5% level of significance and 496 genes were differentially expressed at 1% level of significance using one way analysis of variance (ANOVA). The genes clustered using PCA and clustering analysis were explored in the paper to understand HF and a small number of differentially expressed genes related to HF were identified.     

Daily stem growth patterns in irrigated Eucalyptus globulus and E. nitens in relation to climate

Daily increments in stem radius were determined from hourly dendrometer measurements in each of three irrigated Eucalyptus nitens and E. globulus trees. Multiple regressions determined from daily weather variables accounted for 40–50% of the variance in increment. The use of weather variables lagged by 1–2 days increased the variance explained. The diurnal variation in stem radius was resolved into three mathematically defined phases: shrinkage, recovery and increment. The positive daily net increment in stem radius, by definition, occurred in the increment phase. Average weather conditions during this phase (predominantly night-time) did not explain any more variance in increment than the average daily conditions, determined over a 24 h period. Daily increment was resolved into a rate of stem radius increase during the increment phase and the duration (hours) of that phase. Significant species by month interactions were evident with growth in summer characterised by faster rates of stem expansion over shorter time periods within each diurnal cycle. E. nitens tended to have longer increment phases in spring and autumn, and faster phase rates in autumn than E. globulus. Interactions between weather variables and cambial growth were complicated and varied over the year. The correlation between temperature and stem growth varied from positive in spring to zero or negative during summer. The data indicate a need to understand weather-by- climate interactions at the level of whole tree physiology in order to fully understand the effect of weather on cambial activity and therefore stem increment and wood properties. Received: 12 April 1999 / Accepted: 6 July 1999     

A power analysis of microsatellite-based statistics for inferring past population growth

We present results concerning the power to detect past population growth using three microsatellite-based statistics available in the current literature: (1) that based on between-locus variability, (2) that based on the shape of allele size distribution, and (3) that based on the imbalance between variance and heterozygosity at a locus. The analysis is based on the single-step stepwise mutation model. The power of the statistics is evaluated for constant, as well as variable, mutation rates across loci. The latter case is important, since it is a standard procedure to pool data collected at a number of loci, and mutation rates at microsatellite loci are known to be different. Our analysis indicates that the statistic based on the imbalance between allele size variance and heterozygosity at a locus has the highest power for detection of population growth, particularly when mutation rates vary across loci.     

Numerical simulation and graphical analysis of in vitro benign tumor growth: application of single-particle state bosonic matter equation with length scaling

We describe the application of a non-linear single-particle state bosonic condensate equation to simulate multicellular tumor growth by treating it as a coupling of two classical wave equations with real components. With one component representing the amplitude of the cells in their volume growth phase and the other representing the amplitude of the cells in their proliferation or mitosis phase, the two components of the coupled equation feed each other during the time evolution and are coupled together through diffusion and other linear and non-linear terms. The features of quiescent and necrotic cells, which result from poor nutrient diffusion into a tumor, have been found to correspond quite well to experimental data when they are modeled as depending on higher cell density. Classical hallmarks of benign tumor growth, such as the initial rapid growth, followed by a dramatic collapse in the proliferating cell count and a strong re-growth thereafter appear quite encouragingly in the theoretical results. A tool for graphical analysis of the tumor simulation results has been developed to provide morphological information about tumors at various growth stages. The model and the graphical analysis can be extended further to create an effective tool to predict/monitor tumor growth. 1 Screen shot from the graphical analysis tool showing simulation results after ten days: clustering of cells of the tumor (up); cell density profile (down) Dedicated to Professor Dr. Paul von Ragué Schleyer on the occasion of his 75th birthday     

Effect of growth phase on survival of bromegrass suspension cells following cryopreservation and abiotic stresses

BACKGROUND AND AIMS: Cryopreservation is a practical method of preserving plant cell cultures and their genetic integrity. It has long been believed that cryopreservation of plant cell cultures is best performed with cells at the late lag or early exponential growth phase. At these stages the cells are small and non-vacuolated. This belief was based on studies using conventional slow prefreezing protocols and survival determined with fluorescein diacetate staining or 2,3,5-triphenyltetrazolium chloride assays. This classical issue was revisited here to determine the optimum growth phase for cryopreserving a bromegrass (Bromus inermis) suspension culture using more recently developed protocols and regrowth assays for determination of survival. METHODS: Cells at different growth phases were cryopreserved using three protocols: slow prefreezing, rapid prefreezing and vitrification. Stage-dependent trends in cell osmolarity, water content and tolerance to freezing, heat and salt stresses were also determined. In all cases survival was assayed by regrowth of cells following the treatments. KEY RESULTS: Slow prefreezing and rapid prefreezing protocols resulted in higher cell survival compared with the vitrification method. For all the protocols used, the best regrowth was obtained using cells in the late exponential or early stationary phase, whereas lowest survival was obtained for cells in the late lag or early exponential phase. Cells at the late exponential phase were characterized by high water content and high osmolarity and were most tolerant to freezing, heat and salt stresses, whereas cells at the early exponential phase, characterized by low water content and low osmolarity, were least tolerant. CONCLUSIONS: The results are contrary to the classical concept which utilizes cells in the late lag or early exponential growth phase for cryopreservation. The optimal growth phase for cryopreservation may depend upon the species or cell culture being cryopreserved and requires re-investigation for each cell culture. Stage-dependent survival following cryopreservation was proportionally correlated with the levels of abiotic stress tolerance in bromegrass cells.     

Metabolomic and physiological changes of <Emphasis Type="Italic">Chlamydomonas reinhardtii</Emphasis> (Chlorophyceae,Chlorophyta) during batch culture development

During mixotrophic batch culturing, the microalga Chlamydomonas reinhardtii goes through S-shaped growth kinetics and cells consistently transit from division to death. Photosynthesis and respiration had two simultaneous maxima at the first half of the exponential growth phase and at the border of the stationary phase. GC-MS analysis detected about 300 compounds of which about 100 were identified. Differences in metabolite profiles were observed between cells sampled at different time points of the growth curve. Several data mining methods clearly indicated that metabolomes tended to group together in a time-dependent manner. Clustering analysis revealed three major groups of metabolites varied in concentration dynamic. The alterations in lipophilic compounds and carbohydrates took place even within the same phase of culture growth, which indicated complex rearrangements in cell biochemistry and physiology. Special attention was paid to alterations in the ratios between metabolite groups. The most significant ratio changes were discovered for pools of amino and fatty acids.