生态学研究中常见的统计学问题分析

在当代生态学研究中统计学方法的应用日益广泛,对于生态科学的发展和研究水平的提高起到了积极的作用。但是不容忽视的是在生态学研究应用统计学方法的过程中存在若干问题,主要表现在:1)回归分析方面的问题。直线回归方程用相关指数R²来描述直线回归的显著性;曲线回归方程往往用相关系数r来表示显著性;多元线性回归方程只对方程进行显著性检验,没有对每一个回归系数进行显著性检验。2)方差分析方面的问题。当处理数超过2时,不恰当地使用t_检验比较平均数的差异显著性。该文分析了产生这些问题的原因,提出了改进的对策。     

用中国汉族男性髓骨推断身高的研究

本文研究了以中国汉族男性航骨推断身高的方法．研究样本来自公安部第二研究所法医室近年收集的２４８对已知确切身高的汉族成年男性完整干燥防骨．依据人体测量学方法,共测量了１２项指标．相关分析表明,所测指标与身高的相关系数的统计学检验均有非常显著的意义．进而建立了航骨推断身高的直线回归方程及多元回归方程．并用３０对国人脱骨对各方程进行了盲测．结果表明,助骨推算身高的直线回归方程与多元日归方程所得结果与实际身高相近．效果较好．并且田骨推算身高的一元回归方程与多元回归方程的实用价值基本相同．     

用中国汉族男性髋骨推断向往身高的研究

本文研究了以中国汉族男性髋骨推断身高的方法。研究样本来自公安部第二研究所法医室近年收集的２４８对已知确切身高的汉族成年男性完整干燥髋骨。依据人体测量学方法,共测量了１２项指标。相关分析表明,所测指标与身高的相关系数的统计学检验均有非常显著的意义。进而建立了髋骨推断身高的直线回归方程及多元回归方程。并用３０对国人髋骨对各方程进行了盲测。结果表明,髋骨推算身高的直线回归方程。并用３０对国人髋骨对各方程     

从中指骨长度推算身高的研究

作者对近年在华南地区收集的,已知生前身高的汉族成年男性骨骼的中指骨近节、中节进行了测量。用直线回归方程、多元回归方程对从中指骨长度推算身高进行了研究。并用50例国人骨骼标本对这些推算身高的方法作了检验。结果表明,中指骨与四肢大型长骨,以及从中指骨长度推算身高的直线回归方程与多元回归方程,对推算身高的价值都是相同的。     

基于野外观测检验动物廊道选址模型的准确性——以白头叶猴为例

廊道构建是减少栖息地破碎化负面影响的重要策略之一。目前，已经有许多模型用于动物廊道的选址，而"选址模型是否能准确预测动物迁移的实际发生位置"一直是保护生物学最为关注的问题。最小成本路径模型（LCP）和条件最小成本廊道模型（CMTC）是两种较为常用的廊道选址模型。以白头叶猴（Trachypithecus leucocephalus）为目标物种，分别运用LCP和CMTC模拟生成白头叶猴迁移廊道，将模拟结果与野外观测廊道进行对比，检验两种方法的准确性。结果表明：与野外观测实际廊道相比，LCP模型模拟结果的完全准确率为46.7%，部分准确率为20%，完全不准确率为33.3%；CMTC模型模拟结果的完全准确率为26.7%，其余73.3%为部分准确，无完全不准确的结果；总体上看，CMTC廊道的准确率较LCP高，因而CMTC模型模拟白头叶猴实际迁移廊道位置的准确性优于LCP模型。输入"源"要素类型、阻力面栅格尺度设定、栖息地土地利用类型变化以及动物迁移行为复杂性4个因素是影响该模拟结果准确性的主要原因。     

鄂尔多斯高原植物群落季节生长格局模拟

影响大尺度空间生态模型模拟结果与资源管理整合的因素主要有两种:一是一些模型生态学意义不明确,二是一些模型所需要的生态输入信息过于复杂。建立一个基于基本的生态学公理且输入较为简单的生态学模型,便于更加有效地服务于资源环境管理。该模型用于模拟发生严重荒漠化的鄂尔多斯高原植物群落的季节及年生长、叶片投影盖度、蒸发系数。模型首先基于降雨、蒸散、渗漏及土壤水分特性与蒸发系数(k)的关系,采用迭代的计算方法,模拟植物群落蒸散与土壤可利用水分达到平衡状态时的k值,进而采用得到广泛验证的经验公式计算植物群落的其它参数。野外N PP观察数据对模型的验证表明:模拟结果与观察值相符较好。模拟结果表明:蒸发系数小于0 .35×10 - 2 ,显示鄂尔多斯高原气候较为干燥;叶片投影盖度低于5 0 % ;除东部的准格尔旗外,植物群落净第一性生产力均低于1t/(hm2·a) ,近90 %的N PP累积集中于5至8月份。根据该文的模拟结果,在进行植被恢复时,恢复植被密度必须低于5 0 % ,放牧密度以0 .8～2 .0个/hm2 羊单位为宜     

物种在异质性空间的传播可能性与传播速度研究

为了讨论单一物种在异质性景观中的空间传播可能性与传播速度,利用元包自动机模型模拟异质空间结构,建立边沿偶对近似模型,将其入侵速度结果与元宝自动机模型模拟的结果进行对比研究.本研究首先运用元包自动机建立理想模型,模拟物种在异质空间的传播可能性,之后比较在全局密度和局域密度变化时边沿偶对近似模型的入侵速度,以细胞自动机模型的模拟结果为依据,判断边沿偶对近似模型是否能够很好的预测细胞自动机模型的结果.     

基于地形因素的新疆荒漠植被-气候模型应用研究

本研究在新疆荒漠植被型分类的基础上,用植被与气候Holdridge生命带模型进行荒漠植被型的模拟,并用Kappa检验系数进行结果检验,模拟结果很差(0.19),将地形作为模拟模型具体考虑的一个因素,对重新分类的气候区进行二次植被模拟。二次模拟结果Kappa检验系数平均值为0.45,二次模拟整体荒漠植被型模拟结果的Kappa检验系数为0.64,极大地提高了模型模拟的准确度。模型模拟准确度的提高在于将影响新疆水分分配的地形因素作为改进Holdridge生命带模型的参数,该参数的引入为提高Holdridge生命带模型的准确度提供了新的思路,也为较准确地模拟新疆地区的植被提供了新途径。     

基于源库生长单位的温室番茄干物质生产-分配模拟

为了量化研究温室番茄果穗间干物质的分配,提高温室番茄栽培的效益,采用源库生长单位的测定方法,将经典的单叶同化物生产模型与GreenLab模型相结合,构建了干物质向源库生长单位内茎节、叶片、果实分配的动态模型,利用越冬茬、早春茬和春夏茬温室番茄各器官的干物质测定数据对模型进行了验证.结果表明:所构建的模型模拟结果与实测结果吻合性较好,不同茬口同化物生产模拟值与实测值的回归方程斜率为0.93,R~2为0.92;源库生长单位内茎节、叶片、果实以及根系的模拟值与实测值间回归方程斜率在0.85～0.89之间,其相对误差(R_e)均值分别为5.3%、5.6%、8.1%和3.6%,说明模型的模拟准确度较高,可为不同茬口温室番茄栽培管理提供理论依据和决策支持.     

改进Biome-BGC模型模拟哈佛森林地区水、碳通量

Biome-BGC模型通过耦合植被、土壤与大气间的水分与CO2交换过程,实现植被生产力的模拟,但土壤水平衡模块的不够完善,导致在长时间无降水情况下植被生产力模拟存在较大误差.针对这一问题,本文对Biome-BGC模型中土壤水分胁迫气孔导度方程、蒸散计算公式及土壤水分流失过程等3方面进行了改进和调整,利用改进的Biome-BGC模型模拟美国哈佛森林地区蒸散、植被生产力,并与地面通量观测值进行了比较.结果表明,改进后模拟精度有明显的提高,蒸散、植被生态系统生产力(NEE)与观测值间的决定系数分别由0.483和0.658提高到0.617和O.813,蒸散逐年均方根误差平均下降了48.7％,NEE逐年误差平方和平均下降了39.8％.改进后的模型模拟结果更接近观测值.     

When mechanism matters: Bayesian forecasting using models of ecological diffusion

Ecological diffusion is a theory that can be used to understand and forecast spatio‐temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white‐tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression‐based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.     

DELAYED‐RESPONSE PHYLOGENETIC CORRELATION: AN OPTIMIZATION‐BASED METHOD TO TEST COVARIATION OF CONTINUOUS CHARACTERS

A new phylogenetic comparative method is proposed, based on mapping two continuous characters on a tree to generate data pairs for regression or correlation analysis, which resolves problems of multiple character reconstructions, phylogenetic dependence, and asynchronous responses (evolutionary lags). Data pairs are formed in two ways (tree‐down and tree‐up) by matching corresponding changes, Δx and Δy. Delayed responses (Δy occurring later in the tree than Δx) are penalized by weighting pairs using nodal or branch‐length distance between Δx and Δy; immediate (same‐node) responses are given maximum weight. All combinations of character reconstructions (or a random sample thereof) are used to find the observed range of the weighted coefficient of correlation r (or weighted slope b). This range is used as test statistic, and the null distribution is generated by randomly reallocating changes (Δx and Δy) in the topology. Unlike randomization of terminal values, this procedure complies with Generalized Monte Carlo requirements while saving considerable computation time. Phylogenetic dependence is avoided by randomization without data transformations, yielding acceptable type‐I error rates and statistical power. We show that ignoring delayed responses can lead to falsely nonsignificant results. Issues that arise from considering delayed responses based on optimization are discussed.     

A Primer on Interpreting Regression Models

Abstract: We perceive a need for more complete interpretation of regression models published in the wildlife literature to minimize the appearance of poor models and to maximize the extraction of information from good models. Accordingly, we offer this primer on interpretation of parameters in single- and multi-variable regression models. Using examples from the wildlife literature, we illustrate how to interpret linear zero-intercept, simple linear, semi-log, log-log, and polynomial models based on intercepts, coefficients, and shapes of relationships. We show how intercepts and coefficients have biological and management interpretations. We examine multiple linear regression models and show how to use the signs (+, -) of coefficients to assess the merit and meaning of a derived model. We discuss 3 methods of viewing the output of 3-dimensional models (y, x₁, x₂) in 2-dimensional space (sheet of paper) and illustrate graphical model interpretation with a 4-dimensional logistic regression model. Statistical significance or Akaike best-ness does not prevent the appearance of implausible regression models. We recommend that members of the peer review process be sensitive to full interpretation of regression models to forestall bad models and maximize information retrieval from good models     

Forecasting of the flowering time for wild species observed at Guidonia, central Italy

It is well known that forecasting the flowering time of wild vegetation is useful for various sectors of human activity, particularly for all agricultural practices. Therefore, continuing previous work by Cenci et al., we will present here three new phenoclimatic models of the flowering time for a set of wild species, based on an original data sample of flowering dates for more than 500 species, observed at Guidonia (42° N in central Italy) by Montelucci in the period 1960–1982. However, on applying the bootstrap technique to each species sample to check its basic statistical parameters, we found only about 200 to have data samples with an approximately Gaussian distribution. Eventually only 57 species (subdivided into eight monthly subsets from February to September) were used to formulate the models satisfactorily. The flowering date (represented by the z variable), is expressed in terms of two variables x and y by a nonlinear equation of the form z=αx ^β +γy. The x variable represents either the degree-day sum (in model 1), or the daily-maximum-temperature sum (in model 2), or the daily-global-insolation sum (in model 3), while y for all three models corresponds to the rainy-day sum. Note that all summations involved in the computation of the variables x and y take place over a certain period of time (preceding the flowering phase), which is a parameter to be determined by the fitting procedure. This parameter, together with the threshold temperature (needed to compute the degree-days in model 1), represents the two implicit parameters of the process, thus the total number of parameters (including these last two) becomes respectively, five for model 1, and four for the other two models. The preliminary results of this work were reported at the XVI International Botanical Congress (1–7 August 1999, St. Louis, Missouri USA). Received: 4 November 1999 / Revised: 10 May 2000 / Accepted: 10 May 2000     

Effects of light leaf spot (Pyrenopeziza brassicae) on yield of winter oilseed rape (Brassica napus)

The relationship between development of light leaf spot and yield loss in winter oilseed rape was analysed, initially using data from three experiments at sites near Aberdeen in Scotland in the seasons 1991/92, 1992/93 and 1993/94, respectively. Over the three seasons, single-point models relating yield to light leaf spot incidence (% plants with leaves with light leaf spot) at GS 3.3 (flower buds visible) generally accounted for more of the variance than single-point models at earlier or later growth stages. Only in 1992/93, when a severe light leaf spot epidemic developed on leaves early in the season, did the single-point model for disease severity on leaves at GS 3.5/4.0 account for more of the variance than that for disease incidence at GS 3.3. In 1991/92 and 1992/3, when reasonably severe epidemics developed on stems, the single-point model for light leaf spot incidence (stems) at GS 6.3 accounted for as much of the variance. Two-point (disease severity at GS 3.3 and GS 4.0) and AUDPC models (disease incidence/severity) accounted for more of the variance than the single-point model based on disease incidence at GS 3.3 in 1992/93 but not in the other two seasons. Therefore, a simple model using the light leaf spot incidence at GS 3.3 (x) as the explanatory variable was selected as a predictive model to estimate % yield loss (y_r): y_r= 0.32x– 0.57. This model fitted all three data sets from Scotland, When data sets from Rothamsted, Rosemaund and Thurloxton in England were used to test it, this single-point predictive model generally fitted the data well, except when yield loss was clearly not related to occurrence of light leaf spot. However, the regression lines relating observed yield loss to light leaf spot incidence at GS 3.3 often had smaller slopes than the line produce, by the model based on Scottish data.     

Radioligand assays — Methods and applications. IV. Uniform regression of hyperbolic and linear radioimmunoassay calibration curves

In order to handle all types of radioimmunoassay (RIA) calibration curves obtained in our laboratory in the same way, we tried to find a non-linear expression for their regression which allows calibration curves with different degrees of curvature to be fitted. Considering the two boundary cases of the incubation protocol we derived a hyperbolic inverse regression function: x = a₁ya₀ + a_?1y^?1, where x is the total concentration of antigen, a_i constants, and y is the specifically bound radioactivity. An RIA evaluation procedure based on this function is described providing a fitted inverse RIA calibration curve and some statistical quality parameters. The latter are on an order which is normal for RIA systems. There is an excellent agreement between fitted and experimentally obtained calibration curves having a different degree of curvature.     

On the use of log‐transformation versus nonlinear regression for analyzing biological power laws

Xiao and colleagues re‐examined 471 datasets from the literature in a major study comparing two common procedures for fitting the allometric equation y = ax^b to bivariate data (Xiao et al., 2011). One of the procedures was the traditional allometric method, whereby the model for a straight line fitted to logarithmic transformations of the original data is back‐transformed to form a two‐parameter power function with multiplicative, lognormal, heteroscedastic error on the arithmetic scale. The other procedure was standard nonlinear regression, whereby a two‐parameter power function with additive, normal, homoscedastic error is fitted directly to untransformed data by nonlinear least squares. Xiao and colleagues articulated a simple (but explicit) protocol for fitting and comparing the alternative models, and then used the protocol to examine each of the datasets in their compilation. The traditional method was said to provide a better fit in 69% of the cases and an equivalent fit in another 15%, so the investigation appeared to validate findings from a large majority of prior studies on allometric variation. However, focus for the investigation by Xiao and colleagues was overly narrow, and statistical models apparently were not validated graphically in the scale of measurement. The present study re‐examined a subset of the cases using a larger pool of candidate models and graphical validation, and discovered complexities that were overlooked in their investigation. Some datasets that appeared to be described better by the traditional method actually were unsuited for use in an allometric analysis, whereas other datasets were not described adequately by a two‐parameter power function, regardless of how the model was fitted. Thus, conclusions reached by Xiao and colleagues are not well supported and their paradigm for fitting allometric equations is unreliable. Future investigations of allometric variation should adopt a more holistic approach and incorporate graphical validation on the original arithmetic scale. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 113 , 1167–1178.     

The Role of Polarization on 2D Plasmonic Crystals

In this paper, the polarization effects on surface plasmon resonance (SPR) in azimuthally rotated 2D square lattice plasmonic crystal (PCL) are reported. By controlling the polarization angle (α) of the incoming beam, the SPR coupling strength can be fully enhanced when optimized α is used for different momentum lattice vectors (x-, y-axis and diagonal direction). This value can be obtained by adjusting the polarization angle until the deepest dip in SPR reflectivity spectrum can be observed. This will lead to a much easier way for determining the optimum surface plasmon polariton excitation condition for each crystal momentum in 2D PCL.     

River phytoplankton prediction model by Artificial Neural Network: Model performance and selection of input variables to predict time-series phytoplankton proliferations in a regulated river system

In this study, a comparison between statistical regression model and Artificial Neural Network (ANN) is given on the effectiveness of ecological model of phytoplankton dynamics in a regulated river. From the results of the study, the effectiveness of ANN over statistical method was proposed. Also feasible direction of increasing ANN models' performance was provided. A hypertrophic river data was used to develop prediction models (chlorophyll a (chl. a) 41.7 ± 56.8 μg L^− 1; n = 406). Higher time-series predictability was found from the ANN model. Failure of statistical methods would be due to the complex nature of ecological data in the regulated river ecosystems. Reduction of ANN model size by decreasing the number of input variables according to the sensitivity analysis did not have effectiveness with respect to the predictability on testing data set (RMSE of the ANN with all 27 variables, 25.7; 47.9 from using 2 highly sensitive variables; 42.9 from using 5 sensitive variables; 33.1 from using 15 variables). Even though the ANN model presented high performance in prediction accuracy, more efficient methods of selecting feasible input information are strongly requested for the prediction of freshwater ecological dynamics.     

Linkage between loci of quantitative traits and marker loci: multi-trait analysis with a single marker

An efficient approach to increase the resolution power of linkage analysis between a quantitative trait locus (QTL) and a marker is described in this paper. It is based on a counting of the correlations between the QTs of interest. Such correlations may be caused by the segregation of other genes, environmental effects and physiological limitations. Let a QT locus A/a affect two correlated traits, x and y. Then, within the framework of mixture models, the accuracy of the parameter estimates may be seriously increased, if bivariate densities f _aa(x, y), f _Aa(x, y) and f _AA(x, y) rather than the marginals are considered as the basis for mixture decomposition. The efficiency of the proposed method was demonstrated employing Monte-Carlo simulations. Several types of progeny were considered, including backcross, F₂ and recombinant inbred lines. It was shown that provided the correlation between the traits involved was high enough, a good resolution to the problem is possible even if the QTL groups are strongly overlapping for their marginal densities.