土壤速效养分空间变异的尺度效应

在GIS技术支持下,运用经典统计学和地统计学的方法,从经典统计分析、变异函数和Kriging插值图等方面探讨了禹城市耕地土壤速效磷(AP)、速效钾(AK)在县级和镇级两个不同采样尺度下的空间变异特征.结果表明:在两个采样尺度下,AP、AK都服从对数正态分布,它们的变异系数范围为26.5%～36.6%,均属中等变异强度,随着采样尺度的缩小,土壤AP、AK的变异系数都增大.两个采样尺度下,土壤AP和AK均在一定范围内存在空间相关关系,县级采样尺度下土壤AP和AK的空间自相关距离较大,分别为9.0 km和26.5 km,镇级采样尺度下土壤AP和AK的空间自相关距离明显变小,分别为1.7 km和2.8 km.两个采样尺度下的土壤AP和AK受结构性因素和随机性因素的影响,表现出明显不同的分布规律.     

北京地区植被景观中斑块大小的分布特征

利用GIS软件ARC/INFO将北京地区的1∶20万植被图数字化，并提取各斑块的面积信息。该图包含72个基本的斑块类型，它们又分属于森林、灌丛、草地、果园、农田和水体6大类型。这些大类又分别包含20、28、4、7、11和2个基本类型。选用斑块个数、总面积、平均斑块面积、标准差、变异系数、中值、最大斑块面积、最小斑块面积、极差和偏态系数等几个描述统计量，以及Γ-分布、对数正态分布、Weibull分布、指数分布和正态分布等5个概率分布来刻画斑块大小的分布特征。结果表明除具有很少斑块的少数基本类型以外，其它基本类型以及所有6个大类的斑块大小的分布都不是对称的，而是右偏的。因此，普通的正态分布不能对它们加以刻画；其他4种概率分布也只能刻画部分类型，并且服从对数正态分布的类型最多，服从负指数分布的斑块类型最少。     

北京地区植被景观中斑块大小的分布特征

利用GIS软件ARC／INFO将北京地区的1：20万植被图数字化,并提取各斑块的面积信息。该图包含72个基本的斑块类型,它们又分属于森林、灌丛、草地、果园、农田和水体6大类型。这些大类又分别包含20、28、4、7、11和2个基本类型。选用斑块个数、总面积、平均斑块面积、标准差、变异系数、中值、最大斑块面积、最小斑块面积、极差和偏态系数等几个描述统计量,以及厂一分布、对数正态分布、Weibull分布、指数分布和正态分布等5个概率分布来刻画斑块大小的分布特征。结果表明：除具有很少斑块的少数基本类型以外,其它基本类型以及所有6个大类的斑块大小的分布都不是对称的,而是右偏的。因此,普通的正态分布不能对它们加以刻画;其他4种概率分布也只能刻画部分类型,并且服从对数正态分布的类型最多,服从负指数分布的斑块类型最少。     

中亚热带杉木人工林细根生物量空间变异与取样数量估算

林木细根生物量具有一定的空间异质性,因此采用合理的细根取样策略对精确估算细根生物量十分重要。通过在福建省三明杉木人工林林内采用土钻法随机选取100个取样点,分析不同细根类型(杉木、林下植被、总细根)生物量的空间变异特征,并对细根生物量所需的取样数量进行估计。结果表明:不同细根类型单位面积生物量随径级(0—1、1—2 mm)及土层深度的增加变异增大,所需的取样数量也相应增加。Shapiro-Wilk检验表明,仅0—2 mm杉木细根和总细根单位面积生物量符合正态分布,其余各个细根类型不同径级不同土层单位面积生物量均不符合正态分布,均呈明显的右偏分布。蒙特卡罗统计模拟分析表明:在置信水平为95%、精度为80%的条件下,直径为0—1 mm、1—2 mm和0—2 mm的细根,杉木采集95、96、32个样品可以满足测定单位面积生物量的需要,林下植被分别采集98、98、63个样品可以满足测定单位面积生物量的需要,而总细根分别采集93、93、18个样品可以满足测定单位面积生物量的需要。     

南亚热带森林群落种-多度的对数正态分布模型研究

通过对地处南亚热带的广东省黑石顶自然保护区森林群落的定点研究结果的分析表明：当用１,２,３,…分组每种个体数ｒ时,５个不同类型的群落样地的种一多度分布的直方图都呈明显的倒Ｊ－形;经Ｐｒｅｓｔｏｎ“倍程（ｏｃｔａｖｅｓ）”法分组ｒ后,其种－多度都服从对数正态分布。由种－多度模型可以推出另一新的模型一个体一多度分布模型,即Ｉ（Ｒ）＝２R0ＳＯＥＸＰ［［１ｎ２）２／４ａ２〕ＥＸＰ｛－ａ２（Ｒ－（ＲＯ＋１ｎ２／２ａ２）］２｝,它也符合对数正态分布。另外,还运用积分方法推导出估计总体（整个群落）中总种数Ｓ*和总个体数Ｉ*理论值的公式,用此公式估计的结果较为合理。     

闽北地区森林群落物种多样性的测定

采用8个物种多样性指数对闽北地区的8个森林群落类型物种多样性进行测定,并选用4个种一多度关系模型(对数正态分布、Weibull分布、对数级数分布、生态位优先占领模型)分析其物种-多度关系,把多样性指数与对数正态分布、Weibull分布和生态位优先占领模型的有关参数进行线性回归,以分析多度模型参数描述物种多样性的可行性。结果表明：(1)多数物种多样性指数对群落的测度是一致的,(2)对数正态分布、Weibull分布和生态位优先占领模型对8个群落的物种多度拟合效果很好;(3)对数正态分布、Weibull分布和生态位优先占领模型有关模型参数与部分物种多样性指数的线性关系达显著或极显著水平。通过闽北地区8个类型森林群落物种多样性指数测定,使生物多样性较准确地数量化,同时还说明采用改进单纯形法进行非线性分布函数的拟合是简单有效的,可推广应用。     

不同采样密度下县域森林碳储量仿真估计

采用浙江省台州市仙居县森林资源二类调查样地实测地上部分碳储量数据,结合Landsat TM影像数据,利用序列高斯协同仿真(SGCS)算法、序列高斯块协同仿真(SGBCS)算法,以4种地面采样密度(SD)SD_1=0.012%、SD_2=0.010%、SD_3=0.007%、SD_4=0.005%,估计全县森林碳储量及其空间分布,分析不同地面采样密度对区域森林碳储量及其分布格局估计精度的影响。结果表明:1)不同采样密度下SGCS和SGBCS估计的森林碳储量分布趋势相似,SGCS估计在采样密度为SD_2时可以满足精度要求,且均值与实测最相符;SGBCS估计受采样密度影响较小,在四种采样密度下均可满足精度要求。2)SGCS、SGBCS估计的不确定性随着采样密度的降低均呈现出整体升高的趋势,增长速率在SD_2采样密度时最低,相对SD_1分别升高1.08%、-1.71%;当SGBCS算法的采样密度由SD_2变为SD_3时,样地数的减少对不确定性影响最大,但对区域空间变异格局估计没有实质性影响。3)将采样密度控制在SD_2(0.010%)水平,利用SGCS和SGBCS算法均能得到准确可靠的森林碳储量及其分布信息,同时能节省至少20%左右的森林调查工作量。     

关中平原田间土壤含水量的空间变异性

为了明确田块尺度土壤含水量的空间变异特征,制定合理准确的土壤采样方法,支持田间精准灌溉,分7个日期对陕西省杨凌区曹新庄试验区土壤样品进行采集,利用经典统计学和地统计学方法,分析了0～60 cm不同土层土壤含水量的空间变异特点。结果表明: 田块尺度土壤含水量空间分布呈弱变异或中等偏弱变异;土壤含水量在11.7%～20.1%时,其值越低,空间变异性越强。采样间距显著影响土壤含水量空间变异性的计算精度,采样间距设置为东西方向间距27 m和南北方向间距9 m时的土壤含水量变异系数比采样间距设置为东西方向间距9 m和南北方向间距18 m大3.3%。随着采样密度的增大,土壤含水量分布的等值线变化增大;表征田块尺度土壤含水量空间变异性最少的网格数量为21个点。采样间距为东西方向间距18 m和南北方向间距9 m时,田块尺度土壤含水量具有较高的空间相关性,田块中间位置的土壤含水量比四周高3%～5%。本研究可为关中平原田间测定土壤含水量确定合理的采样方法,并为实现农业精准灌溉提供参考。     

基于估计准度和调查费用的渔业资源调查采样设计优化

合理的调查采样设计及优化可以降低调查费用,确保调查数据的准确性,实现调查采样效益的最大化。本研究量化了调查费用,在考虑估计准确度基础上,将调查费用作为评价指标加入到采样设计优化中,应用计算机模拟重抽样方法和模拟退火算法进行航线规划。基于2013—2015年春、秋季海州湾渔业资源底拖网调查数据,使用克里金插值法模拟了该海域星康吉鳗(Conger myriaster)、方氏云鳚(Enedrias fangi)和大泷六线鱼(Hexagrammos otakii)在春、秋季的相对资源量分布,作为其分布的“真值”。应用分层随机抽样模拟不同样本量下的调查采样,估计各目标鱼种的资源量指数,以相对偏差(RB)的绝对值来评价目标鱼种资源量指数估计的准确度,以调查费用、超标概率作为费用评价指标,以综合评价指标(IEI)作为衡量准确度和费用的综合指标。结果表明: 各鱼种资源量指数估计的RB值随样本量增加而降低,但各鱼种的RB值不同。不同评价指标确定的最优站位数不同,按RB值确定的最优站位数较高,调查费用超过预算;按调查费用确定的站位数较低,但无法有效保证资源量指数估计的准确性;按IEI确定的最优站位数处于中间水平,能兼顾调查费用和资源量指数估计准度。综合考虑调查费用和航线规划的采样设计不仅能确定最优站位数,还可以确定调查设计的站位空间位置、站位调查顺序和调查费用。调查者可以根据实际费用预算,从模拟方案中选择费用低、RB低的理想采样设计方案开展调查。     

黑河中游绿洲区不同土地利用类型表层土壤水分空间变异的尺度效应

了解表层土壤水分空间变异及其尺度效应,可获取土壤水分真实变异,并可为客观揭示土壤水分空间变异制定合理采样方案提供参考.用“再采样”方法对黑河中游张掖绿洲区林地和农地表层土壤水分空间变异的尺度性进行研究.结果表明： 研究区林地和农地表层土壤水分变异程度随土壤水分含量的增加而增加;变异系数随采样尺度的增大而更接近真实变异值.在干旱和湿润条件下,当采样幅度在一定范围内增大时,林地和农地土壤水分的变异系数、Moran I指数、块金值、基台值及林地变程均不断变大,而农地在干旱条件下的变程无固定变化规律.当采样密度在一定范围内增大时,块金值、变程不断增大,但变异系数、Moran I指数、基台值均不受影响.
     

Characterization and Simulation of Uncertain Frequency Distributions: Effects of Distribution Choice,Variability, Uncertainty,and Parameter Dependence

We use bootstrap simulation to characterize uncertainty in parametric distributions, including Normal, Lognormal, Gamma, Weibull, and Beta, commonly used to represent variability in probabilistic assessments. Bootstrap simulation enables one to estimate sampling distributions for sample statistics, such as distribution parameters, even when analytical solutions are not available. Using a two-dimensional framework for both uncertainty and variability, uncertainties in cumulative distribution functions were simulated. The mathematical properties of uncertain frequency distributions were evaluated in a series of case studies during which the parameters of each type of distribution were varied for sample sizes of 5, 10, and 20. For positively skewed distributions such as Lognormal, Weibull, and Gamma, the range of uncertainty is widest at the upper tail of the distribution. For symmetric unbounded distributions, such as Normal, the uncertainties are widest at both tails of the distribution. For bounded distributions, such as Beta, the uncertainties are typically widest in the central portions of the distribution. Bootstrap simulation enables complex dependencies between sampling distributions to be captured. The effects of uncertainty, variability, and parameter dependencies were studied for several generic functional forms of models, including models in which two-dimensional random variables are added, multiplied, and divided, to show the sensitivity of model results to different assumptions regarding model input distributions, ranges of variability, and ranges of uncertainty and to show the types of errors that may be obtained from mis-specification of parameter dependence. A total of 1,098 case studies were simulated. In some cases, counter-intuitive results were obtained. For example, the point value of the 95th percentile of uncertainty for the 95th percentile of variability of the product of four Gamma or Weibull distributions decreases as the coefficient of variation of each model input increases and, therefore, may not provide a conservative estimate. Failure to properly characterize parameter uncertainties and their dependencies can lead to orders-of-magnitude mis-estimates of both variability and uncertainty. In many cases, the numerical stability of two-dimensional simulation results was found to decrease as the coefficient of variation of the inputs increases. We discuss the strengths and limitations of bootstrap simulation as a method for quantifying uncertainty due to random sampling error.     

Species range size distributions for some marine taxa in the Atlantic Ocean. Effect of latitude and depth

The range size distributions of 6643 species in ten different fish and invertebrate taxa dwelling in pelagic (latitudinal range sizes) and benthic (latitudinal and depth range sizes) habitats on both sides of the Atlantic Ocean (80°N?70°S) were studied. The objectives were to analyse: (1) the range size distribution patterns for the various taxa and whether they have right/left skewed or lognormal distributions; (2) the geographical species distributions, to ascertain whether the distribution ranges change with latitude (Rapoport's rule); and (3) the relationship between the depth ranges of benthic species and their maximum depth of occurrence and how depth range size distributions change with latitude. The pelagic taxa exhibited larger range sizes than did the benthic taxa, continental slope/rise species excepted. On the other hand, the boundaries between geographical provinces for both benthic taxa and pelagic taxa tended to occur in association with major oceanographic processes. The shape of the latitudinal range frequency distributions (LRFDs) of the pelagic organisms were distinctly left‐skewed, and the LRFDs for most taxa were significantly different from lognormal. There was no common pattern for the distributions of the benthic organisms, which were lognormal in Cephalopoda, Stomatopoda, and Crustacea Decapoda and tended to be left‐skewed and significantly different from lognormal in Pisces. The applicability of Rapoport's rule was not clearly inferable from the results, and the rule appears to be conditioned by the location of biogeographical boundaries and the endemism rate in the different biogeographical provinces. A clear increase in depth range size with maximum depth range was observable for benthic species, confirming previous studies. Species’ depth range distributions displayed a discernible latitudinal pattern, right‐skewed at high latitudes and left‐skewed at low latitudes. The location of biogeographical boundaries, and endemism rate by biogeographical province were considered to be the factors most useful in explaining species’ distribution patterns and their conformity or nonconformity to Rapoport's rule. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society, 2003, 80 , 437–455.     

Soil Ingestion Distributions for Monte Carlo Risk Assessment in Children

Monte Carlo environmental risk assessment requires estimates of the exposure distributions. An exposure of principal concern is often soil ingestion among children. We estimate the long-term (annual) average soil ingestion exposure distribution using daily soil ingestion estimates from children who participated in a mass-balance study at Anaconda, MT. The estimated distribution is accompanied by uncertainty estimates. The estimates take advantage of developing knowledge about bias in soil ingestion estimates and are robust. The estimates account for small particle size soil, use the median trace element estimate for subject days, account for the small sample variance of the median estimates, and use best linear unbiased predictors to estimate the cumulative long term soil ingestion distribution. Bootstrapping is used to estimate the uncertainty of the distribution estimates. The median soil ingestion is estimated as 24?mg/d (sd = 4?mg/d), with the 95 percentile soil ingestion estimated as 91?mg/d (sd = 16.6?mg/d). Strategies are discussed for use of these estimates in Monte Carlo risk assessment.     

Exact propagation of uncertainties in multiplicative models

Propagation of uncertainties has been widely accepted as an integral component in health risk assessments. Historically, the approximations based on Taylor series expansions have been applied, but they are valid only when the model is linear or the coefficients of variation are small. Another approximation approach is Monte Carlo analysis. It is simpler and more practical for risk management but may become cumbersome if the model involves many variables containing large uncertainties. Recently, the exact log transform technique has been proposed for multiplicative models with lognormal uncertainties. The purpose of this paper is to present a novel exact analytical method as a complementary approach to simulation for general multiplicative models with independent variables, without a constraint on the types of uncertainty distributions. It also provides good estimates of the mean and variance of highly skewed distributions, determination of their existence, and verification of sufficient simulation sample size for simulation method. Two case examples are given to demonstrate the applications.     

The size distribution of human hematogenous metastases.

The development of primary cancers and their subsequent metastases occur through a complex sequence of discrete steps. A hypothesis is proposed here whereby the time available for the growth of metastases is normally distributed, presumably as a consequence of the summation of multiple independently distributed time intervals from each of the steps and of the Central Limit Theorem. For exponentially growing metastases, the corresponding size distribution would be lognormal; Gompertzian growth would imply a modified (Gompertz-normal) distribution, where larger metastases would occur less frequently as a consequence of a decreased growth rate. These two size distributions were evaluated against 18 human autopsy cases where precise size measurements had been collected from over 3900 macroscopic hematogenous organ metastases. The lognormal distribution provided an approximate agreement. Its main deficiency was a tendency to over-represent metastases greater than 10 mm diameter. The Gompertz-normal distribution provided more stringent agreement, correcting for this over-representation. These observations supported the hypothesis of normally distributed growth times, and qualified the utility of the lognormal and Gompertz-normal distributions for the size distribution of metastases.     

Intraspecific body size frequency distributions of insects

Although interspecific body size frequency distributions are well documented for many taxa, including the insects, intraspecific body size frequency distributions (IaBSFDs) are more poorly known, and their variation among mass-based and linear estimates of size has not been widely explored. Here we provide IaBSFDs for 16 species of insects based on both mass and linear estimates and large sample sizes (n ≥ 100). In addition, we review the published IaBSFDs for insects, though doing so is complicated by their under-emphasis in the literature. The form of IaBSFDs can differ substantially between mass-based and linear measures. Nonetheless, in non-social insects they tend to be normally distributed (18 of 27 species) or in fewer instances positively skewed. Negatively skewed distributions are infrequently reported and log transformation readily removes the positive skew. Sexual size dimorphism does not generally cause bimodality in IaBSFDs. The available information on IaBSFDs in the social insects suggests that these distributions are usually positively skewed or bimodal (24 of 30 species). However, only c. 15% of ant genera are polymorphic, suggesting that normal distributions are probably more common, but less frequently investigated. Although only 57 species, representing seven of the 29 orders of insects, have been considered here, it appears that whilst IaBSFDs are usually normal, other distribution shapes can be found in several species, though most notably among the social insects. By contrast, the interspecific body size frequency distribution is typically right-skewed in insects and in most other taxa.     

麻城黄山松天然林直径分布

为研究黄山松天然次生林直径分布特征,以麻城市黄山松天然次生林为研究对象,采用标准样地调查,计算林分直径的偏度、峰度,林分直径分布的Shannon-Weiner和Simpson指数,运用负指数分布、normal分布、lognormal分布、logistic分布和Weibull分布等5种概率密度函数对黄山松天然次生林林分直...     

Abundance patterns of European breeding birds

The frequency distribution of national population sizes of breeding birds was examined for each of 48 European countries, including autonomous regions, using data from the European Bird Database. The frequency distribution of logarithmically transformed abundance was left skewed in 40 countries: there was significant left skew in 10, and positive skew, in 2 countries. The inclusion of data classed as of low quality did not alter the conclusion that abundance patterns were predominantly left skewed. Abundance patterns of resident and migrant breeding birds differed; residents were left skewed, migrants were lognormal. Skewness was correlated negatively the number of species within a country. At low sample size, both left and right skews were evident, but left skews predominated at larger samples sizes. This pattern was driven partly by a difference between breeding populations on islands and on continental countries. Resampling procedures with fixed sample size showed that resident and migrant birds differed consistently in their patterns of skew, independent of sample size. If the birds of Europe were treated as a single assemblage, their abundance pattern was left skewed but this was driven by a very small number of vagrant breeders.     

Estimation of Sample Size for Reference Interval Studies

The currently used criterion for sample size calculation in a reference interval study is not well stated and leads to imprecise control of the ratio in question. We propose a generalization of the criterion used to determine sufficient sample size in reference interval studies. The generalization allows better estimation of the required sample size when the reference interval estimation will be using a power transformation or is nonparametric. Bootstrap methods are presented to estimate sample sizes required by the generalized criterion. Simulation of several distributions both symmetric and positively skewed is presented to compare the sample size estimators. The new method is illustrated on a data set of plasma glucose values from a 50‐g oral glucose tolerance test. It is seen that the sample sizes calculated from the generalized criterion leads to more reliable control of the desired ratio.