土地利用类型的分维值和稳定性指数空间变异分析

土地利用类型是一种在自然和人类活动双重作用下的产物,具有不规则、相对不稳定性和复杂性特征,可以利用分形方法进行探讨;分形理论在土地结构研究中的应用涉及土地利用类型分数维的计算、土地利用结构分形研究方法、土地利用结构及其动态变化的分形描述、区域景观结构的分形模型等方面;但土地利用类型的分形机制的空间差异研究少见报道。综合考虑广东省的自然地理环境和社会经济发展状况,文章选择韶关、潮州、汕头、广州作为不同类型区域的代表,基于分形理论计算了耕地、园地、林地、草地、居民点及工矿用地、道路用地、水体和未利用土地8种地类分维值(D)和稳定性指数(Si)以及平均分维值和稳定性指数,从影响土地利用结构的地貌和人文因素两个方面出发,对比和分析了地域之间的D值、Si值的关系,并从中得到了D值和Si值的变化规律。结果表明:(1)复杂的地貌类型是影响土地利用类型D值和Si值的最主要因素;(2)社会经济发展水平一定程度上影响土地利用类型的分维值和稳定性指数;(3)区域土地利用类型的平均分维值、稳定性指数的大小是土地利用结构的综合反映。     

A state-space model approach to optimum spatial sampling design based on entropy

We consider the spatial sampling design problem for a random field X. This random field is in general assumed not to be directly observable, but sample information from a related variable Y is available. Our purpose in this paper is to present a state-space model approach to network design based on Shannon's definition of entropy, and describe its main points with regard to some of the most common practical problems in spatial sampling design. For applications, an adaptation of Ko et al.'s (1995) algorithm for maximum entropy sampling in this context is provided. We illustrate the methodology using piezometric data from the Velez aquifer (Malaga, Spain). © Rapid Science 1998     

Bayesian entropy for spatial sampling design of environmental data

We develop a spatial statistical methodology to design national air pollution monitoring networks with good predictive capabilities while minimizing the cost of monitoring. The underlying complexity of atmospheric processes and the urgent need to give credible assessments of environmental risk create problems requiring new statistical methodologies to meet these challenges. In this work, we present a new method of ranking various subnetworks taking both the environmental cost and the statistical information into account. A Bayesian algorithm is introduced to obtain an optimal subnetwork using an entropy framework. The final network and accuracy of the spatial predictions is heavily dependent on the underlying model of spatial correlation. Usually the simplifying assumption of stationarity, in the sense that the spatial dependency structure does not change location, is made for spatial prediction. However, it is not uncommon to find spatial data that show strong signs of nonstationary behavior. We build upon an existing approach that creates a nonstationary covariance by a mixture of a family of stationary processes, and we propose a Bayesian method of estimating the associated parameters using the technique of Reversible Jump Markov Chain Monte Carlo. We apply these methods for spatial prediction and network design to ambient ozone data from a monitoring network in the eastern US.     

三江平原典型小叶章种群地上生物量的空间结构分形特征

2005年5月至10月,应用分形几何学的原理和方法对三江平原典型小叶章种群地上生物量与株高的空间结构分形关系进行了研究。结果表明,典型草甸小叶章和沼泽化草甸小叶章的地上生物量与株高存在良好的静态分形关系,其分形维数(D)是对地上生物量在各器官中积累规律的表征;二者地上生物量与株高的对数值线性相关,相关系数分别介于0.579～0.919和0.655～0.914之间(P<0.01,D值介于1.778～3.414和2.238～3.924之间,各时期地上生物量均以株高的幂函数形式积累;二者地上生物量与株高静态分形关系D值的季节动态基本一致,其变化均符合抛物线模型(P<0.05),而局部波动又与地上生物量的变化有关;生长季内,二者地上生物量与株高动态分形关系的D值分别为2.749和2.738,说明地上生物量的积累具有自相似性,符合幂函数增长的分形生长过程。研究还表明,仅用D值来刻画不同植物地上生物量的空间积累与展布存在一定的局限性,它只能用于测度和描述一种植物体生物量的空间积累及其对空间的占据,而一般不能用于植物间相应指标的类比;导致不同植物D值差异的原因可能与植物生长所处生境、外在因素以及模型参数(C)有关。     

Diversity pattern and spatial scale: a study of a tropical rain forest of Malaysia

Scale is emerging as one of the critical problems in ecology because our perception of most ecological variables and processes depends upon the scale at which the variables are measured. A conclusion obtained at one scale may not be valid at another scale without sufficient knowledge of the scaling effect, which is also a source of misinterpretation for many ecological problems, such as the design of reserves in conservation biology.This paper attempts to study empirically how scaling may affect the spatial patterns of diversity (tree density, richness and Shannon diversity) that we may perceive in tropical forests, using as a test-case a 50 ha forest plot in Malaysia. The effect of scale on measurements of diversity patterns, the occurrence of rare species, the fractal dimension of diversity patterns, the spatial structure and the nearest-neighbour autocorrelation of diversity are addressed. The response of a variable to scale depends on the way it is measured and the way it is distributed in space.We conclude that, in general, the effect of scaling on measures of biological diversity is non-linear; heterogeneity increases with the size of the sampling units, and fine-scale information is lost at a broad scale. Our results should lead to a better understanding of how ecological variables and processes change over scale.     

景观格局破碎化的粒度特征及其变异的分形定量研究

文章构建一种用于定量测度景观破碎化指标空间粒度特征的分形方法.该方法基于景观粒度特征中的幂律关系,利用双对数线性回归方法,获取了景观破碎化指标在粒度变换过程中的2个数量关系:拟合优度R2与分维数D,分别刻画景观指标粒度变换的分形特性和随空间粒度变化的程度.以1992—2011年间上海市景观破碎化的过程为例,利用提出的分形方法进行分析.研究显示,总体上内部生境面积破碎化指标FI1和FI2没有清晰的分形特性;均匀性指标EI在1992年分形特性显著而在2011年分形特性却不清晰;斑块形状破碎化指标FS1其分形特性同样不清晰,而指标FS2呈现显著的分形特性,并且分维数D表现为正值,即随空间粒度的增大景观指标FS2的值减小.结果表明,拟合优度R2与分维数D的有机组合,能够定量地刻画景观破碎化中的粒度变化特征.研究同时发现,景观指标随空间粒度的变化特征,受指标内在特性、研究数据、研究区域的景观结构以及实验数据重采样方法和方案的影响.该分形方法不但可以用来测度所例举的5种景观破碎化指标的粒度特征,更适用于测度Fragstats中被广泛使用的各种景观指标.     

Phased sampling for soil remediation

In phased sampling, data obtained in one phase is used to design the sampling network for the next phase. GivenN total observations, 1, ...,N phases are possible. Experiments were conducted with one-phase, two-phase, andN-phase design algorithms on surrogate models of sites with contaminated soils. The sampling objective was to identify through interpolation, subunits of the site that required remediation. The cost-effectiveness of alternate methods was compared by using a loss function. More phases are better, but in economic terms, the improvement is marginal. The optimal total number of samples is essentially independent of the number of phases. For two phase designs, 75% of samples in the first phase is near optimal; 20% or less is actually counterproductive.The U.S. Environmental Protection Agency (EPA) through its Office of Research and Development (ORD), partially funded and collaborated in the research described here. It has been subjected to the Agency's peer review and has been approved as an EPA publication. The U.S. Government has a non-exclusive, royalty-free licence in and to any copyright covering this article.     

Markov Chain Monte Carlo on optimal adaptive sampling selections

Under a Bayesian population model with a given prior distribution, the optimal sampling strategy with a fixed sample size n is an n-phase adaptive one. That is, the selection of the next sampling units should sequentially depend on the information obtained from the previously selected units, including the observed values of interest. Such an optimal strategy is in general not executable in practice due to its intensive computation. In many survey sampling situations, an important problem is that one would like to select a set of units in addition to a certain number of sampling units which have been observed. If the optimal strategy is an adaptive one, the selection of the additional units should take both the labels and the observed values of the already selected units into account. Hence, a simpler optimal two-phase adaptive sampling strategy under a Bayesian population model is proposed in this article for practical interest. A Markov chain Monte Carlo method is used to approximate the posterior joint distribution of the unobserved population units after the first phase sampling, for the optimal selection of the second phase sample. This approximation method is found to be successful to select the optimal second-phase sample. Finally, this optimal strategy is applied to a set of data from a study of geothermal CO₂ emissions in Yellowstone National Park as a practical illustrative example.     

Estimator bias and efficiency for adaptive cluster sampling with order statistics and a stopping rule

Practical problems facing adaptive cluster sampling with order statistics (acsord) are explored using Monte Carlo simulation for three simulated fish populations and two known waterfowl populations. First, properties of an unbiased Hansen-Hurwitz (HH) estimator and a biased alternative Horvitz-Thompson (HT) estimator are evaluated. An increase in the level of population aggregation or the initial sample size increases the efficiencies of the two acsord estimators. For less aggregated fish populations, the efficiencies decrease as the order statistic parameter r (the number of units about which adaptive sampling is carried out) increases; for the highly aggregated fish and waterfowl populations, they increase with r. Acsord is almost always more efficient than simple random sampling for the highly aggregated populations. Positive bias is observed for the HT estimator, with the maximum bias usually occurring at small values of r. Secondly, a stopping rule at the Sth iteration of adaptive sampling beyond the initial sampling unit was applied to the acsord design to limit the otherwise open-ended sampling effort. The stopping rule induces relatively high positive bias to the HH estimator if the level of the population aggregation is high, the stopping level S is small, and r is large. The bias of HT is not very sensitive to the stopping rule and its bias is often reduced by the stopping rule at smaller values of r. For more aggregated populations, the stopping rule often reduces the efficiencies of the estimators compared to the non-stopping-rule scheme, but acsord still remains more efficient than simple random sampling. Despite its bias and lack of theoretical grounding, the HT estimator is usually more efficient than the HH estimator. In the stopping rule case, the HT estimator is preferable, because its bias is less sensitive to the stopping level.     

Space-time statistics for environmental and agricultural related phenomena

This paper presents an overview of space-time statistical procedures to analyse agricultural and environmental related phenomena. It starts with an application on root-rot development in cotton. Dependence modelling in space and time is done with the space-time variogram. Various kriging interpolators are presented for making predictions in space and time. Simulated annealing is used to design an optimal monitoring network for estimation of space-time variograms. In the application no clear indication was found for anisotropy, although strong evidence exists that the disease not only proceeds within rows but also jumps between rows. The optimal sampling scheme showed a spatial clustering of observations at the first and the last monitoring day and less observations at intermediate times.     

Cost analysis of composite sampling for classification

When an environmental sampling objective is to classify all the sample units as contaminated or not, composite sampling with selective retesting can substantially reduce costs by reducing the number of units that require direct analysis. The tradeoff, however, is increased complexity that has its own hidden costs. For this reason, we propose a model for assessing the relative cost, expressed as the ratio of total expected cost with compositing to total expected cost without compositing (initial exhaustive testing). Expressions are derived for the following retesting protocols: (i) exhaustive, (ii) sequential and (iii) binary split. The effects of both false positive and false negative rates are also derived and incorporated. The derived expressions of relative cost are illustrated for a range of values for various cost components that reflect typical costs incurred with hazardous waste site monitoring. Results allow those who are designing sampling plans to evaluate if any of these compositing/retesting protocols will be cost effective for particular applications.     

Stack sampling for organic emissions

Along with increased activity in source sampling for organics, there have been many improvements in the methods of acquiring samples. Much has been learned about how best to proceed, and a number of potentially serious pitfalls have been discovered, characterized, and circumvented. Unfortunately, communication of all of this new technology has not always been effective.

This paper reviews some of the more important fundamental principles involved in stack sampling for organics, briefly describes and discusses recently developed equipment, and points out a few of the more serious pitfalls to be avoided. Extensive references are provided, many of which are often overlooked by newcomers to the field. The conclusion is reached that it is possible to consistently obtain high‐quality samples of organic materials from stationary source stacks, even though knowledge and caution are necessary.     

Comparison between Hansen-Hurwitz and Horvitz-Thompson estimators for adaptive cluster sampling

Thompson (1990) introduced the adaptive cluster sampling design. This sampling design has been shown to be a useful sampling method for parameter estimation of a clustered and scattered population (Roesch, 1993; Smith et al., 1995; Thompson and Seber, 1996). Two estimators, the modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators, are available to estimate the mean or total of a population. Empirical results from previous researches indicate that the modified HT estimator has smaller variance than the modified HH estimator. We analytically compare the properties of these two estimators. Some results are obtained in favor of the modified HT estimator so that practitioners are strongly recommended to use the HT estimator despite easiness of computations for the HH estimator.     

Spatial sampling and the environment: some issues and directions

In this paper we summarize research issues for spatial environmental sampling stemming from a NISS/USEPA workshop held on 21-22 September 1994 at Chapel Hill, NC.     

Variance estimation in the EMAP strategy for sampling discrete ecological resources

The United States Environmental Protection Agency's Environmental Monitoring and Assessment Program (EMAP) is designed to describe status, trends and spatial pattern of indicators of condition of the nation's ecological resources. The proposed sampling design for EMAP is based on a triangular systematic grid and employs both variable probability and double sampling. The Horvitz-Thompson estimator provides the foundation of the design-based estimation strategy used in EMAP. However, special features of EMAP designed to accommodate the complexity of sampling environmental resources on a national scale require modifications of standard variance estimation procedures as well as development of new techniques. An overview of variance estimation methods proposed for application to EMAP's sampling strategy for discrete resources is presented.     

Null models reveal preferential sampling, spatial autocorrelation and overfitting in habitat suitability modelling

Nowadays, species are driven to extinction at a high rate. To reduce this rate it is important to delineate suitable habitats for these species in such a way that these areas can be suggested as conservation areas. The use of habitat suitability models (HSMs) can be of great importance for the delineation of such areas. In this study MaxEnt, a presence-only modelling technique, is used to develop HSMs for 223 nematode species of the Southern Bight of the North Sea. However, it is essential that these models are beyond discussion and they should be checked for potential errors. In this study we focused on two categories (1) errors which can be attributed to the database such as preferential sampling and spatial autocorrelation and (2) errors induced by the modelling technique such as overfitting, In order to quantify these adverse effects thousands of nulls models were created. The effect of preferential sampling (i.e. some areas where visited more frequenty than others) was investigated by comparing model outcomes based from null models sampling the actual sampling stations and null models sampling the entire mapping area (Raes and ter Steege, 2007). Overfitting is exposed by a fivefold cross-validation and the influence of spatial autocorrelation is assessed by separating test and training sets in space. Our results clearly show that all these effects are present: preferential sampling has a strong effect on the selection of non-random species models. Crossvalidation seems to have less influence on the model selection and spatial autocorrelation is also strongly present. It is clear from this study that predefined thresholds are not readily applicable to all datasets and additional tests are needed in model selection.     

Comparison of distribution function estimators for forestry applications following variable probability sampling

Practical considerations often motivate employing variable probability sampling designs when estimating characteristics of forest populations. Three distribution function estimators, the Horvitz-Thompson estimator, a difference estimator, and a ratio estimator, are compared following variable probability sampling in which the inclusion probabilities are proportional to an auxiliary variable, X. Relative performance of the estimators is affected by several factors, including the distribution of the inclusion probabilities, the correlation () between X and the response Y, and the position along the distribution function being estimated. Both the ratio and difference estimators are superior to the Horvitz-Thompson estimator. The difference estimator gains better precision than the ratio estimator toward the upper portion of the distribution function, but the ratio estimator is superior toward the lower end of the distribution function. The point along the distribution function at which the difference estimator becomes more precise than the ratio estimator depends on the sampling design, as well as the coefficient of variation of X and . A simple confidence interval procedure provides close to nominal coverage for intervals constructed from both the difference and ratio estimators, with the exception that coverage may be poor for the lower tail of the distribution function when using the ratio estimator.     

Improved strategies for coverage estimation by using replicated line-intercept sampling

Coverage, i.e., the area covered by the target attribute in the study region, is a key parameter in many surveys. Coverage estimation is usually performed by adopting a replicated protocol based on line-intercept sampling coupled with a suitable linear homogeneous estimator. Since coverage is a parameter which may be interestingly represented as the integral of a suitable function, improved Monte Carlo strategies for implementing the replicated protocol are introduced in order to achieve estimators with small variance rates. In addition, new specific theoretical results on Monte Carlo integration methods are given to deal with the integrand functions arising in the special coverage estimation setting.

A foundation for developing a methodology for social network sampling

Researchers are increasingly turning to network theory to understand the social nature of animal populations. We present a computational framework that is the first step in a series of works that will allow us to develop a quantitative methodology of social network sampling to aid ecologists in their social network data collection. To develop our methodology, we need to be able to generate networks from which to sample. Ideally, we need to perform a systematic study of sampling protocols on different known network structures, as network structure might affect the robustness of any particular sampling methodology. Thus, we present a computational tool for generating network structures that have user-defined distributions for network properties and for key measures of interest to ecologists. The user defines the values of these measures and the tool will generate appropriate network randomizations with those properties. This tool will be used as a framework for developing a sampling methodology, although we do not present a full methodology here. We describe the method used by the tool, demonstrate its effectiveness, and discuss how the tool can now be utilized. We provide a proof-of-concept example (using the assortativity measure) of how such networks can be used, along with a simulated egocentric sampling regime, to test the level of equivalence of the sampled network to the actual network. This contribution is part of the special issue “Social Networks: new perspectives” (Guest Editors: J. Krause, D. Lusseau and R. James).     

The use of replicated plot,line and point sampling for estimating species abundance and ecological diversity

The paper deals with the problem of estimating diversity indexes for an ecological community. First the species abundances are unbiasedly and consistently estimated using designs based on n random and independent selections of plots, points or lines over the study area. The problem of sampling elusive populations is also considered. Finally, the diversity index estimates are obtained as functions of the abundance estimates. The resulting estimators turn out to be asymptotically (n large) unbiased, even if a considerable bias may occur for a small n. Accordingly, the method of jackknifing is made use of in order to reduce bias.