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.     

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.     

The National Resources Inventory: a long-term multi-resource monitoring programme

Interest in natural resources and the environment has led to the development of new federal monitoring efforts, the expansion of existing federal inventory programmes, and discussions of inter-agency collaboration for natural resource assessment data collection. As federal programmes evolve, knowledge gained from existing long-term survey programmes can provide valuable contributions to statistical and operational aspects of survey efforts. This paper describes the National Resources Inventory (NRI), which has been conducted by the US Department of Agriculture's Natural Resources Conservation Service in cooperation with the Iowa State University Statistical Laboratory for several decades. The current NRI is a longitudinal survey of soil, water, and related environmental resources designed to assess conditions and trends every five years on non-federal US lands. An historical overview is provided highlighting the development of the survey programme. Sample design, data collection, and estimation procedures used in the 1992 NRI are described, and statistical issues related to long-term monitoring are discussed.     

Complex national sampling design for long-term monitoring of protected dry grasslands in Switzerland

We describe a probabilistic sampling design of circular permanent plots for the long-term monitoring of protected dry grasslands in Switzerland. The population under study is defined by the perimeter of a national inventory. The monitoring focus is on the species composition of the protected grassland vegetation and derived conservation values. Efficient trend estimations are required for the whole country and for some predefined target groups (six biogeographical regions and eleven vegetation types). The target groups are equally important regardless of their size. Consequently, intensified sampling of the less frequent groups is essential for sample efficiency. The prior information needed to draw a targeted sample is obtained from the sampling frame and external databases. The logistics and generalized delineation of the target population may pose further problems. Thus, investments in fieldwork and travel time should be well balanced by selecting a cluster sample. Second, any access problems in the field and non-target units in the sample should be compensated for by selecting reserve plots as they otherwise may considerably reduce the effective sample size. Finally, the design has to be flexible as the sampling frame may change over time and sampling intensity might have to be adjusted to redefined budgets or requirements. Likewise, the variables and biological items of interest may change. To fulfil all these constraints and to optimally use the available prior information, we propose a multi-stage self-weighted unequal probability sampling design. The design uses modern techniques such as: balanced sampling, spreading, stratified balancing, calibration, unequal probability sampling and power allocation. This sampling design meets the numerous requirements of this study and provides a very efficient estimator.     

Propagation functions for monitoring distributional changes

In environmental assessment and monitoring, a primary objective of the investigator is to describe the changes occurring in the environmentally important variables over time. Propagation functions have been proposed to describe the distributional changes occurring in the variable of interest at two different times. McDonald et al. (1992, 1995) proposed an estimator of propagation function under the assumption of normality. We conduct a detailed sensitivity analysis of inference based on the normal model. It turns out that this model is appropriate only for small departures from normality whereas, for moderate to large departures, both estimation and testing of hypothesis break down. Non-parametric estimation of the propagation function based on kernel density estimation is also considered and the robustness of the choice of bandwidth for kernel density estimation is investigated. Bootstrapping is employed to obtain confidence intervals for the propagation function and also to determine the critical regions for testing the significance of distributional changes between two sampling epochs. Also studied briefly is the mathematical form and graphical shape of the propagation function for some parametric bivariate families of distributions. Finally, the proposed estimation techniques are illustrated on a data set of tree ring widths.     

Identifying the largest individual sample value from a two-way composite sampling design

Composite sampling techniques for identifying the largest individual sample value seem to be cost effective when the composite samples are internally homogeneous. However, since it is not always possible to form homogeneous composite samples, these methods can lead to higher costs than expected. In this paper we propose a two-way composite sampling design as a way to improve on the cost effectiveness of the methods available to identify the largest individual sample value.     

Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling

Many of the most popular sampling schemes used in forestry are probability proportional to size methods. These methods are also referred to as size-biased because sampling is actually from a weighted form of the underlying population distribution. Length- and area-biased sampling are special cases of size-biased sampling where the probability weighting comes from a lineal or areal function of the random variable of interest, respectively. Often, interest is in estimating a parametric probability density of the data. In forestry, the Weibull function has been used extensively for such purposes. Estimating equations for method of moments and maximum likelihood for two- and three-parameter Weibull distributions are presented. Fitting is illustrated with an example from an area-biased angle-gauge sample of standing trees in a woodlot. Finally, some specific points concerning the form of the size-biased densities are reported.     

Lessons for ecological policy design: A case study of ecosystem management

This paper explores the prospects for combining elements of the ecological and policy sciences to form a substantive and effective science of ecological policy design. This exploration is made through a case study whose specific focus is the management problem posed by competition between man and an insect (the spruce budworm, Choristoneura fumiferana) for utilization of coniferous forests in the Canadian Province of New Brunswick. We used this case study as a practical testing ground in which we examined the relative strengths, weaknesses, and complementarities of various aspects of the policy design process. Where existing approaches proved wanting, we sought to develop alternatives and to test them in turn. In particular, we used a combination of simulation modeling and topological approaches to analyze the space-time dynamics of this ecosystem under a variety of natural and managed conditions. Explicit consideration was given to the development of invalidation tests for establishing the limits of model credibility. An array of economic, social, and environmental indicators was generated by the model, enabling managers and policy makers to evaluate meaningfully the performance of the system under a variety of management proposals. Simplified versions of the models were constructed to accomodate several optimization procedures, including dynamic programming, which produced trial policies for a range of possible objectives. These trial policies were tested in the more complex model versions and heuristically modified in dialogue with New Brunswick's forest managers. We explored the role of utility functions for simplifying and contrasting policy performance measures, paying special attention to questions of time preferences and discounting. Finally, the study was shaped by a commitment to transfer the various models and policy design capabilities from their original academic setting to the desks and minds of the practicing managers and politicians. An array of workshops, model gaming sessions, and nontraditional communication formats was developed and tested in pursuit of this goal.This paper reports some specific management policies developed, and some general lessons for ecological policy design learned in the course of the study.     

Ranked set sample design for environmental investigations

Ranked set sampling can provide an efficient basis for estimating parameters of environmental variables, particularly when sampling costs are intrinsically high. Various ranked set estimators are considered for the population mean and contrasted in terms of their efficiencies and useful- ness, with special concern for sample design considerations. Specifically, we consider the effects of the form of the underlying random variable, optimisation of efficiency and how to allocate sampling effort for best effect (e.g. one large sample or several smaller ones of the same total size). The various prospects are explored for two important positively skew random variables (lognormal and extreme value) and explicit results are given for these cases. Whilst it turns out that the best approach is to use the largest possible single sample and the optimal ranked set best linear estimator (ranked set BLUE), we find some interesting qualitatively different conclusions for the two skew distributions     

西南岩溶山区景观生态特征与景观生态建设

探讨了西南岩溶山区景观生态结构与功能以及景观生态过程的不同于其他区域的基本特征，尝试从景观角度认识西南岩溶区生态空间特性与演化过程。受地质地貌和土地利用的影响。西南岩溶山区景观基质脆弱、景观格局分异明显，具破碎化与景观结构粗粒化、景观动态变化范围大且速度快、整体退化明显的特点，以石漠化为特征的景观演化削弱了岩溶生态系统的生态服务功能。岩溶山区的景观生态建设须充分认识岩溶山区资源环境优势，充分利用当地的适生植物资源，协调生态效应和水文效应，促进水土资源的有效保持向高效利用发展，形成新的高效、和谐的人工自然景观。今后应把景观格局与生态过程结合起来、与人文因子和地学背景结合起来，加强小尺度的景观变化研究。     

Estimation of the mean in line intercept sampling

Ratio estimation of the parametric mean for a characteristic measured on plants sampled by a line intercept method is presented and evaluated via simulation using different plant dispersion patterns (Poisson, regular cluster, and Poisson cluster), plant width variances, and numbers of lines. The results indicate that on average the estimates are close to the parametric mean under all three dispersion patterns. Given a fixed number of lines, variability of the estimates is similar across dispersion patterns with variability under the Poisson pattern slightly smaller than varia-bility under the cluster patterns. No variance estimates were negative under the Poisson pattern, but some estimates were negative under the cluster patterns for smaller numbers of lines. Variance estimates become closer to zero similarly for all spatial patterns as the number of lines increases. Ratio estimation of the parametric mean in line intercept sampling works better, from the viewpoint of approximate unbiasedness and variability of estimates, under the Poisson pattern with larger numbers of lines than other combinations of spatial patterns, plant width variances and numbers of lines.     

Measures of preferred direction for environmental and ecological circular data

Circular or angular variables indicating direction or cyclical time can be of great interest to scientists studying ecology, biology or environmental issues. A common problem of interest in circular data is estimating a preferred direction and its corresponding distribution. This problem is complicated by the so-called “wrap-around effect” on the circle, which exists because there is no natural minimum or maximum. The usual statistics employed for linear data are inappropriate for directional data, as they do not account for its circular nature. Three choices for summarizing the preferred direction (the sample circular mean, sample circular median and a circular analog of the Hodges–Lehmann estimator) are discussed, with examples from environmental and ecological applications. Similar to the linear data case, the relative emphases of different methods sometimes yield different measures of preferred direction in the presence of outliers or lack of symmetry in the original data. Received: November 2003 / Revised: June 2004     

Problems associated with ecological assessment of packaging

Current trends in the development of the world packaging market and the place of ecological tendencies in them suggest the need to analyse the present status of studies on the ecological assessment of packaging materials and packaging. The aim of this study is to present some aspects of ecological assessment of packaging. The methods and criteria of ecological assessment of packaging, including Life Cycle Analysis (LCA) and ecological classification of packaging proposed by COBRO (Polish Packaging Research and Development Centre) in Warsaw were used. The considerations presented in the paper related to the general assumptions of ecological assessment of packaging materials and packaging point to the complexity of the problem and, at the same time, to the immediate interest and importance of studies in this field, particularly in terms of implementing a specific environmental protection policy.     

Mark-recapture estimators for dual frame population size of prominent nesting structures: the effect of uncertain detection probability

The combined mark-recapture and line transect sampling methodology proposed by Alpizar-Jara and Pollock [Journal of Environmental and Ecological Statistics, 3(4), 311–327, 1996; In Marine Mammal Survey and Assessment Methods Symposium. G.W. Garner, S.C. Amstrup, J.L. Laake, B.F.J. Manly, L.L. McDonald, and D.C. Robertson (Eds.), A.A. Balkema, Rotterdam, Netherlands, pp. 99–114, 1999] is used to illustrate the estimation of population size for populations with prominent nesting structures (i.e., bald eagle nests). In the context of a bald eagle population, the number of nests in a list frame corresponds to a pre-marked sample of nests, and an area frame corresponds to a set of transect strips that could be regularly monitored. Unlike previous methods based on dual frame methodology using the screening estimator [Haines and Pollock (Journal of Environmental and Ecological Statistics, 5, 245–256, 1998a; Survey Methodology, 24(1), 79–88, 1998b)], we no longer need to assume that the area frame is complete (i.e., all the nests in the sampled sites do not need to be seen). One may use line transect sampling to estimate the probability of detection in a sampled area. Combining information from list and area frames provides more efficient estimators than those obtained by using data from only one frame. We derive an estimator for detection probability and generalize the screening estimator. A simulation study is carried out to compare the performance of the Chapman modification of the Lincoln–Petersen estimator to the screening estimator. Simulation results show that although the Chapman estimator is generally less precise than the screening estimator, the latter can be severely biased in presence of uncertain detection. The screening estimator outperforms the Chapman estimator in terms of mean squared error when detection probability is near 1 wheareas the Chapman estimator outperforms the screening estimator when detection probability is lower than a certain threshold value depending on particular scenarios.     

Data-directed modelling of Daphnia dynamics in a long-term micro-ecosystem experiment

The micro-ecosystem under consideration consists of three compartments forming a closed chain in which water circulates. Three trophic levels are represented in different compartments: autotrophs (algae, mainly Chlorella vulgaris), herbivores (Daphnia magna) and microbial decomposers. From a 20 years experiment with this system, data has been selected for this study. The dynamics of algae and Daphnia magna in only one of the compartments were modeled by different systems of differential and difference equations. We describe the successive steps in the process of model development, and the fitting of parameters using a Nelder-Mead simplex calibration method. Identification problems were overcome by taking values for physiological parameters in agreement with the literature. It turned out that a logistic type of model gives the best result for the structured Daphnia population because of the set up of the experiment: algae grow and reproduce in the upstream compartment. For this reason well-known plant–herbivore models did not comply with the data. The results of the parameter estimation procedure are discussed. The estimated grazing rate by Daphnia was smaller than expected. Possibly the Daphnia fed also on detritus and decomposing algae which were not measured.     

向日葵光合特性及其对不同生态条件的响应

对向日葵光合特性及其对不同生态条件响应的研究结果表明 :向日葵光饱和点为 1 70 0 μE·m-2 ·s-1 ,光补偿点为 95～ 1 2 0 μE·m-2 ·s-1 ;向日葵在光饱和点范围内 ,净光合速率随着光强的增加而增加 ,但随着相对湿度的增加而减小 ;向日葵光合适温为 2 3～ 33℃ ;气孔导度不是导致向日葵光合“午休”的主要影响因素 ,而光合有机物质可溶性糖的积累所产生的抑制作用才是光合“午休”的主要原因。     

重视生态策略在建筑设计中的运用

建筑既作用于生态环境，也作用于人类，它始终持续地影响着周围的环境和使用者的生活，特别是对于我国高速发展的城市来说，其影响更是巨大。生态建筑将成为21世纪建筑设计的主流。建筑与可持续发展的三个重要方面(环境保护、经济发展和社会进步)密切相关，生态建筑应是可持续发展的一个组成部分。文章针对我国生态环境与建筑设计中存在的主要问题，提出在建筑设计中要注重生态策略的运用，推动生态建筑设计要依靠全社会生态意识的提高，增强人与自然环境的沟通，完善生态建筑设计的法律规范。     

Line transect sampling of Karner blue butterflies ( Lycaeides melissa samuelis)

Line transect sampling is an effective survey method for estimating butterfly densities because it provides unbiased estimates of site-density (provided key assumptions are met), and estimates are comparable among sites. For monitoring Karner blue butterflies in Wisconsin, USA, comparable estimates are required because each year a different selection of sites will be monitored. Annual state-wide indices of species abundance can be derived from the site-surveys and compared to previous year's indices to monitor trends. We advocate that line transect sampling is preferable to Pollard-Yates transects as a survey technique for monitoring Karner blue butter- flies. The Pollard-Yates surveys do not adjust for diferences in site detectability. As a consequence, estimates of among-site from Pollard-Yates surveys can be biased. © Rapid Science 1998     

Coregionalization analysis with a drift for multi-scale assessment of spatial relationships between ecological variables 1. Estimation of drift and random components

In two articles, we present ‘coregionalization analysis with a drift’ (CRAD), a method to assess the multi-scale variability of and relationships between ecological variables from a multivariate spatial data set. In phase I of CRAD (the first article), a deterministic drift component representing the large-scale pattern and a random component modeled as a second-order stationary process are estimated for each variable separately. In phase II (this article), a linear model of coregionalization (LMC) is fitted by estimated generalized least squares to the direct and cross experimental variograms of residuals (i.e., after the removal of estimated drifts). Structural correlations and coefficients of determination at smaller scales are then computed from the estimated coregionalization matrices, while the estimated drifts are used to calculate pseudo coefficients at large scale. The performance of five procedures in estimating correlations and coefficients of determination was compared using a Monte Carlo study. In four CRAD procedures, drift estimation was based on local polynomials of order 0, 1, 2 (L₀, L₁, L₂) or a global polynomial with forward selection of the basis functions; the fifth procedure was coregionalization analysis (CRA), in which large-scale patterns were modeled as a supplemental component in the LMC. In bivariate and multivariate analyses, the uncertainty in the estimation of correlations and coefficients of determination could be related to the interference between spatial components within a bounded sampling domain. In the bivariate case, most procedures provided acceptable estimates of correlations. In regionalized redundancy analysis, uncertainty was highest for CRA, while L₁ provided the best results overall. In a forest ecology example, the identification of scale-specific correlations between plant species diversity and soil and topographical variables illustrated the potential of CRAD to provide unique insight into the functioning of complex ecosystems.