Model-based combination of spatial information for stream networks

Evolutionary improvements in Geographic Information Systems (GIS) now routinely allow the management and mapping of spatial-temporal information. In response, the development of statistical models to combine information of different types and spatial support is of vital importance to environmental science. In this paper we develop a hierarchical spatial statistical model for environmental indicators of stream and river systems in the United States Mid-Atlantic Region by combining information from separate monitoring surveys, available contextual information on hydrologic units and remote sensing information. These models are used to estimate the indicators throughout the riverine system based on information from multiple sources and aggregate scales. The analysis is based on information underlying the Landscape Atlas of the mid-Atlantic region produced by the US Environmental Monitoring and Assessment Program (EMAP). We also combine information from two overlapping separate monitoring surveys, the EMAP Stream and River Survey and the Maryland Biological Streams Survey. We present a general framework for comparative distributional analysis based on the concept of a relative spatial distribution. As an application, the spatial model is used to predict spatial distributions and relative spatial distributions for a watershed.     

Triangulation based inclusion probabilities: a design-unbiased sampling approach

A probabilistic sampling approach for design-unbiased estimation of area-related quantitative characteristics of spatially dispersed population units is proposed. The developed field protocol includes a fixed number of 3 units per sampling location and is based on partial triangulations over their natural neighbors to derive the individual inclusion probabilities. The performance of the proposed design is tested in comparison to fixed area sample plots in a simulation with two forest stands. Evaluation is based on a general approach for areal sampling in which all characteristics of the resulting population of possible samples is derived analytically by means of a complete tessellation of the areal sampling frame. The example simulation shows promising results. Expected errors under this design are comparable to sample plots including a much greater number of trees per plot.     

The memory of spatial patterns: changes in local abundance and aggregation in a tropical forest

The current spatial pattern of a population is the result of previous individual birth, death, and dispersal events. We present a simple model followed by a comparative analysis for a species-rich plant community to show how the current spatial aggregation of a population may hold information about recent population dynamics. Previous research has shown how locally restricted seed dispersal often leads to stronger aggregation in less abundant populations than it does in more abundant populations. In contrast, little is known about how changes in the local abundance of a species may affect the spatial distribution of individuals. If the level of aggregation within a species depends to some extent on the abundance of the species, then changes in abundance should lead to subsequent changes in aggregation. However, an overall change of spatial pattern relies on many individual birth and death events, and a surplus of deaths or births may have short-term effects on aggregation that are opposite to the long-term change predicted by the change in abundance. The change in aggregation may therefore lag behind the change in abundance, and consequently, the current aggregation may hold information about recent population dynamics. Using an individual-based simulation model with local dispersal and density-dependent competition, we show that, on average, recently growing populations should be more aggregated than shrinking populations of the same current local abundance. We tested this hypothesis using spatial data on individuals from a long-term tropical rain forest plot, and find support for this relationship in canopy trees, but not in understory and shrub species. On this basis we argue that current spatial aggregation is an important characteristic that contains information on recent changes in local abundance, and may be applied to taxonomic groups where dispersal is limited and within-species aggregation is observed.     

Habitat association studies in conjunction with adaptive cluster samples

Habitat association studies investigate the relationships between habitat characteristics and animal usage of study regions. These studies are often conducted in conjunction with surveys designed primarily to estimate population totals. This paper shows that habitat association studies may proceed from surveys using adaptive cluster sampling. The manner in which units appear in the sample turns out not be relevant to the habitat association study, which proceeds as though the units came from a simple random sample. However, it is also shown that the information about the habitat association parameters is greater than one would expect from a simple random sample of the same general size.     

Halton iterative partitioning: spatially balanced sampling via partitioning

A new spatially balanced sampling design for environmental surveys is introduced, called Halton iterative partitioning (HIP). The design draws sample locations that are well spread over the study area. Spatially balanced designs are known to be efficient when surveying natural resources because nearby locations tend to be similar. The HIP design uses structural properties of the Halton sequence to partition a resource into nested boxes. Sample locations are then drawn from specific boxes in the partition to ensure spatial diversity. The method is conceptually simple and computationally efficient, draws spatially balanced samples in two or more dimensions and uses standard design-based estimators. Furthermore, HIP samples have an implicit ordering that can be used to define spatially balanced over-samples. This feature is particularly useful when sampling natural resources because we can dynamically add spatially balanced units from the over-sample to the sample as non-target or inaccessible units are discovered. We use several populations to show that HIP sampling draws spatially balanced samples and gives precise estimates of population totals.     

Analysis of neighborhood dynamics of forest ecosystems using likelihood methods and modeling.

Advances in computing power in the past 20 years have led to a proliferation of spatially explicit, individual-based models of population and ecosystem dynamics. In forest ecosystems, the individual-based models encapsulate an emerging theory of "neighborhood" dynamics, in which fine-scale spatial interactions regulate the demography of component tree species. The spatial distribution of component species, in turn, regulates spatial variation in a whole host of community and ecosystem properties, with subsequent feedbacks on component species. The development of these models has been facilitated by development of new methods of analysis of field data, in which critical demographic rates and ecosystem processes are analyzed in terms of the spatial distributions of neighboring trees and physical environmental factors. The analyses are based on likelihood methods and information theory, and they allow a tight linkage between the models and explicit parameterization of the models from field data. Maximum likelihood methods have a long history of use for point and interval estimation in statistics. In contrast, likelihood principles have only more gradually emerged in ecology as the foundation for an alternative to traditional hypothesis testing. The alternative framework stresses the process of identifying and selecting among competing models, or in the simplest case, among competing point estimates of a parameter of a model. There are four general steps involved in a likelihood analysis: (1) model specification, (2) parameter estimation using maximum likelihood methods, (3) model comparison, and (4) model evaluation. Our goal in this paper is to review recent developments in the use of likelihood methods and modeling for the analysis of neighborhood processes in forest ecosystems. We will focus on a single class of processes, seed dispersal and seedling dispersion, because recent papers provide compelling evidence of the potential power of the approach, and illustrate some of the statistical challenges in applying the methods.     

Bridging the gap between ecophysiological and genetic knowledge to assess the adaptive potential of European beech

In this study we aimed to combine knowledge of the ecophysiology and genetics of European beech to assess the potential of this species to adapt to environmental change. Therefore, we performed field and experimental studies on the genetic and ecophysiological functioning of beech. This information was integrated through a coupled genetic–ecophysiological model for individual trees that was parameterized with information derived from our own studies or from the literature. Using the model, we evaluated the adaptive response of beech stands in two ways: firstly, through sensitivity analyses (of initial genetic diversity, pollen dispersal distance, heritability of selected phenotypic traits, and forest management, representing disturbances) and secondly, through the evaluation of the responses of phenotypic traits and their genetic diversity to four management regimes applied to 10 study plots distributed over Western Europe. The model results indicate that the interval between recruitment events strongly affects the rate of adaptive response, because selection is most severe during the early stages of forest development. Forest management regimes largely determine recruitment intervals and thereby the potential for adaptive responses. Forest management regimes also determine the number of mother trees that contribute to the next generation and thereby the genetic variation that is maintained. Consequently, undisturbed forests maintain the largest amount of genetic variation, as recruitment intervals approach the longevity of trees and many mother trees contribute to the next generation. However, undisturbed forests have the slowest adaptive response, for the same reasons.Gene flow through pollen dispersal may compensate for the loss in genetic diversity brought about by selection. The sensitivity analysis showed that the total genetic diversity of a 2 ha stand is not affected by gene flow if the pollen distance distribution is varied from highly left-skewed to almost flat. However, a stand with a prevailing short-distance gene flow has a more pronounced spatial genetic structure than stands with equal short- and long-distance gene flows. The build-up of a spatial genetic structure is also strongly determined by the recruitment interval. Overall, the modelling results indicate that European beech has high adaptive potential to environmental change if recruitment intervals are short and many mother trees contribute to the next generation.The findings have two implications for modelling studies on the impacts of climate change on forests. Firstly: it cannot be taken for granted that parameter values remain constant over a time horizon of even a few generations – this is particularly important for threshold values subject to strong selection, like budburst, frost hardiness, drought tolerance, as used in species area models. Secondly: forest management should be taken into account in future assessments, as management affects the rate of adaptive response and thereby the response on trees and forests to environmental change, and because few forests are unmanaged. We conclude that a coupled ecophysiological and quantitative genetic tree model is a useful tool for such studies.     

抚育间伐对栓皮栎种群空间分布格局的影响

抚育间伐是一种重要的改善林木生长条件的经营措施,对林分结构和动态具有重要影响。为研究抚育间伐对林木种群空间结构与格局影响的内在机制,以间伐和未间伐的栓皮栎人工林为研究对象,通过设置2个100 m×100 m样地并进行每木定位和调查,在采用径级结构代替年龄结构方法将栓皮栎种群划分为幼树(2 cm≤DBH<5 cm)、小树(5 cm≤DBH<13 cm)和大树(DBH≥13 cm)3个生长阶段的基础上,分别采用Ripley’s K函数衍生的g(r)函数和双变量g12(r)函数,对栓皮栎种群空间分布点格局及不同生长阶段栓皮栎种群之间的关联性进行了研究。结果表明,间伐和未间伐样地栓皮栎种群空间分布点格局分别在0-16 m和0-33 m距离尺度内呈聚集分布,而分别在大于16 m和33 m距离尺度内呈随机分布;间伐和未间伐样地栓皮栎幼树、小树和大树的株数比分别为8?741?699和261?1134?683,且间伐样地栓皮栎幼树、小树和大树种群分别在0-14、1-16、0-6 m距离尺度内呈现均匀或聚集分布,而在其他距离尺度上表现为随机分布;栓皮栎幼树、小树和大树之间仅在间伐样地0-6 m距离尺度内呈现一定的相关性,而在未间伐样地更大的距离尺度内有显著的关联性,如栓皮栎幼树和大树之间在6-38 m距离尺度上呈显著正相关。因此,抚育间伐一定程度上使得栓皮栎种群在更大距离尺度上呈现出随机分布状态,并弱化了不同生长阶段的林木栓皮栎种群的关联性,这调整了栓皮栎种群空间竞争关系,有利于大径级林木个体的培育。该研究可以为开展抚育间伐对林木种群的影响的研究提供理论依据,也可以为制定科学合理的抚育技术措施提供参考。     

Resampling methods for estimating dispersion indices in random and adaptive designs

In many surveys in environmental and natural phenomena the aim is to evaluate the heterogeneity, and the skewness of the distribution of the number point-objects in the study area opportunely partitioned in sub-regions. For this purpose, in this paper the estimation of dispersion indices is considered by using simple random sampling and adaptive sampling with initial simple random sampling selected with replacement or without replacement. The jackknife and the bootstrap procedures are proposed in both cases for reducing bias. Finally, both a simulation study and a case study on biological population referred to a Oidium tuckeri contamination in a growing vineyard is performed to assess the accuracy of the proposed estimators.     

Spatial methods for plot-based sampling of wildlife populations

Classical sampling methods can be used to estimate the mean of a finite or infinite population. Block kriging also estimates the mean, but of an infinite population in a continuous spatial domain. In this paper, I consider a finite population version of block kriging (FPBK) for plot-based sampling. The data are assumed to come from a spatial stochastic process. Minimizing mean-squared-prediction errors yields best linear unbiased predictions that are a finite population version of block kriging. FPBK has versions comparable to simple random sampling and stratified sampling, and includes the general linear model. This method has been tested for several years for moose surveys in Alaska, and an example is given where results are compared to stratified random sampling. In general, assuming a spatial model gives three main advantages over classical sampling: (1) FPBK is usually more precise than simple or stratified random sampling, (2) FPBK allows small area estimation, and (3) FPBK allows nonrandom sampling designs.     

Chilean Blue Whales as a Case Study to Illustrate Methods to Estimate Abundance and Evaluate Conservation Status of Rare Species

Abstract: Often abundance of rare species cannot be estimated with conventional design‐based methods, so we illustrate with a population of blue whales (Balaenoptera musculus) a spatial model‐based method to estimate abundance. We analyzed data from line‐transect surveys of blue whales off the coast of Chile, where the population was hunted to low levels. Field protocols allowed deviation from planned track lines to collect identification photographs and tissue samples for genetic analyses, which resulted in an ad hoc sampling design with increased effort in areas of higher densities. Thus, we used spatial modeling methods to estimate abundance. Spatial models are increasingly being used to analyze data from surveys of marine, aquatic, and terrestrial species, but estimation of uncertainty from such models is often problematic. We developed a new, broadly applicable variance estimator that showed there were likely 303 whales (95% CI 176–625) in the study area. The survey did not span the whales' entire range, so this is a minimum estimate. We estimated current minimum abundance relative to pre‐exploitation abundance (i.e., status) with a population dynamics model that incorporated our minimum abundance estimate, likely population growth rates from a meta‐analysis of rates of increase in large baleen whales, and two alternative assumptions about historic catches. From this model, we estimated that the population was at a minimum of 9.5% (95% CI 4.9–18.0%) of pre‐exploitation levels in 1998 under one catch assumption and 7.2% (CI 3.7–13.7%) of pre‐exploitation levels under the other. Thus, although Chilean blue whales are probably still at a small fraction of pre‐exploitation abundance, even these minimum abundance estimates demonstrate that their status is better than that of Antarctic blue whales, which are still <1% of pre‐exploitation population size. We anticipate our methods will be broadly applicable in aquatic and terrestrial surveys for rarely encountered species, especially when the surveys are intended to maximize encounter rates and estimate abundance.     

Testing the effectiveness of capture mark recapture population estimation techniques using a computer simulation with known population size

Estimation of small mammal population sizes is important for monitoring ecosystem condition and for conservation. Here, we test the accuracy of standard methods of population size estimation using Capture-Mark-Recapture (CMR) on a simulated population of agents. The use of a computer simulation allows complete control of population sizes and behaviors, thereby avoiding assumptions that may be violated in real populations. We find that the recommended protocol for CMR sampling, using uniformly distributed traps, consistently overestimates population sizes by as much as 100% when studies are conducted over only two trapping periods. More than 20 trapping periods are required before this method, or that of placing traps randomly, gives an accurate estimation of population size (i.e., within a 95% confidence limit of the actual value). Non-random sampling, by placing traps on runways used by small mammals, produces the most accurate, and least variable, estimates of population. However, we show that around 10 trapping periods are still required to produce an accurate population estimate using this method. Given that most real populations do not comply with the ‘ideal’ assumptions made by CMR, we suggest that population estimates based on CMR may be fundamentally flawed, and recommend that protocols for CMR population estimation methods may need revising.     

Estimation of rare and clustered population mean using stratified adaptive cluster sampling

For many clustered populations, the prior information on an initial stratification exists but the exact pattern of the population concentration may not be predicted. Under this situation, the stratified adaptive cluster sampling (SACS) may provide more efficient estimates than the other conventional sampling designs for the estimation of rare and clustered population parameters. For practical interest, we propose a generalized ratio estimator with the single auxiliary variable under the SACS design. The expressions of approximate bias and mean squared error (MSE) for the proposed estimator are derived. Numerical studies are carried out to compare the performances of the proposed generalized estimator over the usual mean and combined ratio estimators under the conventional stratified random sampling (StRS) using a real population of redwood trees in California and generating an artificial population by the Poisson cluster process. Simulation results show that the proposed class of estimators may provide more efficient results than the other estimators considered in this article for the estimation of highly clumped population.

     

Remote sensing: Using the spatial domain

Objects in the terrestrial environment interact differentially with electromagnetic radiation according to their essential physical, chemical and biological properties. This differential interaction is manifest as variability in scattered radiation according to wavelength, location, time, geometries of illumination and observation and polarization. If the population of scattered radiation could be measured, then estimation of these essential properties would be straightforward. The only problem would be linking such estimates to environmental variables of interest. This review paper is divided into three parts. Part 1 is an overview of the attempts that have been made to sample the five domains of scattered radiation (spectral, spatial, temporal, geometrical, polarization) and then to use the results of this sampling to estimate environmental variables of interest. Part one highlights three issues: first, that relationships between remotely sensed data and environmental variables of interest are indirect; second, our ability to estimate these environmental variables is dependent upon our ability to capture a sound representation of variability in scattered radiation and third, a considerable portion of the useful information in remotely sensed images resides in the spatial domain (within the relations between the pixels in the image). This final point is developed in Part 2 that explores ways in which the spatial domain is utilized to describe spatial variation in remotely sensed and ground data; to design optimum sampling schemes for image data and ground data and to increase the accuracy with which remotely sensed data can be used to estimate both discontinuous and continuous variables. Part 3 outlines two specific uses of information in the spatial domain; first, to select an optimum spatial resolution and second, to inform an image classification.     

Simulation and analysis of outbreaks of bark beetle infestations and their management at the stand level

Outbreaks of bark beetles in forests can result in substantial economic losses. Understanding the factors that influence the development and spread of bark beetle outbreaks is crucial for forest management and for predicting outbreak risks, especially with the expected global warming. Although much research has been done on the ecology and phenology of bark beetles, the complex interplay between beetles, host trees, beetle antagonists and forest management makes predicting beetle population development especially difficult. Using the recent infestations of the European Spruce Bark Beetle (Ips typographus L. Col. Scol.) in the Bavarian Forest National Park (Germany) as a case study, we developed a spatially explicit agent-based simulation model (SAMBIA) that takes into account individual trees and beetles. This model primarily provides a tool for analysing and understanding the spatial and temporal aspects of bark beetles outbreaks at the stand scale. Furthermore, the model should allow an estimation of the effectiveness of concurrent impacts of both antagonists and management to confine outbreak dynamics in practice. We also used the model to predict outbreak probabilities in various settings. The simulation results indicated a distinct threshold behaviour of the system in response to pressure by antagonists or management of the bark beetle population. Despite the different scenarios considered, we were able to extract from the simulations a simple rule of thumb for the successful control of an outbreak: if roughly 80% of individual beetles are killed by antagonists or foresters, outbreaks will rarely take place. Our model allows the core dynamics of this complex system to be reduced to this inherent common denominator.     

Elephants as agents of habitat creation for small vertebrates at the patch scale

Ecologists increasingly recognize the ability of certain species to influence ecological processes by engineering the physical environment, but efforts to develop a predictive understanding of this phenomenon are in their early stages. While many believe that the landscape-scale effects of ecosystem engineers will be to increase habitat diversity and therefore the abundance and richness of other species, few generalities exist about the effects of engineering at the scale of the engineered patch. According to one hypothesis, activities that increase structural habitat complexity within engineered patches will have positive effects on the abundance or diversity of other organisms. Here I show that, by damaging trees and increasing their structural complexity, browsing elephants create refuges used by a common arboreal lizard. Observational surveys and a lizard transplant experiment revealed that lizards preferentially occupy trees with real or simulated elephant damage. A second experiment showed that lizards vacate trees when elephant-engineered refuges are removed. Furthermore, local lizard densities increased with (and may be constrained by) local densities of elephant-damaged trees. This facilitative effect of elephants upon lizards via patch-scale habitat modification runs contrary to previously documented negative effects of the entire ungulate guild on lizards at the landscape scale, suggesting that net indirect effects of large herbivores comprise opposing trophic and engineering interactions operating at different spatial scales. Such powerful megaherbivore-initiated interactions suggest that anthropogenic changes in large-mammal densities will have important cascading consequences for ecological communities.     

Spatially-balanced sampling versus unbalanced stratified sampling for assessing forest change: evidences in favour of spatial balance

Large-scale remote sensing-based inventories of forest cover are usually carried out by combining unsupervised classifications of satellite pixels into forest/non forest classes (map data) with subsequent time-consuming visual on-screen imagery classification of a probabilistic sample of pixels taken as the ground truth (reference data). In this paper the estimation of forest change from a sample of reference data is approached by: (i) exploiting map data to construct strata in which changes are occurred, and then adopting the stratified sampling joined with the HT estimator with most sampling effort devoted to strata where changes are occurred irrespective of their size, as suggested in most remote sensing literature regarding land change assessments; (ii) adopting a spatial scheme ensuring spatially balanced samples, as suggested in most recent statistical literature regarding spatial surveys, and exploiting the map data in the difference estimator. The results of a comparison performed on an artificial population of reference data generated from a real population of map data recorded in Sardinia (Italy) discourage the use of unbalanced stratified samples that achieve the worst precision. The best results are obtained by means of spatially balanced samples or stratification with nearly proportional allocation to strata.     

Modeling species-habitat relationships with spatially autocorrelated observation data.

Spatial autocorrelation in wildlife observation data arises when extrinsic environmental processes and patterns that influence the spatial distribution of wildlife are themselves spatially structured, or when species are subject to intrinsic population processes, causing contagion or dispersion effects. Territoriality, Allee effects, dispersal limitations, and social clustering are examples of intrinsic processes. Both forms of autocorrelation can violate the assumptions of generalized linear regression models, resulting in biased estimation of model coefficients and diminished predictive performance. Such consequences may be avoided for extrinsic autocorrelation when autocorrelated environmental variables are available for use as model covariates, whereas intrinsic spatial autocorrelation requires an alternative modeling approach. The autologistic model provides an approach suited to the binary observations often obtained in wildlife surveys, but its performance has not been tested across widely varying sampling intensities or strengths of intrinsic spatial structure. Here we use simulated data to test the autologistic model under a range of sampling conditions. The autologistic model obtains better fits and substantially better predictive performance than the standard logistic regression model over the full range of sampling designs and intensities tested. We provide a simple Bayesian implementation of the autologistic model, which until now has not been achieved with standard statistical software alone. A step-by-step procedure is given for characterizing and modeling spatial autocorrelation in binary observation data, along with computer code for fitting autologistic models in WinBUGS, a freeware Bayesian analysis package. This approach avoids normal approximations to the pseudo-likelihood, in contrast to previous Bayesian applications of the autologistic model. We provide a sample application of the autologistic model, fitted to survey data for a gliding marsupial in southeastern Australia.     

Modeling and spatial prediction of pre-settlement patterns of forest distribution using witness tree data

At the time of European settlement, land surveys were conducted progressively westward throughout the United States. Outside of the original 13 colonies, surveys generally followed the Public Land Survey system in which trees, called witness trees, were regularly recorded at 1 mi by 1 mi grid intersections. This unintentional sampling provides insight into the composition and structure of pre-European settlement forests, which is used as baseline data to assess forest change following settlement. In this paper, a model for the Public Land Surveys of east central Alabama is developed. Assuming that the locations of trees of each species are realized from independent Poisson processes whose respective log intensities are linear functions of environmental covariates (i.e., elevation, landform, and physiographic province), the species observed at the survey grid intersections are independently sampled from a generalized logistic regression model. If all 68 species found in the survey were included, the model would be highly over-parameterized, so only the distribution of the most common taxon, pines, will be considered at this time. To assess the impact of environmental factors not included in the model, a hidden Gaussian random field shall be added as a random effect. A Markov Chain Monte Carlo algorithm is developed for Bayesian inference on model parameters, and for Bayes posterior prediction of the spatial distribution of pines in east central Alabama. Received: June 2004 / Revised: November 2004     

Learning habitat models for the diatom community in Lake Prespa

Habitat suitability modelling studies the influence of abiotic factors on the abundance or diversity of a given taxonomic group of organisms. In this work, we investigate the effect of the environmental conditions of Lake Prespa (Republic of Macedonia) on diatom communities. The data contain measurements of physical and chemical properties of the environment as well as the relative abundances of 116 diatom taxa. In addition, we create a separate dataset that contains information only about the top 10 most abundant diatoms. We use two machine learning techniques to model the data: regression trees and multi-target regression trees. We learn a regression tree for each taxon separately (from the top 10 most abundant) to identify the environmental conditions that influence the abundance of the given diatom taxon. We learn two multi-target regression trees: one for modelling the complete community and the other for the top 10 most abundant diatoms. The multi-target regression trees approach is able to detect the conditions that affect the structure of a diatom community (as compared to other approaches that can model only a single target variable). We interpret and compare the obtained models. The models present knowledge about the influence of metallic ions and nutrients on the structure of the diatom community, which is consistent with, but further extends existing expert knowledge.