Bayesian spatial prediction

This paper presents a complete Bayesian methodology for analyzing spatial data, one which employs proper priors and features diagnostic methods in the Bayesian spatial setting. The spatial covariance structure is modeled using a rich class of covariance functions for Gaussian random fields. A general class of priors for trend, scale, and structural covariance parameters is considered. In particular, we obtain analytic results that allow easy computation of the predictive distribution for an arbitrary prior on the parameters of the covariance function using importance sampling. The computations, as well as model diagnostics and sensitivity analysis, are illustrated with a set of precipitation data.     

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.     

Finite area smoothing with generalized distance splines

Most conventional spatial smoothers smooth with respect to the Euclidean distance between observations, even though this distance may not be a meaningful measure of spatial proximity, especially when boundary features are present. When domains have complicated boundaries leakage (the inappropriate linking of parts of the domain which are separated by physical barriers) can occur. To overcome this problem, we develop a method of smoothing with respect to generalized distances, such as within domain distances. We obtain the generalized distances between our points and then use multidimensional scaling to find a configuration of our observations in a Euclidean space of 2 or more dimensions, such that the Euclidian distances between points in that space closely approximate the generalized distances between the points. Smoothing is performed over this new point configuration, using a conventional smoother. To mitigate the problems associated with smoothing in high dimensions we use a generalization of thin plate spline smoothers proposed by Duchon (Constructive theory of functions of several variables, pp 85–100, 1977). This general method for smoothing with respect to generalized distances improves on the performance of previous within-domain distance spatial smoothers, and often provides a more natural model than the soap film approach of Wood et al. (J R Stat Soc Ser B Stat Methodol 70(5):931–955, 2008). The smoothers are of the linear basis with quadratic penalty type easily incorporated into a range of statistical models.     

小流域土壤有机质和全磷空间变异分析——以安徽省舒城县龙潭小流域为例

为了解土壤的地域差异性,基于地统计学半方差函数理论和GIS空间克立格插值定量分析了安徽省舒城县龙潭小流域有机质、全磷的各向同性、各向异性变异特征及分布格局.结果表明,有机质、全磷的半方差拟合模型均为指数模型,两者的分布都显示了强烈的空间自相关,自相关距离分别为642 m、435 m.有机质、全磷变异的各向异性都比较显著,有机质在0°、50°方向上变异程度明显大于90°、145°方向;全磷则在0°、145°方向的变异程度更加突出.有机质、全磷的分布呈明显的块状和带状,其中有机质中部含量高,南部、西部含量低;全磷则是南部、西北含量高,西部、东北含量低.     

Applying the Patuxent Landscape Unit Model to human dominated ecosystems: the case of agriculture

Non-spatial dynamics are core to landscape simulations. Unit models simulate system interactions aggregated within one space unit of resolution used within a spatial model. For unit models to be applicable to spatial simulations they have to be formulated in a general enough way to simulate all habitat elements within the landscape. Within the Patuxent River watershed, human dominated land uses, such as agriculture and urban land, are already 50% of the current land use, while urban land is replacing forests, agriculture and wetlands at a rapid rate. The Patuxent Landscape Model (PLM) with the Patuxent General Unit Model as core (Pat-GEM) was developed as a predictive policy tool to estimate environmental impacts of such land use changes. The Pat-GEM is based on the General Ecosystem Model (GEM) developed by [Ecol. Modelling 88 1996 263]. Previous calibrations of the Pat-GEM for anthropogenic land uses have not been satisfactory due to the scarcity of appropriate data. This paper shows Pat-GEM simulations of biomass growth and nutrient uptake for crops typical within the Patuxent watershed. The Pat-GEM was expanded to include processes and fluxes that characterize agricultural land use. The most important extension was to include crop rotation into the model. Additionally, we refined the processes for planting, harvesting and fertilization by introducing specific growth parameters. Our revised Pat-GEM was calibrated against the results from Erosion Productivity Impact Calculator (EPIC) a widely used and calibrated agricultural model. We achieved high correlation between results generated with Pat-GEM and EPIC. The correlation coefficients (r²) varied between 0.87 and 0.98, with the simulation results for winter wheat showing the lowest correlation coefficients. Intercalibration using EPIC is a powerful method for calibrating the Pat-GEM model for agricultural land use. EPIC was able (a) to provide about 30% of the input data required for running the Pat-GEM model; and (b) to provide time series output data (with a daily time step) to calibrate the output variables biomass production and nutrient uptake.     

Changes in the spatial distribution of spawning activity by north-east Atlantic mackerel in warming seas: 1977–2010

Migratory species with a broad geographic range, such as north-east Atlantic mackerel, may be amongst the fauna most able to respond to warming seas, typically with a poleward shift in range. Habitat heterogeneity could, however, produce more complex patterns than a simple polewards translation in distribution. We tested for changes in the central location and spatial spread of mackerel spawning over a 33-year period. Spatial statistics [centre of gravity (CoG) of egg production, spatial variance, and degree of anisotropy] were used to summarise interannual changes in the spawning locations of the western spawning stock of north-east Atlantic mackerel (NEA-WSC) using data from the ICES triennial egg survey. A northwards shift in CoG of egg production estimates was observed, related to both an expansion in the distribution in survey effort and warming waters of the north-east Atlantic. Sea surface temperature (SST) had a significant positive association with the observed northward movement of NEA-WSC mackerel, equivalent to a displacement of 37.7 km °C^?1 (based on spring mean SST for the region). The spatial distribution of spawning around the CoG also changed significantly with SST, with a less elongated spatial spread in warm years. An increase in the proportion of spawning over the Porcupine Bank demonstrated how habitat interacts with positional shifts to affect how north-east Atlantic mackerel are distributed around the centre of their spawning range.     

A note on a non-stationary point source spatial model

A point source, non-stationary covariance structure model is proposed, having only one additional parameter over a standard, stationary covariance structure, spatial model. Additionally, the proposed model is demonstrated to fit better than the three extra parameter, point source, non-stationary spatial model proposed by Ecker and De Oliveira (Commun Stat Theory Methods 37:2066–2078, 2008). The proposed model is fit from a Bayesian perspective and illustrated using a house sales dataset from Cedar Falls, Iowa.     

A zero-inflated Bayesian spatial model with near-locating measurements

Zero-inflated data arise in many contexts. In this paper, we develop a zero-inflated Bayesian hierarchical model which deals with spatial effects, correlation among near-locating measurements as well as excess zeros simultaneously. Inference, including the sampling from the posterior distributions, predictions at new locations, and model selection, is carried out by using computationally efficient Markov chain Monte Carlo techniques. The posterior distributions are simulated using a Gibbs sampler with the embedded ratio-of-uniform method and the slice sampling algorithm. The approach is illustrated via an application to herbaceous data collected in the Missouri Ozark Forest Ecosystem Project. The results from the proposed model are compared with those generated from a non-zero inflated model. The proposed model fully incorporates the information from data collection and provides more reliable inference. A predictive $p$ value is computed for model checking and it indicates that the proposed model fits the data well.     

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.     

Efficacy of extracting indices from large‐scale acoustic recordings to monitor biodiversity

Passive acoustic monitoring could be a powerful way to assess biodiversity across large spatial and temporal scales. However, extracting meaningful information from recordings can be prohibitively time consuming. Acoustic indices (i.e., a mathematical summary of acoustic energy) offer a relatively rapid method for processing acoustic data and are increasingly used to characterize biological communities. We examined the relationship between acoustic indices and the diversity and abundance of biological sounds in recordings. We reviewed the acoustic‐index literature and found that over 60 indices have been applied to a range of objectives with varying success. We used 36 of the most indicative indices to develop a predictive model of the diversity of animal sounds in recordings. Acoustic data were collected at 43 sites in temperate terrestrial and tropical marine habitats across the continental United States. For terrestrial recordings, random‐forest models with a suite of acoustic indices as covariates predicted Shannon diversity, richness, and total number of biological sounds with high accuracy (R² ≥ 0.94, mean squared error [MSE] ≤170.2). Among the indices assessed, roughness, acoustic activity, and acoustic richness contributed most to the predictive ability of models. Performance of index models was negatively affected by insect, weather, and anthropogenic sounds. For marine recordings, random‐forest models poorly predicted Shannon diversity, richness, and total number of biological sounds (R² ≤ 0.40, MSE ≥ 195). Our results suggest that using a combination of relevant acoustic indices in a flexible model can accurately predict the diversity of biological sounds in temperate terrestrial acoustic recordings. Thus, acoustic approaches could be an important contribution to biodiversity monitoring in some habitats.     

Mouse lemurs in space and time: a test of the socioecological model

Socioecological theory predicts that the distribution of fertile females in space and time is the major determinant of male spacing behavior and mating strategies. Using a small nocturnal Malagasy primate, the gray mouse lemur (Microcebus murinus), we determined the spatiotemporal distribution of estrous females during the brief annual mating season to examine the predictive power of the socioecological model for male mating strategies. Mouse lemurs are particularly interesting in this respect because this polygynous species is characterized by seasonal reproduction, seasonally reversed sexual dimorphism, and relatively large testes. All resident animals in our 8-ha study area, a total of 30 adult males and 27 adult females, were individually marked and regularly recaptured to determine female reproductive status and to obtain home range data. We found that the mating season is limited to 4 weeks following female emergence from hibernation. Only 3-9 females could have synchronized estruses during a given week, indicating a moderately high male monopolization potential. However, receptive females were not spatially clumped and male ranges overlapped with those of many other rivals. Therefore, we suggest that individual powerful males may be unable to defend exclusive permanent access to receptive females because of prohibitive costs of range defense resulting from the strongly male-biased operational sex ratio and the corresponding intruder pressure. Our general conclusions are (1) that the socioecological model provides a useful heuristic framework for the study of mating systems, but that (2) it does not specify the degree of spatiotemporal clumping of receptive females at which male mating strategies switch among mate guarding, spatial exclusion of rivals, and roaming, and that (3) the operational sex ratio can have profound effects on male mating strategies as well.     

Fractal properties of spatial distribution of intertidal benthic communities

We studied the spatial distribution of intertidal macrozoobenthos, microphytobenthos (diatom algae) and sediments at scales from decimeters to kilometers using an index of spatial homogeneity, D _I. Sediments were found to be randomly distributed, making up a mosaic of silty and sandy sites. On the contrary, the estimated spatial variability of macrofauna within all the scales up to 5500 m depended upon neither extent (total area covered) nor grain (finest spatial resolution) but only their ratio. We treat this as evidence of statistical self-similarity (fractal property) of the pattern. For diatoms, spatial heterogeneity of community structure was also self-similar in the range from 0.25 to 75 m (within a single bight). At larger scales, microalgae showed a combination of patchy structure with pronounced gradient along the shoreline from brackish-water to marine flora. Thus, fractal properties of both groups became manifested at scales corresponding to their mean body size. The ranges of fractal patterns were approximately equal to 10³–10⁵ if measured in body size units. We suggest that fractal-like spatial structures may be a general feature of communities, and speculate on the nature of such patterns. Received: 16 February 1999 / Accepted: 30 December 1999     

Evolving social influence in large populations

Darwinian studies of collective human behaviour, which deal fluently with change and are grounded in the details of social influence among individuals, have much to offer “social” models from the physical sciences which have elegant statistical regularities. Although Darwinian evolution is often associated with selection and adaptation, “neutral” models of drift are equally relevant. Building on established neutral models, we present a general, yet highly parsimonious, stochastic model, which generates an entire family of real-world, right-skew socio-economic distributions, including exponential, winner-take-all, power law tails of varying exponents, and power laws across the whole data. The widely used Barabási and Albert (1999) Science 286: 509-512 “B-A” model of preferential attachment is a special case of this general model. In addition, the model produces the continuous turnover observed empirically within these distributions. Previous preferential attachment models have generated specific distributions with turnover using arbitrary add-on rules, but turnover is an inherent feature of our model. The model also replicates an intriguing new relationship, observed across a range of empirical studies, between the power law exponent and the proportion of data represented in the distribution.     

Estimating the spatial covariance structure using the geoadditive model

In geostatistics, both kriging and smoothing splines are commonly used to generate an interpolated map of a quantity of interest. The geoadditive model proposed by Kammann and Wand (J R Stat Soc: Ser C (Appl Stat) 52(1):1–18, 2003) represents a fusion of kriging and penalized spline additive models. Complex data issues, including non-linear covariate trends, multiple measurements at a location and clustered observations are easily handled using the geoadditive model. We propose a likelihood based estimation procedure that enables the estimation of the range (spatial decay) parameter associated with the penalized splines of the spatial component in the geoadditive model. We present how the spatial covariance structure (covariogram) can be derived from the geoadditive model. In a simulation study, we show that the underlying spatial process and prediction of the spatial map are estimated well using the proposed likelihood based estimation procedure. We present several applications of the proposed methods on real-life data examples.     

Size and spatial arrangement of home range of checkered snapper <Emphasis Type="Italic">Lutjanus decussatus</Emphasis> (Lutjanidae) in an Okinawan coral reef determined using a portable GPS receiver

Although snappers (Lutjanidae) are commercially important fishery resources in tropical and subtropical waters, their home range size and its spatial arrangement have not been sufficiently clarified. In the present study, the size and spatial arrangement of the home range of the reef-associated checkered snapper Lutjanus decussatus (Lutjanidae) were investigated by use of a portable GPS receiver. In a 120 m × 120 m quadrat established on a section of the fringing reef of Ishigaki Island, 29 individuals of the species were identified by their color pattern and individuals were divided into five arbitrary size classes (class 1 <10 cm TL ≤ class 2 <15 cm TL ≤ class 3 <20 cm TL ≤ class 4 <25 cm TL ≤ class 5). Fish tracking by snorkeling was conducted with the portable GPS receiver. Site fidelity of this species was high. Home range size ranged from 93.0 to 3638.4 m², and there was a significant positive correlation between the home range size and fish total length. Home ranges of the same-sized individuals abutted each other (8.8% area overlap), whereas those of different-sized individuals overlapped (44.0% area overlap). Agonistic behavior (attack and agonistic display) was more frequently found among same-sized individuals (times of agonistic behavior/times of all encounters × 100 = 71.3%), whereas such agonistic behavior was rarely found among different-sized individuals (times of agonistic behavior/times of all encounters × 100 = 6.9%). These results suggest that home ranges of Lutjanus decussatus can be regarded as territories against same-sized individuals, but not different-sized individuals. The usefulness of the fish tracking by snorkeling using a portable GPS receiver for home range size estimation and the function of the overlapping territory of the species are discussed.     

城市可持续发展评价的分指数及综合指数公式

在指标按特征分类的基础上，提出了城市可持续发展评价分类指标的分指数公式和多类别组合的综合指数公式。应用遗传算法对公式中的参数进行优化，得到简单而适用的城市可持续发展评价模型。模型应用于全国“七五”，“八五”可持续发展评价结果与实际分析结果一致。该模型具有可比性强，通用性好和简单，实用的特点。     

Effects of time since fire on birds: how informative are generalized fire response curves for conservation management?

Fire is both a widespread natural disturbance that affects the distribution of species and a tool that can be used to manage habitats for species. Knowledge of temporal changes in the occurrence of species after fire is essential for conservation management in fire-prone environments. Two key issues are: whether postfire responses of species are idiosyncratic or if multiple species show a limited number of similar responses; and whether such responses to time since fire can predict the occurrence of species across broad spatial scales. We examined the response of bird species to time since fire in semiarid shrubland in southeastern Australia using data from surveys at 499 sites representing a 100-year chronosequence. We used nonlinear regression to model the probability of occurrence of 30 species with time since fire in two vegetation types, and compared species' responses with generalized response shapes from the literature. The occurrence of 16 species was significantly influenced by time since fire: they displayed six main responses consistent with generalized response shapes. Of these 16 species, 15 occurred more frequently in mid- or later-successional vegetation (> 20 years since fire), and only one species occurred more often in early succession (< 5 years since fire). The models had reasonable predictive ability for eight species, some predictive ability for seven species, and were little better than random for one species. Bird species displayed a limited range of responses to time since fire; thus a small set of fire ages should allow the provision of habitat for most species. Postfire successional changes extend for decades and management of the age class distribution of vegetation will need to reflect this timescale. Response curves revealed important seral stages for species and highlighted the importance of mid- to late-successional vegetation (> 20 years). Although time since fire clearly influences the distribution of numerous bird species, predictive models of the spatial distribution of species in fire-prone landscapes need to incorporate other factors in addition to time since fire.     

A general random walk model for the leptokurtic distribution of organism movement: Theory and application

The movement of organisms is usually leptokurtic in which some individuals move long distances while the majority remains at or near the area they are released. There has been extensive research into the origin of such leptokurtic movement, but one important aspect that has been overlooked is that the foraging behaviour of most organisms is not Brownian as assumed in most existing models. In this paper we show that such non-Brownian foraging indeed gives rise to leptokurtic distribution. We first present a general random walk model to describe the organism movement by breaking the foraging of each individual into events of active movement and inactive stationary period; its foraging behaviour is therefore fully characterized by a joint probability of how far the individual can move in each active movement and the duration it remains stationary between two consecutive movements. The spatio-temporal distribution of the organism can be described by a generalized partial differential equation, and the leptokurtic distribution is a special case when the stationary period is not exponentially distributed. Empirical observations of some organisms living in different habitats indicated that their rest time shows a power-law distribution, and we speculate that this is general for other organisms. This leads to a fractional diffusion equation with three parameters to characterize the distributions of stationary period and movement distance. A method to estimate the parameters from empirical data is given, and we apply the model to simulate the movement of two organisms living in different habitats: a stream fish (Cyprinidae: Nocomis leptocephalus) in water, and a root-feeding weevil, Sitona lepidus in the soil. Comparison of the simulations with the measured data shows close agreement. This has an important implication in ecology that the leptokurtic distribution observed at population level does not necessarily mean population heterogeneity as most existing models suggested, in which the population consists of different phenotypes; instead, a homogeneous population moving in homogeneous habitat can also lead to leptokurtic distribution.