Density dependence in marine fish populations revealed at small and large spatial scales

Experimental manipulation of population density has frequently been used to demonstrate demographic density dependence. However, such studies are usually small scale and typically provide evidence of spatial (within-generation) density dependence. It is often unclear whether small-scale, experimental tests of spatial density dependence will accurately describe temporal (between-generation) density dependence required for population regulation. Understanding the mechanisms generating density dependence may provide a link between spatial experiments and temporal regulation of populations. In this study, I manipulated the density of recently settled kelp rockfish (Sebastes atrovirens) in both the presence and absence of predators to test for density-dependent mortality and whether predation was the mechanism responsible. I also examined mortality of rockfish cohorts within kelp beds throughout central California to evaluate temporal (between-generation) density dependence in mortality. Experiments suggested that short-term behavioral responses of predators and/or a shortage of prey refuges caused spatial density dependence. Temporal density dependence in mortality was also detected at larger spatial scales for several species of rockfish. It is likely that short-term responses of predators generated both spatial and temporal density dependence in mortality. Spatial experiments that describe the causal mechanisms generating density dependence may therefore be valuable in describing temporal density dependence and population regulation.     

Time-varying models for extreme values

We propose a new approach for modeling extreme values that are measured in time and space. First we assume that the observations follow a Generalized Extreme Value (GEV) distribution for which the location, scale or shape parameters define the space–time structure. The temporal component is defined through a Dynamic Linear Model (DLM) or state space representation that allows to estimate the trend or seasonality of the data in time. The spatial element is imposed through the evolution matrix of the DLM where we adopt a process convolution form. We show how to produce temporal and spatial estimates of our model via customized Markov Chain Monte Carlo (MCMC) simulation. We illustrate our methodology with extreme values of ozone levels produced daily in the metropolitan area of Mexico City and with rainfall extremes measured at the Caribbean coast of Venezuela.     

A GIS-based approach to spatio-temporal analysis of environmental pollution in urban areas: A case study of Prague's environment extended by LIDAR data

Environmental pollution of urban areas is one of key factors that state authorities and local agencies have to consider in the decision-making process. To find a compromise among many criteria, spatial analysis extended by geostatistical methods and dynamic models has to be carried out. In this case, spatial analysis includes processing of a wide range of air, water and soil pollution data and possibly noise assessment and waste management data. Other spatial inputs consist of data from remote sensing and GPS field measurements. Integration and spatial data management are carried out within the framework of a geographic information system (GIS). From a modeling point of view, GIS is used mainly for the preprocessing and postprocessing of data to be displayed in digital map layers and visualized in 3D scenes. Moreover, for preprocessing and postprocessing, deterministic and geostatistical methods (IDW, ordinary kriging) are used for spatial interpolation; geoprocessing and raster algebra are used in multi-criteria evaluation and risk assessment methods. GIS is also used as a platform for spatio-temporal analyses or for building relationships between the GIS database and stand-alone modeling tools. A case study is presented illustrating the application of spatial analysis to the urban areas of Prague. This involved incorporating environmental data from monitoring networks and field measurements into digital map layers. Extra data inputs were used to represent the 3D concentration fields of air pollutants (ozone, NO₂) measured by differential absorption LIDAR. ArcGIS was used to provide spatial data management and analysis, extended by modeling tools developed internally in the ArcObjects environment and external modules developed with MapObjects. Ordinary kriging methods were employed to predict ozone concentrations in selected 3D locations together with estimates of variability. Higher ozone concentrations were found above crossroads with their heavy traffic than above the surrounding areas. Ozone concentrations also varied with height above the digital elevation model. Processed data, spatial analysis and models are integrated within the framework of the GIS project, providing an approach that state and local authorities can use to address environmental protection issues.     

Hierarchical Bayesian space-time models

Space-time data are ubiquitous in the environmental sciences. Often, as is the case with atmo- spheric and oceanographic processes, these data contain many different scales of spatial and temporal variability. Such data are often non-stationary in space and time and may involve many observation/prediction locations. These factors can limit the effectiveness of traditional space- time statistical models and methods. In this article, we propose the use of hierarchical space-time models to achieve more flexible models and methods for the analysis of environmental data distributed in space and time. The first stage of the hierarchical model specifies a measurement- error process for the observational data in terms of some 'state' process. The second stage allows for site-specific time series models for this state variable. This stage includes large-scale (e.g. seasonal) variability plus a space-time dynamic process for the anomalies'. Much of our interest is with this anomaly proc ess. In the third stage, the parameters of these time series models, which are distributed in space, are themselves given a joint distribution with spatial dependence (Markov random fields). The Bayesian formulation is completed in the last two stages by speci- fying priors on parameters. We implement the model in a Markov chain Monte Carlo framework and apply it to an atmospheric data set of monthly maximum temperature.     

Detecting and Modeling Spatial and Temporal Dependence in Conservation Biology

Abstract: Due to the structuring forces and large-scale physical processes that shape our biosphere, we often find that environmental and ecological data are either spatially or temporally—or both spatially and temporally—dependent. When these data are analyzed, statistical techniques and models are frequently applied that were developed for independent data. We describe some of the detrimental consequences, such as inefficient parameter estimators, biased hypothesis test results, and inaccurate predictions, of ignoring spatial and temporal data dependencies, and we cite an example of adverse statistical results occurring when spatial dependencies were disregarded. We also discuss and recommend available techniques used to detect and model spatial and temporal dependence, including variograms, covariograms, autocorrelation and partial autocorrelation plots, geostatistical techniques, Gaussian autoregressive models, K functions, and ARIMA models, in environmental and ecological research to avoid the aforementioned difficulties.     

A nonparametric procedure for analyzing repeated measures of spatially correlated data

Many agricultural, biological, and environmental studies involve detecting temporal changes of a response variable, based on data observed at sampling sites in a spatial region and repeatedly over several time points. That is, data are repeated measures over time and are potentially correlated across space. The traditional repeated-measures analysis allows for time dependence but assumes that the observations at different sampling sites are mutually independent, which may not be suitable for field data that are correlated across space. In this paper, a nonparametric large-sample inference procedure is developed to assess the time effects while accounting for the spatial dependence using a block bootstrap. For illustration, the methodology is applied to describe the population changes of root-lesion nematodes over time in a production field in Wisconsin.     

A simple non-separable,non-stationary spatiotemporal model for ozone

The past two decades have witnessed an increasing interest in the use of space-time models for a wide range of environmental problems. The fundamental tool used to embody both the temporal and spatial components of the phenomenon in question is the covariance model. The empirical estimation of space-time covariance models can prove highly complex if simplifying assumptions are not employed. For this reason, many studies assume both spatiotemporal stationarity, and the separability of spatial and temporal components. This second assumption is often unrealistic from the empirical point of view. This paper proposes the use of a model in which non-separability arises from temporal non-stationarity. The model is used to analyze tropospheric ozone data from the Emilia-Romagna Region of Italy.     

State space models with spatial deformation

Space deformation has been proposed to model space-time varying observation processes with non-stationary spatial covariance structure under the hypothesis of temporal stationarity. In real applications, however, the temporal stationarity assumption is inappropriate and unrealistic. In this work we propose a spatial-temporal model whose temporal trend is modeled through state space models and a spatially varying anisotropy is modeled through spatial deformation, under the Bayesian approach. A distinctive feature of our approach is the consideration of model uncertainty in an unified framework. Our model has a clear advantage over the ones proposed so far in the literature when the main objective of the study is to perform spatial interpolation for fixed points in time. Approximations of the posterior distributions of the model parameters are obtained via Markov chain Monte Carlo methods. This allows for prediction of the process values in space and time as well as handling of missing values. Two applications are presented: the first one to model concentrations of sulfur dioxide in the eastern United States and the second one to model monthly minimum temperatures in the State of Rio de Janeiro.     

Combining data and simulated data for space–time fields: application to ozone

This paper presents a theory for modeling random environmental spatial-temporal fields that allows simulated data (numerical-physical model output) to be combined with measurements made at fixed monitoring sites. That theory involves Bayesian hierarchical models that provide temporal forecasts and spatial predictions along with appropriate credibility intervals. A by-product is a method for re-calibrating the simulated data to bring it into line with the measurements for certain applications. While the approach covers a broad domain of potential applications, this paper addresses a field of particular importance, ground level ozone concentrations over the eastern and central USA. A univariate model is developed and illustrated with hourly ozone fields. A multivariate alternative is also provided and illustrated with daily concentration fields. The forecasts and predictions they provide are compared with those from other approaches.     

Spatial and temporal modeling of community non-timber forest extraction

This paper examines the interaction of spatial and dynamic aspects of resource extraction from forests by local people. Highly cyclical and varied across space and time, the patterns of resource extraction resulting from the spatial–temporal model bear little resemblance to the patterns drawn from focusing either on spatial or temporal aspects of extraction alone. Ignoring this variability inaccurately depicts villagers’ dependence on different parts of the forest and could result in inappropriate policies. Similarly, the spatial links in extraction decisions imply that policies imposed in one area can have unintended consequences in other areas. Combining the spatial–temporal model with a measure of success in community forest management—the ability to avoid open-access resource degradation—characterizes the impact of incomplete property rights on patterns of resource extraction and stocks.     

Spatiotemporal modeling of irregularly spaced aerosol optical depth data

Many advancements have been introduced to tackle spatial and temporal structures in data. When the spatial and/or temporal domains are relatively large, assumptions must be made to account for the sheer size of the data. The large data size, coupled with realities that come with observational data, make it difficult for all of these assumptions to be met. In particular, air quality data are very sparse across geographic space and time, due to a limited air pollution monitoring network. These “missing” values make it difficult to incorporate most dimension reduction techniques developed for high-dimensional spatiotemporal data. This article examines aerosol optical depth (AOD), an indirect measure of radiative forcing, and air quality. The spatiotemporal distribution of AOD can be influenced by both natural (e.g., meteorological conditions) and anthropogenic factors (e.g., emission from industries and transport). After accounting for natural factors influencing AOD, we examine the spatiotemporal relationship in the remaining human influenced portion of AOD. The presented data cover a portion of India surrounding New Delhi from 2000–2006. The proposed method is demonstrated showing how it can handle the large spatiotemporal structure containing so much missing data for both meteorologic conditions and AOD over time and space.     

The scale and cause of spatial heterogeneity in strength of temporal density dependence

The importance of density dependence in natural communities continues to spark much debate because it is fundamental to population regulation. We used temporal manipulations of density to explore potentially stabilizing density dependence in early survivorship among six local populations of a tropical damselfish (Dascyllus flavicaudus). Specifically, we tested the premise that spatial heterogeneity in the strength of temporal density dependence would reflect variation in density of predators, the agent of mortality. Our field manipulations revealed that mortality among successive cohorts of young fishes was density dependent at each reef, but that its strength varied by approximately 1.5 orders of magnitude. This spatial heterogeneity was well predicted by variation among the six reefs in the density of predatory fishes that consume juvenile damselfishes. Because density dependence arose from competition for enemy-free space within a shelter coral, the mortality consequence of the competition depended on the neighborhood density of predators. Thus, the scale of heterogeneity in the density dependence largely reflected attributes of the environment that shaped the local abundance of predators. These results have important implications for how ecologists explore regulatory processes in nature. Failure to account for spatial variation could frequently yield misleading conclusions regarding density dependence as a stabilizing process, obscure underlying mechanisms influencing its strength, and provide no insight into the spatial scale of the heterogeneity. Further, models of population dynamics will be improved when experimental approaches better estimate the magnitude and causes of variation in strength of stabilizing density dependence.     

Analytical solution of two-dimensional advection–dispersion equation with spatio-temporal coefficients for point sources in an infinite medium using Green’s function method

In the present study analytical solutions of a two-dimensional advection–dispersion equation (ADE) with spatially and temporally dependent longitudinal and lateral components of the dispersion coefficient and velocity are obtained using Green’s Function Method (GFM). These solutions describe solute transport in infinite horizontal groundwater flow, assimilating the spatio-temporal dependence of transport properties, dependence of dispersion coefficient on velocity, and the particulate heterogeneity of the aquifer. The solution is obtained in the general form of temporal dependence and the source term, from which solutions for instantaneous and continuous point sources are derived. The spatial dependence of groundwater velocity is considered non-homogeneous linear, whereas the dispersion coefficient is considered proportional to the square of spatial dependence of velocity. An asymptotically increasing temporal function is considered to illustrate the proposed solutions. The solutions are validated with the existing solutions derived from the proposed solutions in three special cases. The effect of spatially/temporally dependent heterogeneity on the solute transport is also demonstrated. To use the GFM, the ADE with spatio-temporally dependent coefficients is reduced to a dispersion equation with constant coefficients in terms of new position variables introduced through properly developed coordinate transformation equations. Also, a new time variable is introduced through a known transformation.     

Statistical hypothesis testing formulations for U.S. environmental regulatory standards for ozone

Environmental regulatory standards are intended to protect human health and environmental welfare. Current standards are based on scientific and policy considerations but appear to lack rigorous statistical foundations and may have unintended regulatory consequences. We examine current and proposed U.S. environmental regulatory standards for ozone from the standpoint of their formulation and performance within a statistical hypothesis testing framework. We illustrate that the standards can be regarded as representing constraints on a percentile of the ozone distribution, where the percentile involved depends on the defined length of ozone season and the constraint is stricter in regions with greater variability. A hypothesis testing framework allows consideration of error rates (probability of false declaration of violation and compliance) and we show that the existing statistics on which the standards are based can be improved upon in terms of bias and variance. Our analyses also raise issues relating to network design and the possibilities of defining a regionally based standard that acknowledges and accounts for spatial and temporal variability in the ozone distribution.     

天津臭氧浓度与气象因素的相关性及其预测方法

气象因素在影响夏季臭氧浓度水平和变化特征方面扮演着重要作用.通过对2008年夏季天津地面臭氧体积浓度和气象因素的相关分析,揭示高浓度臭氧发生时的典型气象特征,并初步建立了预测地面臭氧浓度的气象学方法.结果表明:影响臭氧浓度的主要气象因素是气温、相对湿度和风速、风向,当14时气温大于30℃,相对湿度低于60%,风向为偏西或偏南时,高浓度臭氧的发生概率较高.采用14时气温、相对湿度和风速等气象参数拟合臭氧体积浓度,效果良好.     

Network-based exploration and visualisation of ecological data

Networks – structured graphs consisting of sets of nodes connected by edges – provide a rich framework for data visualisation and exploratory analyses. Although rarely used for the visualisation of ecological data, networks are well suited to this purpose, including data that one might not normally think of as a network. We present a simple method for transforming a data matrix into network format, and show how this can be used as the basis for interactive exploratory analyses of ecological data.The method is demonstrated using a database of marine zooplankton samples acquired in the Southern Ocean. The network analyses revealed zooplankton community structures that are in good agreement with previously published results. Variations in community structure were observed to be related to the temporal and spatial pattern of sampling, as well as to physical environmental factors such as sea ice cover. The analyses also revealed a number of errors in the data, including taxon identification errors and instrument failures.The method allows the analyst to generate networks from different combinations of variables in the data set, and to examine the effects of varying parameters such as the scales of spatial, temporal, and taxonomic aggregation. This flexibility allows the analyst to rapidly gain a number of perspectives on the data and provides a powerful mechanism for exploration.     

An adjoint data assimilation approach for estimating parameters in a three-dimensional ecosystem model

In this paper an ecosystem model, including phytoplankton, zooplankton, nitrate, ammonium, phosphate and detritus, is described. The model is driven by physical fields derived from a three-dimensional physical transport model. Simulation includes nitrate input from a river. Simulated results are then sampled and the sampled data are used in sequential numerical experiments to assess the ability of using an adjoint data assimilation approach for estimating the poorly known parameters of the ecosystem model, such as growth and death rate, half-saturation constant of nutrients, etc. Data with different spatial and temporal resolution over 1 week are assimilated into the ecosystem model. Assimilation of data at 30 grid stations with a sampling interval of 6 h is proved to be adequate for recovering all the parameters of the ecosystem model. Both the spatial and temporal resolution of the data are mutually complementary in the assimilative model. Thus, improvement of either of them can result in improvement of model parameter recoveries. The assimilation of phytoplankton data is essential to recover the model parameters. Phytoplankton is the core of the food web and without the information on phytoplankton, the structure of the ecosystem cannot be constructed correctly. The adjoint method can work well with the noisy data. In the twin experiments with noisy data, the parameters can be recovered but the error is increased. The results of the model and parameter recovery are sensitive to the initial conditions of state variables, so the determination of the initial condition is as important as that of the model parameter. The spatial and temporal resolution and the data type of the observations in Analysis and Modelling Research of the Ecosystem in the Bohai Sea (AMREB) are suitable for the recovery of the model parameters used in this study.     

Spatial and temporal variability modify density dependence in populations of large herbivores

A central challenge in ecology is to understand the interplay of internal and external controls on the growth of populations. We examined the effects of temporal variation in weather and spatial variation in vegetation on the strength of density dependence in populations of large herbivores. We fit three subsets of the model ln(Nt) = a + (1 + b) x ln(N(t-1)) + c x ln(N(t-2)) to five time series of estimates (Nt) of abundance of ungulates in the Rocky Mountains, USA. The strength of density dependence was estimated by the magnitude of the coefficient b. We regressed the estimates of b on indices of temporal heterogeneity in weather and spatial heterogeneity in resources. The 95% posterior intervals of the slopes of these regressions showed that temporal heterogeneity strengthened density-dependent feedbacks to population growth, whereas spatial heterogeneity weakened them. This finding offers the first empirical evidence that density dependence responds in different ways to spatial heterogeneity and temporal heterogeneity.     

A two-step local smoothing approach for exploring spatio-temporal patterns with application to the analysis of precipitation in the mainland of China during 1986–2005

There has been a growing interest on using local modelling techniques for the analysis of spatio-temporal data because of their powerfulness in extracting the underlying local patterns in the data. In this study, we propose a two-step local smoothing approach to explore spatial patterns and temporal trends of spatio-temporal data via combining the geographically weighted regression and the local polynomial smoothing procedure. The proposed method incorporates both spatial and temporal information into the calibration process and makes it easier to implement visualization of the results. A simulation experiment is conducted to assess the performance of the proposed method and the results show that the method works satisfactorily. A real-world spatio-temporal data set is analyzed to demonstrate the practical usefulness of the method.