Model selection in demographic time series using VC-bounds

The problem of distinguishing density-independent (DI) from density-dependent (DD) demographic time series is important for understanding the mechanisms that regulate populations of animals and plants. We address this problem in a novel way by means of Statistical Learning Theory (SLT); SLT is built around the idea of VC-dimension, a complexity index for classes of parameterized functions. Though VC-dimensions of nonlinear models are generally unknown, in the linear case VC-dimension actually corresponds to the number of free parameters; this allows one to straightforwardly apply the model selection framework developed within SLT, and called Structural Risk Minimization (SRM). We generate noisy artificial time series, both DI and DD, and use SRM to recognize the model underlying the data, choosing among a suite of both density-dependent and independent demographies. We show that SRM significantly outperforms traditional model selection approaches, such as the Schwartz Information Criterion and Final Prediction Error in recognizing both density-dependence and independence.     

Spectral analysis of forest model time series

The use of spectral analysis to elucidate the cyclic behavior in time series generated by a forest stand growth simulation model is discussed. A stand-level simulator, FORET, for an Appalachian deciduous forest is described. An estimate of the power spectral density of the total biomass time series is calculated. The power spectral density estimate indicates a dominant cyclic behavior with a period of about 200 years. In addition the spectral density is approximately bandlimited. This characteristic makes possible the application of the sampling theorem for analysis of sampling rates.     

Cross-correlation bias in lag analysis of aquatic time series

Cross-correlation analysis is the most valuable and widely used statistical tool for evaluating the strength and direction of time-lagged relationships between ecological variables. Although it is well understood that temporal autocorrelation can inflate estimates of cross correlations and cause high rates of incorrectly concluding that lags exist among time series (i.e. type I error), in this study we show that a problem we term intra-multiplicity can cause substantial bias in cross-correlation analysis even in the absence of autocorrelation. Intra-multiplicity refers to the numerous time lags examined and cross-correlation coefficients computed within a pair of time series during cross-correlation analysis. We show using Monte Carlo simulations that intra-multiplicity can spuriously inflate estimates of cross correlations by identifying incorrect time lags. Further, unlike autocorrelation, which generally identifies lags close to the true lag, intra-multiplicity can erroneously identify lags anywhere in the time series and commonly results in a direction change of the correlation (i.e. positive or negative). Using Monte Carlo simulations we develop formulas that quantify the bias introduced by intra-multiplicity as a function of sample size, true cross correlation between the series, and the number of time lags examined. A priori these formulas enable researchers to determine the sample size needed to minimize the biases introduced by intra-multiplicity. A posteriori the formulas can be used to predict the expected bias and type I error rate associated with the data at hand, as well as the maximum number of time lags that can be analyzed to minimize the effects of intra-multiplicity. We examine the relationship between commercial catch of chum salmon and surface temperatures of the North Pacific (1925–1992) to illustrate the problems of intra-multiplicity in fisheries studies and the application of our formulas. These analyses provide a more robust framework to assess the temporal relationships between ecological variables. Received: 28 July 2000 / Accepted: 6 December 2000     

Procedures for outlier detection in circular time series models

It is known that the occurrence of outliers in linear or non-linear time series models may have adverse effects on the modelling and statistical inference of the data. Consequently, extensive research has been conducted on developing outlier detection procedures so that outliers may be properly managed. However, no work has been done on the problem of outliers in circular time series data. This problem is the focus of this paper. The main objective is to develop novel numerical and graphical procedures for detecting these outliers in circular time series data.A number of circular time series models have been proposed including the circular autoregressive model. We extend the iterative outlier detection procedure which has been successfully used in linear time series models to the circular autoregressive model. The proposed procedure shows a good performance when investigated via simulation for the circular autoregressive model of order one. At the same time, several statistical techniques have been used to detect the change of preferred trend in time series data using SLIME and CUSUM plots. While the methods fail to indicate directly the outliers in circular time series data, we use the ideas employed to develop three novel graphical procedures for identifying the outliers. For illustration, we apply the procedures to a particular set of wind direction data. An agreement between the results of the graphical and iterative detection procedures is observed. These procedures could be very useful in improving the modelling and inferential processes for circular time series data.     

月径流时间序列的混沌特性分析

研究根据混沌理论,分别采用功率谱分析方法、G-P关联维识别合水水库月径流量的混沌特性,并且得出主要的混沌特性指标.以Tanks嵌入定理为理论基础,进行短期预测,能够取得精度较高的预测结果.研究表明:月径流序列存在一定的混沌特性,其最小嵌入维数在m=8对应的吸引子维数D=-0.95,最大李雅谱诺夫指数σ=0.325,采用加权一阶权域方法预测时,预测最大时限为4个月,其预测精度均在5%以内.     

Hidden Markov models for circular and linear-circular time series

We introduce a new class of circular time series based on hidden Markov models. These are compared with existing models, their properties are outlined and issues relating to parameter estimation are discussed. The new models conveniently describe multi-modal circular time series as dependent mixtures of circular distributions. Two examples from biology and meteorology are used to illustrate the theory. Finally, we introduce a hidden Markov model for bivariate linear-circular time series and use it to describe larval movement of the fly Drosophila. Received: September 2003 / Revised: March 2004     

Analysis of the global warming dynamics from temperature time series

Global warming is the observed increase of the average temperature of the Earth. The primary cause of this phenomenon is the release of the greenhouse gases by burning of fossil fuels, land cleaning, agriculture, among others, leading to the increase of the so-called greenhouse effect. An approach to deal with this important problem is the time series analysis. In this regard, different techniques can be applied to evaluate the global warming dynamics. This kind of analysis allows one to make better predictions increasing our comprehension of the phenomenon. This article applies nonlinear tools to analyze temperature time series establishing state space reconstruction and prediction. Since noise contamination is unavoidable in data acquisition, it is important to employ robust techniques. The method of delay coordinates is employed for state space reconstruction and delay parameters are evaluated using the method of average mutual information and the method of false nearest neighbors. Afterwards, the simple nonlinear prediction method is employed to estimate temperatures of the future. Temperature time series from different places of the planet are used. Initially, the approach is verified considering known parts of the time series and afterwards, results are extrapolated for future values estimating temperature until 2028. Results show that these techniques are interesting to estimate temperature time history, presenting coherent estimations.     

Estimating survival rates with time series of standing age-structure data

It has long been recognized that age-structure data contain useful information for assessing the status and dynamics of wildlife populations. For example, age-specific survival rates can be estimated with just a single sample from the age distribution of a stable, stationary population. For a population that is not stable, age-specific survival rates can be estimated using techniques such as inverse methods that combine time series of age-structure data with other demographic data. However, estimation of survival rates using these methods typically requires numerical optimization, a relatively long time series of data, and smoothing or other constraints to provide useful estimates. We developed general models for possibly unstable populations that combine time series of age-structure data with other demographic data to provide explicit maximum likelihood estimators of age-specific survival rates with as few as two years of data. As an example, we applied these methods to estimate survival rates for female bison (Bison bison) in Yellowstone National Park, USA. This approach provides a simple tool for monitoring survival rates based on age-structure data.     

Strength of evidence for density dependence in abundance time series of 1198 species

Population limitation is a fundamental tenet of ecology, but the relative roles of exogenous and endogenous mechanisms remain unquantified for most species. Here we used multi-model inference (MMI), a form of model averaging, based on information theory (Akaike's Information Criterion) to evaluate the relative strength of evidence for density-dependent and density-independent population dynamical models in long-term abundance time series of 1198 species. We also compared the MMI results to more classic methods for detecting density dependence: Neyman-Pearson hypothesis-testing and best-model selection using the Bayesian Information Criterion or cross-validation. Using MMI on our large database, we show that density dependence is a pervasive feature of population dynamics (median MMI support for density dependence = 74.7-92.2%), and that this holds across widely different taxa. The weight of evidence for density dependence varied among species but increased consistently, with the number of generations monitored. Best-model selection methods yielded similar results to MMI (a density-dependent model was favored in 66.2-93.9% of species time series), while the hypothesis-testing methods detected density dependence less frequently (32.6-49.8%). There were no obvious differences in the prevalence of density dependence across major taxonomic groups under any of the statistical methods used. These results underscore the value of using multiple modes of analysis to quantify the relative empirical support for a set of working hypotheses that encompass a range of realistic population dynamical behaviors.     

Comparison of sequential monitoring methods for environmental time series with stochastic cycle

The paper compares recursive methods for detecting change points in environmental time series. Timely identification of peaks and troughs is important for planning defense actions and preventing risks. We consider linear nonparametric methods, such as time-varying coefficients, double exponential smoothers and prediction error statistics. These methods are often used in surveillance, forecasting and control, and their common features are sequential computation and exponential weighting of data. The new approach proposed here is to select their coefficients by maximizing the difference between subsequent peaks and troughs detected on past data. We compare the methods with applications to meteorological, astronomical and ecological data, and Monte-Carlo simulations.     

论生态环境用水与生态环境需水的区别与计算问题

针对生态环境用水与生态环境需水概念和计算中存在的问题，从生态与环境概念分析入手，对生态环境用水、生态环境需水的概念进行界定和区分，对其内涵和计算关键问题进行评述。文章认为生态环境用水与生态环境需水既有区别又有联系，生态环境用水是其“实际用水”之意，生态环境需水是其“需求水”之意，生态环境需水是生态环境达到某一水平时的“用水量”。文章还介绍了生态环境用（需）水的分类及计算方法，指出生态环境用（需）水计算的两个关键问题，即尺度问题和阈值问题，认为生态环境用（需）水总量不是分类或分区生态环境用（需）水量的简单相加；提出了“基于水循环模拟的生态环境用（需）水量计算方法”的初步思想。     

Geospatial analysis of vulnerable beach-foredune systems from decadal time series of lidar data

Time series of lidar data, acquired over the past decade along the North American East Coast, provide opportunities to gain new insights into 3D evolution of barrier islands and their beach and dune systems. GIS-based per grid cell statistics and map algebra was applied to time series of Digital Surface Models representing two sections of North Carolina barrier islands to quantify elevation change trends, map dynamic and stable locations, identify new and lost buildings, measure relative volume evolution in the beach and foredune systems and analyze shoreline dynamics. Results show a relatively small stable core in both study areas, with beaches and the ocean side of the dunes exhibiting systematic high rates of elevation loss while areas landward from the dunes increase slightly in elevation. Significant number of new homes have been built at locations with very small core surface elevation, and homes built within the shoreline dynamics band have already been lost. The raster-based methodology used in this study can be applied to perform similar analyses in other coastal areas where time series of lidar data are available.     

保水剂对番茄生长及水分利用效率的影响

在砂与木屑复合基质中加入不同用量的保水剂,测定基质物理性状,并进行不同水分处理条件下番茄盆栽试验,以研究保水剂对番茄生长及水分利用效率的影响。结果表明:在每1 L基质分别加入1、2、4、8 g保水剂时,与对照(未加保水剂)相比,基质持水量分别增加16.35%、34.00%、61.29%和135.16%,容重分别降低3.61%、5.37%、9.42%和14.64%;在水分耗竭试验中,番茄萎蔫天数分别延长13.92%、22.79%、31.65%和45.5%,干物质量分别增加7.90%、21.60%、57.08%、179.50%,株高、叶片数、茎粗、鲜质量也都随保水剂用量的增加而明显增加;在基质相对水分质量分数分别为55%、70%、85%及100%4种处理下的番茄水分胁迫试验中,每1 L基质施用2 g保水剂时,与对照(未加保水剂)相比,水分利用效率分别提高29.93%、28.06%、14.36%、7.42%,株高、生物量也随水分胁迫程度加重而明显提高。     

Ecological footprint and biological capacity time series assessment for a forest region in northeastern China

Anthropogenic disturbances have caused major landscape changes in the forests of northeastern China during the past 50 years. In particular, continuous over-deforestation has greatly decreased the region's forest quality. Ecological footprint analysis generates aggregated information about a population's demand on nature and the population regional biological capacity. To show the forest change and the population's ecological demand on the study area, this paper presents an ecological footprint time series for the Songling Forestry Bureau in northeastern China from 1965 to 2000. The paper shows conventional ecological footprint time series and area demand time series – under global, Chinese and local yearly yields – to study the biological productivity of Songling. In this study, biological capacity was calculated based on a conventional approach. The results demonstrate that the ecological footprint has increased slightly and continuously during the 35-year timespan, while the biological capacity has decreased dramatically. These effects have been caused mainly by the depletion of forest resources. The results also yield much information about natural changes and socioeconomic dynamics, as well as the driving factors for these changes, of which the most important is forest management policy.     

Air pollution effects on hospital admissions: a statistical analysis of parallel time series

A statistical model for longitudinal count data is used to examine the potential adverse health effects of ambient air pollution. Daily respiratory admissions to 164 acute care hospitals in Ontario are obtained for the period 1983 to 1988. Estimates of ozone levels in the vicinity of each hospital are determined from air pollution monitoring stations maintained by the Ontario Ministry of the Environment. Generalized estimating equation methods are used to make inferences about the regression and overdispersion parameters. The admission data display little evidence of serial correlation and extra Poisson variation. However, admission rates vary considerably among hospitals. This latter source of variation needs to be taken into account in examining the effects of air pollution on respiratory health status.     

Detecting the order of population dynamics from time series: nonlinearity causes spurious diagnosis

Partial autocorrelation and partial rate correlation functions are frequently used to detect the order of the endogenous process generating an observed population time series. Here we uncover a problem with this approach: the diagnosis of spurious second order autocorrelation due to strong nonlinearity in a first order endogenous process, as exemplified by time series data from a population of Soay sheep. Causes and a possible solution are discussed.     

Watershed land use effects on lake water quality in Denmark

Mitigating nutrient losses from anthropogenic nonpoint sources is today of particular importance for improving the water quality of numerous freshwater lakes worldwide. Several empirical relationships between land use and in-lake water quality variables have been developed, but they are often weak, which can in part be attributed to lack of detailed information about land use activities or point sources. We examined a comprehensive data set comprising land use data, point-source information, and in-lake water quality for 414 Danish lakes. By excluding point-source-influenced lakes (n = 210), the strength in relationship (R2) between in-lake total nitrogen (TN) and total phosphorus (TP) concentrations and the proportion of agricultural land use in the watershed increased markedly, from 10-12% to 39-42% for deep lakes and from 10-12% to 21-23% for shallow lakes, with the highest increase for TN. Relationships between TP and agricultural land use were even stronger for lakes with rivers in their watershed (55%) compared to lakes without (28%), indicating that rivers mediate a stronger linkage between landscape activity and lake water quality by providing a "delivery" mechanism for excess nutrients in the watershed. When examining the effect of different near-freshwater land zones in contrast to the entire watershed, relationships generally improved with size of zone (25, 50, 100, 200, and 400 m from the edge of lake and streams) but were by far strongest using the entire watershed. The proportion of agricultural land use in the entire watershed was best in explaining lake water quality, both relative to estimated nutrient surplus at agricultural field level and near-lake land use, which somewhat contrasts typical strategies of management policies that mainly target agricultural nutrient applications and implementation of near-water buffer zones. This study suggests that transport mechanisms within the whole catchment are important for the nutrient export to lakes. Hence, the whole watershed should be considered when managing nutrient loadings to lakes, and future policies should ideally target measures that reduce the proportion of cultivated land in the watershed to successfully improve lake water quality.