A closure test for time-specific capture-recapture data

The assumption of demographic closure in the analysis of capture-recapture data under closed-population models is of fundamental importance. Yet, little progress has been made in the development of omnibus tests of the closure assumption. We present a closure test for time-specific data that, in principle, tests the null hypothesis of closed-population model M_t against the open-population Jolly-Seber model as a specific alternative. This test is chi-square, and can be decomposed into informative components that can be interpreted to determine the nature of closure violations. The test is most sensitive to permanent emigration and least sensitive to temporary emigration, and is of intermediate sensitivity to permanent or temporary immigration. This test is a versatile tool for testing the assumption of demographic closure in the analysis of capture-recapture data.     

Erlangian models for capture-recapture data

Models for the analysis of capture-recapture data based on Erlangian distributions reflecting assumptions about the times at which individuals enter and leave the population are described. A procedure for fitting such models by the method of maximum likelihood is illustrated.     

Maximum likelihood inference for the band-read error model for capture-recapture data with misidentification

Environmental and Ecological Statistics - Misidentification of animals is a common problem for many capture-recapture experiments. Considerably misleading inference may be obtained when traditional...     

Optimal model averaging by data perturbation for spatial noisy data

Geostatistical models play an important role in spatial data analysis, in which model selection is inevitable. Model selection methods, such as AIC and BIC, are popular for selecting appropriate models. In recent years, some model averaging methods, such as smoothed AIC and smoothed BIC, are also applied to spatial data models. However, the corresponding averaging estimators are outperformed by optimal model averaging estimators (Hansen in Econometrica 75:1175–1189, 2007) for the ordinary linear models. Therefore, this paper focuses on the optimal model averaging method for geostatistical models. We propose a weight choice criterion for the model averaging estimator on the basis of the generalized degrees of freedom and data perturbation technique. We further theoretically prove the resultant estimator is asymptotically optimal in terms of the mean squared error, and numerically demonstrate its satisfactory performance. Finally, the proposed method is applied to a mercury data set.     

A capture-recapture model with heterogeneity and behavioural response

We develop the non-parametric maximum likelihood estimator (MLE) of the full M_bh capture-recapture model which utilizes both initial capture and recapture data and permits both heterogeneity (h) between animals and behavioural (b) response to capture. Our MLE procedure utilizes non-parametric maximum likelihood estimation of mixture distributions (Lindsay, 1983; Lindsay and Roeder, 1992) and the EM algorithm (Dempsteret al., 1977). Our MLE estimate provides the first non-parametric estimate of the bivariate capture-recapture distribution.Since non-parametric maximum likelihood estimation exists for submodels M_h (allowing heterogeneity only), Mb (allowing behavioural response only) and M₀ (allowing no changes), we develop maximum likelihood-based model selection, specifically the Akaike information criterion (AIC) (Akaike, 1973). The AIC procedure does well in detecting behavioural response but has difficulty in detecting heterogeneity.     

A combination line transect and capture-recapture sampling model for multiple observers in aerial surveys

We present a robust sampling methodology to estimate population size using line transect and capture-recapture procedures for aerial surveys. Aerial surveys usually underestimate population density due to animals being missed. A combination of capture-recapture and line transect sampling methods with multiple observers allows violation of the assumption that all animals on the centreline are sighted from the air. We illustrate our method with an example of inanimate objects which shows evidence of failure of the assumption that all objects on the centreline have probability 1 of being detected. A simulation study is implemented to evaluate the performance of three variations of the Lincoln-Petersen estimator: the overall estimator, the stratified estimator, and the general stratified estimator based on the combined likelihood proposed in this paper. The stratified Lincoln-Petersen estimator based on the combined likelihood is found to be generally superior to the other estimators.     

A model examining hierarchical wetland networks for watershed stormwater management

There is increasing awareness that solutions to degraded quality and excessive quantity of stormwater and resulting impacts on downstream water bodies may require a watershed approach to management rather that the incremental approach that is now common. Examination of low-relief watersheds characteristic of the southeastern coastal plain reveals common hierarchical patterns of surface water convergence that may be emulated in developed watersheds to enhance the efficacy of peak-flow attenuation and pollutant removal. A dynamic systems model was developed to compare stormwater management using a hierarchical network of treatment wetlands with the standard incremental approach wherein treatment systems are designed considering only site-level effluent criteria. The model simulates watershed hydrology, suspended sediment transport and phosphorus removal and transformation. Results indicate that watershed planning of stormwater collection and treatment systems using hierarchical networks can greatly enhance overall effectiveness (annual retention improvements of 31% for flow, 36% for sediment and 27% for phosphorus) with respect to an equal area of uniformly sized wetlands. Further, network proportions can be adjusted to specific runoff characteristics. Distinct roles were observed for each wetland size class: small headwater wetlands effectively removed sediment, medium-sized mid-reach wetlands retained phosphorus, while large wetlands primarily stored and attenuated long-period hydrologic flows.     

A general model for analyzing Taylor's spatial scaling laws

Taylor's spatial scaling law concerns the relation between the variance and the mean population counts within areas of a given size. For a range of area sizes, the log of the variance often is an approximately linear function of the mean with a slope between 1 and 2, depending on the range of areas considered. In this paper, we investigate this relationship theoretically for random quadrat samples within a large area. The model makes a distinction between the local point process determining the position of each individual and the population density described by a spatial covariance function. The local point process and the spatial covariance of population density both contribute to the general relationship between the mean and the variance in which the slope may begin at 1, increase to 2, and decrease to 1 again. It is demonstrated by an example that the slope theoretically may exceed 2 by a small amount for very regular patterns that generate spatial covariance functions that increase in certain intervals. We also show how properties of population dynamics in space and time determine this relationship.     

A spatial zero-inflated poisson regression model for oak regeneration

Ecological counts data are often characterized by an excess of zeros and spatial dependence. Excess zeros can occur in regions outside the range of the distribution of a given species. A zero-inflated Poisson regression model is developed, under which the species range is determined by a spatial probit model, including physical variables as covariates. Within that range, species counts are independently drawn from a Poisson distribution whose mean depends on biotic variables. Bayesian inference for this model is illustrated using data on oak seedling counts. Received: May 2004 / Revised: December 2004     

Ordinary kriging for function-valued spatial data

In various scientific fields properties are represented by functions varying over space. In this paper, we present a methodology to make spatial predictions at non-data locations when the data values are functions. In particular, we propose both an estimator of the spatial correlation and a functional kriging predictor. We adapt an optimization criterion used in multivariable spatial prediction in order to estimate the kriging parameters. The curves are pre-processed by a non-parametric fitting, where the smoothing parameters are chosen by cross-validation. The approach is illustrated by analyzing real data based on soil penetration resistances.     

A spatial model of phytoplankton patchiness

The one-dimensional theory of critical-length scales of phytoplankton patchiness is developed to include phytoplankton growth and herbivore grazing as functions of time and space. The critical-length scale L _c for the pathch is then determined by the initial spatial distribution and concentration of the limiting nutrient and herbivores in addition to the daily averaged values of the growth and loss processes. The response of an initial phytoplankton patch to the stresses of turbulent diffusion, nutrient depletion, light periodicity, and nocturnal or continuous herbivore grazing is investigated numerically for several oceanic conditions. Nocturnal grazing, while less stressful on primary production than continous grazing, results in lower phytoplankton standing stocks. Increase in biomass of vertically migrating zooplankton results in a net loss of nutrient which might otherwise be egested, recycled, and utilized in the euphotic zone under continuous grazing conditions. The Ivlev constant is shown via sensitivity analysis to be a significant parameter ultimately influencing phytoplankton production. It is demonstrated numerically that diffusion of phytoplankton cells from areas of high concentration to low concentration prevents the local extinction of the standing stock, thereby rendering a positive herbivore grazing-threshold unnecessary for ecosystem stability.     

Combining multistate capture-recapture data with tag recoveries to estimate demographic parameters

Matrix population models that allow an animal to occupy more than one state over time are important tools for population and evolutionary ecologists. Definition of state can vary, including location for metapopulation models and breeding state for life history models. For populations whose members can be marked and subsequently reencountered, multistate mark-recapture models are available to estimate the survival and transition probabilities needed to construct population models. Multistate models have proved extremely useful in this context, but they often require a substantial amount of data and restrict estimation of transition probabilities to those areas or states subjected to formal sampling effort. At the same time, for many species, there are considerable tag recovery data provided by the public that could be modeled in order to increase precision and to extend inference to a greater number of areas or states. Here we present a statistical model for combining multistate capture-recapture data (e.g., from a breeding ground study) with multistate tag recovery data (e.g., from wintering grounds). We use this method to analyze data from a study of Canada Geese (Branta canadensis) in the Atlantic Flyway of North America. Our analysis produced marginal improvement in precision, due to relatively few recoveries, but we demonstrate how precision could be further improved with increases in the probability that a retrieved tag is reported.     

An EM algorithm for capture-recapture estimation

Analysis of capture—recapture data often involves maximizing a complex likelihood function with many unknown parameters. Statistical inference based on selection of a proper model depends on successful attainment of this maximum. An EM algorithm is developed for obtaining maximum likelihood estimates of capture and survival probabilities conditional on first capture from standard capture—recapture data. The algorithm does not require the use of numerical derivatives which may improve precision and stability relative to other estimation schemes. The asymptotic covariance matrix of the estimated parameters can be obtained using the supplemented EM algorithm. The EM algorithm is compared to a more traditional Newton-Raphson algorithm with both a simulated and a real dataset. The two algorithms result in the same parameter estimates, but Newton-Raphson variance estimates depend on a numerically estimated Hessian matrix that is sensitive to step size choice.     

A geostatistical approach for mapping thematic classification accuracy and evaluating the impact of inaccurate spatial data on ecological model predictions

Spatial information in the form of geographical information system coverages and remotely sensed imagery is increasingly used in ecological modeling. Examples include maps of land cover type from which ecologically relevant properties, such as biomass or leaf area index, are derived. Spatial information, however, is not error-free: acquisition and processing errors, as well as the complexity of the physical processes involved, make remotely sensed data imperfect measurements of ecological attributes. It is therefore important to first assess the accuracy of the spatial information being used and then evaluate the impact of such inaccurate information on ecological model predictions. In this paper, the role of geostatistics for mapping thematic classification accuracy through integration of abundant image-derived (soft) and sparse higher accuracy (hard) class labels is presented. Such assessment leads to local indices of map quality, which can be used for guiding additional ground surveys. Stochastic simulation is proposed for generating multiple alternative realizations (maps) of the spatial distribution of the higher accuracy class labels over the study area. All simulated realizations are consistent with the available pieces of information (hard and soft labels) up to their validated level of accuracy. The simulated alternative class label representations can be used for assessing joint spatial accuracy, i.e., classification accuracy regarding entire spatial features read from the thematic map. Such realizations can also serve as input parameters to spatially explicit ecological models; the resulting distribution of ecological responses provides a model of uncertainty regarding the ecological model prediction. A case study illustrates the generation of alternative land cover maps for a Landsat Thematic Mapper (TM) subscene, and the subsequent construction of local map quality indices. Simulated land cover maps are then input into a biogeochemical model for assessing uncertainty regarding net primary production (NPP).     

Trend analyses of hierarchical pin-point cover data

The use of state-space models for analyzing longitudinal hierarchical pin-point plant cover data is demonstrated. The main advantages of using a state-space model are (1) that the observed variance is separated into sampling variance and the more interesting structural variance which are needed for quantifying prediction uncertainty, (2) that missing values or an unbalanced sampling design readily may be accounted for, and (3) that the structural equation easily may be expanded and made as complex as necessary for modeling longitudinal pin-point cover data, thus allowing the incorporation of the most important ecological processes in the state-space model without technical difficulties. Typically, there is considerable spatial variation in plant abundance, and this variation is modeled using the Pólya-Eggenberger distribution (a generalization of the beta-binomial distribution). To illustrate this method, longitudinal hierarchical pin-point data of Erica tetralix in wet Danish heathlands were analyzed, including and excluding autocorrelation and an environmental covariable in the state-space model. The pin-point plant cover data showed a significant decrease in the plant cover of E. tetralix in the period from 2004 to 2009, with an annual decrease of about 10% in the logit-transformed cover. The distribution of predicted plant cover at a given site the following year was calculated, including and excluding the information of an environmental covariable.     

A multiscale hierarchical Markov transition matrix model for generating and analyzing thematic raster maps

A model is described for generating hierarchically scaled spatial pattern as represented in a thematic raster map. The model involves a series of Markov transition matrices, one for each level in the scaling hierarchy. In full generality, the model allows the transition matrices to be different at each level, potentially making available a large number of parameters for landscape characterization. The model is self-similar when the transition matrices are all equal. A method is presented for fitting the model to data that take the form of a single-resolution thematic raster map. Explicit analytic solutions are obtained for the fitted parameters. The fitting method is based on a relationship between the hierarchical transitions in the model and spatial transitions at varying distance scales in the data map, a categorical analogy of the geostatistical variogram.