Using Scalar Models for Precautionary Assessments of Threatened Species

Abstract:  Scalar population models, commonly referred to as count-based models, are based on time-series data of population sizes and may be useful for screening-level ecological risk assessments when data for more complex models are not available. Appropriate use of such models for management purposes, however, requires understanding inherent biases that may exist in these models. Through a series of simulations, which compared predictions of risk of decline of scalar and matrix-based models, we examined whether discrepancies may arise from different dynamics displayed due to age structure and generation time. We also examined scalar and matrix-based population models of 18 real populations for potential patterns of bias in population viability estimates. In the simulation study, precautionary bias (i.e., overestimating risks of decline) of scalar models increased as a function of generation time. Models of real populations showed poor fit between scalar and matrix-based models, with scalar models predicting significantly higher risks of decline on average. The strength of this bias was not correlated with generation time, suggesting that additional sources of bias may be masking this relationship. Scalar models can be useful for screening-level assessments, which should in general be precautionary, but the potential shortfalls of these models should be considered before using them as a basis for management decisions.     

Database-driven models of the world's Large Marine Ecosystems

We present a new methodology for database-driven ecosystem model generation and apply the methodology to the world's 66 currently defined Large Marine Ecosystems. The method relies on a large number of spatial and temporal databases, including FishBase, SeaLifeBase, as well as several other databases developed notably as part of the Sea Around Us project. The models are formulated using the freely available Ecopath with Ecosim (EwE) modeling approach and software. We tune the models by fitting to available time series data, but recognize that the models represent only a first-generation of database-driven ecosystem models. We use the models to obtain a first estimate of fish biomass in the world's LMEs. The biggest hurdles at present to further model development and validation are insufficient time series trend information, and data on spatial fishing effort.     

Estimating wildfire growth from noisy and incomplete incident data using a state space model

Wildfire behaviors are complex and are of interest to fire managers and scientists for a variety of reasons. Many of these important behaviors are directly measured from the cumulative burn area time series of individual wildfires; however, estimating cumulative burn area time series is challenging due to the magnitude of measurement errors and missing entries. To resolve this, we introduce two state space models for reconstructing wildfire burn area using repeated observations from multiple data sources that include different levels of measurement error and temporal gaps. The constant growth parameter model uses a few parameters and assumes a burn area time series that follows a logistic growth curve. The non-constant growth parameter model uses a time-varying logistic growth curve to produce detailed estimates of the burn area time series that permit sudden pauses and pulses of growth. We apply both reconstruction models to burn area data from 13 large wildfire incidents to compare the quality of the burn area time series reconstructions and computational requirements. The constant growth parameter model reconstructs burn area time series with minimal computational requirements, but inadequately fits observed data in most cases. The non-constant growth parameter model better describes burn area time series, but can also be highly computationally demanding. Sensitivity analyses suggest that in a typical application, the reconstructed cumulative burn area time series is fairly robust to minor changes in the prior distributions.     

Reconstructing historical marine ecosystems using food web models: Northern British Columbia from Pre-European contact to present

Mass-balance trophic models (Ecopath with Ecosim) are developed for the marine ecosystem of northern British Columbia (BC) for the historical periods 1750, 1900, 1950 and 2000 AD. Time series data are compiled for catch, fishing mortality and biomass using fisheries statistics and literature values. Using the assembled dataset, dynamics of the 1950-based simulations are fitted to agree with observations over 50 years to 2000 through the manipulation of trophic flow parameters and the addition of climate factors: a primary production anomaly and herring recruitment anomaly. The predicted climate anomalies reflect documented environmental series, most strongly sea surface temperature and the Pacific Decadal Oscillation index. The best-fit predator–prey interaction parameters indicate mixed trophic control of the ecosystem. Trophic flow parameters from the fitted 1950 model are transferred to the other historical periods assuming stationarity in density-dependent foraging tactics. The 1900 model exhibited an improved fit to data using this approach, which suggests that the pattern of trophic control may have remained constant over much of the last century. The 1950 model is driven forward 50 years using climate and historical fishing drivers. The resulting ecosystem is compared to the 2000 model, and the dynamics of these models are compared in a predictive forecast to 2050. The models suggest similar restoration trajectories after a hypothetical release from fishing.     

Modeling and forecasting daily maximum hourly ozone concentrations using the RegAR model with skewed and heavy-tailed innovations

This paper considers the modeling and forecasting of daily maximum hourly ozone concentrations in Laranjeiras, Serra, Brazil, through dynamic regression models. In order to take into account the natural skewness and heavy-tailness of the data, a linear regression model with autoregressive errors and innovations following a member of the family of scale mixture of skew-normal distributions was considered. Pollutants and meteorological variables were considered as predictors, along with some deterministic factors, namely week-days and seasons. The Oceanic Niño Index was also considered as a predictor. The estimated model was able to explain satisfactorily well the correlation structure of the ozone time series. An out-of-sample forecast study was also performed. The skew-normal and skew-t models displayed quite competitive point forecasts compared to the similar model with gaussian innovations. On the other hand, in terms of forecast intervals, the skewed models presented much better performance with more accurate prediction intervals. These findings were empirically corroborated by a forecast Monte Carlo experiment.     

Testing the robustness of primary production models in shallow coastal areas: a case study

In this paper we investigate the robustness of a dynamic model, which describes the dynamic of the seagrass Zostera marina, with respect to the inter-annual variability of the two main forcing functions of primary production models in eutrophicated environments. The model was previously applied to simulate the seasonal evolution of this species in the Lagoon of Venice during a specific year and calibrated against time series of field data. In the this paper, we present and discuss the results which were obtained by forcing the model using time series of site-specific daily values concerning the solar radiation intensity and water temperature. The latter was estimated by means of a regression model, whose input variable was a site-specific time series of the air temperature. The regression model was calibrated using a year-long time series of hourly observations. The Z. marina model was first partially recalibrated against the same data set that was used in the original paper. Subsequently, the model was forced using a 7-year-long time series of the driving functions, in order to check the reliability of its long-term predictions. Even though the calibration gave satisfactory results, the multi-annual trends of the output variables were found to be in contrast with the observed evolution of the seagrass biomasses. Since detailed information about the air temperature and solar radiation are often available, these findings suggest that the testing of the ecological consistency of the evolution of primary production models in the long term would provide additional confidence in their results, particularly in those cases in which the scarcity of field data does not allow one to perform a formal corroboration/validation of these models.     

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.     

Space-time modeling of environmental monitoring data

This study describes and applies statistical methods for space-time modeling of data from environmental monitoring programs, e.g., within areas such as climate change, air pollution and aquatic environment. Such data are often characterized by sparse sampling in both the temporal and spatial dimensions. In order to improve the amount of information on the physical system in question we suggest using statistical modeling methods for monitoring data. Model predictions combined with observations could be analyzed directly to assess the environmental state or as forcing functions for time series models and deterministic, hydrodynamic models. To illustrate the approach we applied the proposed modeling methods to data from the Danish and Swedish marine monitoring programs. Time series with a weekly resolution were predicted from observations of dissolved inorganic nitrogen (DIN) from the Kattegat basin (1993–1997). DIN observations were sparse, irregularly distributed and comprised approximately 10% of the generated time series.     

Empirical study of GARCH models with leverage effect in an environmental application

Atmospheric carbon dioxide concentration (ACDC) level is an important factor for predicting temperature and climate changes. We analyze the conditional variance of a function of ACDC level known as ACDC level growth rate (ACDCGR) using the generalised autoregressive conditional heteroskedasticity (GARCH) and GARCH models with leverage effect. The data are a subset of the well known Mauna Loa atmosphere carbon dioxide record. We test for the presence of stylized facts in the ACDCGR time series. The performance of GARCH models are compared to EGARCH, TGARCH and PGARCH models. Model fit measures AIC, BIC and likelihood is calculated for each fitted model. The results do confirm the presence of some of important stylized facts in the ACDCGR time series, but the presence of leverage effect is not significant . The out of sample one step ahead forecasting performances of the models based on RMSE and MAE metrics are evaluated. EGARCH model with student $t$ disturbances showed the best fit and a valid forecasting performance. A bootstrap algorithm is employed to calculate confidence intervals for future values of ACDCGR time series and its volatility. The constructed bootstrap confidence intervals showed a reasonable performance.     

Sampling variability and estimates of density dependence: a composite-likelihood approach

It is well known that sampling variability, if not properly taken into account, affects various ecologically important analyses. Statistical inference for stochastic population dynamics models is difficult when, in addition to the process error, there is also sampling error. The standard maximum-likelihood approach suffers from large computational burden. In this paper, I discuss an application of the composite-likelihood method for estimation of the parameters of the Gompertz model in the presence of sampling variability. The main advantage of the method of composite likelihood is that it reduces the computational burden substantially with little loss of statistical efficiency. Missing observations are a common problem with many ecological time series. The method of composite likelihood can accommodate missing observations in a straightforward fashion. Environmental conditions also affect the parameters of stochastic population dynamics models. This method is shown to handle such nonstationary population dynamics processes as well. Many ecological time series are short, and statistical inferences based on such short time series tend to be less precise. However, spatial replications of short time series provide an opportunity to increase the effective sample size. Application of likelihood-based methods for spatial time-series data for population dynamics models is computationally prohibitive. The method of composite likelihood is shown to have significantly less computational burden, making it possible to analyze large spatial time-series data. After discussing the methodology in general terms, I illustrate its use by analyzing a time series of counts of American Redstart (Setophaga ruticilla) from the Breeding Bird Survey data, San Joaquin kit fox (Vulpes macrotis mutica) population abundance data, and spatial time series of Bull trout (Salvelinus confluentus) redds count data.     

Reliability of Absolute and Relative Predictions of Population Persistence Based on Time Series

Abstract:  Conventional population viability analysis (PVA) is often impractical because data are scarce for many threatened species. For this reason, simple count-based models are being advocated. The simplest of these models requires nothing more than a time series of abundance estimates, from which variance and autocorrelation in growth rate are estimated and predictions of population persistence are generated. What remains unclear, however, is how many years of data are needed to generate reliable estimates of these parameters and hence reliable predictions of persistence. By analyzing published and simulated time series, we show that several decades of data are needed. Predictions based on short time series were very unreliable mainly because limited data yielded biased, unreliable estimates of variance in growth rate, especially when growth rate was strongly autocorrelated. More optimistically, our results suggest that count-based PVA is sometimes useful for relative risk assessment (i.e., for ranking populations by extinction risk), even when time series are only a decade long. However, some conditions consistently lead to backward rankings. We explored the limited conditions under which simple count-based PVA may be useful for relative risk assessment.     

Prediction of non-methane hydrocarbons in Kuwait using regression and Bayesian kriged Kalman model

This article describes the hierarchical Bayesian approach for predicting average hourly concentrations of ambient non-methane hydrocarbons (NMHC) in Kuwait where records of six monitor stations located in different sites are observed at successive time points. Our objective is to predict the concentration level of NMHC in unmonitored areas. Here an attempt is made for the prediction of unmeasured concentration of NMHC at two additional locations in Kuwait. We will implement a kriged Kalman filter (KKF) hierarchical Bayesian approach assuming a Gaussian random field, a technique that allows the pooling of data from different sites in order to predict the exposure of the NMHC in different regions of Kuwait. In order to increase the accuracy of the KKF we will use other statistical models such as imputation, regression, principal components, and time series analysis in our approach. We considered four different types of imputation techniques to address the missing data. At the primary level, the logarithmic field is modeled as a trend plus Gaussian stochastic residual model. The trend model depends on hourly meteorological predictors which are common to all sites. The residuals are then modeled using KKF, and the prediction equation is derived conditioned on adjoining hours. On this basis we developed a spatial predictive distribution for these residuals at unmonitored sites. By transforming the predicted residuals back to the original data scales, we can impute Kuwait’s hourly non-methane hydrocarbons field.     

Selecting a binary Markov model for a precipitation process

This paper uses rth-order categorical Markov chains to model the probability of precipitation. Several stationary and non-stationary high-order Markov models are proposed and compared using BIC. The number of parameters increases exponentially by adding the Markov order. Several classes of high-order Markov models are proposed which their increase of number of parameters are modest. For example models that use the number of precipitation days in a period prior to date, temperature of the previous day and sines/cosines periodic functions (to model the seasonality) are considered. The theory of partial likelihood is used to estimate the parameters. Parsimonious non-stationary first order Markov models with few seasonal terms are found optimal using BIC and temperature does not turn out to be a useful covariate. However BIC seems to underestimate the number of seasonal terms. We have also compared the results with AIC in some cases which tends to pick parsimonious models with more seasonal terms and higher order. We also show that ignoring seasonal terms result in picking higher order Markov chains. Finally we apply the methods to build confidence intervals for the probability of periods with no precipitation or low number of precipitation days in Calgary using historical data from 1980 to 2000.     

Impact of time series data on calibration and prediction uncertainty for a deterministic hydrogeochemical model

Model calibration is fundamental in applications of deterministic process-based models. Uncertainty in model predictions depends much on the input data and observations available for model calibration. Here we explored how model predictions (forecasts) and their uncertainties vary with the length of time series data used in calibration. As an example we used the hydrogeochemical model MAGIC and data from Birkenes, a small catchment in southern Norway, to simulate future water chemistry under a scenario of reduced acid deposition. A Bayesian approach with a Markov Chain Monte Carlo (MCMC) technique was used to calibrate the model to different lengths of observed data (4–29 years) and to estimate the prediction uncertainty each calibration. The results show that the difference between modelled and observed water chemistry (calibration goodness of fit) in general decreases with increasing length of the time series used in calibration. However, there are considerable differences for different time series of the same length. The results also show that the uncertainties in predicted future acid neutralizing capacity were lowest (i.e. the distribution peak narrowest) when using the longest time series for calibration. As for calibration success, there were considerable differences between the future distributions (prediction uncertainty) for the different calibrations.     

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.     

Two-compartment model of radionuclide accumulation into marine organisms. I. Accumulation from a medium of constant activity

The interpretation of kinetics of radionuclide accumulation into biological organisms can be performed by using the well-known multicompartment models. The application of a two-compartment model in the interpretation of radionuclide accumulation into marine organisms, when this does not markedly deplete the medium, is considered. It has been found that most of the loss experiments cannot be interpreted without the use of uptake data. The agreement between the uptake and loss parameters is discussed. Explicit expressions for different kinds of two-compartment models are evaluated. The interpretation of irreversible and other special cases is proposed.     

Improved statistical downscaling models based on canonical correlation analysis, for generating temperature scenarios over Greece

This study attempts to improve upon statistical downscaling (Sd) models based on the classical approach which uses canonical correlation analysis, in order to generate temperature scenarios over Greece. Considering the long-term trends of the predictor variables (1,000–500 hPa thickness field geopotential heights—using NCEP data) and the predictand variables (observed mean maximum summer temperatures over Greece), a new Sd model is constructed. Regression models using generalized least square estimators are developed in order to eliminate the trends within the time series. The advantages of the suggested method compared to the classical method are quantified in terms of a number of distinct performance criteria, e.g., Mean squared error which is the basic criterion of the estimated downscaled values relative to the observed. Finally, the suggested Sd models are used to evaluate the effects of a future climate scenario (IPCC-SRES: A2) on mean maximum summer temperatures over Greece. The results from the climate projection indicate a temperature increase for the period 2070–2100 which is smaller than the corresponding increase from the classical approach.     

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.     

Fitting complex population models by combining particle filters with Markov chain Monte Carlo

We show how a recent framework combining Markov chain Monte Carlo (MCMC) with particle filters (PFMCMC) may be used to estimate population state-space models. With the purpose of utilizing the strengths of each method, PFMCMC explores hidden states by particle filters, while process and observation parameters are estimated using an MCMC algorithm. PFMCMC is exemplified by analyzing time series data on a red kangaroo (Macropus rufus) population in New South Wales, Australia, using MCMC over model parameters based on an adaptive Metropolis-Hastings algorithm. We fit three population models to these data; a density-dependent logistic diffusion model with environmental variance, an unregulated stochastic exponential growth model, and a random-walk model. Bayes factors and posterior model probabilities show that there is little support for density dependence and that the random-walk model is the most parsimonious model. The particle filter Metropolis-Hastings algorithm is a brute-force method that may be used to fit a range of complex population models. Implementation is straightforward and less involved than standard MCMC for many models, and marginal densities for model selection can be obtained with little additional effort. The cost is mainly computational, resulting in long running times that may be improved by parallelizing the algorithm.     

A method for assigning species into groups based on generalized Mahalanobis distance between habitat model coefficients

Habitat association models are commonly developed for individual animal species using generalized linear modeling methods such as logistic regression. We considered the issue of grouping species based on their habitat use so that management decisions can be based on sets of species rather than individual species. This research was motivated by a study of western landbirds in northern Idaho forests. The method we examined was to separately fit models to each species and to use a generalized Mahalanobis distance between coefficient vectors to create a distance matrix among species. Clustering methods were used to group species from the distance matrix, and multidimensional scaling methods were used to visualize the relations among species groups. Methods were also discussed for evaluating the sensitivity of the conclusions because of outliers or influential data points. We illustrate these methods with data from the landbird study conducted in northern Idaho. Simulation results are presented to compare the success of this method to alternative methods using Euclidean distance between coefficient vectors and to methods that do not use habitat association models. These simulations demonstrate that our Mahalanobis-distance-based method was nearly always better than Euclidean-distance-based methods or methods not based on habitat association models. The methods used to develop candidate species groups are easily explained to other scientists and resource managers since they mainly rely on classical multivariate statistical methods.