Performance of a Bayesian state-space model of semelparous species for stock-recruitment data subject to measurement error

Measurement errors in spawner abundance create problems for fish stock assessment scientists. To deal with measurement error, we develop a Bayesian state-space model for stock-recruitment data that contain measurement error in spawner abundance, process error in recruitment, and time series bias. Through extensive simulations across numerous scenarios, we compare the statistical performance of the Bayesian state-space model with that of standard regression for a traditional stock-recruitment model that only considers process error. Performance varies depending on the information content in data, as determined by stock productivity, types of harvest situations, and amount of measurement error. Overall, in terms of estimating optimal spawner abundance S_MSY, the Ricker density-dependence parameter β, and optimal harvest rate h_MSY, the Bayesian state-space model works best for informative data from low and variable harvest rate situations for high-productivity salmon stocks. The traditional stock-recruitment model (TSR) may be used for estimating α and h_MSY for low-productivity stocks from variable and high harvest rate situations. However, TSR can severely overestimate S_MSY when spawner abundance is measured with large error in low and variable harvest rate situations. We also found that there is substantial merit in using h_MSY (or benchmarks derived from it) instead of S_MSY as a management target.     

A frontier model for landscape ecology: the tapir in Honduras

We borrow a frontier specification from the econometrics literature to make inferences about the tolerance of the tapir to human settlements. We estimate the width of an invisible band surrounding human settlements which would act as a frontier or exclusion zone to the tapir to be around 290 metres.     

Dealing with collinearity in behavioural and ecological data: model averaging and the problems of measurement error

There has been a great deal of recent discussion of the practice of regression analysis (or more generally, linear modelling) in behaviour and ecology. In this paper, I wish to highlight two factors that have been under-considered, collinearity and measurement error in predictors, as well as to consider what happens when both exist at the same time. I examine what the consequences are for conventional regression analysis (ordinary least squares, OLS) as well as model averaging methods, typified by information theoretic approaches based around Akaike’s information criterion. Collinearity causes variance inflation of estimated slopes in OLS analysis, as is well known. In the presence of collinearity, model averaging reduces this variance for predictors with weak effects, but also can lead to parameter bias. When collinearity is strong or when all predictors have strong effects, model averaging relies heavily on the full model including all predictors and hence the results from this and OLS are essentially the same. I highlight that it is not safe to simply eliminate collinear variables without due consideration of their likely independent effects as this can lead to biases. Measurement error is also considered and I show that when collinearity exists, this can lead to extreme biases when predictors are collinear, have strong effects but differ in their degree of measurement error. I highlight techniques for dealing with and diagnosing these problems. These results reinforce that automated model selection techniques should not be relied on in the analysis of complex multivariable datasets.     

Uncertainty and measurement error in welfare models for risk changes

Most welfare models of environmental or mortality risk reductions assume that risks are exogenously determined and known with certainty. However, a growing body of research suggests that uncertainty about risks can affect choices over risky prospects. I present a decision-weighted random-utility model that decomposes welfare losses into those attributable to an increase in the deterministic component of risk and those attributable to uncertainty about risk. I apply the model to an illustrative dataset of subjects' perceived mortality risk and willingness to accept the risk of nuclear-waste transport. I estimate the model using Lewbel's (2000) strictly exogenous regressor approach to account for endogeneity bias and measurement error. Subjects display aversion to both risk and uncertainty about the risk of a transport accident, so that increases in either leads to social-welfare losses. Roughly 12% of the external cost of nuclear-waste transport is attributable to the public's uncertainty about transport risk.     

Regression model under skew-normal error with applications in predicting groundwater arsenic level in the Mekong Delta Region

Environmental and Ecological Statistics - Recently there has been some renewed interest in skew-normal distribution (SND) because it provides a nice and natural generalization (in terms of...     

Bayesian testing for trend in a power model for clustered binary data

Developmental toxicity studies are widely used to investigate the potential risk of environmental hazards. In dose–response experiments, subjects are randomly allocated to groups receiving various dose levels. Tests for trend are then often applied to assess possible dose effects. Recent techniques for risk assessment in this area are based on fitting dose–response models. The complexity of such studies implies a number of non-trivial challenges for model development and the construction of dose-related trend tests, including the hierarchical structure of the data, litter effects inducing extra variation, the functional form of the dose–response curve, the adverse event at dam or at fetus level, the inference paradigm, etc. The purpose of this paper is to propose a Bayesian trend test based on a non-linear power model for the dose effect and using an appropriate model for clustered binary data. Our work is motivated by the analysis of developmental toxicity studies, in which the offspring of exposed and control rodents are examined for defects. Simulations show the performance of the method over a number of samples generated under typical experimental conditions.     

A Bayesian mixture model for missing data in marine mammal growth analysis

Much of what is known about bottle nose dolphin (Tursiops truncatus) anatomy and physiology is based on necropsies from stranding events. Measurements of total body length, total body mass, and age are used to estimate growth. It is more feasible to retrieve and transport smaller animals for total body mass measurement than larger animals, introducing a systematic bias in sampling. Adverse weather events, volunteer availability, and other unforeseen circumstances also contribute to incomplete measurement. We have developed a Bayesian mixture model to describe growth in detected stranded animals using data from both those that are fully measured and those not fully measured. Our approach uses a shared random effect to link the missingness mechanism (i.e. full/partial measurement) to distinct growth curves in the fully and partially measured populations, thereby enabling drawing of strength for estimation. We use simulation to compare our model to complete case analysis and two common multiple imputation methods according to model mean square error. Results indicate that our mixture model provides better fit both when the two populations are present and when they are not. The feasibility and utility of our new method is demonstrated by application to South Carolina strandings data.     

Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology.     

Accounting for large-scale factors in the study of understory vegetation using a conditional logistic model

Local-scale and large-scale factors can affect the presence of a species of understory vegetation in the forest. Local-scale factors may be the influence of surrounding trees, while climate and latitude are typically considered large-scale factors. A model for the presence of a species needs to take into account both scales. A conditional logistic model is proposed for those studies where only the local-scale factors are of interest and that avoids estimating the large-scale parameters. Conditioning is carried out by the number of quadrats in the plot where the vegetation is found. As the latter is a sufficient statistic for the large-scale factors, a model free from these parameters is obtained. Data gathered in the permanent sample plots of the 1985–1986 National Forest Inventory of Finland is used for illustration, where the local-scale factor of interest is the influence of the trees, quantified by an index based on the size and location of the trees. The model fitted to Vaccinium vitis-idaea showed a significant and positive influence of Scots pine on the presence of this species, while for Calamagrostis arundinacea, a decrease in the odds ratio was observed due to the influence of Norway spruce.     

Inferring linear feature use in the presence of GPS measurement error

Global Positioning System (GPS) collars are increasingly used to study animal movement and habitat use. Measurement error is defined as the difference between the observed and true value being measured. In GPS data measurement error is referred to as location error and leads to misclassification of observed locations into habitat types. This is particularily true when studying habitats of small spatial extent with large amounts of edge, such as linear features (e.g. roads and seismic lines). However, no consistent framework exists to address the effect of measurement error on habitat classification of observed locations and resulting biological inference. We developed a mechanistic, empirically-based method for buffering linear features that minimizes the underestimation of animal use introduced by GPS measurement error. To do this we quantified the distribution of measurement error and derived an explicit formula for buffer radius which incorporated the error distribution, the width of the linear feature, and a predefined amount of acceptable type I error in location classification. In our empirical study we found the GPS measurement error of the Lotek GPS_3300 collar followed a bivariate Laplace distribution with parameter ρ = 0.1123. When we applied our method to a simulated landscape, type I error was reduced by 57%. This study highlights the need to address the effect of GPS measurement error in animal location classification, particularily for habitats of small spatial extent.     

Nutrient criteria for lakes,ponds, and reservoirs: A Bayesian TREED model approach

We develop regional-scale eutrophication models for lakes, ponds, and reservoirs to investigate the link between nutrients and chlorophyll-a. The Bayesian TREED (BTREED) model approach allows association of multiple environmental stressors with biological responses, and quantification of uncertainty sources in the empirical water quality model. Nutrient data for lakes, ponds, and reservoirs across the United States were obtained from the Environmental Protection Agency (EPA) National Nutrient Criteria Database. The nutrient data consist of measurements for both stressor variables (such as total nitrogen and total phosphorus), and response variables (such as chlorophyll-a), used in the BTREED model. Markov chain Monte Carlo (McMC) posterior exploration guides a stochastic search through a rich suite of candidate trees toward models that better fit the data. The Bayes factor provides a goodness of fit criterion for comparison of resultant models. We randomly split the data into training and test sets; the training data were used in model estimation, and the test data were used to evaluate out-of-sample predictive performance of the model. An average relative efficiency of 1.02 between the training and test data for the four highest log-likelihood models suggests good out-of-sample predictive performance. Reduced model uncertainty relative to over-parameterized alternative models makes the BTREED models useful for nutrient criteria development, providing the link between nutrient stressors and meaningful eutrophication response.     

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...     

Model selection and model averaging in behavioural ecology: the utility of the IT-AIC framework

Behavioural ecologists often study complex systems in which multiple hypotheses could be proposed to explain observed phenomena. For some systems, simple controlled experiments can be employed to reveal part of the complexity; often, however, observational studies that incorporate a multitude of causal factors may be the only (or preferred) avenue of study. We assess the value of recently advocated approaches to inference in both contexts. Specifically, we examine the use of information theoretic (IT) model selection using Akaike’s information criterion (AIC). We find that, for simple analyses, the advantages of switching to an IT-AIC approach are likely to be slight, especially given recent emphasis on biological rather than statistical significance. By contrast, the model selection approach embodied by IT approaches offers significant advantages when applied to problems of more complex causality. Model averaging is an intuitively appealing extension to model selection. However, we were unable to demonstrate consistent improvements in prediction accuracy when using model averaging with IT-AIC; our equivocal results suggest that more research is needed on its utility. We illustrate our arguments with worked examples from behavioural experiments.     

A Bayesian hierarchical model for monitoring harbor seal changes in Prince William Sound, Alaska

Bayesian hierarchical models were used to assess trends of harbor seals, Phoca vitulina richardsi, in Prince William Sound, Alaska, following the 1989 Exxon Valdez oil spill. Data consisted of 4–10 replicate observations per year at 25 sites over 10 years. We had multiple objectives, including estimating the effects of covariates on seal counts, and estimating trend and abundance, both per site and overall. We considered a Bayesian hierarchical model to meet our objectives. The model consists of a Poisson regression model for each site. For each observation the logarithm of the mean of the Poisson distribution was a linear model with the following factors: (1) intercept for each site and year, (2) time of year, (3) time of day, (4) time relative to low tide, and (5) tide height. The intercept for each site was then given a linear trend model for year. As part of the hierarchical model, parameters for each site were given a prior distribution to summarize overall effects. Results showed that at most sites, (1) trend is down; counts decreased yearly, (2) counts decrease throughout August, (3) counts decrease throughout the day, (4) counts are at a maximum very near to low tide, and (5) counts decrease as the height of the low tide increases; however, there was considerable variation among sites. To get overall trend we used a weighted average of the trend at each site, where the weights depended on the overall abundance of a site. Results indicate a 3.3% decrease per year over the time period.     

Random forests for classification in ecology

Classification procedures are some of the most widely used statistical methods in ecology. Random forests (RF) is a new and powerful statistical classifier that is well established in other disciplines but is relatively unknown in ecology. Advantages of RF compared to other statistical classifiers include (1) very high classification accuracy; (2) a novel method of determining variable importance; (3) ability to model complex interactions among predictor variables; (4) flexibility to perform several types of statistical data analysis, including regression, classification, survival analysis, and unsupervised learning; and (5) an algorithm for imputing missing values. We compared the accuracies of RF and four other commonly used statistical classifiers using data on invasive plant species presence in Lava Beds National Monument, California, USA, rare lichen species presence in the Pacific Northwest, USA, and nest sites for cavity nesting birds in the Uinta Mountains, Utah, USA. We observed high classification accuracy in all applications as measured by cross-validation and, in the case of the lichen data, by independent test data, when comparing RF to other common classification methods. We also observed that the variables that RF identified as most important for classifying invasive plant species coincided with expectations based on the literature.     

The value of virtual conferencing for ecology and conservation

The objectives of conservation science and dissemination of its research create a paradox: Conservation is about preserving the environment, yet scientists spread this message at conferences with heavy carbon footprints. Ecology and conservation science depend on global knowledge exchange—getting the best science to the places it is most needed. However, conference attendance from developed countries typically outweighs that from developing countries that are biodiversity and conservation hotspots. If any branch of science should be trying to maximize participation while minimizing carbon emissions, it is conservation. Virtual conferencing is common in other disciplines, such as education and humanities, but it is surprisingly underused in ecology and conservation. Adopting virtual conferencing entails a number of challenges, including logistics and unified acceptance, which we argue can be overcome through planning and technology. We examined 4 conference models: a pure‐virtual model and 3 hybrid hub‐and‐node models, where hubs stream content to local nodes. These models collectively aim to mitigate the logistical and administrative challenges of global knowledge transfer. Embracing virtual conferencing addresses 2 essential prerequisites of modern conferences: lowering carbon emissions and increasing accessibility for remote, time‐ and resource‐poor researchers, particularly those from developing countries.