Bayesian hierarchical mixture models for otolith microchemistry analysis

The field of fisheries research commonly uses classical statistical classification methods to estimate the proportion of fish that return to natal spawning grounds to spawn. With the advent of otolith microchemical analysis, researchers are able to extract information from fish ear stones (otoliths) about the chemical composition of water in which fish have spent distinct periods of their lives. Here we present a method of analysis set in the Bayesian statistical paradigm which enables explicit incorporation of habitat information into the analysis. The ecological system is seen as arising from a mixture of disparate fish populations and information from the biological relationships inherent in otolith formation is exploited through the hierarchical model structure. We present the model and motivation, demonstrate the validity of the model through simulation studies, and conclude with an analysis of a data set from Lake Erie.     

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 new context-based approach to assess marine mammal behavioral responses to anthropogenic sounds

Acute effects of anthropogenic sounds on marine mammals, such as from military sonars, energy development, and offshore construction, have received considerable international attention from scientists, regulators, and industry. Moreover, there has been increasing recognition and concern about the potential chronic effects of human activities (e.g., shipping). It has been demonstrated that increases in human activity and background noise can alter habitats of marine animals and potentially mask communications for species that rely on sound to mate, feed, avoid predators, and navigate. Without exception, regulatory agencies required to assess and manage the effects of noise on marine mammals have addressed only the acute effects of noise on hearing and behavior. Furthermore, they have relied on a single exposure metric to assess acute effects: the absolute sound level received by the animal. There is compelling evidence that factors other than received sound level, including the activity state of animals exposed to different sounds, the nature and novelty of a sound, and spatial relations between sound source and receiving animals (i.e., the exposure context) strongly affect the probability of a behavioral response. A more comprehensive assessment method is needed that accounts for the fact that multiple contextual factors can affect how animals respond to both acute and chronic noise. We propose a three-part approach. The first includes measurement and evaluation of context-based behavioral responses of marine mammals exposed to various sounds. The second includes new assessment metrics that emphasize relative sound levels (i.e., ratio of signal to background noise and level above hearing threshold). The third considers the effects of chronic and acute noise exposure. All three aspects of sound exposure (context, relative sound level, and chronic noise) mediate behavioral response, and we suggest they be integrated into ecosystem-level management and the spatial planning of human offshore activities.     

A Bayesian approach to line-transect analysis for estimating abundance

Line-transect analysis is a widely used method of estimating plant and animal density and abundance. A Bayesian approach to a basic line-transect analysis is developed for a half-normal detection function. We extend the model of Karunamuni and Quinn [Karunamuni, R.J., Quinn II, T.J., 1995. Bayesian estimation of animal abundance for line-transect sampling. Biometrics 51, 1325–1337] by including a binomial likelihood function for the number of objects detected. The method computes a joint posterior distribution on the effective strip width and the density of objects in the sampled area. Analytical and computational methods for binned and unbinned perpendicular distance data are provided. Existing information about effective strip width and density can be brought into the analysis via prior distributions. The Bayesian approach is compared to a standard line-transect analysis using both real and simulated data. Results of the Bayesian and non-Bayesian analyses are similar when there are no prior data on effective strip width or density, but the Bayesian approach performs better when such data are available from previous or related studies. Practical methods for including prior data on effective strip width and density are suggested. A numerical example shows how the Bayesian approach can provide valid estimates when the sample size is too small for the standard approach to work reliably. The proposed Bayesian approach can form the basis for developing more advanced analyses.     

A general bioeconomic simulation model for annual-crop marine fisheries

A generalized bioeconomic simulation model of annual-crop marine fisheries is described and its use in marine fisheries management is demonstrated. The biological submodel represents the recruitment of new organisms into the fishery, the movement of organisms from one fishing area to another and from one depth to another, the growth of organisms and the mortality of organisms resulting both from natural causes and from fishing. The economic submodel represents the fishing effort exerted on each resource species, the monetary costs of fishing, the value of the harvest and the rent (or excess profits) to the fishery.Basic dynamics of the model results from changes in the number of organisms in the fishery over time, which can be summarized as a set of difference equations of the general form ΔN/Δt = R + I ? E ? M ? F where ΔN/Δt is the net change in number of organisms in the fishery over time, R is recruitment, I is immigration, E is emigration, M is natural mortality and F is fishing mortality. R is a driving variable, whereas I, E, M and F are functions of the state of the system at any given point in time. The model can be run in a deterministic or stochastic mode. Values for parameters affecting rates of recruitment, movement, growth, natural mortality and fishing mortality can be selected from uniform, triangular or normal distributions.Use of the model within a fisheries-management framework is demonstrated by evaluating several management alternatives for the pink shrimp (Penaeus duorarum) fishery on the Tortugas grounds in the Gulf of Mexico. Steps involved in use of the model, including parameterization, validation, sensitivity analysis and stochastic simulations of management policies, are explained.     

Bayesian analysis of abundance for binomial sighting data with unknown number of marked individuals

The mark-resight method for estimating the size of a closed population can in many circumstances be a less expensive and less invasive alternative to traditional mark-recapture. Despite its potential advantages, one major drawback of traditional mark-resight methodology is that the number of marked individuals in the population available for resighting needs to be known exactly. In real field studies, this can be quite difficult to accomplish. Here we develop a Bayesian model for estimating abundance when sighting data are acquired from distinct sampling occasions without replacement, but the exact number of marked individuals is unknown. By first augmenting the data with some fixed number of individuals comprising a marked “super population,” the problem may then be reformulated in terms of estimating the proportion of this marked super population that was actually available for resighting. This then allows the data for the marked population available for resighting to be modeled as random realizations from a binomial logit-normal distribution. We demonstrate the use of our model to estimate the New Zealand robin (Petroica australis) population size in a region of Fiordland National Park, New Zealand. We then evaluate the performance of the proposed model relative to other estimators via a series of simulation experiments. We generally found our model to have advantages over other models when sample sizes are smaller with individually heterogeneous resighting probabilities. Due to limited budgets and the inherent variability between individuals, this is a common occurrence in mark-resight population studies. WinBUGS and R code to carry out these analyses is available from .     

A hierarchical model for spatial capture-recapture data

Estimating density is a fundamental objective of many animal population studies. Application of methods for estimating population size from ostensibly closed populations is widespread, but ineffective for estimating absolute density because most populations are subject to short-term movements or so-called temporary emigration. This phenomenon invalidates the resulting estimates because the effective sample area is unknown. A number of methods involving the adjustment of estimates based on heuristic considerations are in widespread use. In this paper, a hierarchical model of spatially indexed capture-recapture data is proposed for sampling based on area searches of spatial sample units subject to uniform sampling intensity. The hierarchical model contains explicit models for the distribution of individuals and their movements, in addition to an observation model that is conditional on the location of individuals during sampling. Bayesian analysis of the hierarchical model is achieved by the use of data augmentation, which allows for a straightforward implementation in the freely available software WinBUGS. We present results of a simulation study that was carried out to evaluate the operating characteristics of the Bayesian estimator under variable densities and movement patterns of individuals. An application of the model is presented for survey data on the flat-tailed horned lizard (Phrynosoma mcallii) in Arizona, USA.     

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 zero-inflated Bayesian spatial model with near-locating measurements

Zero-inflated data arise in many contexts. In this paper, we develop a zero-inflated Bayesian hierarchical model which deals with spatial effects, correlation among near-locating measurements as well as excess zeros simultaneously. Inference, including the sampling from the posterior distributions, predictions at new locations, and model selection, is carried out by using computationally efficient Markov chain Monte Carlo techniques. The posterior distributions are simulated using a Gibbs sampler with the embedded ratio-of-uniform method and the slice sampling algorithm. The approach is illustrated via an application to herbaceous data collected in the Missouri Ozark Forest Ecosystem Project. The results from the proposed model are compared with those generated from a non-zero inflated model. The proposed model fully incorporates the information from data collection and provides more reliable inference. A predictive $p$ value is computed for model checking and it indicates that the proposed model fits the data well.     

Towards a global model of in situ weight-specific growth in marine planktonic copepods

The dependency of in situ weight-specific fecundity of adult females (as egg production) and growth of juveniles (as somatic production) upon individual body weight in marine planktonic copepods was examined. A compilation was made of results where wild-caught individuals were incubated in natural seawater (often pre-screened to remove large organisms), at near in situ temperatures, over short periods of the order of 24 h. The results demonstrate that for the adult broadcast-spawning group weight-specific fecundity rates are dependent upon body weight, but independent of temperature. We postulate this may be the result of global patterns in available phytoplankton. Weight-specific growth rates are dependent upon individual temperature and body weight in juvenile broadcast-spawners, with rates declining as body weight increases. Sac-spawners have growth/fecundity rates that are independent of body weight in adults, juveniles, and both combined, but which are temperature-dependent. Globally applicable equations are derived which may be used to predict growth and production of marine copepods using easily quantifiable parameters, namely size-distributed biomass and temperature. Some of the variability in growth which remained unaccounted for is the result of variations in food quantity and quality in the natural environment. Comparisons of the rates compiled here over the temperature range 10 to 20 °C with previously compiled food-saturated rates over the same temperature interval, revealed that in situ rates are typically sub-optimal. Adults appear to be more food-limited than juveniles, adult rates in situ being 32 and 40% of those under food saturation in broadcasters and sac-spawners, respectively, while juvenile in situ rates are on average ∼70% of those at food saturation in both broadcasters and sac-spawners. Received: 18 September 1997 / Accepted: 13 May 1998     

A mechanistic model of GPS collar location data: Implications for analysis and bias mitigation

Global positioning system (GPS) collars have revolutionized the collection of animal location data; however, it is well-recognized that considerable bias can be present in these data due to habitat or behavior-induced obstruction of satellite signals resulting in inaccurate or missing locations. To date, no explicit theoretical framework of GPS fix acquisition specific to animal telemetry has been presented, and studies make differing assumptions regarding factors influencing GPS fix acquisition and how these data should be analyzed. Inappropriate statistical models have been used, interaction effects have been misunderstood, and the implementation of bias mitigation techniques has been problematic. Herein we outline current conceptual and analytical problems in the GPS animal telemetry literature, and subsequently present a theoretical model-based framework for GPS fix acquisition that clarifies the single and interactive effects of habitat and behavioral obstruction, fix interval, and collar model on GPS collar performance. By recognizing that GPS fix acquisition is a Bernoulli process, it becomes apparent that all forms of obstruction inherently interact with each other, making generalizations across study areas, study species, and collar models problematic. Stationary collar tests to determine the probability of fix acquisition (PFA), location accuracy, and the response to sources of obstruction are thus of limited applicability to animal-deployed collars. Bias mitigation techniques that extrapolate PFA models across samples, especially those using stationary collar tests to correct animal-deployed collars, are theoretically unsound. It is also demonstrated that nonlinearities in the relationships between sources of obstruction and PFA complicate PFA modeling with limited data and that even slight model misspecification can lead to considerable errors in correction factors, especially when using inverse weighting to mitigate bias. By emphasizing the importance of GPS collar sensitivity and ephemeris retention, the theoretical framework predicts that newer, more sensitive GPS collars will be less severely biased by sources of obstruction than reported for the older, less sensitive collars that have been used in the majority of GPS performance studies to date and we expect this trend to continue. This heuristic modeling exercise should be of value to researchers planning and analyzing studies using GPS collars and it also establishes a starting point for future theoretical investigations into GPS collar performance and bias mitigation.     

Pivotal discrepancy measures for Bayesian modelling of spatio-temporal data

Environmental and Ecological Statistics - Within the field of geostatistics, Gaussian processes are a staple for modelling spatial and spatio-temporal data. Statistical literature is rich with...     

Bayesian entropy for spatial sampling design of environmental data

We develop a spatial statistical methodology to design national air pollution monitoring networks with good predictive capabilities while minimizing the cost of monitoring. The underlying complexity of atmospheric processes and the urgent need to give credible assessments of environmental risk create problems requiring new statistical methodologies to meet these challenges. In this work, we present a new method of ranking various subnetworks taking both the environmental cost and the statistical information into account. A Bayesian algorithm is introduced to obtain an optimal subnetwork using an entropy framework. The final network and accuracy of the spatial predictions is heavily dependent on the underlying model of spatial correlation. Usually the simplifying assumption of stationarity, in the sense that the spatial dependency structure does not change location, is made for spatial prediction. However, it is not uncommon to find spatial data that show strong signs of nonstationary behavior. We build upon an existing approach that creates a nonstationary covariance by a mixture of a family of stationary processes, and we propose a Bayesian method of estimating the associated parameters using the technique of Reversible Jump Markov Chain Monte Carlo. We apply these methods for spatial prediction and network design to ambient ozone data from a monitoring network in the eastern US.     

Bayesian methods for analyzing movements in heterogeneous landscapes from mark-recapture data

Spatially referenced mark-recapture data are becoming increasingly available, but the analysis of such data has remained difficult for a variety of reasons. One of the fundamental problems is that it is difficult to disentangle inherent movement behavior from sampling artifacts. For example, in a typical study design, short distances are sampled more frequently than long distances. Here we present a modeling-based alternative that combines a diffusion-based process model with an observation model to infer the inherent movement behavior of the species from the data. The movement model is based on classifying the landscape into a number of habitat types, and assuming habitat-specific diffusion and mortality parameters, and habitat selection at edges between the habitat types. As the problem is computationally highly intensive, we provide software that implements adaptive Bayesian methods for effective sampling of the posterior distribution. We illustrate the modeling framework by analyzing individual mark-recapture data on the Glanville fritillary butterfly (Melitaea cinxia), and by comparing our results with earlier ones derived from the same data using a purely statistical approach. We use simulated data to perform an analysis of statistical power, examining how accuracy in parameter estimates depends on the amount of data and on the study design. Obtaining precise estimates for movement rates and habitat preferences turns out to be especially challenging, as these parameters can be highly correlated in the posterior density. We show that the parameter estimates can be considerably improved by alternative study designs, such as releasing some of the individuals into the unsuitable matrix, or spending part of the recapture effort in the matrix.     

Bayesian estimation of European sulphur emissions using monitoring data and an acid deposition model

A statistical method for estimating national emissions of acidifying air pollutants in Europe is presented. The method uses an acid deposition model to match official emissions data from European countries and measured depositions from a monitoring network. An application to 1990 sulphate data demonstrates the method and suggests some tendencies in the reported emissions. The proposed framework may prove useful for verifying national compliance with emissions standards, and the method should be applicable also to other substances than sulphur dioxide. The problem of designing an optimal monitoring network may also be assessed within the proposed statistical framework.     

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.     

A goal interval programming model for resource allocation in a marine environmental protection program

A multidimensional “goal programming” model is developed to aid resource allocation decisions in the U. S. Coast Guard's Marine Environmental Protection (MEP) program. It is then extended to a model of “goal interval programming” (GIP ) type where exact values for the indicated goals, as in ordinary goal programming, are replaced by ranges. Deviations outside these ranges are also accommodated by piecewise linear functions with slopes that vary with distance from the goal intervals. Uses and generalizations are discussed in the context of applications to allocating manhours and planning the activities of the Coast Guard's MEP program.