Random versus stratified location of transects or points in distance sampling: theoretical results and practical considerations

A composite approach mixing design-based and model-based inference is considered for analyzing line-transect or point-transect data. In this setting, the properties of the animal abundance estimator stem from the sampling scheme adopted to locate transects or points on the study region, as well as from the modeled detection probabilities. Moreover, the abundance estimation can be viewed as a “generalized” version of Monte Carlo integration. This approach permits to prove the superiority of the stratified placement of transects or points (based on a regular tessellation of the study region) over the uniform random placement. Even if the result was already established for the fixed-area sampling, i.e., when a perfect detection takes place, it was lacking in distance sampling. Comparisons with other widely-applied schemes pursuing an even placement of transects or points are also considered.     

Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.     

Toward accurate and precise estimates of lion density

Reliable estimates of animal density are fundamental to understanding ecological processes and population dynamics. Furthermore, their accuracy is vital to conservation because wildlife authorities rely on estimates to make decisions. However, it is notoriously difficult to accurately estimate density for wide‐ranging carnivores that occur at low densities. In recent years, significant progress has been made in density estimation of Asian carnivores, but the methods have not been widely adapted to African carnivores, such as lions (Panthera leo). Although abundance indices for lions may produce poor inferences, they continue to be used to estimate density and inform management and policy. We used sighting data from a 3‐month survey and adapted a Bayesian spatially explicit capture‐recapture (SECR) model to estimate spatial lion density in the Maasai Mara National Reserve and surrounding conservancies in Kenya. Our unstructured spatial capture‐recapture sampling design incorporated search effort to explicitly estimate detection probability and density on a fine spatial scale, making our approach robust in the context of varying detection probabilities. Overall posterior mean lion density was estimated to be 17.08 (posterior SD 1.310) lions >1 year old/100 km², and the sex ratio was estimated at 2.2 females to 1 male. Our modeling framework and narrow posterior SD demonstrate that SECR methods can produce statistically rigorous and precise estimates of population parameters, and we argue that they should be favored over less reliable abundance indices. Furthermore, our approach is flexible enough to incorporate different data types, which enables robust population estimates over relatively short survey periods in a variety of systems. Trend analyses are essential to guide conservation decisions but are frequently based on surveys of differing reliability. We therefore call for a unified framework to assess lion numbers in key populations to improve management and policy decisions.     

Poor-data and data-poor species stock assessment using a Bayesian hierarchical approach

Appropriate inference for stocks or species with low-quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small-area, small-sample-size estimation problems because they allow poor-data species to borrow strength from species with good-quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor-data and data-poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70-80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state-space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species-specific data, because the poor-data species can borrow strength from the species with good data, making the estimation more stable and robust.     

Density estimation in tiger populations: combining information for strong inference

A productive way forward in studies of animal populations is to efficiently make use of all the information available, either as raw data or as published sources, on critical parameters of interest. In this study, we demonstrate two approaches to the use of multiple sources of information on a parameter of fundamental interest to ecologists: animal density. The first approach produces estimates simultaneously from two different sources of data. The second approach was developed for situations in which initial data collection and analysis are followed up by subsequent data collection and prior knowledge is updated with new data using a stepwise process. Both approaches are used to estimate density of a rare and elusive predator, the tiger, by combining photographic and fecal DNA spatial capture-recapture data. The model, which combined information, provided the most precise estimate of density (8.5 +/- 1.95 tigers/100 km2 [posterior mean +/- SD]) relative to a model that utilized only one data source (photographic, 12.02 +/- 3.02 tigers/100 km2 and fecal DNA, 6.65 +/- 2.37 tigers/100 km2). Our study demonstrates that, by accounting for multiple sources of available information, estimates of animal density can be significantly improved.     

Cost‐effective conservation of an endangered frog under uncertainty

How should managers choose among conservation options when resources are scarce and there is uncertainty regarding the effectiveness of actions? Well‐developed tools exist for prioritizing areas for one‐time and binary actions (e.g., protect vs. not protect), but methods for prioritizing incremental or ongoing actions (such as habitat creation and maintenance) remain uncommon. We devised an approach that combines metapopulation viability and cost‐effectiveness analyses to select among alternative conservation actions while accounting for uncertainty. In our study, cost‐effectiveness is the ratio between the benefit of an action and its economic cost, where benefit is the change in metapopulation viability. We applied the approach to the case of the endangered growling grass frog (Litoria raniformis), which is threatened by urban development. We extended a Bayesian model to predict metapopulation viability under 9 urbanization and management scenarios and incorporated the full probability distribution of possible outcomes for each scenario into the cost‐effectiveness analysis. This allowed us to discern between cost‐effective alternatives that were robust to uncertainty and those with a relatively high risk of failure. We found a relatively high risk of extinction following urbanization if the only action was reservation of core habitat; habitat creation actions performed better than enhancement actions; and cost‐effectiveness ranking changed depending on the consideration of uncertainty. Our results suggest that creation and maintenance of wetlands dedicated to L. raniformis is the only cost‐effective action likely to result in a sufficiently low risk of extinction. To our knowledge we are the first study to use Bayesian metapopulation viability analysis to explicitly incorporate parametric and demographic uncertainty into a cost‐effective evaluation of conservation actions. The approach offers guidance to decision makers aiming to achieve cost‐effective conservation under uncertainty.     

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.     

Field-scale roles of density, temperature, nitrogen, and predation on aphid population dynamics

Robust analyses of noisy, stage-structured, irregularly spaced, field-scale data incorporating multiple sources of variability and nonlinear dynamics remain very limited, hindering understanding of how small-scale studies relate to large-scale population dynamics. We used a novel, complementary Bayesian and frequentist state-space model analysis to ask how density, temperature, plant nitrogen, and predators affect cotton aphid (Aphis gossypii) population dynamics in weekly data from 18 field-years and whether estimated effects are consistent with small-scale studies. We found clear roles of density and temperature but not of plant nitrogen or predators, for which Bayesian and frequentist evidence differed. However, overall predictability of field-scale dynamics remained low. This study demonstrates stage-structured state-space model analysis incorporating bottom-up, top-down, and density-dependent effects for within-season (nearly continuous time), nonlinear population dynamics. The analysis combines Bayesian posterior evidence with maximum-likelihood estimation and frequentist hypothesis testing using average one-step-ahead residuals.     

A Bayesian framework for stable isotope mixing models

Stable isotope sourcing is used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets and plant nutrient use. Statistical methods for inference on the diet proportions using stable isotopes have focused on the linear mixing model. Existing frequentist methods provide inferences when the diet proportion vector can be uniquely solved for in terms of the isotope ratios. Bayesian methods apply for arbitrary numbers of isotopes and diet sources but existing models are somewhat limited as they assume that trophic fractionation or discrimination is estimated without error or that isotope ratios are uncorrelated. We present a Bayesian model for the estimation of mean diet that accounts for uncertainty in source means and discrimination and allows correlated isotope ratios. This model is easily extended to allow the diet proportion vector to depend on covariates, such as time. Two data sets are used to illustrate the methodology. Code is available for selected analyses.     

Habitat selection models to account for seasonal persistence in radio telemetry data

Models for the analysis of habitat selection data incorporate covariates in an independent multinomial selections model (McCracken et al. 1998) Ramsey and Usner 2003 and an extension of that model to include a persistence parameter (2003). In both cases, all parameters are assumed to be fixed through time. Radio telemetry data collected for habitat selection studies typically consist of animal relocations through time, suggesting the need for an extension to these models. We use a Bayesian approach that allows for the habitat selection probabilities, persistence parameter, or both, to change with season. These extensions are particularly important when movement patterns are expected to differ seasonally and/or when availabilities of habitats change throughout the study period due to weather or migration. We implement and compare the models using radio telemetry data for westslope cutthroat trout in two streams in eastern Oregon.     

Spatial statistics for modeling of abundance and distribution of wildlife species in the Masai Mara ecosystem, Kenya

This study illustrates the use of modern statistical procedures for better wildlife management by addressing three key issues: determination of abundance, modeling of animal distributions and variability of diversity in space and time. Prior information in Markov Chain Monte Carlo (MCMC) methods is used to improve estimates of abundance. Measures of autocorrelation are included when modeling distributions of animal counts, and a diversity index to indicate species abundance and richness for large herbivores is developed. Data from the Masai Mara ecosystem in Kenya are used to develop and demonstrate these procedures. The new abundance estimates are up to 35% more accurate than those obtained by existing methods. Significant temporal changes in spatial patterns are found from a space-time analysis of elephant counts over a 20-year period, with strong interactions over 5 km and 6 months space and time separations, respectively. The new diversity index is sensitive to both high abundance and species richness and is also able to capture year to year variation. It indicates an overall marginal decrease in diversity for large herbivores in the Mara ecosystem. The space-time analyses and diversity index can easily be computed thereby providing tools for rapid decision making.     

Effects of anthropogenic disturbance on primate density at the landscape scale

Accurate estimations of the abundance of threatened animal populations are required for assessment of species’ status and vulnerability and conservation planning. However, density estimation is usually difficult and resource demanding, so researchers often collect data at local scales. However, anthropogenic pressures most often have landscape-level effects, for example, through habitat loss and fragmentation. We applied hierarchical distance sampling (HDS) to transect count data to determine the effect of habitat and anthropogenic factors on the density of 3 arboreal primate species inhabiting 5 distinct tropical forests across a landscape of 19,000 km² in the Udzungwa Mountains of Tanzania. We developed a novel, multiregion extension of HDS that allowed us to model density and detectability jointly across forests without losing site-specific information. For all species, the effect of anthropogenic disturbance on density was overwhelmingly negative among metapopulations: −0.63 Angolan colobus (Colobus angolensis palliatus) (95% Bayesian CI −1.03 to −0.27), −0.54 Udzungwa red colobus (Procolobus gordonorum) (−0.89 to −0.22), and −0.33 Sykes' monkey (Cercopithecus mitis monoides) (−0.63 to −0.07). Some responses to habitat factors were shared, notably the negative effect of elevation and the positive effect of climber coverage. These results are important for conservation science and practice because: the among-populations negative responses to anthropogenic disturbance provides a foundation for development of conservation plans that hold at the landscape scale, which is a comprehensive and cost-efficient approach; the among-species consistency in responses suggests conservation measures may be generalized at the guild level, which is especially relevant given the functional importance of primates in tropical rainforests; and the greater primate densities in areas at low elevation, which are closer to human settlements, point to specific management recommendations, such as the creation of buffer zones and prioritization of areas for protection.     

Estimating an homogeneous series of a population abundance indicator despite changes in data collection procedure: A hierarchical Bayesian modelling approach

Abundance indicators are required both to assess and to manage wild populations. As new techniques are developed and teams in charge of gathering the data change, data collection procedures (DCPs) can evolve in space and time. How to estimate an homogeneous series of abundance indicator despite changes in DCP? To tackle this question a hierarchical Bayesian modelling (HBM) approach is proposed. It integrates multiple DCPs in order to derive a single abundance indicator that can be compared over space and time irrespective of the DCP used. Compared to single DCP models, it takes further advantage for abundance estimation of the joint treatment of a larger set of spatio-temporal units. After presenting the general formulation of our HBM approach, it is applied to the juvenile Atlantic salmon (Salmo salar L.) population of the River Nivelle (France). Posterior model checking, using χ² discrepancy measure, do not reveal any inadequacy between the model and the data. Despite a change in the DCP used (successive removals to catch-per-unit of effort), a unique abundance indicator for the 425 spatio-temporal units (site × year) sampled over twenty-four years (1985-2008) is estimated. The HBM approach allows the assessment of precision of the abundance estimates and shows variation between DCPs: a reduction in precision is observed during the most recent years (2005-2008) when only the catch-per-unit of effort DCP was used. The merits and generality of our HBM approach are discussed. We contend it extends previous single DCP models or inter-calibration of two DCPs, and it could be applied to a wide range of specific situations (taxon and DCPs).     

Estimation of population density by spatially explicit capture-recapture analysis of data from area searches

The recent development of capture-recapture methods for estimating animal population density has focused on passive detection using devices such as traps or automatic cameras. Some species lend themselves more to active searching: a polygonal plot may be searched repeatedly and the locations of detected individuals recorded, or a plot may be searched just once and multiple cues (feces or other sign) identified as belonging to particular individuals. This report presents new likelihood-based spatially explicit capture-recapture (SECR) methods for such data. The methods are shown to be at least as robust in simulations as an equivalent Bayesian analysis, and to have negligible bias and near-nominal confidence interval coverage with parameter values from a lizard data set. It is recommended on the basis of simulation that plots for SECR should be at least as large as the home range of the target species. The R package "secr" may be used to fit the models. The likelihood-based implementation extends the spatially explicit analyses available for search data to include binary data (animal detected or not detected on each occasion) or count data (multiple detections per occasion) from multiple irregular polygons, with or without dependence among polygons. It is also shown how the method may be adapted for detections along a linear transect.     

A jellyfish diet for the herbivorous green turtle Chelonia mydas in the temperate SW Atlantic

Feeding ecology of juvenile green turtles (Chelonia mydas) was studied from 2008 to 2011 at Samborombón Bay (35°30′–36°30′S, Argentina), combining data on digestive tract examination and stable isotope analysis through a Bayesian mixing model. We found that animal matter, in particular gelatinous plankton, was consumed in large proportions compared to herbivorous food items such as terrestrial plants and macroalgae. This diet is facilitated by the high abundance of gelatinous plankton in the region, thus confirming the adaptive foraging behaviour of the juveniles according to prey abundance in the SW Atlantic. To our knowledge, this is the first study to employ this combination of techniques and to conclusively demonstrate that animal matter, in particular gelatinous plankton, is important in the diet of the neritic green sea turtles.     

A Bayesian hierarchical framework for calibrating aquatic biogeochemical models

Model practitioners increasingly place emphasis on rigorous quantitative error analysis in aquatic biogeochemical models and the existing initiatives range from the development of alternative metrics for goodness of fit, to data assimilation into operational models, to parameter estimation techniques. However, the treatment of error in many of these efforts is arguably selective and/or ad hoc. A Bayesian hierarchical framework enables the development of robust probabilistic analysis of error and uncertainty in model predictions by explicitly accommodating measurement error, parameter uncertainty, and model structure imperfection. This paper presents a Bayesian hierarchical formulation for simultaneously calibrating aquatic biogeochemical models at multiple systems (or sites of the same system) with differences in their trophic conditions, prior precisions of model parameters, available information, measurement error or inter-annual variability. Our statistical formulation also explicitly considers the uncertainty in model inputs (model parameters, initial conditions), the analytical/sampling error associated with the field data, and the discrepancy between model structure and the natural system dynamics (e.g., missing key ecological processes, erroneous formulations, misspecified forcing functions). The comparison between observations and posterior predictive monthly distributions indicates that the plankton models calibrated under the Bayesian hierarchical scheme provided accurate system representations for all the scenarios examined. Our results also suggest that the Bayesian hierarchical approach allows overcoming problems of insufficient local data by “borrowing strength” from well-studied sites and this feature will be highly relevant to conservation practices of regions with a high number of freshwater resources for which complete data could never be practically collected. Finally, we discuss the prospect of extending this framework to spatially explicit biogeochemical models (e.g., more effectively connect inshore with offshore areas) along with the benefits for environmental management, such as the optimization of the sampling design of monitoring programs and the alignment with the policy practice of adaptive management.     

Parasitism as a determinant of community structure on intertidal flats

The burrowing and movement ability of the New Zealand cockle Austrovenus stutchburyi is reduced when infected by echinostome trematodes. Previous experimental evidence from a single site suggests that this parasite-induced behavioural change of a key bivalve can affect the structure of the surrounding benthic community. By using multiple regression analyses on data collected from 17 intertidal flats, we here show that cockle parasitism is associated with macrozoobenthic community structure on a larger spatial scale. Regressions were performed for animal abundance, biomass, species diversity and species richness separately, entering cockle parasitism (infection intensity), presence/absence of ghost shrimps (Callianassa filholi), cockle density, primary producer abundance and organic content, particle size, sorting coefficient and gravel content of the substrate as predictors. Next to ghost shrimps, cockle parasitism was the best predictor of animal abundance by affecting (mainly positively) 8 of the 49 most widespread species significantly. Cockle parasitism was also associated with the biomass of anthozoans (positively), nemerteans (negatively) and bivalves (positively), whereas overall animal biomass was positively related to the sorting coefficient of the substrate. Species diversity was positively associated with cockle parasitism and gravel content of the substrate. Species richness was significantly associated with cockle parasitism (positively), ghost shrimps (negatively) and abundance of primary producers (positively) in combination. The impact of cockle parasitism on benthic community structure is believed governed directly or indirectly by (1) reduced sediment disturbance, (2) increased surface structural complexity and (3) availability of larval trematodes as an additional food source.     

A new multimodal and asymmetric bivariate circular distribution

Multimodal and asymmetric bivariate circular data arise in several different disciplines and fitting appropriate distribution plays an important role in the analysis of such data. In this paper, we propose a new bivariate circular distribution which can be used to model both asymmetric and multimodal bivariate circular data simultaneously. In fact the proposed density covers unimodality as well as multimodality, symmetry as well as asymmetry of circular bivariate data. A number of properties of the proposed density are presented. A Bayesian approach with MCMC scheme is employed for statistical inference. Three real datasets and a simulation study are provided to illustrate the performance of the proposed model in comparison with alternative models such as finite mixture Cosine model.     

Bayesian model-based cluster analysis for predicting macrofaunal communities

To predict macrofaunal community composition from environmental data a two-step approach is often followed: (1) the water samples are clustered into groups on the basis of the macrofauna data and (2) the groups are related to the environmental data, e.g. by discriminant analysis. For the cluster analysis in step 1 many hard, seemingly arbitrary choices have to be made that nevertheless influence the solution (similarity measure, clustering strategy, number of clusters). The stability of the solution is often of concern, e.g. in clustering by the program. In the discriminant analysis of step 2 it can occur that a water sample is misclassified on the basis of the environmental data but on further inspection happens to be a borderline case in the cluster analysis. One would then rather reclassify such a sample and iterate the two steps. Bayesian latent class analysis is a flexible, extendable model-based cluster analysis approach that recently has gained popularity in the statistical literature and that has the potential to address these problems. It allows the macrofauna and environmental data to be modelled and analyzed in a single integrated analysis. An exciting extension is to incorporate in the analysis prior information on the habitat preferences of the macrofauna taxa such as is available in lists of indicator values. The output of the analysis is not a hard assignment of water samples to clusters but a probabilistic (fuzzy) assignment. The number of clusters is determined on the basis of the Bayes factor. A standard feature of the Bayesian method is to make predictions and to assess their uncertainty. We applied this approach to a data set consisting of 70 water samples, 484 macrofauna taxa and four environmental variables for which previously a five cluster solution had been proposed. The standard for Bayesian estimation, the Gibbs sampler, worked fine on a subset with only 12 selected taxa but did not converge on the full set with 484 taxa. This is due to many configurations in which the assignment probabilities are all very close to either 0 or 1. This convergence problem is comparable with the local optima problem in classical cluster optimization algorithms, including the EM algorithm used in Latent Gold, a Windows program for latent class analysis. The convergence problem needs to be solved before the benefits of Bayesian latent class analysis can come to fruition in this application. We discuss possible solutions.     

Patterns in swimming by a scyphomedusa: a novel approach to quantifying behavior in individuals

Behavior is commonly studied at the group level using several individuals, but there is increasing evidence that the behavior of a few individuals often has a disproportionate effect on the response of a population to its environment. The present study used a suite of statistical techniques, random series analysis, analysis of variance, spectral analysis, and goodness-of-fit tests of frequency histograms, to quantitatively describe the time-dependent changes in individual behavior. Each technique reveals a different facet of the behavior and, when simultaneously applied to the data, distinguishes significant differences among the behaviors of several individuals. The approach was developed and tested on the swimming behavior of four specimens of the scyphomedusa Aurelia aurita (Linnaeus, 1758), which were observed for 19 days, beginning 16 January 1998, and videotaped under identical environmental conditions during that period. The analyses showed that each medusa swam in a unique pattern, varying swimming at characteristic frequencies. Application of the approach to individual-based numerical modeling, to the role of endogenous stimuli in the behavioral repertoire, and to in situ studies of animal behavior is discussed.Communicated by J.P. Grassle, New Brunswick