C. S. Oedekoven

Improving distance sampling: accounting for covariates and non-independency between sampled sites

Summary 1. There is currently much interest in replacing the design-based component of conventional distance sampling methods by a modelling approach where animal densities are related to environmental covariates. These models allow identification of relationships between density and covariates. One of the uses of such models is to assess the effects of some intervention on numbers for species of conservation interest in designed distance sampling experiments. 2. In this context, we use an integrated likelihood approach for modelling sample counts, adopting a Poisson model and allowing imperfect detectability on the sample plots. We use the method of Royle, Dawson & Bates (2004, Ecology, 85, 1591), extended to model heterogeneity in detection probabilities using either multiple covariate distance sampling methods or stratification. Moreover, we include a random effect for site in the plot abundance model to accommodate correlation in repeat counts at a single site. 3. These developments were motivated by a large-scale experimental study to assess the effects of establishing conservation buffers along field margins on indigo buntings in several US states. We analyse the data using an integrated likelihood and include model selection for both the Poisson rate of counts and detection probabilities. We assess model performance by comparing our results with those using a two-stage approach (Buckland et al. 2009, Journal of Agricultural, Biological, and Environmental Statistics, 14, 432) which we extended by including a random effect for site in the plot abundance model. 4. The two methods led to the same selected models and gave similar results for parameters, which revealed significant beneficial effects of buffers on indigo bunting densities. Densities on buffered fields were on average 35% higher than on unbuffered fields. Using a detection function stratified by state captured some of the heterogeneity in detection probabilities between the nine states included in the analyses. 5. Synthesis and applications. We develop and compare two methods for analysing data from large-scale distance sampling experiments with imbalanced repeat measures. By including a random site effect in the plot abundance model, we relax the assumption of independent sample counts which is generally made for distance sampling methods, and we allow inference to be drawn for the wider region that the sites represent.

Distance sampling with a random scale detection function

Distance sampling was developed to estimate wildlife abundance from observational surveys with uncertain detection in the search area. We present novel analysis methods for estimating detection probabilities that make use of random effects models to allow for unmodeled heterogeneity in detection. The scale parameter of the half-normal detection function is modeled by means of an intercept plus an error term varying with detections, normally distributed with zero mean and unknown variance. In contrast to conventional distance sampling methods, our approach can deal with long-tailed detection functions without truncation. Compared to a fixed effect covariate approach, we think of the random effect as a covariate with unknown values and integrate over the random effect. We expand the random scale to a mixed scale model by adding fixed effect covariates. We analyzed simulated data with large sample sizes to demonstrate that the code performs correctly for random and mixed effect models. We also generated replicate simulations with more practical sample sizes (

Attributing changes in the distribution of species abundance to weather variables using the example of British breeding birds

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The Basic Methods

∼100) and compared the random scale half-normal with the hazard rate detection function. As expected each estimation model was best for different simulation models. We illustrate the mixed effect modeling approach using harbor porpoise vessel survey data where the mixed effect model provided an improved model fit in comparison to a fixed effect model with the same covariates. We propose that a random or mixed effect model of the detection function scale be adopted as one of the standard approaches for fitting detection functions in distance sampling.

Modelling Detection Functions

Summary A key aspect of monitoring regional changes in biodiversity is to quantify the temporal turnover in communities. Turnover has traditionally been assessed by observing range change. However, we are often interested in trends in biodiversity of large regions as opposed to single sites, as with Convention for Biological Diversity targets. Extinctions and colonizations tend to be rare events at the regional level; changes in species proportions estimated from spatio-temporal models of species abundance are then more sensitive measures of community change. We investigated three measures for quantifying turnover based on species proportions, and estimated how each varies across Great Britain using data from the British Trust for Ornithologys Breeding Bird Survey. All three measures identify high turnover associated with loss of biodiversity in the south-east of England. This seems to be driven by changes in the farmland bird community, and by turnover in the scarcer species of the woodland bird community. The measures also show evidence of high turnover in the west of Scotland; these changes may be linked to climate change, although precision in our measures for this region is relatively poor due to low survey effort. Policy implications. Turnover in ecological communities may be quantified by modelling species abundance, and measuring how resulting species proportions change over time. When used alongside estimated temporal trends in biodiversity, these can identify areas and communities showing greatest evidence for change. How, and indeed even whether, society should respond to such changes depends on further investigation into the causes of the changes, and the extent to which these are seen as undesirable and avoidable. For those communities with adequate survey data, we recommend that these methods augment the suite of measures used for routine assessment of change, hence acting as a more sensitive trigger to set in motion exploration of causes and consideration of adaptive actions to be taken by land managers and policymakers.

An evaluation of density estimation methods using a multiyear dataset of localized bowhead whale calls

Modelling spatio-temporal changes in species abundance and attributing those changes to potential drivers such as climate, is an important but difficult problem. The standard approach for incorporating climatic variables into such models is to include each weather variable as a single covariate, whose effect is expressed through a low-order polynomial or smoother in an additive model. This, however, confounds the spatial and temporal effects of the covariates. We developed a novel approach to distinguish between three types of change in any particular weather covariate. We decomposed the weather covariate into three new covariates by separating out temporal variation in weather (averaging over space), spatial variation in weather (averaging over years) and a space–time anomaly term (residual variation). These three covariates were each fitted separately in the models. We illustrate the approach using generalized additive models applied to count data for a selection of species from the UKs Breeding Bird Survey, 1994–2013. The weather covariates considered were the mean temperatures during the preceding winter and temperatures and rainfall during the preceding breeding season. We compare models that include these covariates directly with models including decomposed components of the same covariates, considering both linear and smooth relationships. The lowest QAIC values were always associated with a decomposed weather covariate model. Different relationships between counts and the three new covariates provided strong evidence that the effects of changes in covariate values depended on whether changes took place in space, in time, or in the space–time anomaly. These results promote caution in predicting species distribution and abundance in future climate, based on relationships that are largely determined by environmental variation over space. Our methods estimate the effect of temporal changes in weather, while accounting for spatial effects of long-term climate, improving inference on overall and/or localized effects of climate change. With increasing availability of large-scale datasets, need is growing for appropriate analytical tools. The proposed decomposition of the weather variables represents an important advance by eliminating the confounding issue often inherent in analyses of large-scale datasets.

Low tortoise abundances in pine forest plantations in forest-shrubland transition areas

Hierarchical centering has been described as a reparameterization method applicable to random effects models. It has been shown to improve mixing of models in the context of Markov chain Monte Carlo (MCMC) methods. A hierarchical centering approach is proposed for reversible jump MCMC (RJMCMC) chains which builds upon the hierarchical centering methods for MCMC chains and uses them to reparameterize models in an RJMCMC algorithm. Although these methods may be applicable to models with other error distributions, the case is described for a log-linear Poisson model where the expected value λ includes fixed effect covariates and a random effect for which normality is assumed with a zero-mean and unknown standard deviation. For the proposed RJMCMC algorithm including hierarchical centering, the models are reparameterized by modeling the mean of the random effect coefficients as a function of the intercept of the λ model and one or more of the available fixed effect covariates depending on the model. The method is appropriate when fixed-effect covariates are constant within random effect groups. This has an effect on the dynamics of the RJMCMC algorithm and improves model mixing. The methods are applied to a case study of point transects of indigo buntings where, without hierarchical centering, the RJMCMC algorithm had poor mixing and the estimated posterior distribution depended on the starting model. With hierarchical centering on the other hand, the chain moved freely over model and parameter space. These results are confirmed with a simulation study. Hence, the proposed methods should be considered as a regular strategy for implementing models with random effects in RJMCMC algorithms; they facilitate convergence of these algorithms and help avoid false inference on model parameters. We consider a hierarchical centering approach for reversible jump MCMC algorithms.We describe the case for a log-linear Poisson model with mixed effects.The zero-mean of the random effect is replaced with part of the linear predictor.We apply the methods to point transect data of indigo buntings and simulated data.Our methods improve model mixing and inference on parameters.

Variations on a Theme

One of the most common and pervasive questions in applied ecology relates to the size of a given population. How many animals are there? The question is intrinsically interesting, but perhaps even more important from an applied perspective, the actual answer has implications for most ecological processes affecting that population. The effective management of a population is not possible without knowing at least approximately how many individuals it includes. As an example, for a small population, a given mortality rate due to a newly introduced human disturbance might be important and a matter of concern, quickly leading the population to local extinction, but essentially not ecologically relevant for an abundant population. Therefore, knowledge about abundance is required to adequately interpret a wide variety of ecological processes affecting a given population.