Monique MacKenzie

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.

SALSA – a spatially adaptive local smoothing algorithm

We present a nonlinear integer programming formulation for fitting a spline-based regression to two-dimensional data using an adaptive knot-selection approach, with the number and location of the knots being determined in the solution process. However, the nonlinear nature of this formulation makes its solution impractical, so we also outline a knot selection heuristic inspired by the Remes Exchange Algorithm, to produce good solutions to our formulation. This algorithm is intuitive and naturally accommodates local changes in smoothness. Results are presented for the algorithm demonstrating performance that is as good as, or better than, other current methods on established benchmark functions.

The social context of individual foraging behaviour in long-finned pilot whales (Globicephala melas)

Long-finned pilot whales (Globicephala melas) are highly social cetaceans that live in matrilineal groups and acquire their prey during deep foraging dives. We tagged individual pilot whales to record their diving behaviour. To describe the social context of this individual behaviour, the tag data were matched with surface observations at the group level using a novel protocol. The protocol comprised two key components: a dynamic definition of the group centred around the tagged individual, and a set of behavioural parameters quantifying visually observable characteristics of the group. Our results revealed that the diving behaviour of tagged individuals was associated with distinct group-level behaviour at the water’s surface. During foraging, groups broke up into smaller and more widely spaced units with a higher degree of milling behaviour. These data formed the basis for a classification model, using random forest decision trees, which accurately distinguished between bouts of shallow diving and bouts of deep foraging dives based on group behaviour observed at the surface. The results also indicated that members of a group to a large degree synchronised the timing of their foraging periods. This was confirmed by pairs of tagged individuals that nearly always synchronized their diving bouts. Hence, our study illustrates that integration of individual-level and group-level observations can shed new light on the social context of the individual foraging behaviour of animals living in groups.

Complex Region Spatial Smoother (CReSS)

Conventional smoothing over complicated coastal and island regions may result in errors across boundaries, due to the use of Euclidean distances to measure interpoint similarity. The new Complex Region Spatial Smoother (CReSS) method presented here uses estimated geodesic distances, model averaging, and a local radial basis function to provide improved smoothing over complex domains. CReSS is compared, via simulation, with recent related smoothing techniques, Thin Plate Splines (TPS), geodesic low rank TPS (GLTPS), and the Soap film smoother (SOAP). The GLTPS method cannot be used in areas with islands and SOAP can be hard to parameterize. CReSS is comparable with, if not better than, all considered methods on a range of simulations. Supplementary materials for this article are available online.

Regression spline mixed models: A forestry example

In this article, regression splines are used inside linear mixed models to explore nonlinear longitudinal data. The regression spline bases are generated using a single knot chosen using biological information—a knot position supported by an automated knot selection procedure. A variety of inferential procedures are compared. The variance in the data was closely modeled using a flexible model-based covariance structure, a robust method and the nonparametric bootstrap, while the variance was underestimated when independent random effects were assumed.

Using hierarchical centering to facilitate a reversible jump MCMC algorithm for random effects models

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.

Classification of animal dive tracks via automatic landmarking, principal components analysis and clustering

The behaviour of animals and their interactions with the environment can be inferred by tracking their movement. For this reason, biologgers are an important source of ecological data, but analysing the shape of the tracks they record is difficult. In this paper we present a technique for automatically determining landmarks that can be used to analyse the shape of animal tracks. The approach uses a parametric version of the SALSA algorithm to fit regression splines to 1-dimensional curves in N dimensions (in practice N = 2 or 3). The knots of these splines are used as landmarks in a subsequent Principal Components Analysis, and the dives classified via agglomerative clustering. We demonstrate the efficacy of this algorithm on simulated 2-dimensional dive data, and apply our method to real 3-dimensional whale dive data from the Behavioral Response Study (BRS) in the Bahamas. The BRS is a series of experiments to quantify shifts in behavior due to SONAR. Our analysis of 3-dimensional track data supports an ...