Spatial smoothing techniques for the assessment of habitat suitability

Precise knowledge about factors influencing the habitat suitability of a certain species forms the basis for the implementation of effective programs to conserve biological diversity. Such knowledge is frequently gathered from studies relating abundance data to a set of influential variables in a regression setup. In particular, generalised linear models are used to analyse binary presence/absence data or counts of a certain species at locations within an observation area. However, one of the key assumptions of generalised linear models, the independence of observations is often violated in practice since the points at which the observations are collected are spatially aligned. In this paper, we describe a general framework for semiparametric spatial generalised linear models that allows for the routine analysis of non-normal spatially aligned regression data. The approach is utilised for the analysis of a data set of synthetic bird species in beech forests, revealing that ignorance of spatial dependence actually may lead to false conclusions in a number of situations.

A single-chain-based multidimensional Markov chain model for subsurface characterization

Multidimensional Markov chain models in geosciences were often built on multiple chains, one in each direction, and assumed these 1-D chains to be independent of each other. Thus, unwanted transitions (i.e., transitions of multiple chains to the same location with unequal states) inevitably occur and have to be excluded in estimating the states at unobserved locations. This consequently may result in unreliable estimates, such as underestimation of small classes (i.e., classes with smaller than average areas) in simulated realizations. This paper presents a single-chain-based multidimensional Markov chain model for estimation (i.e., prediction and conditional stochastic simulation) of spatial distribution of subsurface formations with borehole data. The model assumes that a single Markov chain moves in a lattice space, interacting with its nearest known neighbors through different transition probability rules in different cardinal directions. The conditional probability distribution of the Markov chain at the location to be estimated is formulated in an explicit form by following the Bayes’ Theorem and the conditional independence of sparse data in cardinal directions. Since no unwanted transitions are involved, the model can estimate all classes fairly. Transiogram models (i.e., 1-D continuous Markov transition probability diagrams) are used to provide transition probability input with needed lags to generalize the model. Therefore, conditional simulation can be conducted directly and efficiently. The model provides an alternative for heterogeneity characterization of subsurface formations.

Trap mortality in mark-recapture studies

When animals die in traps in a mark-recapture study, straightforward likelihood inferences are possible in a class of models. The class includes M₀, M_t, and M_b as reported by White et al. (Los Alamos National Laboratory, LA-8787-NERP, pp 235, 1982), those that do not involve heterogeneity. We include three Markov chain “persistence” models and show that they provide good fits in a trapping study of deer mice in the Cascade-Siskiyou National Monument of Southern Oregon where trapping mortality was high.

Flexible hierarchical mark-recapture modeling for open populations using WinBUGS

Hierarchical mark-recapture models offer three advantages over classical mark-recapture models: (i) they allow expression of complicated models in terms of simple components; (ii) they provide a convenient way of modeling missing data and latent variables in a way that allows expression of relationships involving latent variables in the model; (iii) they provide a convenient way of introducing parsimony into models involving many nuisance parameters. Expressing models using the complete data likelihood we show how many of the standard mark-recapture models for open populations can be readily fitted using the software WinBUGS. We include examples that illustrate fitting the Cormack–Jolly–Seber model, multi-state and multi-event models, models including auxiliary data, and models including density dependence.

A note on non-parametric and semi-parametric modeling of wildfire hazard in Los Angeles County, California

This paper explores the use of, and problems that arise in, kernel smoothing and parametric estimation of the relationships between wildfire incidence and various meteorological variables. Such relationships may be treated as components in separable point process models for wildfire activity. The resulting models can be used for comparative purposes in order to assess the predictive performance of the Burning Index.

A note on data augmentation and iterative simulation for survival rate estimation

In this paper we examine the use of data augmentation techniques for simplifying iterative simulation in the context of both Bayesian and classical statistical inference for survival rate estimation. We examine two distinct model families common in population ecology to illustrate our ideas, ring-recovery models and capture–recapture models, and we present the computational advantage of this approach. We discuss also the fact that problems associated with identifiability in the classical framework can be overcome using data augmentation, but highlight the dangers in doing so under both inferential paradigms.

Behavior of yellowfin (<Emphasis Type="Italic">Thunnus albacares</Emphasis>) and bigeye (<Emphasis Type="Italic">T. obesus</Emphasis>) tuna in a network of fish aggregating devices (FADs)

The influence of multiple anchored fish aggregating devices (FADs) on the spatial behavior of yellowfin (Thunnus albacares) and bigeye tuna (T. obesus) was investigated by equipping all thirteen FADs surrounding the island of Oahu (HI, USA) with automated sonic receivers (“listening stations”) and intra-peritoneally implanting individually coded acoustic transmitters in 45 yellowfin and 12 bigeye tuna. Thus, the FAD network became a multi-element passive observatory of the residence and movement characteristics of tuna within the array. Yellowfin tuna were detected within the FAD array for up to 150 days, while bigeye tuna were only observed up to a maximum of 10 days after tagging. Only eight yellowfin tuna (out of 45) and one bigeye tuna (out of 12) visited FADs other than their FAD of release. Those nine fish tended to visit nearest neighboring FADs and, in general, spent more time at their FAD of release than at the others. Fish visiting the same FAD several times or visiting other FADs tended to stay longer in the FAD network. A majority of tagged fish exhibited some synchronicity when departing the FADs but not all tagged fish departed a FAD at the same time: small groups of tagged fish left together while others remained. We hypothesize that tuna (at an individual or collective level) consider local conditions around any given FAD to be representative of the environment on a larger scale (e.g., the entire island) and when those conditions become unfavorable the tuna move to a completely different area. Thus, while the anchored FADs surrounding the island of Oahu might concentrate fish and make them more vulnerable to fishing, at a meso-scale they might not entrain fish longer than if there were no (or very few) FADs in the area. At the existing FAD density, the ‘island effect’ is more likely to be responsible for the general presence of fish around the island than the FADs. We recommend further investigation of this hypothesis.

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Heteroscedastic semiparametric models for domestic water consumption aggregated data

Heteroscedastic additive and multiplicative models are proposed to disaggregate household data on water consumption from Athens and provide individual consumption estimates. The models adjust for heteroscedasticity assuming that variances relate to covariates. Household characteristics that can influence consumption are also included into models in order to allow for a clearer measurement of individual characteristics effects. Estimation is accomplished through a penalized least squares approach. The method is applied to a sample of real data related to domestic water consumption in Athens. The results show a greater consumption of water for males while the single-female households are these that use the lowest quantities of water. The consumption curves by age and gender are constructed presenting differences between the two sexes.

A stochastic forest fire growth model

We consider a stochastic fire growth model, with the aim of predicting the behaviour of large forest fires. Such a model can describe not only average growth, but also the variability of the growth. Implementing such a model in a computing environment allows one to obtain probability contour plots, burn size distributions, and distributions of time to specified events. Such a model also allows the incorporation of a stochastic spotting mechanism.

Multi-parameter renewal processes and simulation of forest fires

The concept of the renewal property is extended to processes indexed by a multidimensional time parameter. The definition given includes not only partial sum processes, but also Poisson processes and many other point processes whose jump points are not totally ordered. Various properties of renewal processes are discussed. Renewal processes are proposed as a basis for modelling the spread of a forest fire under a prevailing wind.

Testing homogeneity of capture probabilities of animals in a removal experiment

Consider the removal experiment used to estimate population sizes. Statistical methods towards testing the homogeneity of capture probabilities of animals, including a graphical diagnostic and a formal test, are presented and illustrated by real biological examples. Simulation is used to assess the test and compare it with the χ² test.

Seals at sea: modelling seal distribution in the German bight based on aerial survey data

The Wadden Sea is an important habitat for harbour seals and grey seals. They regularly haul-out on sandbanks and islands along the coast. Comparably little is known about the time seals spend at sea and how they use the remainder of the North Sea. Yet, human activity in offshore waters is increasing and information on seal distribution in the North Sea is crucial for conservation and management. Aerial line transect surveys were conducted in the German bight from 2002 to 2007 to investigate the distribution and abundance of marine mammals. Distance sampling methodology was combined with density surface modelling for a spatially explicit analysis of seal distribution in the German North Sea. Depth and distance to coast were found to be relevant predictor variables for seal density. Density surface modelling allowed for a depiction of seal distribution in the study area as well as an abundance estimate. This is the first study to use aerial survey data to develop a density surface model (DSM) for a spatially explicit distribution estimate of seals at sea.

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Hierarchical spatial point process analysis for a plant community with high biodiversity

A complex multivariate spatial point pattern of a plant community with high biodiversity is modelled using a hierarchical multivariate point process model. In the model, interactions between plants with different post-fire regeneration strategies are of key interest. We consider initially a maximum likelihood approach to inference where problems arise due to unknown interaction radii for the plants. We next demonstrate that a Bayesian approach provides a flexible framework for incorporating prior information concerning the interaction radii. From an ecological perspective, we are able both to confirm existing knowledge on species’ interactions and to generate new biological questions and hypotheses on species’ interactions.

Social network analysis and valid Markov chain Monte Carlo tests of null models

Analyses of animal social networks derived from group-based associations often rely on randomisation methods developed in ecology (Manly, Ecology 76:1109–1115, 1995) and made available to the animal behaviour community through implementation of a pair-wise swapping algorithm by Bejder et al. (Anim Behav 56:719–725, 1998). We report a correctable flaw in this method and point the reader to a wider literature on the subject of null models in the ecology literature. We illustrate the importance of correcting the method using a toy network and use it to make a preliminary analysis of a network of associations among eagle rays.

Is bird song a reliable signal of aggressive intent?

In this commentary, we discuss recent experiments on the reliability of bird song as a signal of aggressive intent during territorial conflicts. We outline relevant theoretical views on honest signaling, highlighting the vulnerability handicap hypothesis as a possible explanation for soft song’s reliability in predicting attack. We also sketch possible methods of testing whether soft song agrees with key predictions of the vulnerability handicap hypothesis. Finally, we suggest possible empirical refinements that may be useful in future studies of signals of intent, both in birds and in animals broadly. In particular, we argue that future studies of intent should strive to incorporate the following elements into their experimental design: (1) multi-modal signal components, (2) interaction dynamics, and (3) minimal time intervals. Simulated exchanges using dynamically interactive models may provide a powerful means of incorporating all three of these design features simultaneously.

Using data augmentation via the Gibbs Sampler to incorporate missing covariate structure in linear models for ecological assessments

Missing covariate values in linear regression models can be an important problem facing environmental researchers. Existing missing value treatment methods such as Multiple Imputation (MI), the EM algorithm and Data Augmentation (DA) have the assumption that both observed and unobserved data come from the same distribution, most commonly a multivariate normal or a conditionally multivariate normal family. These methods do try to incorporate the missing data mechanism and rely on the assumption of Missing At Random (MAR). We present a DA method which does not rely on the MAR assumption and can model missing data mechanisms and covariate structure. This method utilizes the Gibbs Sampler as a tool for incorporating these structures and mechanisms. We apply this method to an ecological data set that relates fish condition to environmental variables. Notice that the presented DA method detects relationships that are not detected when other missing data methods are employed.

A spatial clustering perspective on autocorrelation and regionalization

We revisit one of the classical problems in geography and cartography where multiple observations on a lattice (N) need to be grouped into many fewer regions (G), especially when this number of desired regions is unknown a priori. Since an optimization through all possible aggregations is not feasible, a hierarchical classification scheme is proposed with an objective function sensitive to spatial pattern. The objective function to be minimized during the assignment of observations to regions (classification) consists of two terms: the first characterizes accuracy and the second, model complexity. For the latter, we introduce a spatial measure that characterizes the number of homogeneous patches rather than the usual number of classes. A simulation study shows that such a classification procedure is less sensitive to random and spatially correlated error (noise) than non-spatial classification. We also show that for conditional autoregressive error (noise) fields the optimal partitioning is the one that has the highest within-units generalized Moran coefficient. The classifier is implemented in ArcView to demonstrate both a socio-economic and an environmental application to illustrate some potential applications.

Determining the optimum number of increments in composite sampling

Composite sampling can be more cost effective than simple random sampling. This paper considers how to determine the optimum number of increments to use in composite sampling. Composite sampling terminology and theory are outlined and a method is developed which accounts for different sources of variation in compositing and data analysis. This method is used to define and understand the process of determining the optimum number of increments that should be used in forming a composite. The blending variance is shown to have a smaller range of possible values than previously reported when estimating the number of increments in a composite sample. Accounting for differing levels of the blending variance significantly affects the estimated number of increments.

Maximum likelihood fitting of the Poisson lognormal distribution

In this paper some properties and analytic expressions regarding the Poisson lognormal distribution such as moments, maximum likelihood function and related derivatives are discussed. The author provides a sharp approximation of the integrals related to the Poisson lognormal probabilities and analyzes the choice of the initial values in the fitting procedure. Based on these he describes a new procedure for carrying out the maximum likelihood fitting of the truncated Poisson lognormal distribution. The method and results are illustrated on real data. The computer program for calculations is freely available.