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.

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.

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.

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.

---

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.

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.

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.

Confidence limits on one-stage model parameters in benchmark risk assessment

In modern environmental risk analysis, inferences are often desired on those low dose levels at which a fixed benchmark risk is achieved. In this paper, we study the use of confidence limits on parameters from a simple one-stage model of risk historically popular in benchmark analysis with quantal data. Based on these confidence bounds, we present methods for deriving upper confidence limits on extra risk and lower bounds on the benchmark dose. The methods are seen to extend automatically to the case where simultaneous inferences are desired at multiple doses. Monte Carlo evaluations explore characteristics of the parameter estimates and the confidence limits under this setting.

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.

Fiat boundaries: some implications for interpretation,decision-support,and multi-temporal analysis

Polygon-based thematic maps can be composed of boundaries that exist by definition—i.e., bona fide boundaries—or those that exist relative to a specific interpretation of a spatial phenomenon—i.e., fiat boundaries. The construction of maps composed of fiat boundaries is usually based on a subjective interpretive methodology that is affected by the data used to construct the map and the minimum mapping unit employed. That fiat boundaries are not the same as bona fide boundaries affects their use in computer-based spatial decision support tools. This is discussed both in terms of an analysis conducted at one specific moment, and in respect to increasingly common multi-temporal analysis.

Statistics in disease ecology: introduction to a special issue

The three papers included in this special issue represent a set of presentations in an invited session on disease ecology at the 2005 Spring Meeting of the Eastern North American Region of the International Biometric Society. The papers each address statistical estimation and inference for particular components of different disease processes and, taken together, illustrate the breadth of statistical issues arising in the study of the ecology and public health impact of disease. As an introduction, we provide a very brief overview of the area of “disease ecology”, a variety of synonyms addressing different aspects of disease ecology, and present a schematic structure illustrating general components of the underlying disease process, data collection issues, and different disciplinary perspectives ranging from microbiology to public health surveillance.

---

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.

Improved strategies for coverage estimation by using replicated line-intercept sampling

Coverage, i.e., the area covered by the target attribute in the study region, is a key parameter in many surveys. Coverage estimation is usually performed by adopting a replicated protocol based on line-intercept sampling coupled with a suitable linear homogeneous estimator. Since coverage is a parameter which may be interestingly represented as the integral of a suitable function, improved Monte Carlo strategies for implementing the replicated protocol are introduced in order to achieve estimators with small variance rates. In addition, new specific theoretical results on Monte Carlo integration methods are given to deal with the integrand functions arising in the special coverage estimation setting.

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.

Benchmark calculations from summarized data: an example

Benchmark calculations often are made from data extracted from publications. Such data may not be in a form most appropriate for benchmark analysis, and, as a result, suboptimal and/or non-standard benchmark analyses are often applied. This problem can be mitigated in some cases using Monte Carlo computational methods that allow the likelihood of the published data to be calculated while still using an appropriate benchmark dose (BMD) definition. Such an approach is illustrated herein using data from a study of workers exposed to styrene, in which a hybrid BMD calculation is implemented from dose response data reported only as means and standard deviations of ratios of scores on neuropsychological tests from exposed subjects to corresponding scores from matched controls. The likelihood of the data is computed using a combination of analytic and Monte Carlo integration methods.

A model for leveling coalitions among primate males: toward a theory of egalitarianism

We present a simple model of within-group leveling coalitions among male primates. The model assumes that the value of the coalition is the sum of the payoffs of its members, that the individuals payoff is monotonically decreasing with its rank and that coalitions do not cause rank changes. It predicts that mainly mid- to low rankers engage in leveling coalitions, and that most coalition partners are of adjacent ranks. These predictions agree reasonably well with observations in nature. The model also makes the novel predictions that leveling coalitions are found where male mating competition has only a moderate contest component, and that male dominance ranks will become poorly differentiated where leveling coalitions are frequent. Both these predictions are consistent with observations on groups of macaques and baboons. The model also may account for leveling coalitions among egalitarian human foragers, without making additional assumptions about special human capabilities.

Modeling spatio-temporal wildfire ignition point patterns

We analyze and model the structure of spatio-temporal wildfire ignitions in the St. Johns River Water Management District in northeastern Florida. Previous studies, based on the K-function and an assumption of homogeneity, have shown that wildfire events occur in clusters. We revisit this analysis based on an inhomogeneous K-function and argue that clustering is less important than initially thought. We also use K-cross functions to study multitype point patterns, both under homogeneity and inhomogeneity assumptions, and reach similar conclusions as above regarding the amount of clustering. Of particular interest is our finding that prescribed burns seem not to reduce significantly the occurrence of wildfires in the current or subsequent year over this large geographical region. Finally, we describe various point pattern models for the location of wildfires and investigate their adequacy by means of recent residual diagnostics.

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.

Replace the NOAEL and LOAEL with the BMDL01 and BMDL10

Although benchmark-dose methodology has existed for more than 20 years, benchmark doses (BMDs) still have not fully supplanted the no-observed-adverse-effect level (NOAEL) and lowest-observed-adverse-effect level (LOAEL) as points of departure from the experimental dose–response range for setting acceptable exposure levels of toxic substances. Among the issues involved in replacing the NOAEL (LOAEL) with a BMD are (1) which added risk level(s) above background risk should be targeted as benchmark responses (BMRs), (2) whether to apply the BMD methodology to both carcinogenic and noncarcinogenic toxic effects, and (3) how to model continuous health effects that aren’t observed in a natural risk-based context like dichotomous health effects. This paper addresses these issues and recommends specific BMDs to replace the NOAEL and LOAEL.

Some comments on design-based line-intersect sampling with segmented transects

Line-intersect sampling based on segmented transects is adopted in many forest inventories to quantify important ecological indicators such as coarse woody debris attributes. By assuming a design-based approach, Affleck, Gregoire and Valentine (2005, Environ Ecol Stat 12:139–154) have recently proposed a sampling protocol for this line-intersect setting and have suggested an estimation method based on linear homogeneous estimators. However, their proposal does not encompass the estimation procedure currently adopted in some national forest inventories. Hence, the present paper aims to introduce a unifying perspective for both methods. Moreover, it is shown that the two procedures give rise to coincident estimators for almost all the usual field applications. Finally, some strategies for efficient segmented-transect replications are considered.