The fire frequency analysis branch of the pyrostatistics tree: sampling decisions and censoring in fire interval data

Statistical characterization of past fire regimes is important for both the ecology and management of fire-prone ecosystems. Survival analysis—or fire frequency analysis as it is often called in the fire literature—has increasingly been used over the last few decades to examine fire interval distributions. These distributions can be generated from a variety of sources (e.g., tree rings and stand age patterns), and analysis typically involves fitting the Weibull model. Given the widespread use of fire frequency analysis and the increasing availability of mapped fire history data, our goal has been to review and to examine some of the issues faced in applying these methods in a spatially explicit context. In particular, through a case study on the massive Cedar Fire in 2003 in southern California, we examine sensitivities of parameter estimates to the spatial resolution of sampling, point- and area-based methods for assigning sample values, current age surfaces versus historical intervals in generating distributions, and the inclusion of censored (i.e., incomplete) observations. Weibull parameter estimates were found to be roughly consistent with previous fire frequency analyses for shrublands (i.e., median age at burning of ~30–50 years and relatively low age dependency). Results indicate, however, that the inclusion or omission of censored observations can have a substantial effect on parameter estimates, far more than other decisions about specifics of sampling.

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.

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.

Fighting fire with fire: estimating the efficacy of wildfire mitigation programs using propensity scores

This paper examines the effect wildfire mitigation has on broad-scale wildfire behavior. Each year, hundreds of million of dollars are spent on fire suppression and fuels management applications, yet little is known, quantitatively, of the returns to these programs in terms of their impact on wildfire extent and intensity. This is especially true when considering that wildfire management influences and reacts to several, often times confounding factors, including socioeconomic characteristics, values at risk, heterogeneous landscapes, and climate. Due to the endogenous nature of suppression effort and fuels management intensity and placement with wildfire behavior, traditional regression models may prove inadequate. Instead, I examine the applicability of propensity score matching (PSM) techniques in modeling wildfire. This research makes several significant contributions including: (1) applying techniques developed in labor economics and in epidemiology to evaluate the effects of natural resource policies on landscapes, rather than on individuals; (2) providing a better understanding of the relationship between wildfire mitigation strategies and their influence on broad-scale wildfire patterns; (3) quantifying the returns to suppression and fuels management on wildfire behavior.

Spatial pattern and persistence of historical fire boundaries in southern interior British Columbia

Recent ecosystem and fire management research aims to quantify, model and understand historical fire disturbances focusing on their frequency, size and distribution. Less attention, however, has been paid to fire boundaries and their location on the landscape. Our study presents a spatial method to quantify the location, pattern and persistence of historical fire boundaries using tree ring fire scar data in the lower Stein watershed (British Columbia). Data from Pinus ponderosa and Pseudotsuga menziesii collected in 35 one-hectare plots over a 412-hectare study area were analyzed for the period between 1879 and 1947 using local spatial statistics and boundary detection techniques. Results of the analysis using local spatial statistic Moran’s I showed significant clustering of boundaries near topographic breaks. To determine and test whether fire boundaries between plots were persistent, we used boundary detection methods and developed a spatially restricted randomization test. The results revealed that out of 86 possible boundary links, 8 were significantly persistent (P < 0.025) while another 8 were significantly rare (P < 0.025). These spatial methods can help determine the historical spatial configuration of persistent boundaries and can be used to maintain natural forest dynamics.

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.

A Bayesian approach to multi-source forest area estimation

In efforts such as land use change monitoring, carbon budgeting, and forecasting ecological conditions and timber supply, there is increasing demand for regional and national data layers depicting forest cover. These data layers must permit small area estimates of forest area and, most importantly, provide associated error estimates. This paper presents a model-based approach for coupling mid-resolution satellite imagery with plot-based forest inventory data to produce estimates of probability of forest and associated error at the pixel-level. The proposed Bayesian hierarchical model provides access to each pixel’s posterior predictive distribution allowing for a highly flexible analysis of pixel and multi-pixel areas of interest. The paper presents a trial using multiple dates of Landsat imagery and USDA Forest Service Forest Inventory and Analysis plot data. The results describe the spatial dependence structure within the trial site, provide pixel and multi-pixel summaries of probability of forest land use, and explore discretization schemes of the posterior predictive distributions to forest and non-forest classes. Model prediction results of a holdout set analysis suggest the proposed model provides high classification accuracy, 88%, for the trial site.

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.

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.

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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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.

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.

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.

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.

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.

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.

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.

Coastal protected area management and multi-tiered governance: the Cape Cod Model

Policy tools that allow for the coordination of various authorities at different levels of government are important for coastal protected areas. Frequently, multiple authorities manage these areas with varied and sometimes conflicting goals. This study examines a regulatory model implemented on the Cape Cod National Seashore in the US that uses federally-approved zoning to regulate private uses for protection of natural coastal resources. Local authorities implement the zoning which is designed to support national resource protection goals making this a prime model of cross-level governance for conservation. I use case study analysis to evaluate the program’s effectiveness by focusing on implementation and compliance in the context of multi-jurisdictional (i.e., national to local) relations. The analysis and subsequent discussion highlight the difficulties associated with implementation of intergovernmental mandates. Also, theoretical perspectives on compliance give insights about the implementation challenges of this model. The model’s limitations have implications for policymakers considering similar schemes implemented by split and hierarchical authorities with different, and possibly conflicting, coastal management goals.

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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