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.

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.

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.

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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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.

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.

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.

Prospective spatial prediction of infectious disease: experience of New York State (USA) with West Nile Virus and proposed directions for improved surveillance

Infectious disease surveillance has become an international top priority due to the perceived risk of bioterrorism. This is driving the improvement of real-time geo-spatial surveillance systems for monitoring disease indicators, which is expected to have many benefits beyond detecting a bioterror event. West Nile Virus surveillance in New York State (USA) is highlighted as a working system that uses dead American Crows (Corvus brachyrhynchos) to prospectively indicate viral activity prior to human onset. A cross-disciplinary review is then presented to argue that this system, and infectious disease surveillance in general, can be improved by complementing spatial cluster detection of an outcome variable with predictive “risk mapping” that incorporates spatiotemporal data on the environment, climate and human population through the flexible class of generalized linear mixed models.

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.

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.

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.

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.

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.

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.

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.

Components of information for multiple resolution comparison between maps that share a real variable

This paper presents quantitative methods that allow scientists to compare the patterns in two maps that show a shared real variable. Specifically, this paper shows how to budget various components of agreement and disagreement between maps. The components are based on the separation of a map’s information of quantity from its information of location. The technique also examines how variation in resolution influences the measurement of the components of information. The manner in which the measurements change as a function of spatial resolution can be more important and interesting than the results at any single particular resolution, because the results at a single particular resolution may indicate more about the format of the data than about the overall pattern in the landscape. An example illustrates the mathematical concepts, and an application compares mapped vegetation indices in Africa to illustrate the usefulness of the proposed approach vis-à-vis a conventional approach. The results are presented visually in the form of stacked bar graphs that show separable components of information. The entire analysis is performed twice, each time with a different mathematical measurement of deviation: (1) root mean square error, and (2) mean absolute error. This paper compares these two approaches and discusses their relative advantages and disadvantages. Hopefully, this approach of budgeting components of information at multiple resolutions will become adopted as standard practice in the measurement of patterns.

Bootstrap methods for simultaneous benchmark analysis with quantal response data

A primary objective in quantitative risk assessment is the characterization of risk which is defined to be the likelihood of an adverse effect caused by an environmental toxin or chemcial agent. In modern risk-benchmark analysis, attention centers on the “benchmark dose” at which a fixed benchmark level of risk is achieved, with a lower confidence limits on this dose being of primary interest. In practice, a range of benchmark risks may be under study, so that the individual lower confidence limits on benchmark dose must be corrected for simultaneity in order to maintain a specified overall level of confidence. For the case of quantal data, simultaneous methods have been constructed that appeal to the large sample normality of parameter estimates. The suitability of these methods for use with small sample sizes will be considered. A new bootstrap technique is proposed as an alternative to the large sample methodology. This technique is evaluated via a simulation study and examples from environmental toxicology.