Wen-Han Hwang

QUANTIFYING THE EFFECTS OF UNEQUAL CATCHABILITIES ON JOLLY-SEBER ESTIMATORS VIA SAMPLE COVERAGE

Using the concept of sample coverage, we derive an approximation of the bias in the Jolly-Seber population size estimators due to heterogeneity of capture probabilities. The resulting bias is expressed as a function of sample coverage, average capture probability, and the coefficient of variation of individual capture probabilities. The effect of unequal catchabilities on the Jolly-Seber survival rate estimators is also briefly discussed. We propose new population size estimators which incorporate the heterogeneity of capture probabilities. A simulation study investigates the performance of the approximation formulas of biases and the proposed estimation procedure. A real data set of male black-kneed capsids discussed in Jolly (Biometrika 52, 225-247, 1965), Seber (The Estimation of Animal Abundance, 1982), and Burnham (In Estimation of Analysis of Insect Populations, pp. 416-435, 1989) illustrates the method.

Estimating the Richness of a Population When the Maximum Number of Classes Is Fixed: A Nonparametric Solution to an Archaeological Problem

Background Estimating assemblage species or class richness from samples remains a challenging, but essential, goal. Though a variety of statistical tools for estimating species or class richness have been developed, they are all singly-bounded: assuming only a lower bound of species or classes. Nevertheless there are numerous situations, particularly in the cultural realm, where the maximum number of classes is fixed. For this reason, a new method is needed to estimate richness when both upper and lower bounds are known. Methodology/Principal Findings Here, we introduce a new method for estimating class richness: doubly-bounded confidence intervals (both lower and upper bounds are known). We specifically illustrate our new method using the Chao1 estimator, rarefaction, and extrapolation, although any estimator of asymptotic richness can be used in our method. Using a case study of Clovis stone tools from the North American Lower Great Lakes region, we demonstrate that singly-bounded richness estimators can yield confidence intervals with upper bound estimates larger than the possible maximum number of classes, while our new method provides estimates that make empirical sense. Conclusions/Significance Application of the new method for constructing doubly-bound richness estimates of Clovis stone tools permitted conclusions to be drawn that were not otherwise possible with singly-bounded richness estimates, namely, that Lower Great Lakes Clovis Paleoindians utilized a settlement pattern that was probably more logistical in nature than residential. However, our new method is not limited to archaeological applications. It can be applied to any set of data for which there is a fixed maximum number of classes, whether that be site occupancy models, commercial products (e.g. athletic shoes), or census information (e.g. nationality, religion, age, race).

Specimen-Based Modeling, Stopping Rules, and the Extinction of the Ivory-Billed Woodpecker

Assessing species survival status is an essential component of conservation programs. We devised a new statistical method for estimating the probability of species persistence from the temporal sequence of collection dates of museum specimens. To complement this approach, we developed quantitative stopping rules for terminating the search for missing or allegedly extinct species. These stopping rules are based on survey data for counts of co-occurring species that are encountered in the search for a target species. We illustrate both these methods with a case study of the Ivory-billed Woodpecker (Campephilus principalis), long assumed to have become extinct in the United States in the 1950s, but reportedly rediscovered in 2004. We analyzed the temporal pattern of the collection dates of 239 geo-referenced museum specimens collected throughout the southeastern United States from 1853 to 1932 and estimated the probability of persistence in 2011 as <6.4 × 10(-5) , with a probable extinction date no later than 1980. From an analysis of avian census data (counts of individuals) at 4 sites where searches for the woodpecker were conducted since 2004, we estimated that at most 1-3 undetected species may remain in 3 sites (one each in Louisiana, Mississippi, Florida). At a fourth site on the Congaree River (South Carolina), no singletons (species represented by one observation) remained after 15,500 counts of individual birds, indicating that the number of species already recorded (56) is unlikely to increase with additional survey effort. Collectively, these results suggest there is virtually no chance the Ivory-billed Woodpecker is currently extant within its historical range in the southeastern United States. The results also suggest conservation resources devoted to its rediscovery and recovery could be better allocated to other species. The methods we describe for estimating species extinction dates and the probability of persistence are generally applicable to other species for which sufficient museum collections and field census results are available.

Heterogeneous Capture–Recapture Models with Covariates: A Partial Likelihood Approach for Closed Populations

In practice, when analyzing data from a capture-recapture experiment it is tempting to apply modern advanced statistical methods to the observed capture histories. However, unless the analysis takes into account that the data have only been collected from individuals who have been captured at least once, the results may be biased. Without the development of new software packages, methods such as generalized additive models, generalized linear mixed models, and simulation-extrapolation cannot be readily implemented. In contrast, the partial likelihood approach allows the analysis of a capture-recapture experiment to be conducted using commonly available software. Here we examine the efficiency of this approach and apply it to several data sets.

Small-sample estimation of species richness applied to forest communities.

Many well-known methods are available for estimating the number of species in a forest community. However, most existing methods result in considerable negative bias in applications, where field surveys typically represent only a small fraction of sampled communities. This article develops a new method based on sampling with replacement to estimate species richness via the generalized jackknife procedure. The proposed estimator yields small bias and reasonably accurate interval estimation even with small samples. The performance of the proposed estimator is compared with several typical estimators via simulation study using two complete census datasets from Panama and Malaysia.

Theory & Methods: Continuous‐time capture‐recapture models with time variation and behavioural response

This paper develops a likelihood-based inference procedure for continuous-time capture-recapture models. The first-capture and recapture intensities are assumed to be in constant proportion but may otherwise vary arbitrarily through time. The full likelihood is partitioned into two factors, one of which is analogous to the likelihood in a special type of multiplicative intensity model arising in failure time analysis. The remaining factor is free of the non-parametric nuisance parameter and is easily maximized. This factor provides an estimator of population size and an asymptotic variance under a counting process framework. The resulting estimation procedure is shown to be equivalent to that derived from a martingale-based estimating function approach. Simulation results are presented to examine the performance of the proposed estimators.

Estimating the population size with a behavioral response in capture-recapture experiment

A new estimating procedure is suggested to estimate the population size in a capture-recapture experiment. The capture intensities for first-capture and recapture are allowed to be different and time dependent but they are assumed to be proportional. It is shown that the information on the proportionality constant is crucial to the estimation of the population size. Sensitivity analysis with a misspecification of the proportionality constant is conducted. The method has also been extended to the case with an unknown proportionality. A real example is given.

A Varying Coefficient Model to Measure the Effectiveness of Mass Media Anti-Smoking Campaigns in Generating Calls to a Quitline

Background Anti-smoking advertisements are an effective population-based smoking reduction strategy. The Quitline telephone service provides a first point of contact for adults considering quitting. Because of data complexity, the relationship between anti-smoking advertising placement, intensity, and time trends in total call volume is poorly understood. In this study we use a recently developed semi-varying coefficient model to elucidate this relationship. Methods Semi-varying coefficient models comprise parametric and nonparametric components. The model is fitted to the daily number of calls to Quitline in Victoria, Australia to estimate a nonparametric long-term trend and parametric terms for day-of-the-week effects and to clarify the relationship with target audience rating points (TARPs) for the Quit and nicotine replacement advertising campaigns. Results The number of calls to Quitline increased with the TARP value of both the Quit and other smoking cessation advertisement; the TARP values associated with the Quit program were almost twice as effective. The varying coefficient term was statistically significant for peak periods with little or no advertising. Conclusions Semi-varying coefficient models are useful for modeling public health data when there is little or no information on other factors related to the at-risk population. These models are well suited to modeling call volume to Quitline, because the varying coefficient allowed the underlying time trend to depend on fixed covariates that also vary with time, thereby explaining more of the variation in the call model.

Estimation of survival and capture probabilities in open population capture-recapture models when covariates are subject to measurement error

Predictor variables (or covariates) are frequently used in a capture-recapture analysis when estimating demographic quantities such as population size or survival probabilities. If these predictor variables are measured with error and subsequently used in the analysis, then estimates of the model parameters may be biased. Several approaches have been proposed to account for error-in-variables in capture-recapture models, however these methods generally assume the population is closed; hence quantities of interest for open populations such as the survival probabilities do not appear in the likelihood. To account for measurement error in environmental time-varying covariates for open population capture-recapture data, the well-known Cormack-Jolly-Seber model and two statistical methods are considered:?(1) simulation-extrapolation; and?(2) regression calibration, as well as a new method which accounts for correlation (arising from measurement error) between the survival and capture probabilities. Several simulation studies are conducted to examine the method performances, and a case study is presented which uses capture-recapture data on the Little Penguin Eudyptula minor and sea-surface temperature data as an environmental covariate to model their survival and capture probabilities.

Estimation in closed capture-recapture models when covariates are missing at random.

Individual covariates are commonly used in capture-recapture models as they can provide important information for population size estimation. However, in practice, one or more covariates may be missing at random for some individuals, which can lead to unreliable inference if records with missing data are treated as missing completely at random. We show that, in general, such a naive complete-case analysis in closed capture-recapture models with some covariates missing at random underestimates the population size. We develop methods for estimating regression parameters and population size using regression calibration, inverse probability weighting, and multiple imputation without any distributional assumptions about the covariates. We show that the inverse probability weighting and multiple imputation approaches are asymptotically equivalent. We present a simulation study to investigate the effects of missing covariates and to evaluate the performance of the proposed methods. We also illustrate an analysis using data on the bird species yellow-bellied prinia collected in Hong Kong.