Efficient profile-likelihood confidence intervals for capture-recapture models

In a capture-recapture analysis, uncertainty in the parameter estimates is usually expressed by presenting classical Wald-type confidence intervals. This approach involves (1) the assumption that the maximum likelihood estimates are asymptotically normal and (2) numerical computation of the variance-covariance matrix of these estimates. When the sample size is small or when the estimates are on the boundary of their domain, a Wald confidence interval often performs badly. A natural alternative is to use profile-likelihood confidence intervals. In general, these intervals require a greater amount of computation. We propose a new implementation of this approach that is efficient, both in reducing the amount of computation and in coping with boundary estimates. We also show how profile-likelihood confidence intervals can be adjusted for overdispersion. Simulations were used to check whether nominal coverage levels were attained, and allowed us to compare this approach with the classical Wald procedure. We illustrate this work by considering a multi-state model for a sooty shearwater (Puffinus griseus) population.     

Limited-Information Modeling of Loggerhead Turtle Population Size

We attempt to estimate the size of a population of female loggerhead turtles. In traditional capture-recapture experiments to estimate the size of an animal population, individual animals are tagged and the information about which individuals are captured repeatedly is crucial. For these loggerhead turtle data, information about individual turtles is not available. Rather, we observe only the counts of successful and failed nestings at a location over a series of days (in our case, three). We view the turtles’ nesting behavior as an alternating renewal process, model it using parametric distributions, and then derive probability distributions that describe the behavior of the turtles during the three days via a 3-way contingency table. We adopt a Bayesian approach, formulating our model in terms of parameters about which strong prior information is available. We use a Gibbs sampling algorithm to sample from the posterior distribution of our random quantities, the most crucial of which is the number of turtles remaining offshore during the entire sampling period. We illustrate the method using data sets from loggerhead turtle sites along the South Carolina coast. We provide a simulation study which illustrates the quality and robustness of the method and investigates sensitivity to prior parameter specification.     

A nonparametric lower bound for the number of species shared by multiple communities

In biological and ecological statistical inference, it is practically useful to provide a lower bound for species richness in a community. Chao (1984, 1989) derived a non-parametric lower bound for species richness in a single community. However, there have been no lower bounds proposed in the literature for the number of species shared by multiple communities. Based on sample species abundance or replicated incidence records from each of the N communities, we derive in this article a nonparametric approach to constructing a lower bound for the number of species shared by N (N≥2) communities. The approach is valid for all types of species abundance distributions (for abundance data) or species detection probabilities (for replicated incidence data). Variance estimators for the proposed lower bounds are obtained by using typical asymptotic theory. Simulation results are reported to examine the performance of the lower bounds. Replicated incidence data of ciliate species collected in three areas from Namibia, southwest Africa, are used for illustration. We also briefly discuss the application of the proposed method to estimate the size of a shared population (i.e., the number of individuals in the intersection of multiple populations) based on capture-recapture data from each population.     

Composite sampling enhances the confidence of soil microarthropod abundance and species richness estimates

The quantification of abundance and species richness of soil microarthropods is most often severely hindered by extraordinary data variability, highly skewed frequency distributions, many extreme and zero counts, and small sample sizes. We developed a composite sampling technique to enhance the confidence of abundance and species richness estimates. Many soil cores (n ≥ 100) are sampled, animals extracted, the extracts pooled, mixed, and subsamples (aliquots) taken. Compared to the standard (separate sampling units), no microarthropods were lost or mechanically damaged during the compositing procedure. The confidence of abundance estimates was substantially greater in the composite than in the standard, although not for taxa of low abundance (< ≈ 10³ ind.m⁻²). Moreover, compositing was the superior technique in estimating species richness. The number of sampling units needed to recover a certain number of species with the composite was 70% of the standard method. We conclude that composite sampling is a promising alternative to the standard technique and may help to increase the generally low confidence of microarthropod field data. Finally, potential limitations of composite plans are discussed: a great number of field cores from an unbiased sampling plan have to be composited; comparisons between composites of unequal size should be avoided; all information on the variation among field cores is lost by compositing; parallel measurements of fauna and other variables in the same cores are not possible.     

Hierarchical modeling of cluster size in wildlife surveys

Clusters or groups of individuals are the fundamental unit of observation in many wildlife sampling problems, including aerial surveys of waterfowl, marine mammals, and ungulates. Explicit accounting of cluster size in models for estimating abundance is necessary because detection of individuals within clusters is not independent and detectability of clusters is likely to increase with cluster size. This induces a cluster size bias in which the average cluster size in the sample is larger than in the population at large. Thus, failure to account for the relationship between detectability and cluster size will tend to yield a positive bias in estimates of abundance or density. I describe a hierarchical modeling framework for accounting for cluster-size bias in animal sampling. The hierarchical model consists of models for the observation process conditional on the cluster size distribution and the cluster size distribution conditional on the total number of clusters. Optionally, a spatial model can be specified that describes variation in the total number of clusters per sample unit. Parameter estimation, model selection, and criticism may be carried out using conventional likelihood-based methods. An extension of the model is described for the situation where measurable covariates at the level of the sample unit are available. Several candidate models within the proposed class are evaluated for aerial survey data on mallard ducks (Anas platyrhynchos).     

Genetic Introgression and the Survival of Florida Panther Kittens

Estimates of survival for the young of a species are critical for population models. These models can often be improved by determining the effects of management actions and population abundance on this demographic parameter. We used multiple sources of data collected during 1982-2008 and a live-recapture dead-recovery modeling framework to estimate and model survival of Florida panther (Puma concolor coryi) kittens (age 0-1 year). Overall, annual survival of Florida panther kittens was 0.323 ± 0.071 (SE), which was lower than estimates used in previous population models. In 1995, female pumas from Texas (P. c. stanleyana) were released into occupied panther range as part of an intentional introgression program to restore genetic variability. We found that kitten survival generally increased with degree of admixture: F₁ admixed and backcrossed to Texas kittens survived better than canonical Florida panther and backcrossed to canonical kittens. Average heterozygosity positively influenced kitten and older panther survival, whereas index of panther abundance negatively influenced kitten survival. Our results provide strong evidence for the positive population-level impact of genetic introgression on Florida panthers. Our approach to integrate data from multiple sources was effective at improving robustness as well as precision of estimates of Florida panther kitten survival, and can be useful in estimating vital rates for other elusive species with sparse data.     

Bayesian Calibration of Blue Crab (<Emphasis Type="Italic">Callinectes sapidus</Emphasis>) Abundance Indices Based on Probability Surveys

Abundance and standard error estimates in surveys of fishery resources typically employ classical design-based approaches, ignoring the influences of non-design factors such as varying catchability. We developed a Bayesian approach for estimating abundance and associated errors in a fishery survey by incorporating sampling and non-sampling variabilities. First, a zero-inflated spatial model was used to quantify variance components due to non-sampling factors; second, the model was used to calibrate the estimated abundance index and its variance using pseudo empirical likelihood. The approach was applied to a winter dredge survey conducted to estimate the abundance of blue crabs (Callinectes sapidus) in the Chesapeake Bay. We explored the properties of the calibration estimators through a limited simulation study. The variance estimator calibrated on posterior sample performed well, and the mean estimator had comparable performance to design-based approach with slightly higher bias and lower (about 15% reduction) mean squared error. The results suggest that application of this approach can improve estimation of abundance indices using data from design-based fishery surveys.     

Weighing the costs and benefits of reduced sampling resolution in biomonitoring studies: Perspectives from the temperate rocky intertidal

Efficiency in biomonitoring studies is essential to maximize return (i.e. useful data) for investment (e.g. time, training, personnel). Here, we test several options for reducing data resolution when streamlining monitoring protocols, and use the results as a framework to discuss the costs and benefits of decreasing information when sampling intertidal assemblages. Specifically, we ask; (1) Is it necessary to collect species abundance data, or is species presence-absence information sufficient to differentiate sites? (2) Is it necessary to sample organismal abundance at the species-level or is coarser (higher taxon or functional group) resolution sufficient to resolve patterns of difference in intertidal community structure? and (3) How general are these patterns across different oceanic regions? We answer these questions using data from Northeast Atlantic, Northwest Atlantic, Northeast Pacific, and Southwest Pacific intertidal monitoring studies. Results show that compared to species-level sampling, genus-level sampling requires knowledge of 25% fewer taxa, but results in only a 5% difference in the ability to discern between-sample similarities. Likewise, family-level sampling involves 50% fewer taxa, and is accompanied by only an 8% difference in between-sample similarities. Species lists and functional groups were variable in performance, working well for some regions, and poorly for others. These findings will assist in the selection of monitoring protocols with the potential for increased geographic scope and temporal frequency of sampling, resulting in longer time series of data collection, and a reduction in the required taxonomic skills for individuals involved in scientifically useful biomonitoring programs.     

The Jolly-seber model: More than just abundance

The Jolly-Seber model provides estimates of abundance, survival, and capture rates from capture-recapture experiments. This article will describe recent extensions to the following cases: (a) multiple-cohort studies where recruitment rates are compared among cohorts, (b) age-specific breeding proportions, and (c) population growth rates. Finally, new areas of research needed for this model are proposed.     

Analyzing designed experiments in distance sampling

Distance sampling is a survey technique for estimating the abundance or density of wild animal populations. Detection probabilities of animals inherently differ by species, age class, habitats, or sex. By incorporating the change in an observer’s ability to detect a particular class of animals as a function of distance, distance sampling leads to density estimates that are comparable across different species, ages, habitats, sexes, and so on. Increasing interest in evaluating the effects of management practices on animal populations in an experimental context has led to a need for suitable methods of analyzing distance sampling data. We outline a two-stage approach for analyzing distance sampling data from designed experiments, in which a two-step bootstrap is used to quantify precision and identify treatment effects. We illustrate this approach using data from a before—after control-impact experiment designed to assess the effects of large-scale prescribed fire treatments on bird densities in ponderosa pine forests of the southwestern United States.     

A bayesian approach to crop Model calibration under unknown error covariance

Bayesian methods seem well adapted to dynamic system models in general and to crop models in particular, because there is in general prior information about parameter values. The usefulness of a Bayesian approach has often been pointed out, but actual applications are rather rare. A major difficulty is including the elements of the covariance matrix of model errors in the treatment. We treat the specific case of balanced data and an unstructured covariance matrix. In our particular case this is a 3 × 3 matrix. We illustrate two methods for deriving a sample from the joint posterior density for the crop model parameters and the error covariance matrix parameters. The first method is based on importance sampling, the second on Metropolis within Gibbs sampling. We derive an instrumental density for the former and a proposal density for the latter which are adapted to this type of model and data. Both algorithms work well and they give very similar results. The example concerns a model for sunflowers during rapid leaf growth. The ultimate goal is to use the model as a decision aid in predicting disease risk.     

Assessing the Impacts of Time-to-Detection Distribution Assumptions on Detection Probability Estimation

Abundance estimates from animal point-count surveys require accurate estimates of detection probabilities. The standard model for estimating detection from removal-sampled point-count surveys assumes that organisms at a survey site are detected at a constant rate; however, this assumption can often lead to biased estimates. We consider a class of N-mixture models that allows for detection heterogeneity over time through a flexibly defined time-to-detection distribution (TTDD) and allows for fixed and random effects for both abundance and detection. Our model is thus a combination of survival time-to-event analysis with unknown-N, unknown-p abundance estimation. We specifically explore two-parameter families of TTDDs, e.g., gamma, that can additionally include a mixture component to model increased probability of detection in the initial observation period. Based on simulation analyses, we find that modeling a TTDD by using a two-parameter family is necessary when data have a chance of arising from a distribution of this nature. In addition, models with a mixture component can outperform non-mixture models even when the truth is non-mixture. Finally, we analyze an Ovenbird data set from the Chippewa National Forest using mixed effect models for both abundance and detection. We demonstrate that the effects of explanatory variables on abundance and detection are consistent across mixture TTDDs but that flexible TTDDs result in lower estimated probabilities of detection and therefore higher estimates of abundance.Supplementary materials accompanying this paper appear on-line.     

An Integrated Population Model From Constant Effort Bird-Ringing Data

Data from annual bird-ringing programs, in which catch effort is standardized, are routinely used to index abundance, productivity, and adult survival. Efficient models have been developed for each. Such monitoring schemes, based on ringing across a number of sites, are perhaps unique in providing this combination of demographic information and make the data particularly amenable to an integrated approach to population modeling. We develop a Bayesian approach and a deterministic population model uniting abundance, productivity, and survival. The method is applied to sedge warbler Acrocephalus schoenobaenus data from the British Trust for Ornithology’s Constant Effort Sites scheme. The possibility of “transient” birds needs to be incorporated within this analysis. We demonstrate how current methodology can efficiently be extended to use additional data from multiple within year recaptures when controlling for transience. Supplemental materials for this article are available online.     

A robust design mark-resight abundance estimator allowing heterogeneity in resighting probabilities

This article introduces the beta-binomial estimator (BBE), a closed-population abundance mark-resight model combining the favorable qualities of maximum likelihood theory and the allowance of individual heterogeneity in sighting probability (p). The model may be parameterized for a robust sampling design consisting of multiple primary sampling occasions where closure need not be met between primary occasions. We applied the model to brown bear data from three study areas in Alaska and compared its performance to the joint hypergeometric estimator (JHE) and Bowden’s estimator (BOWE). BBE estimates suggest heterogeneity levels were non-negligible and discourage the use of JHE for these data. Compared to JHE and BOWE, confidence intervals were considerably shorter for the AIC_c model-averaged BBE. To evaluate the properties of BBE relative to JHE and BOWE when sample sizes are small, simulations were performed with data from three primary occasions generated under both individual heterogeneity and temporal variation in p. All models remained consistent regardless of levels of variation in p. In terms of precision, the AIC_c model-averaged BBE showed advantages over JHE and BOWE when heterogeneity was present and mean sighting probabilities were similar between primary occasions. Based on the conditions examined, BBE is a reliable alternative to JHE or BOWE and provides a framework for further advances in mark-resight abundance estimation.     

Combining Survey and Non-survey Data for Improved Sub-area Prediction Using a Multi-level Model

Combining information from different sources is an important practical problem in survey sampling. Using a hierarchical area-level model, we establish a framework to integrate auxiliary information to improve state-level area estimates. The best predictors are obtained by the conditional expectations of latent variables given observations, and an estimate of the mean squared prediction error is discussed. Sponsored by the National Agricultural Statistics Service of the US Department of Agriculture, the proposed model is applied to the planted crop acreage estimation problem by combining information from three sources, including the June Area Survey obtained by a probability-based sampling of lands, administrative data about the planted acreage and the cropland data layer, which is a commodity-specific classification product derived from remote sensing data. The proposed model combines the available information at a sub-state level called the agricultural statistics district and aggregates to improve state-level estimates of planted acreages for different crops. Supplementary materials accompanying this paper appear on-line.     

A resource selection model for analyzing pseudoreplicated data due to grouping behavior of animals

Quantifying resource selection is of primary interest in animal ecology. Many analyses of resource selection assume spatial and temporal independence of the sampling unit. Autocorrelation between observations, which is a general property of ecological variables, causes difficulties for most standard statistical procedures of resource selection because autocorrelated data violate the assumption of independence. To overcome this problem, we develop a mixed-effects model to estimate resource selection functions from data that are autocorrelated because of unobserved grouping behavior by animals. In the application of the expectation-maximization (EM) algorithm, the computation of the conditional expectation of the complete-data log-likelihood function does not have a closed-form solution requiring numerical integration. A Monte Carlo EM algorithm with Gibbs sampling can be used effectively in such situations to find exact maximum likelihood estimates. We propose a simple automated Monte Carlo EM algorithm with multiple sequences in which the Monte Carlo sample size is increased when the EM step is swamped by Monte Carlo errors.We demonstrate that the model can detect inherent autocorrelation and provide reasonable variance estimates when applied to nocturnal bird migration data. This approach could also be applied to ecological processes with various types of spatially and temporally autocorrelated data, circumventing serious problems caused by dangerous pseudoreplication.     

Point-Based Mark-Recapture Distance Sampling

Avian surveys using point sampling for abundance estimation have either focused on distance sampling or more commonly mark-recapture to correct for detection bias. Combining mark-recapture and distance sampling (MRDS) has become an effective tool for line transects, but it has been largely ignored in point sampling literature. We describe MRDS and show that the previously published methods for point sampling are special cases. Using simulated data and golden-cheeked warbler (Dendroica chrysoparia) survey data from Texas, we demonstrate large differences in abundance estimates resulting from different independence assumptions. Data and code are provided in supplementary materials.     

Estimation of Population Mean and Total in a Finite Population Setting Using Multiple Auxiliary Variables

This paper introduces a new sampling design in a finite population setting, where potential sampling units have a wealth of auxiliary information that can be used to rank them into partially ordered sets. The proposed sampling design selects a set of sampling units. These units are judgment ranked without measurement by using available auxiliary information. The ranking process allows ties among ranks whenever units cannot be ranked accurately with high confidence. The ranking information from all sources is combined in a meaningful way to construct strength-of-agreement weights. These weights are then used to select a single sampling unit for full measurement in each set. Three different levels of sampling design, level-0, level-1, and level-2, are investigated. They differ in their replacement policies. Level-0 sampling designs construct the sample by sampling with replacement, level-1 sampling designs constructs the sample without replacement of the fully measured unit in each set, and level-2 sampling designs construct the sample without replacement on the entire set. For these three designs, we estimate the first and second order inclusion probabilities and construct estimators for the population total and mean. We develop a bootstrap resampling procedure to estimate the variances of the estimators and to construct percentile confidence intervals for the population mean and total. We show that the new sampling designs provide a substantial amount of efficiency gain over their competitor designs in the literature.     

Environmental monitoring using populations of birds and small mammals: Analyses of sampling effort

Characteristics of bird and small mammal communities can be valuable in monitoring for impacts on specific plots of land. In Utah (USA), significant differences were found among years, habitats and seasons in bird and small mammal abundance, species diversity, and species richness; thus, estimates of these characteristics are consistent and repeatable and can be used for detecting change. Also, bird and small mammal communities are dependent on a wide variety of food resources and habitat characteristics; thus they should reflect a variety of impacts.A comparison is made between two methods of handling bird data from transects: enumeration (individual birds per km) and density (birds per unit area). Correlation between the two was high (r = 0·93). However, density estimates may be necessary to trace an impact to a particular group, guild or species and possibly to its cause.An analysis is made of how much sampling is necessary to make an adequate estimate of the characteristics of bird and small mammal communities. Estimates of bird abundance, species richness and species diversity (from enumeration) may be obtained with three repetitions of 2 km of transect. Three repetitions are also sufficient to estimate abundance of small mammals on 12 by 12 trapping grids. To estimate species richness and species diversity, however, four or more repetitions are needed. Small mammal community characteristics are not well predicted by trapping on transects or small grids except in grids 9 by 9 or larger. These results of sampling effort may only apply to certain habitats but data from bird and small mammal communities should be useful in environmental monitoring at any site.