Improved methods for estimating abundance and related demographic parameters from mark‐resight data

Over the past decade, there has been much methodological development for the estimation of abundance and related demographic parameters using mark‐resight data. Often viewed as a less‐invasive and less‐expensive alternative to conventional mark recapture, mark‐resight methods jointly model marked individual encounters and counts of unmarked individuals, and recent extensions accommodate common challenges associated with imperfect detection. When these challenges include both individual detection heterogeneity and an unknown marked sample size, we demonstrate several deficiencies associated with the most widely used mark‐resight models currently implemented in the popular capture‐recapture freeware Program MARK. We propose a composite likelihood solution based on a zero‐inflated Poisson log‐normal model and find the performance of this new estimator to be superior in terms of bias and confidence interval coverage. Under Pollock's robust design, we also extend the models to accommodate individual‐level random effects across sampling occasions as a potentially more realistic alternative to models that assume independence. As a motivating example, we revisit a previous analysis of mark‐resight data for the New Zealand Robin (Petroica australis) and compare inferences from the proposed estimators. For the all‐too‐common situation where encounter rates are low, individual detection heterogeneity is non‐negligible, and the number of marked individuals is unknown, we recommend practitioners use the zero‐inflated Poisson log‐normal mark‐resight estimator as now implemented in Program MARK.     

Combined hybridization capture and shotgun sequencing for ancient DNA analysis of extinct wild and domestic dromedary camel

The performance of hybridization capture combined with next‐generation sequencing (NGS) has seen limited investigation with samples from hot and arid regions until now. We applied hybridization capture and shotgun sequencing to recover DNA sequences from bone specimens of ancient‐domestic dromedary (Camelus dromedarius) and its extinct ancestor, the wild dromedary from Jordan, Syria, Turkey and the Arabian Peninsula, respectively. Our results show that hybridization capture increased the percentage of mitochondrial DNA (mtDNA) recovery by an average 187‐fold and in some cases yielded virtually complete mitochondrial (mt) genomes at multifold coverage in a single capture experiment. Furthermore, we tested the effect of hybridization temperature and time by using a touchdown approach on a limited number of samples. We observed no significant difference in the number of unique dromedary mtDNA reads retrieved with the standard capture compared to the touchdown method. In total, we obtained 14 partial mitochondrial genomes from ancient‐domestic dromedaries with 17–95% length coverage and 1.27–47.1‐fold read depths for the covered regions. Using whole‐genome shotgun sequencing, we successfully recovered endogenous dromedary nuclear DNA (nuDNA) from domestic and wild dromedary specimens with 1–1.06‐fold read depths for covered regions. Our results highlight that despite recent methodological advances, obtaining ancient DNA (aDNA) from specimens recovered from hot, arid environments is still problematic. Hybridization protocols require specific optimization, and samples at the limit of DNA preservation need multiple replications of DNA extraction and hybridization capture as has been shown previously for Middle Pleistocene specimens.     

The Total Least Squares Method in Individual Bioequivalence Evaluation

We propose a simple method for comparison of series of matched observations. While in all our examples we address “individual bioequivalence” (IBE), which is the subject of much discussion in pharmaceutical statistics, the methodology can be applied to a wide class of cross‐over experiments, including cross‐over imaging. From the statistical point of view the considered models belong to the class of the “error‐in‐variables” models. In computational statistics the corresponding optimization method is referred to as the “least squares distance” and the “total least squares” method. The derived confidence regions for both intercept and slope provide the basis for formulation of the IBE criteria and methods for its assessing. Simple simulations show that the proposed approach is very intuitive and transparent, and, at the same time, has a solid statistical and computational background.     

A roadmap for high‐throughput sequencing studies of wild animal populations using noninvasive samples and hybridization capture

Large‐scale genomic studies of wild animal populations are often limited by access to high‐quality DNA. Although noninvasive samples, such as faeces, can be readily collected, DNA from the sample producers is usually present in low quantities, fragmented, and contaminated by microorganism and dietary DNAs. Hybridization capture can help to overcome these impediments by increasing the proportion of subject DNA prior to high‐throughput sequencing. Here we evaluate a key design variable for hybridization capture, the number of rounds of capture, by testing whether one or two rounds are most appropriate, given varying sample quality (as measured by the ratios of subject to total DNA). We used a set of 1,780 quality‐assessed wild chimpanzee (Pan troglodytes schweinfurthii) faecal samples and chose 110 samples of varying quality for exome capture and sequencing. We used multiple regression to assess the effects of the ratio of subject to total DNA (sample quality), rounds of capture and sequencing effort on the number of unique exome reads sequenced. We not only show that one round of capture is preferable when the proportion of subject DNA in a sample is above ~2%–3%, but also explore various types of bias introduced by capture, and develop a model that predicts the sequencing effort necessary for a desired data yield from samples of a given quality. Thus, our results provide a useful guide and pave a methodological way forward for researchers wishing to plan similar hybridization capture studies.     

Confidence bands for multiplicative hazards models: Flexible resampling approaches

We propose new resampling‐based approaches to construct asymptotically valid time‐simultaneous confidence bands for cumulative hazard functions in multistate Cox models. In particular, we exemplify the methodology in detail for the simple Cox model with time‐dependent covariates, where the data may be subject to independent right‐censoring or left‐truncation. We use simulations to investigate their finite sample behavior. Finally, the methods are utilized to analyze two empirical examples with survival and competing risks data.     

Semiparametric transformation models for multiple continuous biomarkers in ROC analysis

Recent technological advances continue to provide noninvasive and more accurate biomarkers for evaluating disease status. One standard tool for assessing the accuracy of diagnostic tests is the receiver operating characteristic (ROC) curve. Few statistical methods exist to accommodate multiple continuous‐scale biomarkers in the framework of ROC analysis. In this paper, we propose a method to integrate continuous‐scale biomarkers to optimize classification accuracy. Specifically, we develop semiparametric transformation models for multiple biomarkers. We assume that unknown and marker‐specific transformations of biomarkers follow a multivariate normal distribution. Our models accommodate biomarkers subject to limits of detection and account for the dependence among biomarkers by including a subject‐specific random effect. We also propose a diagnostic measure using an optimal linear combination of the transformed biomarkers. Our diagnostic rule does not depend on any monotone transformation of biomarkers and is not sensitive to extreme biomarker values. Nonparametric maximum likelihood estimation (NPMLE) is used for inference. We show that the parameter estimators are asymptotically normal and efficient. We illustrate our semiparametric approach using data from the Endometriosis, Natural History, Diagnosis, and Outcomes (ENDO) study.     

A general modeling framework for open wildlife populations based on the Polya tree prior

Wildlife monitoring for open populations can be performed using a number of different survey methods. Each survey method gives rise to a type of data and, in the last five decades, a large number of associated statistical models have been developed for analyzing these data. Although these models have been parameterized and fitted using different approaches, they have all been designed to either model the pattern with which individuals enter and/or exit the population, or to estimate the population size by accounting for the corresponding observation process, or both. However, existing approaches rely on a predefined model structure and complexity, either by assuming that parameters linked to the entry and exit pattern (EEP) are specific to sampling occasions, or by employing parametric curves to describe the EEP. Instead, we propose a novel Bayesian nonparametric framework for modeling EEPs based on the Polya tree (PT) prior for densities. Our Bayesian nonparametric approach avoids overfitting when inferring EEPs, while simultaneously allowing more flexibility than is possible using parametric curves. Finally, we introduce the replicate PT prior for defining classes of models for these data allowing us to impose constraints on the EEPs, when required. We demonstrate our new approach using capture–recapture, count, and ring-recovery data for two different case studies.     

Multiscale Adaptive Marginal Analysis of Longitudinal Neuroimaging Data with Time‐Varying Covariates

Summary Neuroimaging data collected at repeated occasions are gaining increasing attention in the neuroimaging community due to their potential in answering questions regarding brain development, aging, and neurodegeneration. These datasets are large and complicated, characterized by the intricate spatial dependence structure of each response image, multiple response images per subject, and covariates that may vary with time. We propose a multiscale adaptive generalized method of moments (MA‐GMM) approach to estimate marginal regression models for imaging datasets that contain time‐varying, spatially related responses and some time‐varying covariates. Our method categorizes covariates into types to determine the valid moment conditions to combine during estimation. Further, instead of assuming independence of voxels (the components that make up each subject’s response image at each time point) as many current neuroimaging analysis techniques do, this method “adaptively smoothes” neuroimaging response data, computing parameter estimates by iteratively building spheres around each voxel and combining observations within the spheres with weights. MA‐GMM’s development adds to the few available modeling approaches intended for longitudinal imaging data analysis. Simulation studies and an analysis of a real longitudinal imaging dataset from the Alzheimer’s Disease Neuroimaging Initiative are used to assess the performance of MA‐GMM. Martha Skup, Hongtu Zhu, and Heping Zhang for the Alzheimer’s Disease Neuroimaging Initiative.     

Behavioral phenotypes of genetic mouse models of autism

More than a hundred de novo single gene mutations and copy‐number variants have been implicated in autism, each occurring in a small subset of cases. Mutant mouse models with syntenic mutations offer research tools to gain an understanding of the role of each gene in modulating biological and behavioral phenotypes relevant to autism. Knockout, knockin and transgenic mice incorporating risk gene mutations detected in autism spectrum disorder and comorbid neurodevelopmental disorders are now widely available. At present, autism spectrum disorder is diagnosed solely by behavioral criteria. We developed a constellation of mouse behavioral assays designed to maximize face validity to the types of social deficits and repetitive behaviors that are central to an autism diagnosis. Mouse behavioral assays for associated symptoms of autism, which include cognitive inflexibility, anxiety, hyperactivity, and unusual reactivity to sensory stimuli, are frequently included in the phenotypic analyses. Over the past 10 years, we and many other laboratories around the world have employed these and additional behavioral tests to phenotype a large number of mutant mouse models of autism. In this review, we highlight mouse models with mutations in genes that have been identified as risk genes for autism, which work through synaptic mechanisms and through the mTOR signaling pathway. Robust, replicated autism‐relevant behavioral outcomes in a genetic mouse model lend credence to a causal role for specific gene contributions and downstream biological mechanisms in the etiology of autism.     

A parallel optimization approach for controlling allele diversity in conservation schemes

We propose a novel method to control allelic diversity in conservation schemes based on an optimization problem, characterized by a convex program subject to integer linear constraints. Departing from previous studies considering similar problems, we implement a parallel simulated annealing algorithm to minimize the number of alleles lost across generations. The proposed algorithm shows excellent timing and minimization performances. Execution time decreases linearly with the number of processors used, providing similar results in all cases.     

Log‐gamma linear‐mixed effects models for multiple outcomes with application to a longitudinal glaucoma study

Glaucoma is a progressive disease due to damage in the optic nerve with associated functional losses. Although the relationship between structural and functional progression in glaucoma is well established, there is disagreement on how this association evolves over time. In addressing this issue, we propose a new class of non‐Gaussian linear‐mixed models to estimate the correlations among subject‐specific effects in multivariate longitudinal studies with a skewed distribution of random effects, to be used in a study of glaucoma. This class provides an efficient estimation of subject‐specific effects by modeling the skewed random effects through the log‐gamma distribution. It also provides more reliable estimates of the correlations between the random effects. To validate the log‐gamma assumption against the usual normality assumption of the random effects, we propose a lack‐of‐fit test using the profile likelihood function of the shape parameter. We apply this method to data from a prospective observation study, the Diagnostic Innovations in Glaucoma Study, to present a statistically significant association between structural and functional change rates that leads to a better understanding of the progression of glaucoma over time.     

Estimating multiple time‐fixed treatment effects using a semi‐Bayes semiparametric marginal structural Cox proportional hazards regression model

Marginal structural models for time‐fixed treatments fit using inverse‐probability weighted estimating equations are increasingly popular. Nonetheless, the resulting effect estimates are subject to finite‐sample bias when data are sparse, as is typical for large‐sample procedures. Here we propose a semi‐Bayes estimation approach which penalizes or shrinks the estimated model parameters to improve finite‐sample performance. This approach uses simple symmetric data‐augmentation priors. Limited simulation experiments indicate that the proposed approach reduces finite‐sample bias and improves confidence‐interval coverage when the true values lie within the central “hill” of the prior distribution. We illustrate the approach with data from a nonexperimental study of HIV treatments.     

Mixed‐Effects State‐Space Models for Analysis of Longitudinal Dynamic Systems

Summary The rapid development of new biotechnologies allows us to deeply understand biomedical dynamic systems in more detail and at a cellular level. Many of the subject‐specific biomedical systems can be described by a set of differential or difference equations that are similar to engineering dynamic systems. In this article, motivated by HIV dynamic studies, we propose a class of mixed‐effects state‐space models based on the longitudinal feature of dynamic systems. State‐space models with mixed‐effects components are very flexible in modeling the serial correlation of within‐subject observations and between‐subject variations. The Bayesian approach and the maximum likelihood method for standard mixed‐effects models and state‐space models are modified and investigated for estimating unknown parameters in the proposed models. In the Bayesian approach, full conditional distributions are derived and the Gibbs sampler is constructed to explore the posterior distributions. For the maximum likelihood method, we develop a Monte Carlo EM algorithm with a Gibbs sampler step to approximate the conditional expectations in the E‐step. Simulation studies are conducted to compare the two proposed methods. We apply the mixed‐effects state‐space model to a data set from an AIDS clinical trial to illustrate the proposed methodologies. The proposed models and methods may also have potential applications in other biomedical system analyses such as tumor dynamics in cancer research and genetic regulatory network modeling.     

Applications of hidden hybrid Markov/semi‐Markov models: from stopover duration to breeding success dynamics

Usually in capture–recapture, a model parameter is time or time since first capture dependent. However, the case where the probability of staying in one state depends on the time spent in that particular state is not rare. Hidden Markov models are not appropriate to manage these situations. A more convenient approach would be to consider models that incorporate semi‐Markovian states which explicitly define the waiting time distribution and have been used in previous biologic studies as a convenient framework for modeling the time spent in a given physiological state. Here, we propose hidden Markovian models that combine several nonhomogeneous Markovian states with one semi‐Markovian state and which (i) are well adapted to imperfect and variable detection and (ii) allow us to consider time, time since first capture, and time spent in one state effects. Implementation details depending on the number of semi‐Markovian states are discussed. From a user's perspective, the present approach enhances the toolbox for analyzing capture–recapture data. We then show the potential of this framework by means of two ecological examples: (i) stopover duration and (ii) breeding success dynamics.     

Resin gathering in neotropical resin bugs (Insecta: Hemiptera: Reduviidae): Functional and comparative morphology

Apiomerini (Reduviidae: Harpactorinae) collect plant resins with their forelegs and use these sticky substances for prey capture or maternal care. These behaviors have not been described in detail and morphological structures involved in resin gathering, transfer, and storage remain virtually undocumented. We here describe these behaviors in Apiomerus flaviventris and document the involved structures. To place them in a comparative context, we describe and document leg and abdominal structures in 14 additional species of Apiomerini that represent all but one of the 12 recent genera in the tribe. Based on these morphological data in combination with the behavioral observations on A. flaviventris, we infer behavioral and functional hypotheses for the remaining genera within the tribe Apiomerini. Setal abdominal patches for resin storage are associated with maternal care so far only documented for species of Apiomerus. Based on the occurrence of these patches in several other genera, we propose that maternal care is widespread within the tribe. Ventral abdominal glands are widespread within female Apiomerini. We propose that their products may prevent hardening of stored resins thus providing long‐term supply for egg coating. Judging from the diverse setal types and arrangements on the front legs, we predict six different behavioral patterns of resin gathering within the tribe. J. Morphol., 2011. © 2010 Wiley‐Liss, Inc.     

Search and foraging behaviors from movement data: A comparison of methods

Search behavior is often used as a proxy for foraging effort within studies of animal movement, despite it being only one part of the foraging process, which also includes prey capture. While methods for validating prey capture exist, many studies rely solely on behavioral annotation of animal movement data to identify search and infer prey capture attempts. However, the degree to which search correlates with prey capture is largely untested. This study applied seven behavioral annotation methods to identify search behavior from GPS tracks of northern gannets (Morus bassanus), and compared outputs to the occurrence of dives recorded by simultaneously deployed time–depth recorders. We tested how behavioral annotation methods vary in their ability to identify search behavior leading to dive events. There was considerable variation in the number of dives occurring within search areas across methods. Hidden Markov models proved to be the most successful, with 81% of all dives occurring within areas identified as search. k‐Means clustering and first passage time had the highest rates of dives occurring outside identified search behavior. First passage time and hidden Markov models had the lowest rates of false positives, identifying fewer search areas with no dives. All behavioral annotation methods had advantages and drawbacks in terms of the complexity of analysis and ability to reflect prey capture events while minimizing the number of false positives and false negatives. We used these results, with consideration of analytical difficulty, to provide advice on the most appropriate methods for use where prey capture behavior is not available. This study highlights a need to critically assess and carefully choose a behavioral annotation method suitable for the research question being addressed, or resulting species management frameworks established.     

Trap‐shyness subsidence is a threshold function of mark–recapture interval in brown mudfish Neochanna apoda populations

The influence of capture interval on trap shyness, and temperature, rainfall and drought on capture probability (p) in 827 brown mudfish Neochanna apoda was quantified using mark–recapture models. In particular, it was hypothesized that the loss of trapping memory in marked N. apoda would lead to a capture‐interval threshold required to minimize trap shyness. Neochanna apoda trap shyness approximated a threshold response to capture interval, declining rapidly with increasing capture intervals up to 16·5 days, after which p remained constant. Tests for detecting trap‐dependent capture probability in Cormack–Jolly–Seber models failed to detect trap shyness in N. apoda capture histories with capture intervals averaging 16 days. This confirmed the applicability of the 16 day capture‐interval threshold for mark–recapture studies. Instead, N. apoda p was positively influenced by water temperature and rainfall during capture. These results imply that a threshold capture interval is required to minimize the trade‐off between the competing assumptions of population closure and p homogeneity between capture occasions in closed mark–recapture models. Moreover, environmental factors that influence behaviour could potentially confound abundance indices, and consequently abundance trends should be interpreted with caution in the face of long‐term climate change, such as with global warming.     

Estimating species – area relationships by modeling abundance and frequency subject to incomplete sampling

Models and data used to describe species–area relationships confound sampling with ecological process as they fail to acknowledge that estimates of species richness arise due to sampling. This compromises our ability to make ecological inferences from and about species–area relationships. We develop and illustrate hierarchical community models of abundance and frequency to estimate species richness. The models we propose separate sampling from ecological processes by explicitly accounting for the fact that sampled patches are seldom completely covered by sampling plots and that individuals present in the sampling plots are imperfectly detected. We propose a multispecies abundance model in which community assembly is treated as the summation of an ensemble of species‐level Poisson processes and estimate patch‐level species richness as a derived parameter. We use sampling process models appropriate for specific survey methods. We propose a multispecies frequency model that treats the number of plots in which a species occurs as a binomial process. We illustrate these models using data collected in surveys of early‐successional bird species and plants in young forest plantation patches. Results indicate that only mature forest plant species deviated from the constant density hypothesis, but the null model suggested that the deviations were too small to alter the form of species–area relationships. Nevertheless, results from simulations clearly show that the aggregate pattern of individual species density–area relationships and occurrence probability–area relationships can alter the form of species–area relationships. The plant community model estimated that only half of the species present in the regional species pool were encountered during the survey. The modeling framework we propose explicitly accounts for sampling processes so that ecological processes can be examined free of sampling artefacts. Our modeling approach is extensible and could be applied to a variety of study designs and allows the inclusion of additional environmental covariates.     

A class of latent Markov models for capture-recapture data allowing for time, heterogeneity, and behavior effects

We propose an extension of the latent class model for the analysis of capture-recapture data which allows us to take into account the effect of a capture on the behavior of a subject with respect to future captures. The approach is based on the assumption that the variable indexing the latent class of a subject follows a Markov chain with transition probabilities depending on the previous capture history. Several constraints are allowed on these transition probabilities and on the parameters of the conditional distribution of the capture configuration given the latent process. We also allow for the presence of discrete explanatory variables, which may affect the parameters of the latent process. To estimate the resulting models, we rely on the conditional maximum likelihood approach and for this aim we outline an EM algorithm. We also give some simple rules for point and interval estimation of the population size. The approach is illustrated by applying it to two data sets concerning small mammal populations.     

Latent multinomial models for extended batch-mark data

Batch marking is common and useful for many capture–recapture studies where individual marks cannot be applied due to various constraints such as timing, cost, or marking difficulty. When batch marks are used, observed data are not individual capture histories but a set of counts including the numbers of individuals first marked, marked individuals that are recaptured, and individuals captured but released without being marked (applicable to some studies) on each capture occasion. Fitting traditional capture–recapture models to such data requires one to identify all possible sets of capture–recapture histories that may lead to the observed data, which is computationally infeasible even for a small number of capture occasions. In this paper, we propose a latent multinomial model to deal with such data, where the observed vector of counts is a non-invertible linear transformation of a latent vector that follows a multinomial distribution depending on model parameters. The latent multinomial model can be fitted efficiently through a saddlepoint approximation based maximum likelihood approach. The model framework is very flexible and can be applied to data collected with different study designs. Simulation studies indicate that reliable estimation results are obtained for all parameters of the proposed model. We apply the model to analysis of golden mantella data collected using batch marks in Central Madagascar.