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.     

Use of hidden Markov capture–recapture models to estimate abundance in the presence of uncertainty: Application to the estimation of prevalence of hybrids in animal populations

Estimating the relative abundance (prevalence) of different population segments is a key step in addressing fundamental research questions in ecology, evolution, and conservation. The raw percentage of individuals in the sample (naive prevalence) is generally used for this purpose, but it is likely to be subject to two main sources of bias. First, the detectability of individuals is ignored; second, classification errors may occur due to some inherent limits of the diagnostic methods. We developed a hidden Markov (also known as multievent) capture–recapture model to estimate prevalence in free‐ranging populations accounting for imperfect detectability and uncertainty in individual's classification. We carried out a simulation study to compare naive and model‐based estimates of prevalence and assess the performance of our model under different sampling scenarios. We then illustrate our method with a real‐world case study of estimating the prevalence of wolf (Canis lupus) and dog (Canis lupus familiaris) hybrids in a wolf population in northern Italy. We showed that the prevalence of hybrids could be estimated while accounting for both detectability and classification uncertainty. Model‐based prevalence consistently had better performance than naive prevalence in the presence of differential detectability and assignment probability and was unbiased for sampling scenarios with high detectability. We also showed that ignoring detectability and uncertainty in the wolf case study would lead to underestimating the prevalence of hybrids. Our results underline the importance of a model‐based approach to obtain unbiased estimates of prevalence of different population segments. Our model can be adapted to any taxa, and it can be used to estimate absolute abundance and prevalence in a variety of cases involving imperfect detection and uncertainty in classification of individuals (e.g., sex ratio, proportion of breeders, and prevalence of infected individuals).     

Structural inference in transition measurement error models for longitudinal data

We propose a new class of models, transition measurement error models, to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error. We show that the response variable conditional on the error-prone covariate follows a complex transition mixed effects model. The naive model obtained by ignoring the measurement error correctly specifies the transition part of the model, but misspecifies the covariate effect structure and ignores the random effects. We next study the asymptotic bias in naive estimator obtained by ignoring the measurement error for both continuous and discrete outcomes. We show that the naive estimator of the regression coefficient of the error-prone covariate is attenuated, while the naive estimators of the regression coefficients of the past responses are generally inflated. We then develop a structural modeling approach for parameter estimation using the maximum likelihood estimation method. In view of the multidimensional integration required by full maximum likelihood estimation, an EM algorithm is developed to calculate maximum likelihood estimators, in which Monte Carlo simulations are used to evaluate the conditional expectations in the E-step. We evaluate the performance of the proposed method through a simulation study and apply it to a longitudinal social support study for elderly women with heart disease. An additional simulation study shows that the Bayesian information criterion (BIC) performs well in choosing the correct transition orders of the models.     

Accounting for imperfect detection of groups and individuals when estimating abundance

If animals are independently detected during surveys, many methods exist for estimating animal abundance despite detection probabilities <1. Common estimators include double‐observer models, distance sampling models and combined double‐observer and distance sampling models (known as mark‐recapture‐distance‐sampling models; MRDS). When animals reside in groups, however, the assumption of independent detection is violated. In this case, the standard approach is to account for imperfect detection of groups, while assuming that individuals within groups are detected perfectly. However, this assumption is often unsupported. We introduce an abundance estimator for grouped animals when detection of groups is imperfect and group size may be under‐counted, but not over‐counted. The estimator combines an MRDS model with an N‐mixture model to account for imperfect detection of individuals. The new MRDS‐Nmix model requires the same data as an MRDS model (independent detection histories, an estimate of distance to transect, and an estimate of group size), plus a second estimate of group size provided by the second observer. We extend the model to situations in which detection of individuals within groups declines with distance. We simulated 12 data sets and used Bayesian methods to compare the performance of the new MRDS‐Nmix model to an MRDS model. Abundance estimates generated by the MRDS‐Nmix model exhibited minimal bias and nominal coverage levels. In contrast, MRDS abundance estimates were biased low and exhibited poor coverage. Many species of conservation interest reside in groups and could benefit from an estimator that better accounts for imperfect detection. Furthermore, the ability to relax the assumption of perfect detection of individuals within detected groups may allow surveyors to re‐allocate resources toward detection of new groups instead of extensive surveys of known groups. We believe the proposed estimator is feasible because the only additional field data required are a second estimate of group size.     

Disease‐structured N‐mixture models: A practical guide to model disease dynamics using count data

Obtaining inferences on disease dynamics (e.g., host population size, pathogen prevalence, transmission rate, host survival probability) typically requires marking and tracking individuals over time. While multistate mark–recapture models can produce high‐quality inference, these techniques are difficult to employ at large spatial and long temporal scales or in small remnant host populations decimated by virulent pathogens, where low recapture rates may preclude the use of mark–recapture techniques. Recently developed N‐mixture models offer a statistical framework for estimating wildlife disease dynamics from count data. N‐mixture models are a type of state‐space model in which observation error is attributed to failing to detect some individuals when they are present (i.e., false negatives). The analysis approach uses repeated surveys of sites over a period of population closure to estimate detection probability. We review the challenges of modeling disease dynamics and describe how N‐mixture models can be used to estimate common metrics, including pathogen prevalence, transmission, and recovery rates while accounting for imperfect host and pathogen detection. We also offer a perspective on future research directions at the intersection of quantitative and disease ecology, including the estimation of false positives in pathogen presence, spatially explicit disease‐structured N‐mixture models, and the integration of other data types with count data to inform disease dynamics. Managers rely on accurate and precise estimates of disease dynamics to develop strategies to mitigate pathogen impacts on host populations. At a time when pathogens pose one of the greatest threats to biodiversity, statistical methods that lead to robust inferences on host populations are critically needed for rapid, rather than incremental, assessments of the impacts of emerging infectious diseases.     

Joint generalized models for multidimensional outcomes: A case study of neuroscience data from multimodalities

This paper is motivated from the analysis of neuroscience data in a study of neural and muscular mechanisms of muscle fatigue. Multidimensional outcomes of different natures were obtained simultaneously from multiple modalities, including handgrip force, electromyography (EMG), and functional magnetic resonance imaging (fMRI). We first study individual modeling of the univariate response depending on its nature. A mixed‐effects beta model and a mixed‐effects simplex model are compared for modeling the force/EMG percentages. A mixed‐effects negative‐binomial model is proposed for modeling the fMRI counts. Then, I present a joint modeling approach to model the multidimensional outcomes together, which allows us to not only estimate the covariate effects but also to evaluate the strength of association among the multiple responses from different modalities. A simulation study is conducted to quantify the possible benefits by the new approaches in finite sample situations. Finally, the analysis of the fatigue data is illustrated with the use of the proposed methods.     

A transformation‐based approach to Gaussian mixture density estimation for bounded data

Finite mixture of Gaussian distributions provide a flexible semiparametric methodology for density estimation when the continuous variables under investigation have no boundaries. However, in practical applications, variables may be partially bounded (e.g., taking nonnegative values) or completely bounded (e.g., taking values in the unit interval). In this case, the standard Gaussian finite mixture model assigns nonzero densities to any possible values, even to those outside the ranges where the variables are defined, hence resulting in potentially severe bias. In this paper, we propose a transformation‐based approach for Gaussian mixture modeling in case of bounded variables. The basic idea is to carry out density estimation not on the original data but on appropriately transformed data. Then, the density for the original data can be obtained by a change of variables. Both the transformation parameters and the parameters of the Gaussian mixture are jointly estimated by the expectation‐maximization (EM) algorithm. The methodology for partially and completely bounded data is illustrated using both simulated data and real data applications.     

Integrating sign surveys and telemetry data for estimating brown bear (Ursus arctos) density in the Romanian Carpathians

Accurate population size estimates are important information for sustainable wildlife management. The Romanian Carpathians harbor the largest brown bear (Ursus arctos) population in Europe, yet current management relies on estimates of density that lack statistical oversight and ignore uncertainty deriving from track surveys. In this study, we investigate an alternative approach to estimate brown bear density using sign surveys along transects within a novel integration of occupancy models and home range methods. We performed repeated surveys along 2‐km segments of forest roads during three distinct seasons: spring 2011, fall‐winter 2011, and spring 2012, within three game management units and a Natura 2000 site. We estimated bears abundances along transects using the number of unique tracks observed per survey occasion via N‐mixture hierarchical models, which account for imperfect detection. To obtain brown bear densities, we combined these abundances with the effective sampling area of the transects, that is, estimated as a function of the median (± bootstrapped SE) of the core home range (5.58 ± 1.08 km²) based on telemetry data from 17 bears tracked for 1‐month periods overlapping our surveys windows. Our analyses yielded average brown bear densities (and 95% confidence intervals) for the three seasons of: 11.5 (7.8–15.3), 11.3 (7.4–15.2), and 12.4 (8.6–16.3) individuals/100 km². Across game management units, mean densities ranged between 7.5 and 14.8 individuals/100 km². Our method incorporates multiple sources of uncertainty (e.g., effective sampling area, imperfect detection) to estimate brown bear density, but the inference fundamentally relies on unmarked individuals only. While useful as a temporary approach to monitor brown bears, we urge implementing DNA capture–recapture methods regionally to inform brown bear management and recommend increasing resources for GPS collars to improve estimates of effective sampling area.     

FuzzyID2: A software package for large data set species identification via barcoding and metabarcoding using hidden Markov models and fuzzy set methods

Species identification through DNA barcoding or metabarcoding has become a key approach for biodiversity evaluation and ecological studies. However, the rapid accumulation of barcoding data has created some difficulties: for instance, global enquiries to a large reference library can take a very long time. We here devise a two‐step searching strategy to speed identification procedures of such queries. This firstly uses a Hidden Markov Model (HMM) algorithm to narrow the searching scope to genus level and then determines the corresponding species using minimum genetic distance. Moreover, using a fuzzy membership function, our approach also estimates the credibility of assignment results for each query. To perform this task, we developed a new software pipeline, FuzzyID2, using Python and C++. Performance of the new method was assessed using eight empirical data sets ranging from 70 to 234,535 barcodes. Five data sets (four animal, one plant) deployed the conventional barcode approach, one used metabarcodes, and two were eDNA‐based. The results showed mean accuracies of generic and species identification of 98.60% (with a minimum of 95.00% and a maximum of 100.00%) and 94.17% (with a range of 84.40%–100.00%), respectively. Tests with simulated NGS sequences based on realistic eDNA and metabarcode data demonstrated that FuzzyID2 achieved a significantly higher identification success rate than the commonly used Blast method, and the TIPP method tends to find many fewer species than either FuzztID2 or Blast. Furthermore, data sets with tens of thousands of barcodes need only a few seconds for each query assignment using FuzzyID2. Our approach provides an efficient and accurate species identification protocol for biodiversity‐related projects with large DNA sequence data sets.