Estimating abundance using mark-resight when sampling is with replacement or the number of marked individuals is unknown

Summary .  Although mark–resight methods can often be a less expensive and less invasive means for estimating abundance in long-term population monitoring programs, two major limitations of the estimators are that they typically require sampling without replacement and/or the number of marked individuals available for resighting to be known exactly. These requirements can often be difficult to achieve. Here we address these limitations by introducing the Poisson log and zero-truncated Poisson log-normal mixed effects models (PNE and ZPNE, respectively). The generalized framework of the models allow the efficient use of covariates in modeling resighting rate and individual heterogeneity parameters, information-theoretic model selection and multimodel inference, and the incorporation of individually unidentified marks. Both models may be implemented using standard statistical computing software, but they have also been added to the mark–recapture freeware package Program MARK . We demonstrate the use and advantages of (Z)PNE using black-tailed prairie dog data recently collected in Colorado. We also investigate the expected relative performance of the models in simulation experiments. Compared to other available estimators, we generally found (Z)PNE to be more precise with little or no loss in confidence interval coverage. With the recent introduction of the logit-normal mixed effects model and (Z)PNE, a more flexible and efficient framework for mark–resight abundance estimation is now available for the sampling conditions most commonly encountered in these studies.     

Population Estimation Techniques for Lekking Species

Abstract: With the decline of many lekking species, the need to develop a rigorous population estimation technique is critical for successful conservation and management. We employed mark—resight methods to estimate population size for 2 lekking species: greater sage-grouse (Centrocercus urophasianus) and Gunnison sage-grouse (Centrocercus minimus). We evaluated 2 different estimators: Bowden's estimator and the mixed logit-normal mark—resight model. We captured and marked 75 greater sage-grouse. We counted marked and unmarked birds as they attended 15 known leks. We used 36 and 37 marked Gunnison sage-grouse to estimate population size in 2003 and 2004, respectively. We observed marked and unmarked Gunnison sage-grouse daily as they attended 6 leks in 2003 and 3 leks in 2004. Based on our examination of the assumptions of each mark—resight estimator, relative to behavior and biology of these species, we concluded the mixed logit-normal mark—resight model is preferred. We recommend wildlife managers employ mark—resight approaches when statistically rigorous population estimates are required for management and conservation of lekking species.     

One‐inflation and unobserved heterogeneity in population size estimation

We present the one‐inflated zero‐truncated negative binomial (OIZTNB) model, and propose its use as the truncated count distribution in Horvitz–Thompson estimation of an unknown population size. In the presence of unobserved heterogeneity, the zero‐truncated negative binomial (ZTNB) model is a natural choice over the positive Poisson (PP) model; however, when one‐inflation is present the ZTNB model either suffers from a boundary problem, or provides extremely biased population size estimates. Monte Carlo evidence suggests that in the presence of one‐inflation, the Horvitz–Thompson estimator under the ZTNB model can converge in probability to infinity. The OIZTNB model gives markedly different population size estimates compared to some existing truncated count distributions, when applied to several capture–recapture data that exhibit both one‐inflation and unobserved heterogeneity.     

Field‐readable alphanumeric flags are valuable markers for shorebirds: use of double‐marking to identify cases of misidentification

Implicit assumptions for most mark‐recapture studies are that individuals do not lose their markers and all observed markers are correctly recorded. If these assumptions are violated, e.g., due to loss or extreme wear of markers, estimates of population size and vital rates will be biased. Double‐marking experiments have been widely used to estimate rates of marker loss and adjust for associated bias, and we extended this approach to estimate rates of recording errors. We double‐marked 309 Piping Plovers (Charadrius melodus) with unique combinations of color bands and alphanumeric flags and used multi‐state mark recapture models to estimate the frequency with which plovers were misidentified. Observers were twice as likely to read and report an invalid color‐band combination (2.4% of the time) as an invalid alphanumeric code (1.0%). Observers failed to read matching band combinations or alphanumeric flag codes 4.5% of the time. Unlike previous band resighting studies, use of two resightable markers allowed us to identify when resighting errors resulted in reports of combinations or codes that were valid, but still incorrect; our results suggest this may be a largely unappreciated problem in mark‐resight studies. Field‐readable alphanumeric flags offer a promising auxiliary marker for identifying and potentially adjusting for false‐positive resighting errors that may otherwise bias demographic estimates.     

Toward reliable population density estimates of partially marked populations using spatially explicit mark–resight methods

相似文献   

Zero‐inflated Poisson factor model with application to microbiome read counts

Dimension reduction of high‐dimensional microbiome data facilitates subsequent analysis such as regression and clustering. Most existing reduction methods cannot fully accommodate the special features of the data such as count‐valued and excessive zero reads. We propose a zero‐inflated Poisson factor analysis model in this paper. The model assumes that microbiome read counts follow zero‐inflated Poisson distributions with library size as offset and Poisson rates negatively related to the inflated zero occurrences. The latent parameters of the model form a low‐rank matrix consisting of interpretable loadings and low‐dimensional scores that can be used for further analyses. We develop an efficient and robust expectation‐maximization algorithm for parameter estimation. We demonstrate the efficacy of the proposed method using comprehensive simulation studies. The application to the Oral Infections, Glucose Intolerance, and Insulin Resistance Study provides valuable insights into the relation between subgingival microbiome and periodontal disease.     

Assessment of costs of reproduction in a pelagic seabird using multistate mark-recapture models

We used a long‐term population band‐resight survey database, a parallel reproduction database, and multistate mark–recapture analysis to assess the costs of reproduction, a keystone concept of life‐history evolution, in Nazca boobies (Sula granti) from Punta Cevallos, Isla Española, Galápagos, Ecuador. We used eight years of resight and breeding data to compare models that included sex‐ and state‐specific survival probabilities and probabilities of transition between reproductive states using multistate mark–recapture models. Models that included state‐specific effects were compared with models lacking such effects to evaluate costs of reproduction. The top model, optimizing the trade‐off of model simplicity and fit to the data using the Akaike Information Criterion (AIC), showed evidence of a temporally varying survival cost of reproduction: nonbreeders showed higher annual survival than breeders did in some years. Because increasing investment among breeders showed no negative association with survival and subsequent breeding success, this evidence indicates a cost to both males and females of initiating, but not of continuing, a reproductive attempt. In some cases, breeders reaching the highest reproductive state (fledging an offspring) showed higher survival or subsequent breeding success than did failed breeders, consistent with differences in overall quality that promote both survival and reproduction. Although a male‐biased adult sex ratio was observed in this population of Nazca boobies, models of state‐ and sex‐specific survival and transition probabilities were not supported, indicating that males and females do not incur different costs of reproduction, and that the observed sex ratio bias is not due to sex‐specific adult mortality.     

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.     

Zero‐Inflated Negative Binomial Mixed Regression Modeling of Over‐Dispersed Count Data with Extra Zeros

In many biometrical applications, the count data encountered often contain extra zeros relative to the Poisson distribution. Zero‐inflated Poisson regression models are useful for analyzing such data, but parameter estimates may be seriously biased if the nonzero observations are over‐dispersed and simultaneously correlated due to the sampling design or the data collection procedure. In this paper, a zero‐inflated negative binomial mixed regression model is presented to analyze a set of pancreas disorder length of stay (LOS) data that comprised mainly same‐day separations. Random effects are introduced to account for inter‐hospital variations and the dependency of clustered LOS observations. Parameter estimation is achieved by maximizing an appropriate log‐likelihood function using an EM algorithm. Alternative modeling strategies, namely the finite mixture of Poisson distributions and the non‐parametric maximum likelihood approach, are also considered. The determination of pertinent covariates would assist hospital administrators and clinicians to manage LOS and expenditures efficiently.     

Density estimation in a wolverine population using spatial capture–recapture models

Classical closed-population capture–recapture models do not accommodate the spatial information inherent in encounter history data obtained from camera-trapping studies. As a result, individual heterogeneity in encounter probability is induced, and it is not possible to estimate density objectively because trap arrays do not have a well-defined sample area. We applied newly-developed, capture–recapture models that accommodate the spatial attribute inherent in capture–recapture data to a population of wolverines (Gulo gulo) in Southeast Alaska in 2008. We used camera-trapping data collected from 37 cameras in a 2,140-km² area of forested and open habitats largely enclosed by ocean and glacial icefields. We detected 21 unique individuals 115 times. Wolverines exhibited a strong positive trap response, with an increased tendency to revisit previously visited traps. Under the trap-response model, we estimated wolverine density at 9.7 individuals/1,000 km² (95% Bayesian CI: 5.9–15.0). Our model provides a formal statistical framework for estimating density from wolverine camera-trapping studies that accounts for a behavioral response due to baited traps. Further, our model-based estimator does not have strict requirements about the spatial configuration of traps or length of trapping sessions, providing considerable operational flexibility in the development of field studies. © 2011 The Wildlife Society.     

Capture–recapture models with heterogeneity to study survival senescence in the wild

Detecting senescence in wild populations and estimating its strength raise three challenges. First, in the presence of individual heterogeneity in survival probability, the proportion of high‐survival individuals increases with age. This increase can mask a senescence‐related decrease in survival probability when the probability is estimated at the population level. To accommodate individual heterogeneity we use a mixture model structure (discrete classes of individuals). Second, the study individuals can elude the observers in the field, and their detection rate can be heterogeneous. To account for detectability issues we use capture–mark–recapture (CMR) methodology, mixture models and data that provide information on individuals’ detectability. Last, emigration to non‐monitored sites can bias survival estimates, because it can occur at the end of the individuals’ histories and mimic earlier death. To model emigration we use Markovian transitions to and from an unobservable state. These different model structures are merged together using hidden Markov chain CMR models, or multievent models. Simulation studies illustrate that reliable evidence for survival senescence can be obtained using highly heterogeneous data from non site‐faithful individuals. We then design a tailored application for a dataset from a colony of black‐headed gull Chroicocephalus ridibundus. Survival probabilities do not appear individually variable, but evidence for survival senescence becomes significant only when accounting for other sources of heterogeneity. This result suggests that not accounting for heterogeneity leads to flawed inference and/or that emigration heterogeneity mimics survival heterogeneity and biases senescence estimates.     

Generalized spatial mark–resight models with incomplete identification: An application to red fox density estimates

相似文献   

Marginalized zero‐inflated Poisson models with missing covariates

Unlike zero‐inflated Poisson regression, marginalized zero‐inflated Poisson (MZIP) models for counts with excess zeros provide estimates with direct interpretations for the overall effects of covariates on the marginal mean. In the presence of missing covariates, MZIP and many other count data models are ordinarily fitted using complete case analysis methods due to lack of appropriate statistical methods and software. This article presents an estimation method for MZIP models with missing covariates. The method, which is applicable to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data on the caries preventive effects of a school‐based fluoride mouthrinse program.     

Rejection of Schmidt et al.'s estimators for bear population size

Aerial distance sampling of bears to estimate population size has been used throughout many parts of Alaska. The distance sampling models are complex since they need to account for undetected bears and differences in detection probabilities. This will require covariates and mark‐recapture data. The models proposed by Schmidt et al. do not use covariates or mark‐recapture data and are inappropriate for these surveys.     

Modeling heterogeneity for count data: A study of maternal mortality in health facilities in Mozambique

Count data are very common in health services research, and very commonly the basic Poisson regression model has to be extended in several ways to accommodate several sources of heterogeneity: (i) an excess number of zeros relative to a Poisson distribution, (ii) hierarchical structures, and correlated data, (iii) remaining “unexplained” sources of overdispersion. In this paper, we propose hierarchical zero‐inflated and overdispersed models with independent, correlated, and shared random effects for both components of the mixture model. We show that all different extensions of the Poisson model can be based on the concept of mixture models, and that they can be combined to account for all different sources of heterogeneity. Expressions for the first two moments are derived and discussed. The models are applied to data on maternal deaths and related risk factors within health facilities in Mozambique. The final model shows that the maternal mortality rate mainly depends on the geographical location of the health facility, the percentage of women admitted with HIV and the percentage of referrals from the health facility.     

Improving inference for aerial surveys of bears: The importance of assumptions and the cost of unnecessary complexity

Obtaining useful estimates of wildlife abundance or density requires thoughtful attention to potential sources of bias and precision, and it is widely understood that addressing incomplete detection is critical to appropriate inference. When the underlying assumptions of sampling approaches are violated, both increased bias and reduced precision of the population estimator may result. Bear (Ursus spp.) populations can be difficult to sample and are often monitored using mark‐recapture distance sampling (MRDS) methods, although obtaining adequate sample sizes can be cost prohibitive. With the goal of improving inference, we examined the underlying methodological assumptions and estimator efficiency of three datasets collected under an MRDS protocol designed specifically for bears. We analyzed these data using MRDS, conventional distance sampling (CDS), and open‐distance sampling approaches to evaluate the apparent bias‐precision tradeoff relative to the assumptions inherent under each approach. We also evaluated the incorporation of informative priors on detection parameters within a Bayesian context. We found that the CDS estimator had low apparent bias and was more efficient than the more complex MRDS estimator. When combined with informative priors on the detection process, precision was increased by >50% compared to the MRDS approach with little apparent bias. In addition, open‐distance sampling models revealed a serious violation of the assumption that all bears were available to be sampled. Inference is directly related to the underlying assumptions of the survey design and the analytical tools employed. We show that for aerial surveys of bears, avoidance of unnecessary model complexity, use of prior information, and the application of open population models can be used to greatly improve estimator performance and simplify field protocols. Although we focused on distance sampling‐based aerial surveys for bears, the general concepts we addressed apply to a variety of wildlife survey contexts.     

Estimating abundance of mountain lions from unstructured spatial sampling

Mountain lions (Puma concolor) are often difficult to monitor because of their low capture probabilities, extensive movements, and large territories. Methods for estimating the abundance of this species are needed to assess population status, determine harvest levels, evaluate the impacts of management actions on populations, and derive conservation and management strategies. Traditional mark–recapture methods do not explicitly account for differences in individual capture probabilities due to the spatial distribution of individuals in relation to survey effort (or trap locations). However, recent advances in the analysis of capture–recapture data have produced methods estimating abundance and density of animals from spatially explicit capture–recapture data that account for heterogeneity in capture probabilities due to the spatial organization of individuals and traps. We adapt recently developed spatial capture–recapture models to estimate density and abundance of mountain lions in western Montana. Volunteers and state agency personnel collected mountain lion DNA samples in portions of the Blackfoot drainage (7,908 km²) in west-central Montana using 2 methods: snow back-tracking mountain lion tracks to collect hair samples and biopsy darting treed mountain lions to obtain tissue samples. Overall, we recorded 72 individual capture events, including captures both with and without tissue sample collection and hair samples resulting in the identification of 50 individual mountain lions (30 females, 19 males, and 1 unknown sex individual). We estimated lion densities from 8 models containing effects of distance, sex, and survey effort on detection probability. Our population density estimates ranged from a minimum of 3.7 mountain lions/100 km² (95% CI 2.3–5.7) under the distance only model (including only an effect of distance on detection probability) to 6.7 (95% CI 3.1–11.0) under the full model (including effects of distance, sex, survey effort, and distance × sex on detection probability). These numbers translate to a total estimate of 293 mountain lions (95% CI 182–451) to 529 (95% CI 245–870) within the Blackfoot drainage. Results from the distance model are similar to previous estimates of 3.6 mountain lions/100 km² for the study area; however, results from all other models indicated greater numbers of mountain lions. Our results indicate that unstructured spatial sampling combined with spatial capture–recapture analysis can be an effective method for estimating large carnivore densities. Published 2012. This article is a U.S. Government work and is in the public domain in the USA.     

Analysis of Zero‐Inflated Poisson Data Incorporating Extent of Exposure

When analyzing Poisson count data sometimes a high frequency of extra zeros is observed. The Zero‐Inflated Poisson (ZIP) model is a popular approach to handle zero‐inflation. In this paper we generalize the ZIP model and its regression counterpart to accommodate the extent of individual exposure. Empirical evidence drawn from an occupational injury data set confirms that the incorporation of exposure information can exert a substantial impact on the model fit. Tests for zero‐inflation are also considered. Their finite sample properties are examined in a Monte Carlo study.     

A new multivariate zero‐adjusted Poisson model with applications to biomedicine

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log‐normal model (Aitchison and Ho, 1989) cannot be used to fit multivariate count data with excess zero‐vectors; (ii) The multivariate zero‐inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero‐truncated/deflated count data and it is difficult to apply to high‐dimensional cases; (iii) The Type I multivariate zero‐adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods.     

Are we overestimating recovery of sturgeon populations using mark/recapture surveys?

Mark‐recaptures studies are often conducted to monitor trends in sturgeon populations. However, many of these studies experience low recapture rates, minimal movement between marking‐recapture phases suggesting that sturgeon as a group are not conducive to mark‐recapture techniques. In this study, two mark‐recapture studies that were conducted differently were reviewed. A study was conducted on the Mattagami River using random nets set throughout the study area in both the mark and recapture phases. The other study was conducted on Lake of the Woods and marked sturgeon in tributaries during the spawning period and the recapture phase within the lake and river during the summer foraging period using random nets sets. Sturgeon's conduciveness to mark‐recapture studies was assessed on the Mattagami River mark‐recapture study by determining detection probability (p) using a hierarchical Bayesian model with data augmentation among three effects: individual effect, temporal effects, and behavioural response effects. Detection probability was constant over individuals and temporally suggesting model M₀ (Otis, Burnham, White, & Anderson, 1978 ) was suitable for lake sturgeon in the Mattagami River; only the M₀ would converge for the Lake of the Woods study. For this study, the assumption that “all individuals have the same probability of being captured during the marking phase” was believed to have been violated given approximately 16%–20% of adult Lake Sturgeon from a population spawn within a year. A population estimate accounting for p provided estimates 56% lower than calculated by a Chapman modification of the Peterson estimate for a closed population. Bias was believed to have been introduced as the Lake of the Woods population did not account for the non‐spawning adults that were encountered during the recapture phase and not vulnerable during the initial marking phase. This was not unique to the Lake of the Woods study as other sturgeon studies, especially multi‐year, assumes a closed population which potentially biased estimates and overestimated their recovery.