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.     

Multiple sensitive estimation and optimal sample size allocation in the item sum technique

For surveys of sensitive issues in life sciences, statistical procedures can be used to reduce nonresponse and social desirability response bias. Both of these phenomena provoke nonsampling errors that are difficult to deal with and can seriously flaw the validity of the analyses. The item sum technique (IST) is a very recent indirect questioning method derived from the item count technique that seeks to procure more reliable responses on quantitative items than direct questioning while preserving respondents' anonymity. This article addresses two important questions concerning the IST: (i) its implementation when two or more sensitive variables are investigated and efficient estimates of their unknown population means are required; (ii) the determination of the optimal sample size to achieve minimum variance estimates. These aspects are of great relevance for survey practitioners engaged in sensitive research and, to the best of our knowledge, were not studied so far. In this article, theoretical results for multiple estimation and optimal allocation are obtained under a generic sampling design and then particularized to simple random sampling and stratified sampling designs. Theoretical considerations are integrated with a number of simulation studies based on data from two real surveys and conducted to ascertain the efficiency gain derived from optimal allocation in different situations. One of the surveys concerns cannabis consumption among university students. Our findings highlight some methodological advances that can be obtained in life sciences IST surveys when optimal allocation is achieved.     

Point and Interval Estimation of the Population Size Using a Zero‐Truncated Negative Binomial Regression Model

This paper presents the zero‐truncated negative binomial regression model to estimate the population size in the presence of a single registration file. The model is an alternative to the zero‐truncated Poisson regression model and it may be useful if the data are overdispersed due to unobserved heterogeneity. Horvitz–Thompson point and interval estimates for the population size are derived, and the performance of these estimators is evaluated in a simulation study. To illustrate the model, the size of the population of opiate users in the city of Rotterdam is estimated. In comparison to the Poisson model, the zero‐truncated negative binomial regression model fits these data better and yields a substantially higher population size estimate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A weighted partial likelihood approach for zero‐truncated models

Zero‐truncated data arises in various disciplines where counts are observed but the zero count category cannot be observed during sampling. Maximum likelihood estimation can be used to model these data; however, due to its nonstandard form it cannot be easily implemented using well‐known software packages, and additional programming is often required. Motivated by the Rao–Blackwell theorem, we develop a weighted partial likelihood approach to estimate model parameters for zero‐truncated binomial and Poisson data. The resulting estimating function is equivalent to a weighted score function for standard count data models, and allows for applying readily available software. We evaluate the efficiency for this new approach and show that it performs almost as well as maximum likelihood estimation. The weighted partial likelihood approach is then extended to regression modelling and variable selection. We examine the performance of the proposed methods through simulation and present two case studies using real data.     

Assessing population size and structure for Andean Condor Vultur gryphus in Bolivia using a photographic ‘capture‐recapture’ method

The Andean Condor Vultur gryphus is a globally threatened and declining species. Problems of surveying Andean Condor populations using traditional survey methods are particularly acute in Bolivia, largely because only few roosts are known there. However, similar to other vulture species, Andean Condors aggregate at animal carcasses, and are individually recognizable due to unique morphological characteristics (size and shape of male crests and pattern of wing coloration). This provided us with an opportunity to use a capture‐recapture (‘sighting‐resighting’) modelling framework to estimate the size and structure of an Andean Condor population in Bolivia using photographs of individuals taken at observer‐established feeding stations. Between July and December 2014, 28 feeding stations were established in five different zones throughout the eastern Andean region of Bolivia, where perched and flying Andean Condors were photographed. Between one and 57 (mean = 20.2 ± 14.6 sd) Andean Condors were recorded visiting each feeding station and we were able to identify 456 different individuals, comprising 134 adult males, 40 sub‐adult males, 79 juvenile males, 80 adult females, 30 sub‐adult females and 93 juvenile females. Open population capture‐recapture models produced population estimates ranging from 52 ± 14 (se) individuals to 678 ± 269 individuals across the five zones, giving a total of 1388 ± 413 sd individuals, which is roughly 20% of the estimated Andean Condor global population. Future trials of this method need to consider explicitly knowledge of Andean Condor movements and home‐ranges, habitat preferences when selecting suitable sites as feeding stations, juvenile movements and other behaviours. Sighting‐resighting methods have considerable potential to increase the accuracy of surveys of Andean Condors and other bird species with unique individual morphological characteristics.     

Climate‐driven vital rates do not always mean climate‐driven population

Current climatic changes have increased the need to forecast population responses to climate variability. A common approach to address this question is through models that project current population state using the functional relationship between demographic rates and climatic variables. We argue that this approach can lead to erroneous conclusions when interpopulation dispersal is not considered. We found that immigration can release the population from climate‐driven trajectories even when local vital rates are climate dependent. We illustrated this using individual‐based data on a trans‐equatorial migratory seabird, the Scopoli's shearwater Calonectris diomedea, in which the variation of vital rates has been associated with large‐scale climatic indices. We compared the population annual growth rate λ_i, estimated using local climate‐driven parameters with ρ_i, a population growth rate directly estimated from individual information and that accounts for immigration. While λ_i varied as a function of climatic variables, reflecting the climate‐dependent parameters, ρ_i did not, indicating that dispersal decouples the relationship between population growth and climate variables from that between climatic variables and vital rates. Our results suggest caution when assessing demographic effects of climatic variability especially in open populations for very mobile organisms such as fish, marine mammals, bats, or birds. When a population model cannot be validated or it is not detailed enough, ignoring immigration might lead to misleading climate‐driven projections.     

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.     

One‐inflation and unobserved heterogeneity in population size estimation by Ryan T. Godwin

In this study, we would like to show that the one‐inflated zero‐truncated negative binomial (OIZTNB) regression model can be easily implemented in R via built‐in functions when we use mean‐parameterization feature of negative binomial distribution to build OIZTNB regression model. From the practitioners' point of view, we believe that this approach presents a computationally convenient way for implementation of the OIZTNB regression model.     

Estimation of population size based on additive hazards models for continuous-time recapture experiments

We use the semiparametric additive hazards model to formulate the effects of individual covariates on the capture rates in the continuous-time capture-recapture experiment, and then construct a Horvitz-Thompson-type estimator for the unknown population size. The resulting estimator is consistent and asymptotically normal with an easily estimated variance. Simulation studies show that the asymptotic approximations are adequate for practical use when the average capture probabilities exceed .5. Ignoring covariates would underestimate the population size and the coverage probability is poor. A wildlife example is provided.     

Variations in age‐ and sex‐specific survival rates help explain population trend in a discrete marine mammal population

Understanding the drivers underlying fluctuations in the size of animal populations is central to ecology, conservation biology, and wildlife management. Reliable estimates of survival probabilities are key to population viability assessments, and patterns of variation in survival can help inferring the causal factors behind detected changes in population size. We investigated whether variation in age‐ and sex‐specific survival probabilities could help explain the increasing trend in population size detected in a small, discrete population of bottlenose dolphins Tursiops truncatus off the east coast of Scotland. To estimate annual survival probabilities, we applied capture–recapture models to photoidentification data collected from 1989 to 2015. We used robust design models accounting for temporary emigration to estimate juvenile and adult survival, multistate models to estimate sex‐specific survival, and age models to estimate calf survival. We found strong support for an increase in juvenile/adult annual survival from 93.1% to 96.0% over the study period, most likely caused by a change in juvenile survival. Examination of sex‐specific variation showed weaker support for this trend being a result of increasing female survival, which was overall higher than for males and animals of unknown sex. Calf survival was lower in the first than second year; a bias in estimating third‐year survival will likely exist in similar studies. There was some support first‐born calf survival being lower than for calves born subsequently. Coastal marine mammal populations are subject to the impacts of environmental change, increasing anthropogenic disturbance and the effects of management measures. Survival estimates are essential to improve our understanding of population dynamics and help predict how future pressures may impact populations, but obtaining robust information on the life history of long‐lived species is challenging. Our study illustrates how knowledge of survival can be increased by applying a robust analytical framework to photoidentification data.     

Blood and cloacal swab sampling for avian influenza monitoring has no effect on survival rates of free‐ranging ducks

Concerns about the spread of avian influenza viruses (AIVs) have led to cloacal swab sampling of hundreds of thousands of birds worldwide as part of AIV surveillance schemes, but the effects of cloacal swabbing have not been adequately evaluated. We tested for differences between swabbed, swabbed and bled, and non‐sampled wild ducks in terms of live re‐encounter and dead recoveries for Common Pochard Aythya ferina and Tufted Duck Aythya fuligula, and also determined re‐encounter and recovery rates for Mallard Anas platyrhynchos and Common Teal Anas crecca. No effects of sampling methods were detected, except in Teal. Re‐encounter rates were lower in sampled Teal than in controls, with annual re‐encounter probabilities being 25% and 35% lower in males and females, respectively. Teal possibly left or avoided sampling sites, or sought sites where they were less detectable after sampling. In general, no deleterious effects were found, suggesting that cloacal swabbing and blood sampling are suitable methods for conducting AIV surveillance in ducks.     

Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, “naturally occurring” zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton-Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F₂ intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.     

Experimental evidence of long‐term reproductive costs in a colonial nesting seabird

Trade‐offs between current and future reproduction are central to the evolution of life histories. Experiments that manipulate brood size provide an effective approach to investigating future costs of current reproduction. Most manipulative studies to date, however, have addressed only the short‐term effects of brood size manipulation. Our goal was to determine whether survival or breeding costs of reproduction in a long‐lived species manifest beyond the subsequent breeding season. To this end, we investigated long‐term survival and breeding effects of a multi‐year reproductive cost experiment conducted on black‐legged kittiwakes Rissa tridactyla, a long‐lived colonial nesting seabird. We used multi‐state capture–recapture modeling to assess hypotheses regarding the role of experimentally reduced breeding effort and other factors, including climate phase and colony size and productivity, on future survival and breeding probabilities during the 16‐yr period following the experiment. We found that forced nest failures had a positive effect on breeding probability over time, but had no effect on long‐term survival. This apparent canalization of survival suggests that adult survival is the most important parameter influencing fitness in this long‐lived species, and that adults should pay reproductive costs in ways that do not compromise this critical life history parameter. When declines in adult survival rate are observed, they may indicate populations of conservation concern.     

A spatially explicit capture–recapture estimator for single‐catch traps

Single‐catch traps are frequently used in live‐trapping studies of small mammals. Thus far, a likelihood for single‐catch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capture–recapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. We build on a recently developed continuous‐time model for SECR to derive a likelihood for single‐catch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height of the detection function. By contrast, the single‐catch estimators of density, distribution, and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constant over the survey region, then the multicatch estimator performs well with single‐catch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the single‐catch estimator when trap saturation is above about 60%. The estimator's performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a single‐catch likelihood with unknown capture times remains intractable for now, researchers using single‐catch traps should aim to incorporate timing devices with their traps.