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.     

The one‐inflated positive Poisson mixture model for use in population size estimation

The one‐inflated positive Poisson mixture model (OIPPMM) is presented, for use as the truncated count model in Horvitz–Thompson estimation of an unknown population size. The OIPPMM offers a way to address two important features of some capture–recapture data: one‐inflation and unobserved heterogeneity. The OIPPMM provides markedly different results than some other popular estimators, and these other estimators can appear to be quite biased, or utterly fail due to the boundary problem, when the OIPPMM is the true data‐generating process. In addition, the OIPPMM provides a solution to the boundary problem, by labelling any mixture components on the boundary instead as one‐inflation.     

Semiparametric frailty models for zero‐inflated event count data in the presence of informative dropout

Recurrent events data are commonly encountered in medical studies. In many applications, only the number of events during the follow‐up period rather than the recurrent event times is available. Two important challenges arise in such studies: (a) a substantial portion of subjects may not experience the event, and (b) we may not observe the event count for the entire study period due to informative dropout. To address the first challenge, we assume that underlying population consists of two subpopulations: a subpopulation nonsusceptible to the event of interest and a subpopulation susceptible to the event of interest. In the susceptible subpopulation, the event count is assumed to follow a Poisson distribution given the follow‐up time and the subject‐specific characteristics. We then introduce a frailty to account for informative dropout. The proposed semiparametric frailty models consist of three submodels: (a) a logistic regression model for the probability such that a subject belongs to the nonsusceptible subpopulation; (b) a nonhomogeneous Poisson process model with an unspecified baseline rate function; and (c) a Cox model for the informative dropout time. We develop likelihood‐based estimation and inference procedures. The maximum likelihood estimators are shown to be consistent. Additionally, the proposed estimators of the finite‐dimensional parameters are asymptotically normal and the covariance matrix attains the semiparametric efficiency bound. Simulation studies demonstrate that the proposed methodologies perform well in practical situations. We apply the proposed methods to a clinical trial on patients with myelodysplastic syndromes.     

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.     

A local evaluation of the individual state‐space to scale up Bayesian spatial capture–recapture

Spatial capture–recapture models (SCR) are used to estimate animal density and to investigate a range of problems in spatial ecology that cannot be addressed with traditional nonspatial methods. Bayesian approaches in particular offer tremendous flexibility for SCR modeling. Increasingly, SCR data are being collected over very large spatial extents making analysis computational intensive, sometimes prohibitively so. To mitigate the computational burden of large‐scale SCR models, we developed an improved formulation of the Bayesian SCR model that uses local evaluation of the individual state‐space (LESS). Based on prior knowledge about a species’ home range size, we created square evaluation windows that restrict the spatial domain in which an individual's detection probability (detector window) and activity center location (AC window) are estimated. We used simulations and empirical data analyses to assess the performance and bias of SCR with LESS. LESS produced unbiased estimates of SCR parameters when the AC window width was ≥5σ (σ: the scale parameter of the half‐normal detection function), and when the detector window extended beyond the edge of the AC window by 2σ. Importantly, LESS considerably decreased the computation time needed for fitting SCR models. In our simulations, LESS increased the computation speed of SCR models up to 57‐fold. We demonstrate the power of this new approach by mapping the density of an elusive large carnivore—the wolverine (Gulo gulo)—with an unprecedented resolution and across the species’ entire range in Norway (> 200,000 km²). Our approach helps overcome a major computational obstacle to population and landscape‐level SCR analyses. The LESS implementation in a Bayesian framework makes the customization and fitting of SCR accessible for practitioners working at scales that are relevant for conservation and management.     

Photo‐identification as a simple tool for studying invasive lionfish Pterois volitans populations

Photo‐tagging, i.e. using a specific software to match colour patterns on photographs, was tested as a means to identify individual Indo‐Pacific Pterois volitans to assist with population and movement studies of this invasive species. The stripe pattern on the flank of adult P. volitans (n = 48) was the most individually distinctive of three body regions tested, leading to correct individual identification on 68 and 82% of tests with a single and two images of the reference individual, respectively. Photo‐tagging is inexpensive, logistically simple and can involve citizen scientists, making it a viable alternative to traditional tagging to provide information on P. volitans distribution, movement patterns and recolonization rates after removals.     

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.     

Unified maximum likelihood estimates for closed capture-recapture models using mixtures

Agresti (1994, Biometrics 50, 494-500) and Norris and Pollock (1996a, Biometrics 52, 639-649) suggested using methods of finite mixtures to partition the animals in a closed capture-recapture experiment into two or more groups with relatively homogeneous capture probabilities. This enabled them to fit the models Mh, Mbh (Norris and Pollock), and Mth (Agresti) of Otis et al. (1978, Wildlife Monographs 62, 1-135). In this article, finite mixture partitions of animals and/or samples are used to give a unified linear-logistic framework for fitting all eight models of Otis et al. by maximum likelihood. Likelihood ratio tests are available for model comparisons. For many data sets, a simple dichotomy of animals is enough to substantially correct for heterogeneity-induced bias in the estimation of population size, although there is the option of fitting more than two groups if the data warrant it.     

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 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.     

Comparison of photo‐matching algorithms commonly used for photographic capture–recapture studies

Photographic capture–recapture is a valuable tool for obtaining demographic information on wildlife populations due to its noninvasive nature and cost‐effectiveness. Recently, several computer‐aided photo‐matching algorithms have been developed to more efficiently match images of unique individuals in databases with thousands of images. However, the identification accuracy of these algorithms can severely bias estimates of vital rates and population size. Therefore, it is important to understand the performance and limitations of state‐of‐the‐art photo‐matching algorithms prior to implementation in capture–recapture studies involving possibly thousands of images. Here, we compared the performance of four photo‐matching algorithms; Wild‐ID, I3S Pattern+, APHIS, and AmphIdent using multiple amphibian databases of varying image quality. We measured the performance of each algorithm and evaluated the performance in relation to database size and the number of matching images in the database. We found that algorithm performance differed greatly by algorithm and image database, with recognition rates ranging from 100% to 22.6% when limiting the review to the 10 highest ranking images. We found that recognition rate degraded marginally with increased database size and could be improved considerably with a higher number of matching images in the database. In our study, the pixel‐based algorithm of AmphIdent exhibited superior recognition rates compared to the other approaches. We recommend carefully evaluating algorithm performance prior to using it to match a complete database. By choosing a suitable matching algorithm, databases of sizes that are unfeasible to match “by eye” can be easily translated to accurate individual capture histories necessary for robust demographic estimates.     

Known unknowns in an imperfect world: incorporating uncertainty in recruitment estimates using multi‐event capture–recapture models

Studying the demography of wild animals remains challenging as several of the critical parts of their life history may be difficult to observe in the field. In particular, determining with certainty when an individual breeds for the first time is not always obvious. This can be problematic because uncertainty about the transition from a prebreeder to a breeder state – recruitment – leads to uncertainty in vital rate estimates and in turn in population projection models. To avoid this issue, the common practice is to discard imperfect data from the analyses. However, this practice can generate a bias in vital rate estimates if uncertainty is related to a specific component of the population and reduces the sample size of the dataset and consequently the statistical power to detect effects of biological interest. Here, we compared the demographic parameters assessed from a standard multistate capture–recapture approach to the estimates obtained from the newly developed multi‐event framework that specifically accounts for uncertainty in state assessment. Using a comprehensive longitudinal dataset on southern elephant seals, we demonstrated that the multi‐event model enabled us to use all the data collected (6639 capture–recapture histories vs. 4179 with the multistate model) by accounting for uncertainty in breeding states, thereby increasing the precision and accuracy of the demographic parameter estimates. The multi‐event model allowed us to incorporate imperfect data into demographic analyses. The gain in precision obtained has important implications in the conservation and management of species because limiting uncertainty around vital rates will permit predicting population viability with greater accuracy.     

A comparison of likelihood ratio tests and Rao's score test for three separable covariance matrix structures

The problem of testing the separability of a covariance matrix against an unstructured variance‐covariance matrix is studied in the context of multivariate repeated measures data using Rao's score test (RST). The RST statistic is developed with the first component of the separable structure as a first‐order autoregressive (AR(1)) correlation matrix or an unstructured (UN) covariance matrix under the assumption of multivariate normality. It is shown that the distribution of the RST statistic under the null hypothesis of any separability does not depend on the true values of the mean or the unstructured components of the separable structure. A significant advantage of the RST is that it can be performed for small samples, even smaller than the dimension of the data, where the likelihood ratio test (LRT) cannot be used, and it outperforms the standard LRT in a number of contexts. Monte Carlo simulations are then used to study the comparative behavior of the null distribution of the RST statistic, as well as that of the LRT statistic, in terms of sample size considerations, and for the estimation of the empirical percentiles. Our findings are compared with existing results where the first component of the separable structure is a compound symmetry (CS) correlation matrix. It is also shown by simulations that the empirical null distribution of the RST statistic converges faster than the empirical null distribution of the LRT statistic to the limiting χ² distribution. The tests are implemented on a real dataset from medical studies.