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Few species are distributed uniformly in space, and populations of mobile organisms are rarely closed with respect to movement, yet many models of density rely upon these assumptions. We present a hierarchical model allowing inference about the density of unmarked populations subject to temporary emigration and imperfect detection. The model can be fit to data collected using a variety of standard survey methods such as repeated point counts in which removal sampling, double-observer sampling, or distance sampling is used during each count. Simulation studies demonstrated that parameter estimators are unbiased when temporary emigration is either \"completely random\" or is determined by the size and location of home ranges relative to survey points. We also applied the model to repeated removal sampling data collected on Chestnut-sided Warblers ( Dendroica pensylvancia ) in the White Mountain National Forest, USA. The density estimate from our model, 1.09 birds/ha, was similar to an estimate of 1.11 birds/ha produced by an intensive spot-mapping effort. Our model is also applicable when processes other than temporary emigration affect the probability of being available for detection, such as in studies using cue counts. Functions to implement the model have been added to the R package unmarked .

Occupancy models estimate distributions of imperfectly detected species, but violations of the closure assumption can bias results. However, researchers working with mobile animals may find it impossible to eliminate such violations. Here, we tested the hypothesis that occupancy models fit to realistic sampling data can generate unbiased occupancy estimates for an itinerant Wood Thrush (Hylocichla mustelina) population. In 2013 and 2014, we tracked movements of 41 breeding Wood Thrush males. We modelled territory shift probabilities using logistic exposure models and within‐territory movements using continuous‐time stochastic process models. We then constructed an individual‐based model, simulated (1000 iterations) spatiotemporal locations for individuals and simulated sampling these populations using 162 different point count protocols with variable spatial (sampling radius and point placement method), and temporal (survey length, between‐survey intervals and number of surveys) characteristics. We compared occupancy estimates with true values of instantaneous, daily and seasonal occupancy from the simulations. We parameterized continuous time stochastic process models based on movements within 34 unique territories and estimated a daily territory shift probability of 0.0099 (95% CI: 0.0060, 0.0152). Simulated data indicated that estimates of occupancy ranged from 0.18 (0.06, 1.00) to 0.80 (0.71, 0.89) depending on protocol characteristics. Occupancy estimates increased with increasing survey radius, survey length and between‐survey interval. Protocols using shorter surveys and between‐survey intervals were good estimators for instantaneous occupancy (low bias and mean‐squared error) but poor estimators for daily and seasonal occupancy; longer surveys and intervals generated unbiased estimators of daily occupancy but underestimated seasonal occupancy. Logistic regression models that ignored imperfect detection outperformed occupancy models for estimating instantaneous occupancy but not daily or seasonal occupancy. For mobile animals, occupancy of sampling sites changes in space and time. Consequently, the spatial and temporal aspects of a sampling protocol have strong, but predictable, effects on occupancy model parameter estimates. Our results demonstrate that how these factors interact is critical for designing surveys that produce occupancy estimates representative of the biological process of interest to a researcher.

Population catastrophes are widespread, unpredictable phenomena occurring in natural populations that have important, yet frequently underappreciated, consequences for persistence. As human impacts on ecosystems increase globally, the frequency of catastrophes is likely to rise as increasingly fragmented and depleted populations become more vulnerable. Species with slow life histories are expected to recover slowly from catastrophes because of their longer generation times, and assessing their population recovery requires data spanning long periods. We report results from a long‐term mark–recapture study of snapping turtles (Chelydra serpentina) in Algonquin Provincial Park, Ontario, that experienced a major mortality event from winter predation by river otters. We estimated abundance and survival of nesting females before, during, and 23 yr following the catastrophe. We built multistate mark–recapture models incorporating movement between sites, temporary emigration, and observation effects. We found that during the 3‐yr mortality event, abundance of nesting females declined by 39% overall, and by 49% at our focal nesting area. Apparent survivorship of nesting females during these three years fell from 0.94 before the mortality event to 0.76 at the focal site and 0.86 at adjacent nest sites. Survivorship over the following 23‐yr period averaged 0.972 and 0.940 at the two sampling areas. Despite high post‐catastrophe survivorship and connectivity with other populations, the population failed to recover, displaying consistently reduced abundances across 23 post‐catastrophe years. We discuss the relationship between life‐history attributes and the causes and consequences of local catastrophes and their conservation implications.

Wildlife population estimators often require formal adjustment for imperfect detection of individuals during surveys. Conventional distance sampling (CDS) and its extensions (mark-recapture distance sampling [MRDS], temporary emigration distance sampling [TEDS]) are popular approaches for producing unbiased estimators of wildlife abundance. However, despite extensive discussion and development of distance sampling theory in the literature, deciding which of these alternatives is most appropriate for a particular scenario can be confusing. Some of this confusion may stem from an incomplete understanding of how each approach addresses the components of the detection process. Here we describe the proper application of CDS, MRDS, and TEDS approaches and use applied examples to help clarify their differing assumptions with respect to the components of the detection process. To further aid the practitioner, we summarize the differences in a decision tree that can be used to identify cases where a more complex alternative (e.g., MRDS or TEDS) may be appropriate for a given survey application. Although the more complex approaches can account for additional sources of bias, in practical applications one also must consider estimator precision. Therefore, we also review the concept of total estimator error in the context of comparing competing methods for a given application to aid in the selection of the most appropriate distance sampling approach. Finally, we detail how the use of more advanced techniques (i.e., informed priors, open-population distance sampling models, and integrated modeling approaches) can further reduce total estimator error by leveraging information from existing and ongoing data collection. By synthesizing the existing literature on CDS, MRDS, TEDS and their extensions, in conjunction with the concepts of total estimator error and the components of the detection process, we provide a comprehensive guide that can be used by the practitioner to more efficiently, effectively, and appropriately apply distance sampling in a variety of settings. A menudo los estimadores poblacionales de fauna silvestre necesitan ser modificados formalmente para la detección imperfecta de individuos durante un muestreo. El método convencional de medidas de distancia (CDS por sus siglas in inglés) y sus extensiones (el método de medidas de distancia con marcarecaptura [MRDS] o con emigración temporal [TEDS]) son opciones populares para producir estimadores de abundancia de fauna silvestre sin sesgo. Sin embargo, a pesar de una discusión extensa y el desarrollo de la teoría y aplicación del método de medidas de distancia en la literatura, la decisión sobre cual opción es la más correcta para una situación en particular puede ser confusa. Algunas de estas confusiones surgen de un entendimiento incompleto de cómo cada opción define a los componentes del proceso de detección. Aquí describimos la aplicación correcta de CDS, MRDS y TEDS, y usamos ejemplos para clarificar sus diferentes supuestos en relación con los componentes del proceso de detección. Además, resumimos las diferencias de las 3 opciones en un árbol de decisión que se puede usar para identificar los casos que requieren de opciones más complicadas (p.ej., MRDS o TEDS). Aunque las opciones más complicadas pueden controlar las causas adicionales de sesgo, en las aplicaciones prácticas tenemos que considerar la precisión del estimador. Por consiguiente, examinamos el concepto de error total del estimador paracomparar las diferentes opciones usando una aplicación específica que ayude a seleccionar el método de medida de distancias más apropiado. Por último, brindamos detalles de cómo el uso de métodos más avanzados (i.e., distribuciones previas informadas, modelos de medidas de distancia para poblaciones abiertas, y opciones de modelado integrado) pueden reducir el error total del estimador aprovechando la información de los datos de un muestreo en curso. Ofrecemos una síntesis de la literatura existente sobre CDS, MRDS, TEDS y sus extensiones, conjuntamente con los conceptos de error total del estimador y los componentes del proceso de detección, y proveemos una guía exhaustiva para aplicar el método de medidas de distancia apropiadamente en una variedad de situaciones.

In the Southern Hemisphere, humpback whales ( Megaptera novaeangliae ) migrate along the extended continental coastlines of Australia, South America, and South Africa. This study reports on photo-identification capture–recapture data from a long-term survey conducted in Hervey Bay, Queensland, where a substantial proportion of the population stop over early in the southern migration. Photo-identification data were collected over 10 weeks per year from 1997 to 2009. The migration through Hervey Bay is dominated and led by females with high fidelity to the site. Mature females, yearlings, and immature whales use the Bay during August, while mature lactating females with calves dominate during September and October. Complex social behaviours occur throughout the season and differ between the early and late cohorts. We argue that the composition of the two cohorts and their distinctively different behaviours indicate that Hervey Bay is not simply a resting site but an area of aggregation that serves important social and biological benefits. A multistate open robust design model was fitted to capture–recapture data to estimate the annual number of whales visiting the Bay, the permanent emigration rate, proportions of the visiting population that do not enter the Bay each year, the number present during each week, and their residency times. The number of annual visitors to the Bay increased approximately linearly from 857 in 1997 to 2175 at the end of sampling in 2009 with two-thirds migrating through during the first half of each season. The population rate of growth may have been slowing by 2009, but there was considerable uncertainty in the trajectory and little basis for projection into the future. While it is desirable to know the current status of the Hervey Bay population and what has occurred since 2009, the cost and effort required make further manual collection and matching of images unlikely. The development of AI algorithmic matching software may enable further research in future.

Accurate estimates of population abundance are essential to both theoretical and applied ecology. Rarely are all individuals detected during a survey and abundance models often incorporate some form of imperfect detection. Detection probability, however, consists of three components: probability of presence during a survey, probability of availability given presence, and probability of detection given availability and presence. We develop an integrated model to separate these three detection components and provide abundance estimates for the available, present, and superpopulation of individuals. Our framework integrates several common survey methods for unmarked populations: spatially and temporally replicated counts, distance sampling data, and time‐of‐detection data. Simulations indicated relatively unbiased estimates for detection and availability probabilities. Negative bias in estimated superpopulation abundance was present with three temporally replicated surveys, but greatly reduced with six surveys. In a case study of Island Scrub‐Jays (Aphelocoma insularis), posterior modes for presence, availability, and detection probabilities were 0.78, 0.96, and 0.26, respectively, from 10‐min point counts repeated at 97 sites on three occasions, with noticeable differences among available, present, and superpopulation abundance estimates. This generalizable framework integrates common sampling protocols and provides joint inferences on the components of detection probability, spatial and non‐spatial temporary emigration, and abundance in unmarked populations.

1. Model-based distance sampling is commonly used to understand spatial variation in the density of wildlife species. The standard approach assumes that individuals are distributed uniformly and models spatial variation in density using plot-level effects. Thinned point process (TPP) models for surveys of unmarked populations (spatial distance sampling) better leverage the spatial information underlying individual encounters, and in the presence of within-plot variation in density, may explain a larger proportion of the spatial variation in density. However, existing spatial distance sampling approaches are conditioned on the assumption that all individuals are present and available for sampling. Temporary emigration of individuals can therefore result in biased estimates of abundance. 2. We extended spatial distance sampling models to accommodate temporary emigration (TPP model). Using simulations of a thinned inhomogeneous point process, we assessed the performance of the TPP model relative to the temporary emigration distance sampling (TEDS) model, which implies a uniform distribution of individuals. In addition, we compared inferences between TPP and TEDS models using data for two passerine species in Alaska. 3. Parameter estimates from the TPP model exhibited improved coverage probability and precision relative to the TEDS model including a 26% reduction in the coefficient of variation (CV) of the population size estimate. 4. In the applied example, the TEDS model indicated weak relationships between abundance and habitat covariates, whereas the TPP model indicated strong relationships for those same effects, suggesting that spatial distance sampling models can provide considerably stronger inference in the presence of within-plot variation in density. In addition, the CV of the population size estimates for the two passerine species were 32% and 4% smaller under the TPP model. 5. Synthesis and applications. We expect our extension accommodating temporary emigration will be a critical specification for spatial distance sampling models, particularly for studies assessing changes in the distribution and abundance of highly mobile species including passerines.

Spatial segregation of animals by class (i.e., maturity or sex) within a population due to differential rates of temporary emigration (TE) from study sites can be an important life history feature to consider in population assessment and management. However, such rates are poorly known; new quantitative approaches to address these knowledge gaps are needed. We present a novel application of multi-event models that takes advantage of two sources of detections to differentiate temporary emigration from apparent absence to quantify class segregation within a study population of double-marked (photo-identified and tagged with coded acoustic transmitters) white sharks (Carcharodon carcharias) in central California. We use this model to test if sex-specific patterns in TE result in disparate apparent capture probabilities (p°) between male and female white sharks, which can affect the observed sex ratio. The best-supported model showed a contrasting pattern of Pr(TE) from coastal aggregation sites between sexes (for males Pr[TE] = 0.015 [95% CI = 0.00,0.31] and Pr[TE]= 0.57 [0.40, 0.72] for females), but not maturity classes. Additionally, by accounting for Pr(TE) and imperfect detection, we were able to estimate class-specific values of true capture probability (p*) for tagged and untagged sharks. The best-supported model identified differences between maturity classes but no difference between sexes or tagging impacts (tagged mature sharks p* = 0.55 (0.46-0.63) and sub-adult sharks P* = 0.36 (0.25, 0.50); and untagged mature sharks p* = 0.50 (0.39-0.61) and sub-adults p* = 0.18 (0.10, 0.31). Estimated sex-based differences in p° were linked to sex-specific differences in Pr(TE) but not in p; once the Pr(TE) is accounted for, the p between sexes was not different. These results indicate that the observed sex ratio is not a consequence of unequal detectability and sex-specific values of Pr(TE) are important drivers of the observed male-dominated sex ratio. Our modeling approach reveals complex class-specific patterns in Pr(TE) and p in a mark-recapture data set, and highlights challenges for the population modeling and conservation of white sharks in central California. The model we develop here can be used to estimate rates of temporary emigration and class segregation when two detection methods are used.

The estimation of demographic parameters is a key component of evolutionary demography and conservation biology. Capture–mark–recapture methods have served as a fundamental tool for estimating demographic parameters. The accurate estimation of demographic parameters in capture–mark–recapture studies depends on accurate modeling of the observation process. Classic capture–mark–recapture models typically model the observation process as a Bernoulli or categorical trial with detection probability conditional on a marked individual's availability for detection (e.g., alive, or alive and present in a study area). Alternatives to this approach are underused, but may have great utility in capture–recapture studies. In this paper, we explore a simple concept: in the same way that counts contain more information about abundance than simple detection/non‐detection data, the number of encounters of individuals during observation occasions contains more information about the observation process than detection/non‐detection data for individuals during the same occasion. Rather than using Bernoulli or categorical distributions to estimate detection probability, we demonstrate the application of zero‐inflated Poisson and gamma‐Poisson distributions. The use of count distributions allows for inference on availability for encounter, as well as a wide variety of parameterizations for heterogeneity in the observation process. We demonstrate that this approach can accurately recover demographic and observation parameters in the presence of individual heterogeneity in detection probability and discuss some potential future extensions of this method. In this paper we explore a simple concept: in the same way that counts provide more information about abundance than detection/non‐detection data, counts of the number of observations of uniquely marked individuals can provide more information about demographic parameters than detection/non‐detection data. Zero‐inflated parameterizations of capture–recapture models can decrease runtime, and improve the estimation of heterogeneity in detection probability among individuals.

Knowledge of demographic parameters of most cetacean populations is scarce because of problems associated with sampling open populations of wide-ranging animals. In recent years, capture–recapture models have been developed to address these problems. We used a photo-identification dataset collected from a population of bottlenose dolphinsTursiops truncatusbetween 1999 and 2004 around 2 islands of the Azores archipelago, to demonstrate the use of some of these methods. A variety of open models and Pollock’s robust design were applied to estimate population size, survival probability and emigration rates. Using only the estimates with the lowest coefficients of variation, the annual abundance of adult dolphins varied between 202 (95% CI: 148 to 277) and 334 (95% CI: 237 to 469), according to the Jolly-Seber method, and between 114 (95% CI: 85 to 152) and 288 (95% CI: 196 to 423), according to the robust design. The number of subadult individuals varied from 300 (95% CI: 232 to 387) to 434 (95% CI: 316 to 597) based on the Jolly-Seber method. The open models yielded estimates of adult survival (0.970 ± 0.029 SE) that were significantly higher than those for subadults (0.815 ± 0.083 SE). Movement patterns of dolphins in the Azores seem to follow a Markovian model, in which dolphins seen in the study area in 1 yr show higher probability of emigrating in the following year. Despite some limitations, this is the first study to model transience and temporary emigration in a dolphin population.