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.     

Monitoring tiger populations using intensive search in a capture–recapture framework

Tigers (Panthera tigris) today face multiple threats to their survival in the form of habitat loss, poaching, depletion of wild prey through illegal hunting and loss of connectivity between populations. Monitoring of tigers is crucial to evaluate their status and react adaptively to management problems. Though camera traps are becoming increasingly popular with researchers enumerating cryptic and elusive animals, they have not been embedded in the regular management activities of tiger reserves. Tiger monitoring, though an important part of the management, is usually implemented using the unreliable pugmark approach. Camera trap-based studies are few, usually of short duration, and are generally conducted by individual scientists and organizations. In this study, we integrate photographic mark–recapture with the routine activity of searching and locating tigers for tourist viewing by the park management in meadows of Kanha Tiger Reserve which form a part of the tourism zone. We validate the density estimates from “tiger search approach” against those obtained from camera trapping and radio-telemetry conducted in conjunction in the same area. Tiger density (\( \hat{D} \) (SE [\( \hat{D} \)]) per 100 km² for camera traps and tiger search, respectively, was estimated at 12.0 (1.95) and 12.0 (1.76) when effective trapping area was estimated using the half mean maximum distance moved (½ MMDM), 7.6 (1.94) and 7.5 (1.97) using the home range radius, 7.3 (1.49) and 7.5 (1.97) with the full MMDM, and 8.0 (3.0) and 6.88 (2.39) with the spatial likelihood method in Program DENSITY 4.1. Camera trapping, however, was five times more expensive than the tiger search method. Our study suggests that “tiger search approach” can be used as a regular monitoring tool in the tourism zones of tiger reserves, where often most of the source populations are located.     

Dealing with many correlated covariates in capture–recapture models

Capture–recapture models for estimating demographic parameters allow covariates to be incorporated to better understand population dynamics. However, high-dimensionality and multicollinearity can hamper estimation and inference. Principal component analysis is incorporated within capture–recapture models and used to reduce the number of predictors into uncorrelated synthetic new variables. Principal components are selected by sequentially assessing their statistical significance. We provide an example on seabird survival to illustrate our approach. Our method requires standard statistical tools, which permits an efficient and easy implementation using standard software.     

Evolution and spatial structure interact to influence plant–herbivore population and community dynamics

An individual-based model of plant–herbivore interactions was developed to test the potentially interactive effects of explicit space and coevolution on population and community dynamics. Individual plants and herbivores resided in cells on a lattice and carried linked interaction genes. Interaction strength between individual plants and herbivores depended on concordance between these genes (gene-for-gene coevolution). Mating and dispersal among individuals were controlled spatially within variably sized neighbourhoods. Without evolution we observed high-frequency plant–herbivore oscillations (blue spectra) with small individual neighbourhoods, and stochastic fluctuations (white spectra) with large neighbourhoods. Evolution resulted in decreased interaction strength, decreased herbivore-induced plant mortality, increased population sizes, and longer-term fluctuations (reddened spectra). Small herbivore neighbourhoods led to herbivore extinction only with evolution. To explore the increased population size response to evolution we ran simulations without evolution while tuning plant–herbivore interaction strength from high to none. We found that herbivore populations were maximized at intermediate levels of interaction strength that coincided with the interaction strength achieved when the system tuned itself through evolution. Overall, our model shows that the small-scale details of phenotypically variable individual-level interactions, leading to evolutionary dynamics, affect large-scale population and community dynamics.     

Methods to mark termites with protein for mark–release–recapture and mark–capture type studies

Studies were conducted to investigate the feasibility of marking the southwestern desert subterranean termite, Heterotermes aureus (Snyder), with rabbit immunoglobulin G (IgG) protein for mark–release–recapture (MRR) and mark–capture type studies. Qualitative laboratory studies were conducted to determine how long reagent-grade rabbit IgG is retained on or in H. aureus that were marked either externally with a topical spray, internally by feeding them a rabbit IgG-marked food source, or both internally and externally (double marked). Marked termites were detected by an anti-rabbit IgG enzyme-linked immunosorbent assay. Data indicated that the termites retained the mark for at least 35 days, regardless of the marking procedure. A second series of laboratory studies were conducted to determine how fast H. aureus acquire the mark after feeding on cardboard bait that was either sprayed or soaked in different formulations of rabbit IgG. The IgGs tested were a highly purified and costly reagent grade IgG at 5.0 mg/ml and a less pure and less costly technical grade rabbit IgG at 1.0 mg/ml. The results showed that termites acquired both marks equally well after exposure to the soaked cardboard treatment. The advantages and limitations of protein marking termites with rabbit IgG for MRR or mark–capture termite studies are discussed.     

Estimating local population size of the European Nightjar Caprimulgus europaeus using territory capture–recapture models

Capsule The capture–recapture model M(o) is an efficient way to estimate local population size.

Aims To test if a single capture–recapture modelling approach, combined with a simple survey method, can produce estimates of local population size from a dataset involving large‐scale multi‐observer surveys

Methods We sampled the presence of Nightjars in three separate sessions at three forests. Territory numbers were estimated using conventional territory‐mapping criteria. We ran different capture–recapture models to analyse the detection histories of territories obtained across the three sampling sessions and in the three different forests, using either only registrations of churring birds or all contacts.

Results The capture–recapture model M(o), assuming a constant detection probability, was the most efficient one to produce estimates of local population size. Using only two of the three sampling sessions gave less precise, though quite similar, estimates of the number of territories, with standard deviations representing 5–10% of the estimate values. However, this was reduced to 0.7–3.5%, i.e. three to seven times lower, when using the three sessions.

Conclusion Repeated sampling sessions to map territories can be efficiently used within the capture–recapture model M(o) to estimate detection probability and produce precise estimates of local population size.     

Plant–pollinator population dynamics

We formulate and analyze a multi-generation population dynamics model for pollinators’ mutualism with plants. The centerpiece of our model is an analytical expression for population-level plant–pollinator interactions extrapolated from a model of individual-level flowers and bees interactions. We also show that this analytical expression can be productively approximated by the Beddington–DeAngelis formula—a function used to model trophic interactions in mathematical ecology.     

Does your species have memory? Analyzing capture–recapture data with memory models

We examine memory models for multisite capture–recapture data. This is an important topic, as animals may exhibit behavior that is more complex than simple first‐order Markov movement between sites, when it is necessary to devise and fit appropriate models to data. We consider the Arnason–Schwarz model for multisite capture–recapture data, which incorporates just first‐order Markov movement, and also two alternative models that allow for memory, the Brownie model and the Pradel model. We use simulation to compare two alternative tests which may be undertaken to determine whether models for multisite capture–recapture data need to incorporate memory. Increasing the complexity of models runs the risk of introducing parameters that cannot be estimated, irrespective of how much data are collected, a feature which is known as parameter redundancy. Rouan et al. (JABES, 2009, pp 338–355) suggest a constraint that may be applied to overcome parameter redundancy when it is present in multisite memory models. For this case, we apply symbolic methods to derive a simpler constraint, which allows more parameters to be estimated, and give general results not limited to a particular configuration. We also consider the effect sparse data can have on parameter redundancy and recommend minimum sample sizes. Memory models for multisite capture–recapture data can be highly complex and difficult to fit to data. We emphasize the importance of a structured approach to modeling such data, by considering a priori which parameters can be estimated, which constraints are needed in order for estimation to take place, and how much data need to be collected. We also give guidance on the amount of data needed to use two alternative families of tests for whether models for multisite capture–recapture data need to incorporate memory.     

Spatial capture–recapture models allowing Markovian transience or dispersal

Spatial capture–recapture (SCR) models are a relatively recent development in quantitative ecology, and they are becoming widely used to model density in studies of animal populations using camera traps, DNA sampling and other methods which produce spatially explicit individual encounter information. One of the core assumptions of SCR models is that individuals possess home ranges that are spatially stationary during the sampling period. For many species, this assumption is unlikely to be met and, even for species that are typically territorial, individuals may disperse or exhibit transience at some life stages. In this paper we first conduct a simulation study to evaluate the robustness of estimators of density under ordinary SCR models when dispersal or transience is present in the population. Then, using both simulated and real data, we demonstrate that such models can easily be described in the BUGS language providing a practical framework for their analysis, which allows us to evaluate movement dynamics of species using capture–recapture data. We find that while estimators of density are extremely robust, even to pathological levels of movement (e.g., complete transience), the estimator of the spatial scale parameter of the encounter probability model is confounded with the dispersal/transience scale parameter. Thus, use of ordinary SCR models to make inferences about density is feasible, but interpretation of SCR model parameters in relation to movement should be avoided. Instead, when movement dynamics are of interest, such dynamics should be parameterized explicitly in the model.     

Dispersal, colored environmental noise, and spatial synchrony in population dynamics: analyzing a discrete host–parasitoid population model

Spatial synchrony is common, and its influences and causes have attracted the interest of ecologists. Spatially correlated environmental noise, dispersal, and trophic interactions have been considered as the causes of spatial synchrony. In this study, we developed a spatially structured population model, which is described by coupled-map lattices. Our recent investigation showed that trophic correlation of environmental noise was another important factor that affects spatial synchrony. As a supplement, we considered the influence of the color of the environmental noise on the spatial synchrony in this study. The noise color refers to the temporal correlation in the time series data of the noise, and is expressed as the degree of (first-order) autocorrelation for autoregressive noise. Patterns of spatial synchrony were considered for stable, periodic (quasi-periodic), and chaotic population dynamics. Numerical simulations verified that the color of the environmental noise is another mechanism that causes spatial synchrony. Generally, the effect of the color of the noise on the synchrony is dependent on the type of dynamics (stable, cyclic, chaotic) present in the population. For cyclic dynamics, simulation results clearly demonstrate that reddened noise has higher synchrony than white noise. The importance of our research is that it enriches the theory of potential causes of spatial synchrony.     

Genetic mark–recapture population estimation in black bears and issues of scale

Abundance estimates for black bears (Ursus americanus) are important for effective management. Recently, DNA technology has resulted in widespread use of noninvasive, genetic capture–mark–recapture (CMR) approaches to estimate populations. Few studies have compared the genetic CMR methods to other estimation methods. We used genetic CMR to estimate the bear population at 2 study sites in northern New Hampshire (Pittsburg and Milan) in 2 consecutive years. We compared these estimates to those derived from traditional methods used by the New Hampshire Fish and Game Department (NHFG) using hunter harvest and mortality data. Density estimates produced with genetic CMR methods were similar both years and were comparable to those derived from traditional methods. In 2006, the estimated number of bears in Pittsburg was 79 (95% CI = 60–98) corresponding to a density of 15–24 (95% CI) bears/100 km²; the 2007 estimate was 83 (95% CI = 67–99; density = 16–24 bears/100 km²). In 2006, the estimated number of bears in Milan was 95 (95% CI = 74–117; density = 16–25 bears/100 km²); the 2007 estimate was 96 (95% CI = 77–114; density = 17–25 bears/100 km²). We found that genetic CMR methods were able to identify demographic variation at a local scale, including a strongly skewed sex ratio (2 M:1 F) in the Milan population. Genetic CMR is a useful tool for wildlife managers to monitor populations of local concern, where abundance or demographic characteristics may deviate from regional estimates. Future monitoring of the Milan population with genetic CMR is recommended to determine if the sex ratio bias continues, possibly warranting a change in local harvest regimes. © 2011 The Wildlife Society.     

Erratum to: Using multistate capture–mark–recapture models to quantify effects of predation on age-specific survival and population growth in black-tailed deer

Effective species management and conservation relies on accurate estimates of vital rates and an understanding of their link to environmental variables. We used multistate capture–mark–recapture models to directly quantify effects of predation on age-specific survival of black-tailed deer Odocoileus hemionus columbianus in California, USA. Survival probabilities were derived from individual encounter histories of 136 fawns and 57 adults monitored over 4 years. Based on results from our survival analysis we parameterized a Lefkovitch matrix and used elasticity analyses to investigate contributions of mortality due to predation to changes in population growth. We found strong evidence for age-specific survival including senescence. Survival of females >1 year old was consistently low (0.56 ± 0.18 for yearlings, 0.77 ± 0.13 for prime-aged females, and 0.55 ± 0.08 for senescent individuals), primarily due to high puma Puma concolor predation during summer. Predation from black bears Ursus americanus and coyotes Canis latrans was the primary cause for low annual survival of fawns (0.24 ± 0.16). Resulting estimates of population growth rates were indicative of a strongly declining population (λ = 0.82 ± 0.13). Despite high sensitivity to changes in adult survival, results from a lower-level elasticity analysis suggested that predation on fawns was the most significant individual mortality component affecting population decline. Our results provide a rare, direct link between predation, age-specific survival and the predicted population decline of a common ungulate species. The magnitude of predation was unexpected and suggests that ungulates in multi-predator systems struggle to cope with simultaneous reductions in survival probabilities from predators targeting different age classes.     

Estimating individual fitness in the wild using capture–recapture data

The concept of Darwinian fitness is central in evolutionary ecology, and its estimation has motivated the development of several approaches. However, measuring individual fitness remains challenging in empirical case studies in the wild. Measuring fitness requires a continuous monitoring of individuals from birth to death, which is very difficult to get in part because individuals may or may not be controlled at each reproductive event and recovered at death. Imperfect detection hampers keeping track of mortality and reproductive events over the whole lifetime of individuals. We propose a new statistical approach to estimate individual fitness while accounting for imperfect detection. Based on hidden process modelling of longitudinal data on marked animals, we show that standard metrics to quantify fitness, namely lifetime reproductive success, individual growth rate and lifetime individual contribution to population growth, can be extended to cope with imperfect detection inherent to most monitoring programs in the wild. We illustrate our approach using data collected on individual roe deer in an intensively monitored population.     

Evaluation of childhood acute leukemia incidence and underreporting in Brazil by capture–recapture methodology

Background: Population-based cancer registries (PBCR) are important in cancer epidemiology as they provide the basis for monitoring cancer incidence. Childhood acute lymphoblastic leukemia (ALL) is said to have lower incidence in developing countries, which has implications for its pathogenesis, but there are few studies concerning the completeness of cancer registries in developing countries. This study analyzes the number of cases and incidence of childhood acute lymphoblastic leukemia in three different cities in Brazil and estimates underreporting cases and possible PBCR failures. Methods: We evaluated the completeness of PBCR and the incidence rates of childhood ALL from three different Brazilian cities using the two-source capture–recapture method. The sources used were a population-based registry and databases from a diagnosis reference laboratory in 2001 and the Chapman's formula was used to calculate the estimates. Results: The estimated incidence was 5.76, 6.32 and 5.48 per 100,000 inhabitants for Salvador, Recife and Belo Horizonte, respectively. The estimated completeness of childhood ALL in PBCRs was 15.5%, 35.4% and 29.2%, respectively, for Salvador, Recife and Belo Horizonte. Conclusions: There was a high estimated underreporting of childhood leukemia cases in some Brazilian cities. The relationship between information systems and the capture–recapture method application improved epidemiological estimates. Childhood acute lymphoblastic leukemia incidence rates are similar to those of developed countries.     

Monitoring conformational dynamics with solid-state R 1ρ experiments

A new application of solid-state rotating frame (R _1ρ) relaxation experiments to observe conformational dynamics is presented. Studies on a model compound, dimethyl sulfone (DMS), show that R _1ρ relaxation due to reorientation of a chemical shift anisotropy (CSA) tensor undergoing chemical exchange can be used to monitor slow-to-intermediate timescale conformational exchange processes. Control experiments used d ₆ -DMS and alanine to confirm that the technique is monitoring reorientation of the CSA tensor rather than dipolar interactions or methyl group rotation. The application of this method to proteins could represent a new site-specific probe of conformational dynamics.     

An improved procedure to estimate wolf abundance using non-invasive genetic sampling and capture–recapture mixture models

Non-invasive genetic sampling (NGS) is increasingly used to estimate the abundance of rare or elusive species such as the wolf (Canis lupus), which cannot be directly counted in forested mountain habitats. Wolf individual and familial home ranges are wide, potentially connected by long-range dispersers, and their populations are intrinsically open. Appropriate demographic estimators are needed, because the assumptions of homogeneous detection probability and demographic closeness are violated. We compiled the capture–recapture record of 418 individual wolf genotypes identified from ca. 4,900 non-invasive samples, collected in the northern Italian Apennines from January 2002 to June 2009. We analysed this dataset using novel capture–recapture multievent models for open populations that explicitly account for individual detection heterogeneity (IDH). Overall, the detection probability of the weakly detectable individuals, probably pups, juveniles and migrants (P = 0.08), was ca. six times lower than that of the highly detectable wolves (P = 0.44), probably adults and dominants. The apparent annual survival rate of weakly detectable individuals was lower (Φ = 0.66) than those of highly detectable wolves (Φ = 0.75). The population mean annual finite rate of increase was λ = 1.05 ± 0.11, and the mean annual size ranged from N = 117 wolves in 2003 to N = 233 wolves in 2007. This procedure, combining large-scale NGS and multievent IDH demographic models, provides the first estimates of abundance, multi-annual trend and survival rates for an open large wolf population in the Apennines. These results contribute to deepen our understanding of wolf population ecology and dynamics, and provide new information to implement sound long-term conservation plans.