N-mixture Models Research Articles

Balancing Precision and Risk: Should Multiple Detection Methods Be Analyzed Separately in N-Mixture Models?

Using multiple detection methods can increase the number, kind, and distribution of individuals sampled, which may increase accuracy and precision and reduce cost of population abundance estimates. However, when variables influencing abundance are of interest, if individuals detected via different methods are influenced by the landscape differently, separate analysis of multiple detection methods may be more appropriate. We evaluated the effects of combining two detection methods on the identification of variables important to local abundance using detections of grizzly bears with hair traps (systematic) and bear rubs (opportunistic). We used hierarchical abundance models (N-mixture models) with separate model components for each detection method. If both methods sample the same population, the use of either data set alone should (1) lead to the selection of the same variables as important and (2) provide similar estimates of relative local abundance. We hypothesized that the inclusion of 2 detection methods versus either method alone should (3) yield more support for variables identified in single method analyses (i.e. fewer variables and models with greater weight), and (4) improve precision of covariate estimates for variables selected in both separate and combined analyses because sample size is larger. As expected, joint analysis of both methods increased precision as well as certainty in variable and model selection. However, the single-method analyses identified different variables and the resulting predicted abundances had different spatial distributions. We recommend comparing single-method and jointly modeled results to identify the presence of individual heterogeneity between detection methods in N-mixture models, along with consideration of detection probabilities, correlations among variables, and tolerance to risk of failing to identify variables important to a subset of the population. The benefits of increased precision should be weighed against those risks. The analysis framework presented here will be useful for other species exhibiting heterogeneity by detection method.

Empirical and simulation evaluations of an abundance estimator using unmarked individuals of cryptic forest-dwelling taxa

Conservation and management programs use populations of sentinel taxa, such as stream-associated amphibians, as indicator species due to their perceived sensitivity to environmental change. Estimating population size with traditional tools such as mark–recapture estimators may be impractical for forest-dwelling stream-associated amphibians, many of which are cryptic and have low detection probabilities. In addition, sampling techniques can alter habitat conditions, particularly with repeat sampling, and compromise inferences about management impacts. We used simulated and empirical data and N-mixture models to estimate detection probabilities and abundances for two amphibian genera, giant Dicamptodon and torrent Rhyacotriton salamanders, sampled with a less-invasive approach than other methods. We surveyed forested headwater streams located in western Washington, USA, for salamanders 7 July–27 August 2008. We assessed model sensitivity to changes in animal abundance (5 and 15) and detection probability (0.05–0.5), as well as study design alternatives including number of sample plots (50–150) and number of sampling visits (2–4). We also evaluated the effects of stream temperature and stream order on detection probability using data collected from forested streams in Washington, USA. Precision of detection probability estimates improved as the number of plots and sampling occasions increased. Variability of estimated population sizes decreased with higher detection probability, although species abundance had little effect on precision of detection probability estimates. Detection probability estimated from empirical data ranged from 0.07 to 0.65 for giant salamanders and 0.06–0.67 for torrent salamanders. Giant salamander detection probability was positively associated with stream temperature regardless of stream order, and was higher in second- and third-order streams than first-order streams. Detection probability for torrent salamanders varied with stream temperature, order, and the interaction of those covariates, with detection increasing with temperature for second- and third-order streams but showing a flat or decreasing trend for first-order streams. N-mixture models, paired with careful consideration of study design alternatives, can produce robust estimates of abundance and obviate the traditional reliance on indices of relative abundance for many rare and sensitive taxa. Use of a less invasive technique for sampling stream-associated amphibians resulted in sufficient animal captures for suitable model performance. Our simulation results can inform study design and direct efficient allocation of field effort.

Spatial dynamics of the knob-tailed gecko Nephrurus stellatus in a fragmented agricultural landscape

In fragmented landscapes, a species’ dispersal ability and response to habitat condition are key determinants of persistence. To understand the relative importance of dispersal and condition for survival of Nephrurus stellatus (Gekkonidae) in southern Australia, we surveyed 92 woodland remnants three times. This gecko favours early post-fire succession conditions so may be at risk of extinction in the long-unburnt agricultural landscape. Using N-mixture models, we compared the influence of four measures of isolation, patch area and two habitat variables on the abundance and occurrence of N. stellatus, while taking into account detection probability. Patch occupancy was high, despite the long-term absence of fire from most remnants. Distance to the nearest occupied site was the most informative measure of patch isolation, exhibiting a negative relationship with occupancy. Distance to a nearby conservation park had little influence, suggesting that mainland–island metapopulation dynamics are not important. Abundance and occurrence were positively related to %-cover of spinifex (Triodia), indicating that niche-related factors may also contribute to spatial dynamics. Patterns of patch occupancy imply that N. stellatus has a sequence of spatial dynamics across an isolation gradient, with patchy populations and source-sink dynamics when patches are within 300 m, metapopulations at intermediate isolation, and declining populations when patches are separated by >1–2 km. Considering the conservation needs of the community, habitat condition and connectivity may need to be improved before fire can be reintroduced to the landscape. We speculate that fire may interact with habitat degradation and isolation, increasing the risk of local extinctions.

An evaluation of the Bayesian approach to fitting the N-mixture model for use with pseudo-replicated count data

The N-mixture model proposed by Royle in 2004 may be used to approximate the abundance and detection probability of animal species in a given region. In 2006, Royle and Dorazio discussed the advantages of using a Bayesian approach in modelling animal abundance and occurrence using a hierarchical N-mixture model. N-mixture models assume replication on sampling sites, an assumption that may be violated when the site is not closed to changes in abundance during the survey period or when nominal replicates are defined spatially. In this paper, we studied the robustness of a Bayesian approach to fitting the N-mixture model for pseudo-replicated count data. Our simulation results showed that the Bayesian estimates for abundance and detection probability are slightly biased when the actual detection probability is small and are sensitive to the presence of extra variability within local sites.

Large-scale monitoring of shorebird populations using count data andN-mixture models: Black Oystercatcher (Haematopus bachmani) surveys by land and sea

ABSTRACT. Large-scale monitoring of bird populations is often based on count data collected across spatial scales that may include multiple physiographic regions and habitat types. Monitoring at large spatial scales may require multiple survey platforms (e.g., from boats and land when monitoring coastal species) and multiple survey methods. It becomes especially important to explicitly account for detection probability when analyzing count data that have been collected using multiple survey platforms or methods. We evaluated a new analytical framework, N-mixture models, to estimate actual abundance while accounting for multiple detection biases. During May 2006, we made repeated counts of Black Oystercatchers (Haematopus bachmani) from boats in the Puget Sound area of Washington (n = 55 sites) and from land along the coast of Oregon (n = 56 sites). We used a Bayesian analysis of N-mixture models to (1) assess detection probability as a function of environmental and survey covariates and (2) estimate total...

Using Public Land Cover Data to Determine Habitat Associations of Breeding Birds in Tuskegee National Forest, Alabama

Abstract A decline in the numbers of breeding songbirds is assumed to be related to habitat loss, but for many species, habitat needs during the breeding season are not well understood. Therefore, we developed habitat use models to quantify habitat relationships for breeding birds within a mostlyforested landscape centered on Tuskegee National Forest, Alabama. We conducted bird counts at 338 points and derived habitat characteristics within 100 m of each point using the Alabama Gap Analysis Program land cover map and the National Land Cover Database Tree Canopy Cover map. We modeled avian abundances and habitat associations based on cover type and canopy cover using N-mixture models. We detected more than 16,000 individuals of 85 species, and we present models of abundances for 42 species. Canopy cover was the most influential habitat characteristic, although many species abundances were influenced by cover type. For most species, detection was influenced by observer; date, time, and weather variables were less important in determining detectability. We demonstrate how bird habitat associations can be modeled at a coarse spatial scale using publicly available land cover maps. Our observations regarding the habitat associations of birds in Tuskegee National Forest may be applicable elsewhere within the East Gulf Coastal Plain, but the regional specificity of habitat use should be tested before such extrapolations are justified.

Improving selection of indicator species when detection is imperfect

Indicator species are widely adopted in conservation programs due to their time- and cost-effectiveness, and the indicator value method is a popular approach for selecting species that are indicative of particular site classifications. The indicator value method does not explicitly incorporate detection probability into its abundance or occupancy estimates. We present an approach based on N-mixture models for estimating indicator values with improved accuracy. Simulations with two site classifications demonstrate the importance of accounting for imperfect detection and how ignoring it can alter indicator values. Our simulations also illustrate the sampling conditions under which use of N-mixture models achieves reduced bias in indicator values relative to naïve estimates based on counts and the assumption of perfect detection. Naïve estimates produced greater bias at nearly all probabilities of detection, and exhibited greater sensitivity to low probability of detection in preferred sites compared with N-mixture estimates. Differences between the naïve estimate and the N-mixture estimate were most pronounced when detection probability in the preferred site type was lower than 0.4. A case study with 11 species of songbirds demonstrated modest associations between most species and their “preferred” habitats, and 3 species in which preferred habitats differed between the naïve and N-mixture model approaches. When studying less common species and in instances where detection probability varies strongly among site classifications, we recommend using the approach based on N-mixture models to improve selection and inference regarding indicator species.

Using multilevel spatial models to understand salamander site occupancy patterns after wildfire

Studies of the distribution of elusive forest wildlife have suffered from the confounding of true presence with the uncertainty of detection. Occupancy modeling, which incorporates probabilities of species detection conditional on presence, is an emerging approach for reducing observation bias. However, the current likelihood modeling framework is restrictive for handling unexplained sources of variation in the response that may occur when there are dependence structures such as smaller sampling units that are nested within larger sampling units. We used multilevel Bayesian occupancy modeling to handle dependence structures and to partition sources of variation in occupancy of sites by terrestrial salamanders (family Plethodontidae) within and surrounding an earlier wildfire in western Oregon, USA. Comparison of model fit favored a spatial N-mixture model that accounted for variation in salamander abundance over models that were based on binary detection/non-detection data. Though catch per unit effort was higher in burned areas than unburned, there was strong support that this pattern was due to a higher probability of capture for individuals in burned plots. Within the burn, the odds of capturing an individual given it was present were 2.06 times the odds outside the burn, reflecting reduced complexity of ground cover in the burn. Ther was weak support that true occupancy was lower within the burned area. While the odds of occupancy in the burn were 0.49 times the odds outside the burn among the five species, the magnitude of variation attributed to the burn was small in comparison to variation attributed to other landscape variables and to unexplained, spatially autocorrelated random variation. While ordinary occupancy models may separate the biological pattern of interest from variation in detection probability when all sources of variation are known, the addition of random effects structures for unexplained sources of variation in occupancy and detection probability may often more appropriately represent levels of uncertainty.

Implementation of a long-term monitoring program of the ocellated lizard (Timon lepidus) population on Oleron Island

AbstractThe ocellated lizard Timon lepidus (Sauria; Lacertidae) has declined throughout most of its range. Habitat fragmentation and habitat loss seem to be mainly responsible for the species' decline. The ocellated lizard population of Oleron Island, confined to a longshore dune of 140 ha, is the subject of a long-term monitoring study established in 2007. The monitoring method consists of 70 plots (50 × 50 m) randomly placed within a study area divided into six distinct zones. Three surveys were conducted in the study area over the spring season of 2007. During each survey, we counted the individuals in each plot. These counts were analyzed with the PRESENCE 2.0 and the R package Unmarked software using two different modeling approaches, the 'site-occupancy model' and the 'N-mixture model'. Estimates resulting from our analyses indicated the proportion of occupied plots to be 0.76. Our results indicated that the ocellated lizard has a highly heterogeneous distribution on Oleron Island, with parts of the dune sheltering clusters of lizards, and other areas totally unoccupied. The population size was estimated to be 516 individuals (95% CI 248-783). The relative abundance of ocellated lizards on the island can be principally explained by the presence of permanent shelters (used both during winter and the lizards' active period), including rabbit and rodent burrows and artificial shelters. This monitoring survey will be replicated every three years to enable us to calculate the species' colonization and local extinction probabilities. These results will help in evaluating and guiding management and conservation measures.

Premiers résultats d’un suivi à long terme sur une population de Lézard ocellé Timon lepidus sur l’île d’Oléron

A long-term monitoring program of the ocellated lizard (Timon lepidus) population on Oléron Island. The Ocellated Lizard Timon lepidus (Sauria ; Lacertidae) has declined throughout most of its range. Today it is difficult to assess the extent of this decline. The Ocellated Lizard population of Oléron Island (Charente- Maritime, France) is the subject of a long-term monitoring study established in 2007. This study is repeated every 3 years to follow the population evolution. The population is confined to a long-shore dune of 140 ha. The monitoring method consists of 70 plots (50 x 50 m) randomly placed within a study area divided into six distinct zones. Three surveys were conducted in the study area over the spring season (April, May and June). Results were analysed with PRESENCE 3.0 (Beta) and R 2.8.1. The Ocellated Lizard has a highly heterogeneous distribution on Oléron Island. The site-occupancy model allows us to conclude that the probability of detecting the species in the plots increases over the field. In 2010, this probability was 0.78 in April and 0.97 in May and June. The estimated proportion of occupied sites was 0.83 in 2010 and 0.76 in 2007. Colonization and local extinction are the consequences of the evolution of available shelters (colonization if this resource increases and extinction if it disappears) and of the coastal erosion (habitat loss). The relative abundance of Ocellated Lizards on the island (modeling with the N-mixture model) can be principally explained by the presence of permanent shelters (used both during winter and the lizards’ active period), including rabbit and rodent burrows and artificial shelters. Rabbits are essential and their maintaining is crucial for the Ocellated Lizard conservation. The Ocellated Lizard population size was estimated to be 1025 individuals (95 % CI : 695-1355) in 2010. This monitoring survey will be replicated in 2013. Results will help us in evaluating and guiding management and conservation measures.

Regional Synthesis of Habitat Relationships in Shrubland Birds

Shrubland birds are declining throughout the eastern United States. To manage scrub-shrub habitats for birds, managers need information on avian habitat relationships. Past studies have produced contradictory results in some cases and may be of limited generality because of site- and habitat-specific factors. We studied shrubland birds across 6 habitats in 3 New England states to provide more general information on habitat relationships than has been possible in past studies. Our study sites included all major scrub-shrub habitats in New England: wildlife openings, regenerating clear-cuts, beaver ponds, utility rights-of-way, pitch pine (Pinus rigida) woodlands, and scrub oak (Quercus ilicifolia) barrens and ranged from Connecticut to northern New Hampshire, with research conducted from 2002 to 2007. Using N-mixture models of repeated point counts, we found that 6 of 12 shrubland birds preferred areas with greater shrub cover. An additional 4 species appeared to prefer areas with lower-stature vegetation and greater forb cover. Eight of 10 bird species showed relationships with cover of individual plant species, with Spiraea spp., willows (Salix spp.), alders (Alnus spp.), and invasive exotics being the most important. We recommend that shrubland management for birds focus on providing 2 distinct habitats: 1) areas of tall (>1.5 m) vegetation with abundant shrub cover and 2) areas of lower (<1.5 m) vegetation with abundant forb cover but fewer shrubs.

Models for Estimating Abundance from Repeated Counts of an Open Metapopulation

Using only spatially and temporally replicated point counts, Royle (2004b, Biometrics 60, 108-115) developed an N-mixture model to estimate the abundance of an animal population when individual animal detection probability is unknown. One assumption inherent in this model is that the animal populations at each sampled location are closed with respect to migration, births, and deaths throughout the study. In the past this has been verified solely by biological arguments related to the study design as no statistical verification was available. In this article, we propose a generalization of the N-mixture model that can be used to formally test the closure assumption. Additionally, when applied to an open metapopulation, the generalized model provides estimates of population dynamics parameters and yields abundance estimates that account for imperfect detection probability and do not require the closure assumption. A simulation study shows these abundance estimates are less biased than the abundance estimate obtained from the original N-mixture model. The proposed model is then applied to two data sets of avian point counts. The first example demonstrates the closure test on a single-season study of Mallards (Anas platyrhynchos), and the second uses the proposed model to estimate the population dynamics parameters and yearly abundance of American robins (Turdus migratorius) from a multi-year study.

Modeling abundance using N‐mixture models: the importance of considering ecological mechanisms

Predicting abundance across a species' distribution is useful for studies of ecology and biodiversity management. Modeling of survey data in relation to environmental variables can be a powerful method for extrapolating abundances across a species' distribution and, consequently, calculating total abundances and ultimately trends. Research in this area has demonstrated that models of abundance are often unstable and produce spurious estimates, and until recently our ability to remove detection error limited the development of accurate models. The N-mixture model accounts for detection and abundance simultaneously and has been a significant advance in abundance modeling. Case studies that have tested these new models have demonstrated success for some species, but doubt remains over the appropriateness of standard N-mixture models for many species. Here we develop the N-mixture model to accommodate zero-inflated data, a common occurrence in ecology, by employing zero-inflated count models. To our knowledge, this is the first application of this method to modeling count data. We use four variants of the N-mixture model (Poisson, zero-inflated Poisson, negative binomial, and zero-inflated negative binomial) to model abundance, occupancy (zero-inflated models only) and detection probability of six birds in South Australia. We assess models by their statistical fit and the ecological realism of the parameter estimates. Specifically, we assess the statistical fit with AIC and assess the ecological realism by comparing the parameter estimates with expected values derived from literature, ecological theory, and expert opinion. We demonstrate that, despite being frequently ranked the "best model" according to AIC, the negative binomial variants of the N-mixture often produce ecologically unrealistic parameter estimates. The zero-inflated Poisson variant is preferable to the negative binomial variants of the N-mixture, as it models an ecological mechanism rather than a statistical phenomenon and generates reasonable parameter estimates. Our results emphasize the need to include ecological reasoning when choosing appropriate models and highlight the dangers of modeling statistical properties of the data. We demonstrate that, to obtain ecologically realistic estimates of abundance, occupancy and detection probability, it is essential to understand the sources of variation in the data and then use this information to choose appropriate error distributions.

N-mixture models for estimating population size from spatially replicated counts.

Spatial replication is a common theme in count surveys of animals. Such surveys often generate sparse count data from which it is difficult to estimate population size while formally accounting for detection probability. In this article, I describe a class of models (N-mixture models) which allow for estimation of population size from such data. The key idea is to view site-specific population sizes, N, as independent random variables distributed according to some mixing distribution (e.g., Poisson). Prior parameters are estimated from the marginal likelihood of the data, having integrated over the prior distribution for N. Carroll and Lombard (1985, Journal of American Statistical Association 80, 423-426) proposed a class of estimators based on mixing over a prior distribution for detection probability. Their estimator can be applied in limited settings, but is sensitive to prior parameter values that are fixed a priori. Spatial replication provides additional information regarding the parameters of the prior distribution on N that is exploited by the N-mixture models and which leads to reasonable estimates of abundance from sparse data. A simulation study demonstrates superior operating characteristics (bias, confidence interval coverage) of the N-mixture estimator compared to the Caroll and Lombard estimator. Both estimators are applied to point count data on six species of birds illustrating the sensitivity to choice of prior on p and substantially different estimates of abundance as a consequence.