Spatial Capture-recapture Models Research Articles

Using bear rub data and spatial capture-recapture models to estimate trend in a brown bear population

Trends in population abundance can be challenging to quantify during range expansion and contraction, when there is spatial variation in trend, or the conservation area is large. We used genetic detection data from natural bear rubbing sites and spatial capture-recapture (SCR) modeling to estimate local density and population growth rates in a grizzly bear population in northwestern Montana, USA. We visited bear rubs to collect hair in 2004, 2009—2012 (3,579—4,802 rubs) and detected 249—355 individual bears each year. We estimated the finite annual population rate of change 2004—2012 was 1.043 (95% CI = 1.017—1.069). Population density shifted from being concentrated in the north in 2004 to a more even distribution across the ecosystem by 2012. Our genetic detection sampling approach coupled with SCR modeling allowed us to estimate spatially variable growth rates of an expanding grizzly bear population and provided insight into how those patterns developed. The ability of SCR to utilize unstructured data and produce spatially explicit maps that indicate where population change is occurring promises to facilitate the monitoring of difficult-to-study species across large spatial areas.

Bayesian model selection for spatial capture-recapture models.

A vast amount of ecological knowledge generated over the past two decades has hinged upon the ability of model selection methods to discriminate among various ecological hypotheses. The last decade has seen the rise of Bayesian hierarchical models in ecology. Consequently, commonly used tools, such as the AIC, become largely inapplicable and there appears to be no consensus about a particular model selection tool that can be universally applied. We focus on a specific class of competing Bayesian spatial capture–recapture (SCR) models and apply and evaluate some of the recommended Bayesian model selection tools: (1) Bayes Factor—using (a) Gelfand‐Dey and (b) harmonic mean methods, (2) Deviance Information Criterion (DIC), (3) Watanabe‐Akaike's Information Criterion (WAIC) and (4) posterior predictive loss criterion. In all, we evaluate 25 variants of model selection tools in our study. We evaluate these model selection tools from the standpoint of selecting the “true” model and parameter estimation. In all, we generate 120 simulated data sets using the true model and assess the frequency with which the true model is selected and how well the tool estimates N (population size), a parameter of much importance to ecologists. We find that when information content is low in the data, no particular model selection tool can be recommended to help realize, simultaneously, both the goals of model selection and parameter estimation. But, in general (when we consider both the objectives together), we recommend the use of our application of the Bayes Factor (Gelfand‐Dey with MAP approximation) for Bayesian SCR models. Our study highlights the point that although new model selection tools are emerging (e.g., WAIC) in the applied statistics literature, those tools based on sound theory even under approximation may still perform much better.

Dog days are just starting: the ecology invasion of free-ranging dogs (Canis familiaris) in a protected area of the Atlantic Forest

Free-ranging dogs (Canis familiaris, Linnaeus, 1758) are highly invasive exotic species because of their ecological flexibility and adaptability and their close relationship with humans. They have occupied many protected areas around the world, threatening natural ecosystems and causing environmental damage. To understand the potential pressures of free-ranging dogs, we investigated three main aspects of their population ecology by placing camera traps in ecologically distinct locations of the Augusto Ruschi Biological Reserve (ARBR), southeastern Brazil. In this study, we assessed (i) the daily activity patterns according to circular kernel density function, (ii) the habitat selection according to occupancy models, and (iii) the population density according to spatial capture-recapture models. Free-ranging dogs in the ARBR are active irregularly (cathemeral behavior), display multiple daily activity peaks, and use approximately 73% of the study area. Our results suggest that free-ranging dogs exhibit broad temporal and spatial plasticity, so they can potentially harm a broad array of native species through competition or predation. The high temporal and spatial use range of free-ranging dogs is possibly a consequence of their high population density (0.55 ± SD 0.18 individuals/km2), representing one of the highest such estimates for the Atlantic Forest, and one that is higher than several estimates for ocelots, an ecologically similar native mesocarnivore. Our results suggest that the free-ranging dog population in the ARBR likely comprises a mix of domestic, stray, and feral individuals, with consequent management challenges that should focus on prevention, control, and perhaps eradication strategies.

Reserve design to optimize functional connectivity and animal density.

Ecological distance-based spatial capture-recapture models (SCR) are a promising approach for simultaneously estimating animal density and connectivity, both of which affect spatial population processes and ultimately species persistence. We explored how SCR models can be integrated into reserve-design frameworks that explicitly acknowledge both the spatial distribution of individuals and their space use resulting from landscape structure. We formulated the design of wildlife reserves as a budget-constrained optimization problem and conducted a simulation to explore 3 different SCR-informed optimization objectives that prioritized different conservation goals by maximizing the number of protected individuals, reserve connectivity, and density-weighted connectivity. We also studied the effect on our 3 objectives of enforcing that the space-use requirements of individuals be met by the reserve for individuals to be considered conserved (referred to as home-range constraints). Maximizing local population density resulted in fragmented reserves that would likely not aid long-term population persistence, and maximizing the connectivity objective yielded reserves that protected the fewest individuals. However, maximizing density-weighted connectivity or preemptively imposing home-range constraints on reserve design yielded reserves of largely spatially compact sets of parcels covering high-density areas in the landscape with high functional connectivity between them. Our results quantify the extent to which reserve design is constrained by individual home-range requirements and highlight that accounting for individual space use in the objective and constraints can help in the design of reserves that balance abundance and connectivity in a biologically relevant manner.

Sex‐specific population dynamics of ocelots in Belize using open population spatial capture–recapture

AbstractWe used open population, spatial capture–recapture (SCR) models to estimate sex‐specific density, survival, per capita recruitment, and population growth rate of ocelots (Leopardus pardalis) at five sites in Belize with up to 12 yr of data per site. Open population SCR models enabled us to separate survival and recruitment from migration using an ecologically realistic, spatially explicit movement model. Yearly survival probability across 4 broadleaf forest sites was estimated at 0.73–0.84 for males and 0.81–0.87 for females, with no clear indication of sex differences. Yearly per capita recruitment was estimated across four broadleaf forest sites at 0.06–0.08 recruits/N for males and 0.09–0.12 recruits/N for females, again with no clear indication of sex differences. At a pine forest site with a population comprised largely of males, survival and recruitment estimates were similar to the broadleaf sites. Population densities in the broadleaf forest sites ranged from 6.5 to 14.7 ocelots/100 km2, and 0.9–2.5 ocelots/100 km2 in the pine forest site, with strong evidence of a female‐biased sex ratio in the broadleaf sites and a male‐biased sex ratio in the pine forest site. We also found strong evidence that female within‐year space use at the broadleaf sites was smaller than that of males, and that within‐year space use at the pine forest site was larger than that at broadleaf sites. Between‐year home‐range relocation at broadleaf sites was of a similar spatial scale as within‐year space use, consistent with philopatry. We found evidence of a small population decline (posterior probability > 0.9) at two of four broadleaf sites; however, given the level of uncertainty about decline magnitudes, we suggest continued monitoring of these sites to increase site‐years and gain further precision on population growth rate estimates. Estimating demographic parameters at large spatial and temporal scales is important for establishing reliable baseline estimates for future comparison and for understanding changes in population dynamics. Long‐term data sets like those we collected are of particular importance for long‐lived species living at low densities and large spatial scales, where not many individuals are exposed to capture in any one year.

A Sensitivity Analysis of the Application of Integrated Species Distribution Models to Mobile Species: A Case Study with the Endangered Baird’s Tapir

SummarySpecies distribution models (SDMs) are statistical tools used to develop continuous predictions of species occurrence. ‘Integrated SDMs’ (ISDMs) are an elaboration of this approach with potential advantages that allow for the dual use of opportunistically collected presence-only data and site-occupancy data from planned surveys. These models also account for survey bias and imperfect detection through the use of a hierarchical modelling framework that separately estimates the species–environment response and detection process. This is particularly helpful for conservation applications and predictions for rare species, where data are often limited and prediction errors may have significant management consequences. Despite this potential importance, ISDMs remain largely untested under a variety of scenarios. We performed an exploration of key modelling decisions and assumptions on an ISDM using the endangered Baird’s tapir (Tapirus bairdii) as a test species. We found that site area had the strongest effect on the magnitude of population estimates and underlying intensity surface and was driven by estimates of model intercepts. Selecting a site area that accounted for the individual movements of the species within an average home range led to population estimates that coincided with expert estimates. ISDMs that do not account for the individual movements of species will likely lead to less accurate estimates of species intensity (number of individuals per unit area) and thus overall population estimates. This bias could be severe and highly detrimental to conservation actions if uninformed ISDMs are used to estimate global populations of threatened and data-deficient species, particularly those that lack natural history and movement information. However, the ISDM was consistently the most accurate model compared to other approaches, which demonstrates the importance of this new modelling framework and the ability to combine opportunistic data with systematic survey data. Thus, we recommend researchers use ISDMs with conservative movement information when estimating population sizes of rare and data-deficient species. ISDMs could be improved by using a similar parameterization to spatial capture–recapture models that explicitly incorporate animal movement as a model parameter, which would further remove the need for spatial subsampling prior to implementation.

Estimating Population Density of the White-Tailed Deer in Finland using Non-Invasive Genetic Sampling and Spatial Capture–Recapture

The white-tailed deer is an important game species in Finland. We evaluated the potential of estimating the white-tailed deer pre-harvest density using non-invasive DNA collection within a spatial capture–recapture (SCR) framework. We sampled faeces during three weekly visits in autumn 2015 from 180, 20 × 20 m plots clustered in groups of four. Individual identification was based on 12–14 microsatellites. Of the 245 faecal samples collected, an individual could be identified from only 36 (15%). We identified 27 white-tailed deer individuals of which seven were recaptured. The SCR model produced a plausible density estimate (3.5 indiv. km–2) which was similar to estimates based on dung count and large-scale national estimates, although a posteriori simulation showed the SCR estimate was likely positive biased. Although we found that SCR based on faecal DNA can provide pre-harvest density estimates of the white-tailed deer, the approach is not without challenges and we discuss these suggesting possible solutions.

Simulation-based validation of spatial capture-recapture models: A case study using mountain lions.

Spatial capture-recapture (SCR) models have improved the ability to estimate densities of rare and elusive animals. However, SCR models have seldom been validated even as model formulations diversify and expand to incorporate new sampling methods and/or additional sources of information on model parameters. Information on the relationship between encounter probabilities, sources of additional information, and the reliability of density estimates, is rare but crucial to assessing reliability of SCR-based estimates. We used a simulation-based approach that incorporated prior empirical work to assess the accuracy and precision of density estimates from SCR models using spatially unstructured sampling. To assess the consequences of sparse data and potential sources of bias, we simulated data under six scenarios corresponding to three different levels of search effort and two levels of correlation between search effort and animal density. We then estimated density for each scenario using four models that included increasing amounts of information from harvested individuals and telemetry to evaluate the impact of additional sources of information. Model results were sensitive to the quantity of available information: density estimates based on low search effort were biased high and imprecise, whereas estimates based on high search effort were unbiased and precise. A correlation between search effort and animal density resulted in a positive bias in density estimates, though the bias decreased with increasingly informative datasets. Adding information from harvested individuals and telemetered individuals improved density estimates based on low and moderate effort but had negligible impact for datasets resulting from high effort. We demonstrated that density estimates from SCR models using spatially unstructured sampling are reliable when sufficient information is provided. Accurate density estimates can result if empirical-based simulations such as those presented here are used to develop study designs with appropriate amounts of effort and information sources.

Spatial capture–recapture for categorically marked populations with an application to genetic capture–recapture

AbstractRecently introduced unmarked spatial capture–recapture (SCR), spatial mark–resight (SMR), and 2‐flank spatial partial identity models (SPIMs) extend the domain of SCR to populations or observation systems that do not always allow for individual identity to be determined with certainty. For example, some species do not have natural marks that can reliably produce individual identities from photographs, and some methods of observation produce partial identity samples as is the case with remote cameras that sometimes produce single‐flank photographs. Unmarked SCR, SMR, and SPIM share the feature that they probabilistically resolve the uncertainty in individual identity using the spatial location where samples were collected. Spatial location is informative of individual identity in spatially structured populations because a sample is more likely to have been produced by an individual living near the trap where it was recorded than an individual living further away from the trap. Further, the level of information about individual identity that a spatial location contains is related to two key ecological concepts, population density and home range size, which we quantify using a proposed Identity Diversity Index (IDI). We show that latent and partial identity SCR models produce imprecise and biased density estimates in many high IDI scenarios when data are sparse. We then extend the unmarked SCR model to incorporate categorical, partially identifying covariates, which reduce the level of uncertainty in individual identity, increasing the reliability and precision of density estimates, and allowing reliable density estimation in scenarios with higher IDI values and with more sparse data. We illustrate the performance of this “categorical SPIM” via simulations and by applying it to a black bear data set using microsatellite loci as categorical covariates, where we reproduce the full data set estimates with only slightly less precision using fewer loci than necessary for confident individual identification. We then discuss how the categorical SPIM can be applied to other wildlife sampling scenarios such as remote camera surveys, where natural or researcher‐applied partial marks can be observed in photographs. Finally, we discuss how the categorical SPIM can be added to SMR, 2‐flank SPIM, or other latent identity SCR models.

Divergent population trends following the cessation of legal grizzly bear hunting in southwestern British Columbia, Canada

We conducted DNA capture-recapture monitoring of grizzly bears (Ursus arctos) from 5 to 17 years after hunting was stopped in two adjacent but genetically distinct populations in southwestern British Columbia, Canada. We used spatial capture-recapture and non-spatial Pradel robust design modelling to estimate population density, trends, and the demographic components of population change for each population. The larger population had 21.5 bears/1000 km2 and was growing (λPradel = 1.02 ± 0.02 SE; λsecr = 1.01 ± 4.6 × 10−5 SE) following the cessation of hunting. The adjacent smaller population had 6.3 bears/1000 km2 and was likely declining (λPradel = 0.95 ± 0.03 SE; λsecr = 0.98 ± 0.02 SE). Estimates of apparent survival and apparent recruitment indicated that lower recruitment was the dominant factor limiting population growth in the smaller population. Factors limiting reproductive rates and population density could include poor habitat quality, particularly the abundance of high-energy foods, genetic Allee effects due to a long period of population isolation, or demographic effects affecting infanticide rates. The cessation of hunting was insufficient to promote population recovery for the low density, isolated population. Our research highlights the importance of considering mortality thresholds in addition to small population effects and habitat quality when recovering large carnivore populations.

Big cats at large: Density, structure, and spatio‐temporal patterns of a leopard population free of anthropogenic mortality

AbstractHuman impact is near pervasive across the planet and studies of wildlife populations free of anthropogenic mortality are increasingly scarce. This is particularly true for large carnivores that often compete with and, in turn, are killed by humans. Accordingly, the densities at which carnivore populations occur naturally, and their role in shaping and/or being shaped by natural processes, are frequently unknown. We undertook a camera‐trap survey in the Sabi Sand Game Reserve (SSGR), South Africa, to examine the density, structure and spatio‐temporal patterns of a leopard Panthera pardus population largely unaffected by anthropogenic mortality. Estimated population density based on spatial capture–recapture models was 11.8 ± 2.6 leopards/100 km2. This is likely close to the upper density limit attainable by leopards, and can be attributed to high levels of protection (particularly, an absence of detrimental edge effects) and optimal habitat (in terms of prey availability and cover for hunting) within the SSGR. Although our spatio‐temporal analyses indicated that leopard space use was modulated primarily by “bottom‐up” forces, the population appeared to be self‐regulating and at a threshold that is unlikely to change, irrespective of increases in prey abundance. Our study provides unique insight into a naturally‐functioning carnivore population at its ecological carrying capacity. Such insight can potentially be used to assess the health of other leopard populations, inform conservation targets, and anticipate the outcomes of population recovery attempts.

Satellite-detected forest disturbance forecasts American marten population decline: The case for supportive space-based monitoring

Limited monitoring resources often constrain rigorous monitoring practices to species or populations of conservation concern. Insufficient monitoring can induce a tautology as lack of monitoring resources makes it difficult to determine whether a species or population deserves additional monitoring resources. When in-situ monitoring resources are limited, remote habitat monitoring could be a useful supplementary tool, as linking parameterized species distribution models to spatially explicit time-series of environmental correlates allows iterative prediction of population change. Yet the performance of predictive forecasts or hindcasts has been difficult to evaluate. We paired contemporary field data, historic population estimates, and a remotely-sensed archive of landscape change to evaluate predictions of American marten (Martes americana) population decline owing to habitat loss in Maine, USA. We estimated contemporary spatial patterns in marten density relative to landscape disturbance with spatial capture-recapture models. We compared current density estimates to historical density calculations to evaluate population decline, and compared historical calculations to habitat-based model predictions to evaluate the efficacy of habitat monitoring as a proxy for direct monitoring. Marten density was negatively associated with the proportion of surrounding regenerating forest, and point estimates within focal townships were 50–80% lower than historical calculations. Habitat-based hindcasts of marten density across our entire focal area interest suggested a smaller population decline (roughly 50%) within our focal area. Thus, although habitat-based predictions underpredicted marten decline, they provided correct directional inference. Habitat monitoring and predictions from species distribution models may provide useful inference about population changes given trends in habitat at limited expense when in-situ information is lacking.

Population genetics reveals high connectivity of giant panda populations across human disturbance features in key nature reserve.

The giant panda is an example of a species that has faced extensive historical habitat fragmentation, and anthropogenic disturbance and is assumed to be isolated in numerous subpopulations with limited gene flow between them. To investigate the population size, health, and connectivity of pandas in a key habitat area, we noninvasively collected a total of 539 fresh wild giant panda fecal samples for DNA extraction within Wolong Nature Reserve, Sichuan, China. Seven validated tetra‐microsatellite markers were used to analyze each sample, and a total of 142 unique genotypes were identified. Nonspatial and spatial capture–recapture models estimated the population size of the reserve at 164 and 137 individuals (95% confidence intervals 153–175 and 115–163), respectively. Relatively high levels of genetic variation and low levels of inbreeding were estimated, indicating adequate genetic diversity. Surprisingly, no significant genetic boundaries were found within the population despite the national road G350 that bisects the reserve, which is also bordered with patches of development and agricultural land. We attribute this to high rates of migration, with four giant panda road‐crossing events confirmed within a year based on repeated captures of individuals. This likely means that giant panda populations within mountain ranges are better connected than previously thought. Increased development and tourism traffic in the area and throughout the current panda distribution pose a threat of increasing population isolation, however. Maintaining and restoring adequate habitat corridors for dispersal is thus a vital step for preserving the levels of gene flow seen in our analysis and the continued conservation of the giant panda meta‐population in both Wolong and throughout their current range.

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.

Integrating multiple genetic detection methods to estimate population density of social and territorial carnivores

AbstractSpatial capture–recapture models can produce unbiased estimates of population density, but sparse detection data often plague studies of social and territorial carnivores. Integrating multiple types of detection data can improve estimation of the spatial scale parameter (σ), activity center locations, and density. Noninvasive genetic sampling is effective for detecting carnivores, but social structure and territoriality could cause differential detectability among population cohorts for different detection methods. Using three observation models, we evaluated the integration of genetic detection data from noninvasive hair and scat sampling of the social and territorial coyote (Canis latrans). Although precision of estimated density was improved, particularly if sharing σ between detection methods was appropriate, posterior probabilities of σ and posterior predictive checks supported different σ for hair and scat observation models. The resulting spatial capture–recapture model described a scenario in which scat‐detected individuals lived on and around scat transects, whereas hair‐detected individuals had larger σ and mostly lived off of the detector array, leaving hair but not scat samples. A more supported interpretation is that individual heterogeneity in baseline detection rates (λ0) was inconsistent between detection methods, such that each method disproportionately detected different population cohorts. These findings can be attributed to the sociality and territoriality of canids: Residents may be more likely to strategically mark territories via defecation (scat deposition), and transients may be more likely to exhibit rubbing (hair deposition) to increase mate attraction. Although this suggests that reliance on only one detection method may underestimate population density, integrating multiple sources of genetic detection data may be problematic for social and territorial carnivores. These data are typically sparse, modeling individual heterogeneity in λ0and/or σ with sparse data is difficult, and positive bias can be introduced in density estimates if individual heterogeneity in detection parameters that is inconsistent between detection methods is not appropriately modeled. Previous suggestions for assessing parameter consistency of σ between detection methods using Bayesian model selection algorithms could be confounded by individual heterogeneity in λ0in noninvasive detection data. We demonstrate the usefulness of augmenting those approaches with calibrated posterior predictive checks and plots of the posterior density of activity centers for key individuals.

State space and movement specification in open population spatial capture-recapture models.

With continued global changes, such as climate change, biodiversity loss, and habitat fragmentation, the need for assessment of long‐term population dynamics and population monitoring of threatened species is growing. One powerful way to estimate population size and dynamics is through capture–recapture methods. Spatial capture (SCR) models for open populations make efficient use of capture–recapture data, while being robust to design changes. Relatively few studies have implemented open SCR models, and to date, very few have explored potential issues in defining these models. We develop a series of simulation studies to examine the effects of the state‐space definition and between‐primary‐period movement models on demographic parameter estimation. We demonstrate the implications on a 10‐year camera‐trap study of tigers in India. The results of our simulation study show that movement biases survival estimates in open SCR models when little is known about between‐primary‐period movements of animals. The size of the state‐space delineation can also bias the estimates of survival in certain cases.We found that both the state‐space definition and the between‐primary‐period movement specification affected survival estimates in the analysis of the tiger dataset (posterior mean estimates of survival ranged from 0.71 to 0.89). In general, we suggest that open SCR models can provide an efficient and flexible framework for long‐term monitoring of populations; however, in many cases, realistic modeling of between‐primary‐period movements is crucial for unbiased estimates of survival and density.

The spotted ghost: Density and distribution of serval Leptailurus serval in Namibia

AbstractDespite its IUCN Red List status as “least concern,” relatively few studies have been conducted on serval Leptailurus serval. Within Namibia, serval are detected infrequently, even during prolonged camera trapping surveys, which has been suggested as indicative of low density. Such populations are vulnerable to habitat loss and degradation; therefore, quantifying serval population density and distribution within Namibia is an important first step in establishing conservation needs. We present the first density estimates of serval for Namibia, from Khaudum National Park and the Mudumu North Complex (MNC). Using Bayesian spatial capture–recapture models, density was estimated at 1.28 serval/100 km2 (± 0.23, 0.82–1.56) for Khaudum and 0.63 serval/100 km2 (± 0.51, 0.38–0.90) for the MNC; the lowest serval densities published to date. Photographic records from the two surveys, along with an additional 10 records from MNC captured outside of the survey period and two new records from north‐central Namibia were used to update the Namibian distribution map. This resulted in the highest probability of occurrence along the north‐eastern borders. Such results imply Namibia hosts a low‐density, geographically limited population, potentially vulnerable to habitat fragmentation and other environmental impacts, and therefore requires careful management to ensure its persistence.

Modelling sound attenuation in heterogeneous environments for improved bioacoustic sampling of wildlife populations

AbstractAcoustic sampling methods are becoming increasingly important in biological monitoring. Sound attenuation is one of the most important dynamics affecting the utility of acoustic data as it directly affects the probability of detection of individuals by acoustic sensor arrays and especially the localization of acoustic signals necessary in telemetry studies. Therefore, models of sound attenuation are necessary to make efficient use of acoustic data in ecological monitoring and assessment applications. Models of attenuation in widespread use are based on Euclidean distance between source and sensor, which is justified under spherical attenuation of sound waves in homogeneous environments.In this paper, I develop a model of sound attenuation based on a non‐Euclidean cost‐weighted distance metric which contains attenuation coefficients that characterize the attenuation of sound due to environmental heterogeneity in the vicinity of an acoustic sensor array.I show that parameters of the proposed attenuation model can be estimated by maximum likelihood using experimental data from an array of fixed sources, thus allowing investigators who use bioacoustic methods to devise explicit models of sound attenuationin situand apply them to localization of sources and density estimation. In addition, drawing on analogy with spatial capture–recapture models, I argue that parameters of the non‐Euclidean model of attenuation can be estimated when source locations areunknown. Thus, the models can be applied to real field studies which require estimation of attenuation parameters or localization of signals.Models of heterogeneous sound attenuation allow more accurate descriptions of acoustic monitoring data, and therefore should produce more accurate estimates of ecological parameters of interest, including source locations, density, and movement trajectories. Moreover, the ability to test specific hypotheses about the effects of habitat and landscape structure on sound attenuation can improve the design of acoustic monitoring arrays and lead to more efficient deployment of acoustic sensing technology.

Estimating density for species conservation: Comparing camera trap spatial count models to genetic spatial capture-recapture models

Density estimation is integral to the effective conservation and management of wildlife. Camera traps in conjunction with spatial capture-recapture (SCR) models have been used to accurately and precisely estimate densities of “marked” wildlife populations comprising identifiable individuals. The emergence of spatial count (SC) models holds promise for cost-effective density estimation of “unmarked” wildlife populations when individuals are not identifiable. We evaluated model agreement, precision, and survey costs, between i) a fully marked approach using SCR models fit using non-invasive genetic data, and ii) an unmarked approach using SC models fit using camera trap data, for a recovering population of the mesocarnivore fisher (Pekania pennanti). The SCR density estimates ranged from 2.95 to 3.42 (2.18–5.19 95% BCI) fishers 100 km−2. The SC density estimates were influenced by their priors, ranging from 0.95 (0.65–2.95 95% BCI) fishers 100 km−2 for the uninformative model to 3.60 (2.01–7.55 95% BCI) fishers 100 km−2 for the model informed by prior knowledge of a 16 km2 fisher home range. We caution against using strongly informative priors but instead recommend using a range of unweighted prior knowledge. Thin detection data was problematic for both SCR and SC models, potentially producing biased low estimates. The total cost of the genetic survey ($47 610) was two-thirds of the camera trap survey ($77 080), or comparable ($75 746) if genetic sampling effort was increased to include sex and trap-behaviour covariates in SCR models. Density estimation of unmarked populations continues to be a series of trade-offs but as methods improve and integrate, so will our estimates.

Spatial capture-recapture design and modelling for the study of small mammals.

Spatial capture-recapture modelling (SCR) is a powerful analytical tool to estimate density and derive information on space use and behaviour of elusive animals. Yet, SCR has been seldom applied to the study of ecologically keystone small mammals. Here we highlight its potential and requirements with a case study on common voles (Microtus arvalis). First, we address mortality associated with live-trapping, which can be high in small mammals, and must be kept minimal. We designed and tested a nest box coupled with a classic Sherman trap and show that it allows a 5-fold reduction of mortality in traps. Second, we address the need to adjust the trapping grid to the individual home range to maximize spatial recaptures. In May-June 2016, we captured and tagged with transponders 227 voles in a 1.2-ha area during two monthly sessions. Using a Bayesian SCR with a multinomial approach, we estimated: (1) the baseline detection rate and investigated variation according to sex, time or behaviour (aversion/attraction after a previous capture); (2) the parameter sigma that describes how detection probability declines as a function of the distance to an individual´s activity centre, and investigated variation according to sex; and (3) density and population sex-ratio. We show that reducing the maximum distance between traps from 12 to 9.6m doubled spatial recaptures and improved model predictions. Baseline detection rate increased over time (after overcoming a likely aversion to entering new odourless traps) and was greater for females than males in June. The sigma parameter of males was twice that of females, indicating larger home ranges. Density estimates were of 142.92±38.50 and 168.25±15.79 voles/ha in May and June, respectively, with 2–3 times more females than males. We highlight the potential and broad applicability that SCR offers and provide specific recommendations for using it to study small mammals like voles.