A comparison of three methods for estimating call densities of migrating bowhead whales using passive acoustic monitoring

Environmental and Ecological Statistics - Various methods for estimating animal density from visual data, including distance sampling (DS) and spatially explicit capture-recapture (SECR), have...     

A hierarchical model for spatial capture-recapture data

Estimating density is a fundamental objective of many animal population studies. Application of methods for estimating population size from ostensibly closed populations is widespread, but ineffective for estimating absolute density because most populations are subject to short-term movements or so-called temporary emigration. This phenomenon invalidates the resulting estimates because the effective sample area is unknown. A number of methods involving the adjustment of estimates based on heuristic considerations are in widespread use. In this paper, a hierarchical model of spatially indexed capture-recapture data is proposed for sampling based on area searches of spatial sample units subject to uniform sampling intensity. The hierarchical model contains explicit models for the distribution of individuals and their movements, in addition to an observation model that is conditional on the location of individuals during sampling. Bayesian analysis of the hierarchical model is achieved by the use of data augmentation, which allows for a straightforward implementation in the freely available software WinBUGS. We present results of a simulation study that was carried out to evaluate the operating characteristics of the Bayesian estimator under variable densities and movement patterns of individuals. An application of the model is presented for survey data on the flat-tailed horned lizard (Phrynosoma mcallii) in Arizona, USA.     

Bat-cave catchment areas: using stable isotopes (deltaD) to determine the probable origins of hibernating bats

The application of stable hydrogen isotope (deltaD) techniques has swiftly advanced our understanding of animal movements, but this progression is dominated by studies of birds and relatively long-distance, north-south migrants. This dominance reflects the challenge of incorporating multiple sources of error into geographic assignments and the nature of spatially explicit deltaD models, which possess greater latitudinal than longitudinal resolution. However, recent progress in likelihood-based assignments that incorporate multiple sources of isotopic error and Bayesian approaches that include additional sources of information may advance finer-scale understanding of animal movements. We develop a stable-isotope method for determining probable origins of bats within hibernacula and show that this method produces spatially explicit, continuous assignments with regional resolution. We outline how these assignments can be used to infer hibernacula connectivity, an application that could inform spatial modeling of white-nose syndrome. Additionally, estimates of seasonal and annual flight distances for many cave-dwelling bat species can be derived from this approach. We also discuss how this application can be used in general to provide insights into variable migratory and foraging strategies within bat populations.     

Toward accurate and precise estimates of lion density

Reliable estimates of animal density are fundamental to understanding ecological processes and population dynamics. Furthermore, their accuracy is vital to conservation because wildlife authorities rely on estimates to make decisions. However, it is notoriously difficult to accurately estimate density for wide‐ranging carnivores that occur at low densities. In recent years, significant progress has been made in density estimation of Asian carnivores, but the methods have not been widely adapted to African carnivores, such as lions (Panthera leo). Although abundance indices for lions may produce poor inferences, they continue to be used to estimate density and inform management and policy. We used sighting data from a 3‐month survey and adapted a Bayesian spatially explicit capture‐recapture (SECR) model to estimate spatial lion density in the Maasai Mara National Reserve and surrounding conservancies in Kenya. Our unstructured spatial capture‐recapture sampling design incorporated search effort to explicitly estimate detection probability and density on a fine spatial scale, making our approach robust in the context of varying detection probabilities. Overall posterior mean lion density was estimated to be 17.08 (posterior SD 1.310) lions >1 year old/100 km², and the sex ratio was estimated at 2.2 females to 1 male. Our modeling framework and narrow posterior SD demonstrate that SECR methods can produce statistically rigorous and precise estimates of population parameters, and we argue that they should be favored over less reliable abundance indices. Furthermore, our approach is flexible enough to incorporate different data types, which enables robust population estimates over relatively short survey periods in a variety of systems. Trend analyses are essential to guide conservation decisions but are frequently based on surveys of differing reliability. We therefore call for a unified framework to assess lion numbers in key populations to improve management and policy decisions.     

Simultaneous-count models to estimate abundance from counts of unmarked individuals with imperfect detection

We developed a method to estimate population abundance from simultaneous counts of unmarked individuals over multiple sites. We considered that at each sampling occasion, individuals in a population could be detected at 1 of the survey sites or remain undetected and used either multinomial or binomial simultaneous-count models to estimate abundance, the latter being equivalent to an N-mixture model with one site. We tested model performance with simulations over a range of detection probabilities, population sizes, growth rates, number of years, sampling occasions, and sites. We then applied our method to 3 critically endangered vulture species in Cambodia to demonstrate the real-world applicability of the model and to provide the first abundance estimates for these species in Cambodia. Our new approach works best when existing methods are expected to perform poorly (i.e., few sites and large variation in abundance among sites) and if individuals may move among sites between sampling occasions. The approach performed better when there were >8 sampling occasions and net probability of detection was high (>0.5). We believe our approach will be useful in particular for simultaneous surveys at aggregation sites, such as roosts. The method complements existing approaches for estimating abundance of unmarked individuals and is the first method designed specifically for simultaneous counts.     

Density estimation in tiger populations: combining information for strong inference

A productive way forward in studies of animal populations is to efficiently make use of all the information available, either as raw data or as published sources, on critical parameters of interest. In this study, we demonstrate two approaches to the use of multiple sources of information on a parameter of fundamental interest to ecologists: animal density. The first approach produces estimates simultaneously from two different sources of data. The second approach was developed for situations in which initial data collection and analysis are followed up by subsequent data collection and prior knowledge is updated with new data using a stepwise process. Both approaches are used to estimate density of a rare and elusive predator, the tiger, by combining photographic and fecal DNA spatial capture-recapture data. The model, which combined information, provided the most precise estimate of density (8.5 +/- 1.95 tigers/100 km2 [posterior mean +/- SD]) relative to a model that utilized only one data source (photographic, 12.02 +/- 3.02 tigers/100 km2 and fecal DNA, 6.65 +/- 2.37 tigers/100 km2). Our study demonstrates that, by accounting for multiple sources of available information, estimates of animal density can be significantly improved.     

A capture-recapture model with heterogeneity and behavioural response

We develop the non-parametric maximum likelihood estimator (MLE) of the full M_bh capture-recapture model which utilizes both initial capture and recapture data and permits both heterogeneity (h) between animals and behavioural (b) response to capture. Our MLE procedure utilizes non-parametric maximum likelihood estimation of mixture distributions (Lindsay, 1983; Lindsay and Roeder, 1992) and the EM algorithm (Dempsteret al., 1977). Our MLE estimate provides the first non-parametric estimate of the bivariate capture-recapture distribution.Since non-parametric maximum likelihood estimation exists for submodels M_h (allowing heterogeneity only), Mb (allowing behavioural response only) and M₀ (allowing no changes), we develop maximum likelihood-based model selection, specifically the Akaike information criterion (AIC) (Akaike, 1973). The AIC procedure does well in detecting behavioural response but has difficulty in detecting heterogeneity.     

On the choice of statistical models for estimating occurrence and extinction from animal surveys

In surveys of natural animal populations the number of animals that are present and available to be detected at a sample location is often low, resulting in few or no detections. Low detection frequencies are especially common in surveys of imperiled species; however, the choice of sampling method and protocol also may influence the size of the population that is vulnerable to detection. In these circumstances, probabilities of animal occurrence and extinction will generally be estimated more accurately if the models used in data analysis account for differences in abundance among sample locations and for the dependence between site-specific abundance and detection. Simulation experiments are used to illustrate conditions wherein these types of models can be expected to outperform alternative estimators of population site occupancy and extinction.     

Ecological boundary detection using Bayesian areal wombling

The study of ecological boundaries and their dynamics is of fundamental importance to much of ecology, biogeography, and evolution. Over the past two decades, boundary analysis (of which wombling is a subfield) has received considerable research attention, resulting in multiple approaches for the quantification of ecological boundaries. Nonetheless, few methods have been developed that can simultaneously (1) analyze spatially homogenized data sets (i.e., areal data in the form of polygons rather than point-reference data); (2) account for spatial structure in these data and uncertainty associated with them; and (3) objectively assign probabilities to boundaries once detected. Here we describe the application of a Bayesian hierarchical framework for boundary detection developed in public health, which addresses these issues but which has seen limited application in ecology. As examples, we analyze simulated spread data and the historic pattern of spread of an invasive species, the hemlock woolly adelgid (Adelges tsugae), using county-level summaries of the year of first reported infestation and several covariates potentially important to influencing the observed spread dynamics. Bayesian areal wombling is a promising approach for analyzing ecological boundaries and dynamics related to changes in the distributions of native and invasive species.     

Extinction Rate Estimates for Plant Populations in Revisitation Studies: Importance of Detectability

Abstract:  Many researchers have obtained extinction-rate estimates for plant populations by comparing historical and current records of occurrence. A population that is no longer found is assumed to have gone extinct. Extinction can then be related to characteristics of these populations, such as habitat type, size, or species, to test ideas about what factors may affect extinction. Such studies neglect the fact that a population may be overlooked, however, which may bias estimates of extinction rates upward. In addition, if populations are unequally detectable across groups to be compared, such as habitat type or population size, comparisons become distorted to an unknown degree. To illustrate the problem, I simulated two data sets, assuming a constant extinction rate, in which populations occurred in different habitats or habitats of different size and these factors affected their detectability. The conventional analysis implicitly assumed that detectability equalled 1 and used logistic regression to estimate extinction rates. It wrongly identified habitat and population size as factors affecting extinction risk. In contrast, with capture-recapture methods, unbiased estimates of extinction rates were recovered. I argue that capture-recapture methods should be considered more often in estimations of demographic parameters in plant populations and communities.     

Estimating age from recapture data: integrating incremental growth measures with ancillary data to infer age-at-length

Estimating the age of individuals in wild populations can be of fundamental importance for answering ecological questions, modeling population demographics, and managing exploited or threatened species. Significant effort has been devoted to determining age through the use of growth annuli, secondary physical characteristics related to age, and growth models. Many species, however, either do not exhibit physical characteristics useful for independent age validation or are too rare to justify sacrificing a large number of individuals to establish the relationship between size and age. Length-at-age models are well represented in the fisheries and other wildlife management literature. Many of these models overlook variation in growth rates of individuals and consider growth parameters as population parameters. More recent models have taken advantage of hierarchical structuring of parameters and Bayesian inference methods to allow for variation among individuals as functions of environmental covariates or individual-specific random effects. Here, we describe hierarchical models in which growth curves vary as individual-specific stochastic processes, and we show how these models can be fit using capture-recapture data for animals of unknown age along with data for animals of known age. We combine these independent data sources in a Bayesian analysis, distinguishing natural variation (among and within individuals) from measurement error. We illustrate using data for African dwarf crocodiles, comparing von Bertalanffy and logistic growth models. The analysis provides the means of predicting crocodile age, given a single measurement of head length. The von Bertalanffy was much better supported than the logistic growth model and predicted that dwarf crocodiles grow from 19.4 cm total length at birth to 32.9 cm in the first year and 45.3 cm by the end of their second year. Based on the minimum size of females observed with hatchlings, reproductive maturity was estimated to be at nine years. These size benchmarks are believed to represent thresholds for important demographic parameters; improved estimates of age, therefore, will increase the precision of population projection models. The modeling approach that we present can be applied to other species and offers significant advantages when multiple sources of data are available and traditional aging techniques are not practical.     

A closure test for time-specific capture-recapture data

The assumption of demographic closure in the analysis of capture-recapture data under closed-population models is of fundamental importance. Yet, little progress has been made in the development of omnibus tests of the closure assumption. We present a closure test for time-specific data that, in principle, tests the null hypothesis of closed-population model M _t against the open-population Jolly-Seber model as a specific alternative. This test is chi-square, and can be decomposed into informative components that can be interpreted to determine the nature of closure violations. The test is most sensitive to permanent emigration and least sensitive to temporary emigration, and is of intermediate sensitivity to permanent or temporary immigration. This test is a versatile tool for testing the assumption of demographic closure in the analysis of capture-recapture data.     

Assessing tiger population dynamics using photographic capture-recapture sampling

Although wide-ranging, elusive, large carnivore species, such as the tiger, are of scientific and conservation interest, rigorous inferences about their population dynamics are scarce because of methodological problems of sampling populations at the required spatial and temporal scales. We report the application of a rigorous, noninvasive method for assessing tiger population dynamics to test model-based predictions about population viability. We obtained photographic capture histories for 74 individual tigers during a nine-year study involving 5725 trap-nights of effort. These data were modeled under a likelihood-based, "robust design" capture-recapture analytic framework. We explicitly modeled and estimated ecological parameters such as time-specific abundance, density, survival, recruitment, temporary emigration, and transience, using models that incorporated effects of factors such as individual heterogeneity, trap-response, and time on probabilities of photo-capturing tigers. The model estimated a random temporary emigration parameter of gamma" = gamma' = 0.10 +/- 0.069 (values are estimated mean +/- SE). When scaled to an annual basis, tiger survival rates were estimated at S = 0.77 +/- 0.051, and the estimated probability that a newly caught animal was a transient was tau = 0.18 +/- 0.11. During the period when the sampled area was of constant size, the estimated population size N(t) varied from 17 +/- 1.7 to 31 +/- 2.1 tigers, with a geometric mean rate of annual population change estimated as lambda = 1.03 +/- 0.020, representing a 3% annual increase. The estimated recruitment of new animals, B(t), varied from 0 +/- 3.0 to 14 +/- 2.9 tigers. Population density estimates, D, ranged from 7.33 +/- 0.8 tigers/100 km2 to 21.73 +/- 1.7 tigers/100 km2 during the study. Thus, despite substantial annual losses and temporal variation in recruitment, the tiger density remained at relatively high levels in Nagarahole. Our results are consistent with the hypothesis that protected wild tiger populations can remain healthy despite heavy mortalities because of their inherently high reproductive potential. The ability to model the entire photographic capture history data set and incorporate reduced-parameter models led to estimates of mean annual population change that were sufficiently precise to be useful. This efficient, noninvasive sampling approach can be used to rigorously investigate the population dynamics of tigers and other elusive, rare, wide-ranging animal species in which individuals can be identified from photographs or other means.     

Resources from another place and time: responses to pulses in a spatially subsidized system

As the theoretical bases for the dynamics of spatially subsidized communities emerge, ecologists question whether spatially subsidized communities exhibit similar structure or dynamics to communities that receive strongly pulsed resources. In both cases, communities may be structured by responses to resources that are potentially absent at any given point in time (pulsed communities) or space (subsidized communities), even if pulsed resources are part of the in situ productivity of the system or the subsidies arrive as a relatively constant input from a nearby system. The potential for significant spatial or temporal resource limitation, therefore, may be a key factor influencing in similar ways the persistence of populations, the structure and dynamics of communities, and the evolution of specific life history traits. In most complex systems, however, multiple resources may arrive for various trophic entities at various points in time and from various points in space, and thus it may be difficult to separate or compare the dynamics of spatially subsidized and pulsed systems. In this paper, we explore the effects of interactions between pulses and subsidies in plant and animal populations and communities on highly pulsed and variably subsidized islands in the Gulf of California. While many of the plant and animal communities on the unsubsidized islands in this system respond to pulses of rain in classic ways, responses to these rain pulses on islands subsidized by seabird guano or other marine resources are quite different and variable, and depend on a combination of life history characteristics, physiology, competitive interactions, and trophic relationships. These variable responses to rain pulses then translate into large differences in dynamics and community structure of subsidized vs. unsubsidized islands. Indeed, most systems experience both temporal pulses and spatial subsidies. When considered in tandem, complementary or synergistic effects of the multiple, temporally and spatially variable resources may emerge that help explain complex food web structure and dynamics.     

Modeling misidentification errors that result from use of genetic tags in capture–recapture studies

Misidentification of animals is potentially important when naturally existing features (natural tags) such as DNA fingerprints (genetic tags) are used to identify individual animals. For example, when misidentification leads to multiple identities being assigned to an animal, traditional estimators tend to overestimate population size. Accounting for misidentification in capture–recapture models requires detailed understanding of the mechanism. Using genetic tags as an example, we outline a framework for modeling the effect of misidentification in closed population studies when individual identification is based on natural tags that are consistent over time (non-evolving natural tags). We first assume a single sample is obtained per animal for each capture event, and then generalize to the case where multiple samples (such as hair or scat samples) are collected per animal per capture occasion. We introduce methods for estimating population size and, using a simulation study, we show that our new estimators perform well for cases with moderately high capture probabilities or high misidentification rates. In contrast, conventional estimators can seriously overestimate population size when errors due to misidentification are ignored.     

A combination line transect and capture-recapture sampling model for multiple observers in aerial surveys

We present a robust sampling methodology to estimate population size using line transect and capture-recapture procedures for aerial surveys. Aerial surveys usually underestimate population density due to animals being missed. A combination of capture-recapture and line transect sampling methods with multiple observers allows violation of the assumption that all animals on the centreline are sighted from the air. We illustrate our method with an example of inanimate objects which shows evidence of failure of the assumption that all objects on the centreline have probability 1 of being detected. A simulation study is implemented to evaluate the performance of three variations of the Lincoln-Petersen estimator: the overall estimator, the stratified estimator, and the general stratified estimator based on the combined likelihood proposed in this paper. The stratified Lincoln-Petersen estimator based on the combined likelihood is found to be generally superior to the other estimators.     

A generalized estimating equations approach for capture–recapture closed population models

The estimation of population density animal population parameters, such as capture probability, population size, or population density, is an important issue in many ecological applications. Capture–recapture data may be considered as repeated observations that are often correlated over time. If these correlations are not taken into account then parameter estimates may be biased, possibly producing misleading results. We propose a generalized estimating equations (GEE) approach to account for correlation over time instead of assuming independence as in the traditional closed population capture–recapture studies. We also account for heterogeneity among observed individuals and over-dispersion, modelling capture probabilities as a function of covariates. The GEE versions of all closed population capture–recapture models and their corresponding estimating equations are proposed. We evaluate the effect of accounting for correlation structures on capture–recapture model selection based on the quasi-likelihood information criterion (QIC). An example is used for an illustrative application and for comparison to currently used methodology. A Horvitz–Thompson-like estimator is used to obtain estimates of population size based on conditional arguments. A simulation study is conducted to evaluate the performance of the GEE approach in capture-recapture studies. The GEE approach performs well for estimating population parameters, particularly when capture probabilities are high. The simulation results also reveal that estimated population size varies on the nature of the existing correlation among capture occasions.     

Use of ambiguous detections to improve estimates from species distribution models

As large carnivores recover throughout Europe, their distribution needs to be studied to determine their conservation status and assess the potential for human-carnivore conflicts. However, efficient monitoring of many large carnivore species is challenging due to their rarity, elusive behavior, and large home ranges. Their monitoring can include opportunistic sightings from citizens in addition to designed surveys. Two types of detection errors may occur in such monitoring schemes: false negatives and false positives. False-negative detections can be accounted for in species distribution models (SDMs) that deal with imperfect detection. False-positive detections, due to species misidentification, have rarely been accounted for in SDMs. Generally, researchers use ad hoc data-filtering methods to discard ambiguous observations prior to analysis. These practices may discard valuable ecological information on the distribution of a species. We investigated the costs and benefits of including data types that may include false positives rather than discarding them for SDMs of large carnivores. We used a dynamic occupancy model that simultaneously accounts for false negatives and positives to jointly analyze data that included both unambiguous detections and ambiguous detections. We used simulations to compare the performances of our model with a model fitted on unambiguous data only. We tested the 2 models in 4 scenarios in which parameters that control false-positive detections and true detections varied. We applied our model to data from the monitoring of the Eurasian lynx (Lynx lynx) in the European Alps. The addition of ambiguous detections increased the precision of parameter estimates. For the Eurasian lynx, incorporating ambiguous detections produced more precise estimates of the ecological parameters and revealed additional occupied sites in areas where the species is likely expanding. Overall, we found that ambiguous data should be considered when studying the distribution of large carnivores through the use of dynamic occupancy models that account for misidentification.     

Modeling and inference of animal movement using artificial neural networks

Movement of animals in relation to objects in their environment is important in many areas of ecology and wildlife conservation. Tools for analysis of movement data, however, still remain rather limited. In previous work, we developed nonlinear regression models for movement in relation to a single landscape feature. Here we greatly expand these previous models by using artificial neural networks. The new models add substantial flexibility and capabilities, including the ability to incorporate multiple factors and covariates. We devise a likelihood-based model fitting procedure that utilizes genetic algorithms and demonstrate the approach with movement data for red diamond rattlesnakes. The proposed methodology can be useful for global positioning system tracking data that are becoming more common in studies of animal movement behavior.