Monitoring distributions using call surveys: estimating site occupancy, detection probabilities and inferring absence

Monitoring programs serve to track changes in the distribution and abundance of species. A major problem with most monitoring programs is that species detection is imperfect and some populations are inevitably missed. Therefore, in most monitoring programs the true distribution of a species will be underestimated. Here, we report a field test of the reliability and performance of a commonly used method to monitor the distribution of amphibians (anuran call surveys). We surveyed the distribution of four anuran species in western Switzerland, and estimated detection probabilities to account for imperfect species detection and used these estimates to adjust our estimate of site occupancy (i.e., distribution). Next, we assessed how detection probabilities were affected by weather and how site occupancy was affected by site specific covariates. For one species (Hyla arborea), call surveys proved efficient in determining the regional distribution with only few site visits because detection probabilities were relatively high. The call surveys apparently missed many populations of another common species (Bufo calamita) because detection probabilities were lower. Two other species (Bombina variegata and Alytes obstetricans) were uncommon and strong inference from the analysis is not possible. Thus, multispecies surveys may be inefficient for rare species. Estimates of detection probabilities were used to calculate how many site visits are necessary to infer the absence of a species with some predetermined statistical certainty. The implications of “false absences” are important in ecology as they are known to bias usual habitat suitability models and overestimate extinction/colonization events in metapopulations. Large-scale monitoring programs would benefit from the application of an estimation-based approach to monitoring the distribution of species.     

Cost-effective abundance estimation of rare animals: Testing performance of small-boat surveys for killer whales in British Columbia

Top predators are often rare, subject to anthropogenic mortality, and possess life-history traits that make them inherently vulnerable to extinction. IUCN criteria recognise populations as Critically Endangered when abundance is <250 mature individuals, but estimating abundance of rare species can be more challenging than for common ones. Cost-effective methods are needed to provide robust abundance estimates. In marine environments, small boats are more widely accessible than large ships for researchers conducting sightings surveys with limited funds, but studies are needed into efficacy of small-boat surveys. This study compares line transect and mark-recapture estimates from small-boat surveys in summer 2004 and 2005 for ‘northern resident’ killer whales in British Columbia to true population size, known from censuses conducted by Fisheries and Oceans Canada. The line transect estimate of 195 animals (95% CI 27-559) used model averaging to incorporate uncertainty in the detection function, while the mark-recapture estimate of 239 animals (CI 154-370) used a simple two-sample Chapman estimator. Both methods produced estimates close to the true population size, which numbered 219 animals in 2004 and 235 in 2006, but both suffered from the small sample sizes and violations of some model assumptions that will vex most pilot studies of rare species. Initial abundance estimates from relatively low-cost surveys can be thought of as hypotheses to be tested as new data are collected. For species of conservation concern, any cost-effective attempt to estimate absolute abundance will assist status assessments, as long as estimates are presented with appropriate caveats.     

Hierarchical models of animal abundance and occurrence

Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.     

Hierarchical modeling of cluster size in wildlife surveys

Clusters or groups of individuals are the fundamental unit of observation in many wildlife sampling problems, including aerial surveys of waterfowl, marine mammals, and ungulates. Explicit accounting of cluster size in models for estimating abundance is necessary because detection of individuals within clusters is not independent and detectability of clusters is likely to increase with cluster size. This induces a cluster size bias in which the average cluster size in the sample is larger than in the population at large. Thus, failure to account for the relationship between detectability and cluster size will tend to yield a positive bias in estimates of abundance or density. I describe a hierarchical modeling framework for accounting for cluster-size bias in animal sampling. The hierarchical model consists of models for the observation process conditional on the cluster size distribution and the cluster size distribution conditional on the total number of clusters. Optionally, a spatial model can be specified that describes variation in the total number of clusters per sample unit. Parameter estimation, model selection, and criticism may be carried out using conventional likelihood-based methods. An extension of the model is described for the situation where measurable covariates at the level of the sample unit are available. Several candidate models within the proposed class are evaluated for aerial survey data on mallard ducks (Anas platyrhynchos).     

Modeling co-occurrence of northern spotted and barred owls: Accounting for detection probability differences

Barred owls (Strix varia) have recently expanded their range and now encompass the entire range of the northern spotted owl (Strix occidentalis caurina). This expansion has led to two important issues of concern for management of northern spotted owls: (1) possible competitive interactions between the two species that could contribute to population declines of northern spotted owls, and (2) possible changes in vocalization behavior and detection probabilities of northern spotted owls induced by presence of barred owls. We used a two-species occupancy model to investigate whether there was evidence of competitive exclusion between the two species at study locations in Oregon, USA. We simultaneously estimated detection probabilities for both species and determined if the presence of one species influenced the detection of the other species. Model selection results and associated parameter estimates provided no evidence that barred owls excluded spotted owls from territories. We found strong evidence that detection probabilities differed for the two species, with higher probabilities for northern spotted owls that are the object of current surveys. Non-detection of barred owls is very common in surveys for northern spotted owls, and detection of both owl species was negatively influenced by the presence of the congeneric species. Our results suggest that analyses directed at hypotheses of barred owl effects on demographic or occupancy vital rates of northern spotted owls need to deal adequately with imperfect and variable detection probabilities for both species.     

Incorporating parametric uncertainty into population viability analysis models

Uncertainty in parameter estimates from sampling variation or expert judgment can introduce substantial uncertainty into ecological predictions based on those estimates. However, in standard population viability analyses, one of the most widely used tools for managing plant, fish and wildlife populations, parametric uncertainty is often ignored in or discarded from model projections. We present a method for explicitly incorporating this source of uncertainty into population models to fully account for risk in management and decision contexts. Our method involves a two-step simulation process where parametric uncertainty is incorporated into the replication loop of the model and temporal variance is incorporated into the loop for time steps in the model. Using the piping plover, a federally threatened shorebird in the USA and Canada, as an example, we compare abundance projections and extinction probabilities from simulations that exclude and include parametric uncertainty. Although final abundance was very low for all sets of simulations, estimated extinction risk was much greater for the simulation that incorporated parametric uncertainty in the replication loop. Decisions about species conservation (e.g., listing, delisting, and jeopardy) might differ greatly depending on the treatment of parametric uncertainty in population models.     

Insights Into the Latent Multinomial Model Through Mark-Resight Data on Female Grizzly Bears With Cubs-of-the-Year

Mark-resight designs for estimation of population abundance are common and attractive to researchers. However, inference from such designs is very limited when faced with sparse data, either from a low number of marked animals, a low probability of detection, or both. In the Greater Yellowstone Ecosystem, yearly mark-resight data are collected for female grizzly bears with cubs-of-the-year (FCOY), and inference suffers from both limitations. To overcome difficulties due to sparseness, we assume homogeneity in sighting probabilities over 16 years of bi-annual aerial surveys. We model counts of marked and unmarked animals as multinomial random variables, using the capture frequencies of marked animals for inference about the latent multinomial frequencies for unmarked animals. We discuss undesirable behavior of the commonly used discrete uniform prior distribution on the population size parameter and provide OpenBUGS code for fitting such models. The application provides valuable insights into subtleties of implementing Bayesian inference for latent multinomial models. We tie the discussion to our application, though the insights are broadly useful for applications of the latent multinomial model.     

Models for Jointly Estimating Abundances of Two Unmarked Site-Associated Species Subject to Imperfect Detection

In ecological field surveys, it is often of interest to estimate the abundance of species. It is frequently the case that unmarked animals are counted on different sites over several time occasions. A natural starting point to model these data, while accounting for imperfect detection, is by using Royle’s N-mixture model (Biometrics 60:108–115, 2004). Subsequently, many multivariate extensions have been proposed to model communities as a whole. However, these approaches are used to study species richness and other community-level variables and do not focus on the relationship between two site-associated species. Here, we extend the N-mixture modelling framework to model two site-associated species abundances jointly and propose to measure the influence of one species’ abundance on the populations of the other and study how this changes over time and space. By including a new parameter in the abundance distribution of one of the species, linking it to abundance of the other, our proposed model treats extra variability as an effect induced by an associated species’ abundance and allows one to study how environmental covariates may affect this. Using results from simulation studies, we show that the model is able to recover true parameter estimates. We illustrate our approach using data from bald eagles and mallards obtained in the 2015 survey of the North American Breeding Bird Survey. By using the joint model, we were able to separate overdispersion from mallard-induced variability and hence what would be accounted for with a dispersion parameter in the univariate framework for the eagles was explained by covariates related to mallard abundance in the joint model. Our approach represents an attractive, yet simple, way of modelling site-associated species populations jointly. Conservation ecologists can use the approach to devise management strategies based on the strength of association between species, which may be due to direct interactions and/or environmental effects affecting both species’ populations. Also, mathematical ecologists can use this framework to develop tools for studying population dynamics under different scenarios. Supplementary materials accompanying this paper appear on-line.     

Bayesian capture-recapture analysis and model selection allowing for heterogeneity and behavioral effects

In this article, we present Bayesian analysis of capture-recapture models for a closed population which allows for heterogeneity of capture probabilities between animals and bait/trap effects. We use a flexible discrete mixture model to account for the heterogeneity and behavioral effects. In addition we present a solid model selection criterion. Through illustrations with a motivating dataset, we demonstrate how Bayesian analysis can be applied in this setting and discuss some major benefits which result, including consideration of informative priors based on historical data.     

Extending Ordinal Regression with a Latent Zero-Augmented Beta Distribution

Ecological abundance data are often recorded on an ordinal scale in which the lowest category represents species absence. One common example is when plant species cover is visually assessed within bounded quadrats and then assigned to pre-defined cover class categories. We present an ordinal beta hurdle model that directly models ordinal category probabilities with a biologically realistic beta-distributed latent variable. A hurdle-at-zero model allows ecologists to explore distribution (absence) and abundance processes in an integrated framework. This provides an alternative to cumulative link models when data are inconsistent with the assumption that the odds of moving into a higher category are the same for all categories (proportional odds). Graphical tools and a deviance information criterion were developed to assess whether a hurdle-at-zero model should be used for inferences rather than standard ordinal methods. Hurdle-at-zero and non-hurdle ordinal models fit to vegetation cover class data produced substantially different conclusions. The ordinal beta hurdle model yielded more precise parameter estimates than cumulative logit models, although out-of-sample predictions were similar. The ordinal beta hurdle model provides inferences directly on the latent biological variable of interest, percent cover, and supports exploration of more realistic ecological patterns and processes through the hurdle-at-zero or two-part specification. We provide JAGS code as an on-line supplement. Supplementary materials accompanying this paper appear on-line.     

A hierarchical model for compositional data analysis

This article introduces a hierarchical model for compositional analysis. Our approach models both source and mixture data simultaneously, and accounts for several different types of variation: these include measurement error on both the mixture and source data; variability in the sample from the source distributions; and variability in the mixing proportions themselves, generally of main interest. The method is an improvement on some existing methods in that estimates of mixing proportions (including their interval estimates) are sure to lie in the range [0, 1]; in addition, it is shown that our model can help in situations where identification of appropriate source data is difficult, especially when we extend our model to include a covariate. We first study the likelihood surface of a base model for a simple example, and then include prior distributions to create a Bayesian model that allows analysis of more complex situations via Markov chain Monte Carlo sampling from the likelihood. Application of the model is illustrated with two examples using real data: one concerning chemical markers in plants, and another on water chemistry.     

Bayesian Methods for Hierarchical Distance Sampling Models

The few distance sampling studies that use Bayesian methods typically consider only line transect sampling with a half-normal detection function. We present a Bayesian approach to analyse distance sampling data applicable to line and point transects, exact and interval distance data and any detection function possibly including covariates affecting detection probabilities. We use an integrated likelihood which combines the detection and density models. For the latter, densities are related to covariates in a log-linear mixed effect Poisson model which accommodates correlated counts. We use a Metropolis-Hastings algorithm for updating parameters and a reversible jump algorithm to include model selection for both the detection function and density models. The approach is applied to a large-scale experimental design study of northern bobwhite coveys where the interest was to assess the effect of establishing herbaceous buffers around agricultural fields in several states in the US on bird densities. Results were compared with those from an existing maximum likelihood approach that analyses the detection and density models in two stages. Both methods revealed an increase of covey densities on buffered fields. Our approach gave estimates with higher precision even though it does not condition on a known detection function for the density model.     

Bayesian Calibration of Blue Crab (<Emphasis Type="Italic">Callinectes sapidus</Emphasis>) Abundance Indices Based on Probability Surveys

Abundance and standard error estimates in surveys of fishery resources typically employ classical design-based approaches, ignoring the influences of non-design factors such as varying catchability. We developed a Bayesian approach for estimating abundance and associated errors in a fishery survey by incorporating sampling and non-sampling variabilities. First, a zero-inflated spatial model was used to quantify variance components due to non-sampling factors; second, the model was used to calibrate the estimated abundance index and its variance using pseudo empirical likelihood. The approach was applied to a winter dredge survey conducted to estimate the abundance of blue crabs (Callinectes sapidus) in the Chesapeake Bay. We explored the properties of the calibration estimators through a limited simulation study. The variance estimator calibrated on posterior sample performed well, and the mean estimator had comparable performance to design-based approach with slightly higher bias and lower (about 15% reduction) mean squared error. The results suggest that application of this approach can improve estimation of abundance indices using data from design-based fishery surveys.     

Spatial models for line transect sampling

This article develops methods for fitting spatial models to line transect data. These allow animal density to be related to topographical, environmental, habitat, and other spatial variables, helping wildlife managers to identify the factors that affect abundance. They also enable estimation of abundance for any subarea of interest within the surveyed region, and potentially yield estimates of abundance from sightings surveys for which the survey design could not be randomized, such as surveys conducted from platforms of opportunity. The methods are illustrated through analyses of data from a shipboard sightings survey of minke whales in the Antarctic.     

Abundance and conservation status of the Yangtze finless porpoise in the Yangtze River, China

The Yangtze finless porpoise (Neophocaena phocaenoides asiaeorientalis) is endemic to the middle and lower reaches of the Yangtze River, China. It is the only freshwater population of porpoises in the world and is currently listed as Endangered by IUCN. In November and December 2006 we used two boats and line transect methods to survey the entire current range of the population, except for two lakes (Poyang and Dongting). Sighting results were similar for both boats, so we pooled all data and analyzed them using two line transect models and a strip transect model. All models produced similar estimates of abundance (1111, 1225 and 1000). We then added independent estimates of the number of porpoises from the two lakes for a total estimate of approximately 1800 porpoises. Our findings indicate that the population continues to decline and that its distribution is becoming more fragmented. Our current estimate in the main river is slightly less than half the estimate from surveys between 1984 and 1991 (which was probably an underestimate). We also found an apparent gap in the distribution of porpoises between Yueyang and Shishou (∼150 km), where sightings had previously been common. Continued threats to Yangtze finless porpoises include bycatch in unregulated and unselective fishing, habitat degradation through dredging, pollution and noise, vessel strikes and water development. Immediate protective measures are urgently needed to ensure the persistence of finless porpoises in the Yangtze River. The survey design and analytical methods developed in this study might be appropriate for surveys of cetaceans in other river systems.     

A gamma-shaped detection function for line-transect surveys with mark-recapture and covariate data

We have developed a procedure for estimating animal population size from aerial survey data collected simultaneously by two observers on the same sighting platform. We used a line transect sample design where transects follow elevation contours in mountainous terrain. Because our 10 data sets from aerial line transect surveys, conducted over a terrestrial environment, consistently show unimodal detection shapes, we chose a gamma-shaped detection function that is unimodal and admits covariates. We fit models separately to data from each observer, and then used all of the data to estimate the probabilities at the apex of the detection curves. We used a Horvitz-Thompson estimator to estimate the population size. We illustrate our procedure on a recently collected brown bear data set.     

Improving Estimates of Abundance by Aggregating Sparse Capture-Recapture Data

Inferences about abundance often are based on unadjusted counts of individuals observed, in part, because of the large amount of data required to generate reliable estimates of abundance. Where capture-recapture data are sparse, aggregating data across multiple sample elements by pooling species, locations, and sampling periods increases the information available for modeling detection probability, a necessary step for estimating abundance reliably. The process of aggregating sample elements involves balancing trade-offs related to the number of aggregated elements; although larger aggregates increase the amount of information available for estimation, they often require more complex models. We describe a heuristic approach for aggregating data for studies with multiple sample elements, use simulated data to evaluate the efficacy of aggregation, and illustrate the approach using data from a field study. Aggregating data systematically improved reliability of model selection and increased accuracy of abundance estimates while still providing estimates of abundance for each original sample unit, an important benefit necessary to maintain the design and sampling structure of a study. Within the framework of capture-recapture sampling, aggregating data improves estimates of abundance and increases the reliability of subsequent inferences made from sparse data. Additional tables and datasets may be found in the online supplements.     

Motorways and bird traffic casualties: Carcasses surveys and scavenging bias

Most survey methods developed to estimate abundance of killed animals on motorways may be biased due to the unequal detectability of carcasses, their persistence time on the lanes, and scavengers activities. Unbiased surveys are needed to evaluate the relationships between bird casualties (mortality), motorways characteristics, and the neighbouring avifauna. The present study conducted on four motorways in France, aimed to evaluate factors affecting persistence and encounter probabilities and variations in scavenging activity to obtain unbiased estimates of bird traffic casualties. Each motorway was surveyed once per season during multiple years and we used capture–recapture methods to estimate detection and carcass persistence rates. Results showed that surveys by car were as efficient as surveys by foot in detecting carcasses on the pavement, but less efficient for carcasses on verges. Passeriformes represented the most numerous casualties, and the Barn Owl (Tyto alba) was the most frequently killed species. Encounter probabilities were constant and high (0.957 ± 0.007). Average daily persistence probability was 0.976 ± 0.003. Persistence probabilities were higher for large and old carcasses, during summer, and differed between seasons, but were relatively similar between years. Scavenging activities, estimated using experimental carcasses disposed on the safe lanes of motorways, varied between years, seasons, and differed between diurnal and nocturnal periods. A peak in scavenging activity occurred during diurnal periods in spring. Results suggest that surveys must take into account carcass characteristics and seasonal variability to obtain unbiased estimates of road killed birds on motorways, as well as variation in scavenging rates.     

Point-Based Mark-Recapture Distance Sampling

Avian surveys using point sampling for abundance estimation have either focused on distance sampling or more commonly mark-recapture to correct for detection bias. Combining mark-recapture and distance sampling (MRDS) has become an effective tool for line transects, but it has been largely ignored in point sampling literature. We describe MRDS and show that the previously published methods for point sampling are special cases. Using simulated data and golden-cheeked warbler (Dendroica chrysoparia) survey data from Texas, we demonstrate large differences in abundance estimates resulting from different independence assumptions. Data and code are provided in supplementary materials.