Assessing Estimators of Snow Leopard Abundance

Abstract: The secretive nature of snow leopards (Uncia uncia) makes them difficult to monitor, yet conservation efforts require accurate and precise methods to estimate abundance. We assessed accuracy of Snow Leopard Information Management System (SLIMS) sign surveys by comparing them with 4 methods for estimating snow leopard abundance: predator:prey biomass ratios, capture-recapture density estimation, photo-capture rate, and individual identification through genetic analysis. We recorded snow leopard sign during standardized surveys in the SaryChat Zapovednik, the Jangart hunting reserve, and the Tomur Strictly Protected Area, in the Tien Shan Mountains of Kyrgyzstan and China. During June-December 2005, adjusted sign averaged 46.3 (SaryChat), 94.6 (Jangart), and 150.8 (Tomur) occurrences/km. We used counts of ibex (Capra ibex) and argali (Ovis ammon) to estimate available prey biomass and subsequent potential snow leopard densities of 8.7 (SaryChat), 1.0 (Jangart), and 1.1 (Tomur) snow leopards/100 km². Photo capture-recapture density estimates were 0.15 (n = 1 identified individual/1 photo), 0.87 (n = 4/13), and 0.74 (n = 5/6) individuals/100 km² in SaryChat, Jangart, and Tomur, respectively. Photo-capture rates (photos/100 trap-nights) were 0.09 (SaryChat), 0.93 (Jangart), and 2.37 (Tomur). Genetic analysis of snow leopard fecal samples provided minimum population sizes of 3 (SaryChat), 5 (Jangart), and 9 (Tomur) snow leopards. These results suggest SLIMS sign surveys may be affected by observer bias and environmental variance. However, when such bias and variation are accounted for, sign surveys indicate relative abundances similar to photo rates and genetic individual identification results. Density or abundance estimates based on capture-recapture or ungulate biomass did not agree with other indices of abundance. Confidence in estimated densities, or even detection of significant changes in abundance of snow leopard, will require more effort and better documentation.     

Capture-Recapture Estimators in Epidemiology with Applications to Pertussis and Pneumococcal Invasive Disease Surveillance

IntroductionSurveillance networks are often not exhaustive nor completely complementary. In such situations, capture-recapture methods can be used for incidence estimation. The choice of estimator and their robustness with respect to the homogeneity and independence assumptions are however not well documented.MethodsWe investigated the performance of five different capture-recapture estimators in a simulation study. Eight different scenarios were used to detect and combine case-information. The scenarios increasingly violated assumptions of independence of samples and homogeneity of detection probabilities. Belgian datasets on invasive pneumococcal disease (IPD) and pertussis provided motivating examples.ResultsNo estimator was unbiased in all scenarios. Performance of the parametric estimators depended on how much of the dependency and heterogeneity were correctly modelled. Model building was limited by parameter estimability, availability of additional information (e.g. covariates) and the possibilities inherent to the method. In the most complex scenario, methods that allowed for detection probabilities conditional on previous detections estimated the total population size within a 20–30% error-range. Parametric estimators remained stable if individual data sources lost up to 50% of their data. The investigated non-parametric methods were more susceptible to data loss and their performance was linked to the dependence between samples; overestimating in scenarios with little dependence, underestimating in others. Issues with parameter estimability made it impossible to model all suggested relations between samples for the IPD and pertussis datasets. For IPD, the estimates for the Belgian incidence for cases aged 50 years and older ranged from 44 to58/100,000 in 2010. The estimates for pertussis (all ages, Belgium, 2014) ranged from 24.2 to30.8/100,000.ConclusionWe encourage the use of capture-recapture methods, but epidemiologists should preferably include datasets for which the underlying dependency structure is not too complex, a priori investigate this structure, compensate for it within the model and interpret the results with the remaining unmodelled heterogeneity in mind.     

Assessing Population Viability of Black Bears using Spatial Capture-Recapture Models

The Central Georgia Bear Population (CGP) is the least abundant and most isolated of Georgia's 3 American black bear (Ursus americanus) populations. Beginning in 2011, changes to regulations governing harvest of the CGP resulted in an increase in female bear harvest, creating concern that future harvest could be an important influence on population viability. Hence, our objective was to assess viability of the CGP under various levels of female mortality. During 2012–2016, we used barbed-wire hair snares to collect bear hair samples from within the range of the CGP in Georgia, USA. We used microsatellite genotyping to identify individual bears and created robust-design, spatial detection histories for all female bears detected. We fit open population spatial capture-recapture (SCR) models to the detection histories in a Bayesian framework. We used the Widely Applicable Information Criterion (WAIC) to rank models that varied with respect to sources of variation in detection probability, survival, and per capita recruitment, and used the model with the lowest WAIC to forecast dynamics of the CGP 50 years into the future under various levels of female mortality. We assessed the 50-year extinction probability under a continuation of mortality levels documented during 2012–2016, and under incremental increases in female mortality above this baseline. The top model included density-dependent per capita recruitment, annual variation in detection probability, and a trap-level behavioral response. Abundance increased from 106 (95% CI = 86–132) females in 2012 to 136 (95% CI = 113–161) females in 2013 and remained relatively stable thereafter. Annual female survival was 0.75 (95% CI = 0.69–0.82) and did not vary among years. The per capita recruitment rate decreased over time as density increased, and was 0.49 (95% CI = 0.33–0.66) during the first time interval and 0.29 (95% CI = 0.20–0.38) during the final time interval. Annual growth rate () was 1.28 (95% CI = 1.07–1.52) between 2012 and 2013 but decreased throughout the study, ending at 1.04 (95% CI = 0.93–1.17). Forecasts indicated continuation of the female mortality levels experienced from 2012–2016 were sustainable over 50 years, with the estimated extinction risk being <0.001%. Increasing annual harvest by 5 females introduced a negligible increase in the 50-year probability of extinction, but harvesting an additional 10 females/year caused extinction risk to rise to 1.15%. We recommend that harvest regulations are structured such that mortality rates remain at current levels or do not increase by more than an annual average of 5 females above levels observed during our study. Furthermore, we recommend that managers continue to monitor the population so that harvest regulations and population models can be refined over time. © 2020 The Wildlife Society.     

A Comparison of Grizzly Bear Demographic Parameters Estimated from Non-Spatial and Spatial Open Population Capture-Recapture Models

Capture-recapture studies are frequently used to monitor the status and trends of wildlife populations. Detection histories from individual animals are used to estimate probability of detection and abundance or density. The accuracy of abundance and density estimates depends on the ability to model factors affecting detection probability. Non-spatial capture-recapture models have recently evolved into spatial capture-recapture models that directly include the effect of distances between an animal’s home range centre and trap locations on detection probability. Most studies comparing non-spatial and spatial capture-recapture biases focussed on single year models and no studies have compared the accuracy of demographic parameter estimates from open population models. We applied open population non-spatial and spatial capture-recapture models to three years of grizzly bear DNA-based data from Banff National Park and simulated data sets. The two models produced similar estimates of grizzly bear apparent survival, per capita recruitment, and population growth rates but the spatial capture-recapture models had better fit. Simulations showed that spatial capture-recapture models produced more accurate parameter estimates with better credible interval coverage than non-spatial capture-recapture models. Non-spatial capture-recapture models produced negatively biased estimates of apparent survival and positively biased estimates of per capita recruitment. The spatial capture-recapture grizzly bear population growth rates and 95% highest posterior density averaged across the three years were 0.925 (0.786–1.071) for females, 0.844 (0.703–0.975) for males, and 0.882 (0.779–0.981) for females and males combined. The non-spatial capture-recapture population growth rates were 0.894 (0.758–1.024) for females, 0.825 (0.700–0.948) for males, and 0.863 (0.771–0.957) for both sexes. The combination of low densities, low reproductive rates, and predominantly negative population growth rates suggest that Banff National Park’s population of grizzly bears requires continued conservation-oriented management actions.     

A Bayesian Hierarchical Model for Estimation of Abundance and Spatial Density of Aedes aegypti

Strategies to minimize dengue transmission commonly rely on vector control, which aims to maintain Ae. aegypti density below a theoretical threshold. Mosquito abundance is traditionally estimated from mark-release-recapture (MRR) experiments, which lack proper analysis regarding accurate vector spatial distribution and population density. Recently proposed strategies to control vector-borne diseases involve replacing the susceptible wild population by genetically modified individuals’ refractory to the infection by the pathogen. Accurate measurements of mosquito abundance in time and space are required to optimize the success of such interventions. In this paper, we present a hierarchical probabilistic model for the estimation of population abundance and spatial distribution from typical mosquito MRR experiments, with direct application to the planning of these new control strategies. We perform a Bayesian analysis using the model and data from two MRR experiments performed in a neighborhood of Rio de Janeiro, Brazil, during both low- and high-dengue transmission seasons. The hierarchical model indicates that mosquito spatial distribution is clustered during the winter (0.99 mosquitoes/premise 95% CI: 0.80–1.23) and more homogeneous during the high abundance period (5.2 mosquitoes/premise 95% CI: 4.3–5.9). The hierarchical model also performed better than the commonly used Fisher-Ford’s method, when using simulated data. The proposed model provides a formal treatment of the sources of uncertainty associated with the estimation of mosquito abundance imposed by the sampling design. Our approach is useful in strategies such as population suppression or the displacement of wild vector populations by refractory Wolbachia-infected mosquitoes, since the invasion dynamics have been shown to follow threshold conditions dictated by mosquito abundance. The presence of spatially distributed abundance hotspots is also formally addressed under this modeling framework and its knowledge deemed crucial to predict the fate of transmission control strategies based on the replacement of vector populations.     

Statistical Properties of Parasite Density Estimators in Malaria

Malaria is a global health problem responsible for nearly one million deaths every year around 85% of which concern children younger than five years old in Sub-Saharan Africa. In addition, around million clinical cases are declared every year. The level of infection, expressed as parasite density, is classically defined as the number of asexual parasites relative to a microliter of blood. Microscopy of Giemsa-stained thick blood films is the gold standard for parasite enumeration. Parasite density estimation methods usually involve threshold values; either the number of white blood cells counted or the number of high power fields read. However, the statistical properties of parasite density estimators generated by these methods have largely been overlooked. Here, we studied the statistical properties (mean error, coefficient of variation, false negative rates) of parasite density estimators of commonly used threshold-based counting techniques depending on variable threshold values. We also assessed the influence of the thresholds on the cost-effectiveness of parasite density estimation methods. In addition, we gave more insights on the behavior of measurement errors according to varying threshold values, and on what should be the optimal threshold values that minimize this variability.     

Estimation of In-Water Density and Abundance of Harbor Seals

Ecologists and managers require accurate population estimates of marine mammals to assess potential anthropogenic threats to these animals. We present estimates of in-water density and abundance of a distinct stock of harbor seals (Phoca vitulina richardii) in Hood Canal, Washington, USA. We used aerial line-transect survey data collected from 2013 to 2016 to directly estimate harbor seal density and abundance in the waters of Hood Canal, a deep-water fjord in the Salish Sea. We estimated a correction factor for trackline detection probability from dive and surface time data gathered from regional seal tagging studies, and applied this factor to correct for seals missed on the trackline during surveys. We applied conventional and multiple covariate line-transect approaches in the analysis. The resulting best estimate of in-water density of harbor seals in the Hood Canal study region was 5.80 seals/km², with an estimated abundance of 2,009 seals. We did not derive a correction factor to account for the number of seals on land (i.e., hauled out). Therefore, these estimates do not reflect total stock size but provide a starting point to evaluate potential influences of anthropogenic activities, particularly those involving underwater noise, on this marine mammal stock. © 2021 The Wildlife Society.     

Empirical Bayes analysis of single nucleotide polymorphisms

Background  

An important goal of whole-genome studies concerned with single nucleotide polymorphisms (SNPs) is the identification of SNPs associated with a covariate of interest such as the case-control status or the type of cancer. Since these studies often comprise the genotypes of hundreds of thousands of SNPs, methods are required that can cope with the corresponding multiple testing problem. For the analysis of gene expression data, approaches such as the empirical Bayes analysis of microarrays have been developed particularly for the detection of genes associated with the response. However, the empirical Bayes analysis of microarrays has only been suggested for binary responses when considering expression values, i.e. continuous predictors.     

Empirical Bayes Estimation and Prediction Using Summary-Level Information From External Big Data Sources Adjusting for Violations of Transportability

Large external data sources may be available to augment studies that collect data to address a specific research objective. In this article we consider the problem of building regression models for prediction based on individual-level data from an “internal” study while incorporating summary information from an “external” big data source. We extend the work of Chatterjee et al. (J Am Stat Assoc 111(513):107–117, 2006) by introducing an adaptive empirical Bayes shrinkage estimator that uses the external summary-level information and the internal data to trade bias with variance for protection against departures in the conditional probability distribution of the outcome given a set of covariates between the two populations. We use simulation studies and a real data application using external summary information from the Prostate Cancer Prevention Trial to assess the performance of the proposed methods in contrast to maximum likelihood estimation and the constrained maximum likelihood (CML) method developed by Chatterjee et al. (J Am Stat Assoc 111(513):107–117, 2006). Our simulation studies show that the CML method can be biased and inefficient when the assumption of a transportable covariate distribution between the external and internal populations is violated, and our empirical Bayes estimator provides protection against bias and loss of efficiency.     

Empirical Bayes estimation for combinations of multivariate bioassays

This article presents a new empirical Bayes estimator (EBE) and a shrinkage estimator for determining the relative potency from several multivariate bioassays by incorporating prior information on the model parameters based on Jeffreys' rules. The EBE can account for any extra variability among the bioassays, and if this extra variability is 0, then the EBE reduces to the maximum likelihood estimator for combinations of multivariate bioassays. The shrinkage estimator turns out to be a compromise of the prior information and the estimator from each multivariate bioassay, with the weights depending on the prior variance.     

A Comparison of the MPN and Fisher-Yates Estimators for the Density of Organisms

The method of moments estimator, discussed in FISHER and YATES (1970), for the density of bacteria is compared with the maximum likelihood or MPN estimator: For sample sizes used in practice the estimators are found to be very similar. Estimators which reduce bias are discussed and their use recommended.     

Bayesian Modeling of Prion Disease Dynamics in Mule Deer Using Population Monitoring and Capture-Recapture Data

Epidemics of chronic wasting disease (CWD) of North American Cervidae have potential to harm ecosystems and economies. We studied a migratory population of mule deer (Odocoileus hemionus) affected by CWD for at least three decades using a Bayesian framework to integrate matrix population and disease models with long-term monitoring data and detailed process-level studies. We hypothesized CWD prevalence would be stable or increase between two observation periods during the late 1990s and after 2010, with higher CWD prevalence making deer population decline more likely. The weight of evidence suggested a reduction in the CWD outbreak over time, perhaps in response to intervening harvest-mediated population reductions. Disease effects on deer population growth under current conditions were subtle with a 72% chance that CWD depressed population growth. With CWD, we forecasted a growth rate near one and largely stable deer population. Disease effects appear to be moderated by timing of infection, prolonged disease course, and locally variable infection. Long-term outcomes will depend heavily on whether current conditions hold and high prevalence remains a localized phenomenon.     

Using Time Series to Estimate Rates of Population Change from Abundance Data

Abstract: Assessing the dynamics of wild populations often involves an estimate of the finite rate of population increase (λ) or the instantaneous rate of increase (r). However, a pervasive problem in trend estimation is that many analytical techniques assume independent errors among the observations. To be valid, variance estimates around λ (or r) must account for serial correlation that exists in abundance data. Time series analysis provides a method for estimating population trends and associated variances when serial correlation of errors occurs. We offer an approach and present an example for estimating λ and its associated variance when observations are correlated over time. We present a simplified time series method and variance estimator to account for autocorrelation based on a moving average process. We illustrate the procedure using a spectacled eider (Somateria fischeri) data set of estimated annual abundances from aerial transect surveys conducted from 1957 to 1995. The analytic variance estimator provides a way to plan future studies to reduce uncertainty and bias in estimates of population growth rates. Demographic studies with policy implications or those involving species of conservation concern should especially consider the correlated nature of population trend data.     

Empirical Bayes estimation of gene-specific effects in micro-array research

Micro-array technology allows investigators the opportunity to measure expression levels of thousands of genes simultaneously. However, investigators are also faced with the challenge of simultaneous estimation of gene expression differences for thousands of genes with very small sample sizes. Traditional estimators of differences between treatment means (ordinary least squares estimators or OLS) are not the best estimators if interest is in estimation of gene expression differences for an ensemble of genes. In the case that gene expression differences are regarded as exchangeable samples from a common population, estimators are available that result in much smaller average mean-square error across the population of gene expression difference estimates. We have simulated the application of such an estimator, namely an empirical Bayes (EB) estimator of random effects in a hierarchical linear model (normal-normal). Simulation results revealed mean-square error as low as 0.05 times the mean-square error of OLS estimators (i.e., the difference between treatment means). We applied the analysis to an example dataset as a demonstration of the shrinkage of EB estimators and of the reduction in mean-square error, i.e., increase in precision, associated with EB estimators in this analysis. The method described here is available in software that is available at .