Distance models as a tool for modelling detection probability and density of native bumblebees

Effective monitoring of native bee populations requires accurate estimates of population size and relative abundance among habitats. Current bee survey methods, such as netting or pan trapping, may be adequate for a variety of study objectives but are limited by a failure to account for imperfect detection. Biases due to imperfect detection could result in inaccurate abundance estimates or erroneous insights about the response of bees to different environments. To gauge the potential biases of currently employed survey methods, we compared abundance estimates of bumblebees (Bombus spp.) derived from hierarchical distance sampling models (HDS) to bumblebee counts collected from fixed‐area net surveys (“net counts”) and fixed‐width transect counts (“transect counts”) at 47 early‐successional forest patches in Pennsylvania. Our HDS models indicated that detection probabilities of Bombus spp. were imperfect and varied with survey‐ and site‐covariates. Despite being conspicuous, Bombus spp. were not reliably detected beyond 5 m. Habitat associations of Bombus spp. density were similar across methods, but the strength of association with shrub cover differed between HDS and net counts. Additionally, net counts suggested sites with more grass hosted higher Bombus spp. densities whereas HDS suggested that grass cover was associated with higher detection probability but not Bombus spp. density. Density estimates generated from net counts and transect counts were 80%–89% lower than estimates generated from distance sampling. Our findings suggest that distance modelling provides a reliable method to assess Bombus spp. density and habitat associations, while accounting for imperfect detection caused by distance from observer, vegetation structure, and survey covariates. However, detection/non‐detection data collected via point‐counts, line‐transects and distance sampling for Bombus spp. are unlikely to yield species‐specific density estimates unless individuals can be identified by sight, without capture. Our results will be useful for informing the design of monitoring programs for Bombus spp. and other pollinators.     

Evaluating Survey Methods for Monitoring a Rare Vertebrate,the Sonoran Desert Tortoise

Abstract: Effective conservation requires strategies to monitor populations efficiently, which can be especially difficult for rare or elusive species where field surveys require high effort and considerable cost. Populations of many reptiles, including Sonoran desert tortoises (Gopherus agassizii), are challenging to monitor effectively because they are cryptic, they occur at low densities, and their activity is limited both seasonally and daily. We compared efficiency and statistical power of 2 survey methods appropriate for tortoises and other rare vertebrates, line-transect distance sampling and site occupancy. In 2005 and 2006 combined, we surveyed 120 1-km transects to estimate density and 40 3-ha plots 5 times each to estimate occupancy of Sonoran desert tortoises in 2 mountain ranges in southern Arizona, USA. For both mountain ranges combined, we estimated density to be 0.30 adult tortoises/ha (95% CI = 0.17–0.43) and occupancy to be 0.72 (95% CI = 0.56–0.89). For the sampling designs we evaluated, monitoring efforts based on occupancy were 8–36% more efficient than those based on density, when contrasting only survey effort, and 17–30% more efficient when contrasting total effort (surveying, hiking to and from survey locations, and radiotracking). Occupancy had greater statistical power to detect annual declines in the proportion of area occupied than did distance sampling to detect annual declines in density. For example, we estimated that power to detect a 5% annual decline with 10 years of annual sampling was 0.92 (95% CI = 0.75–0.98) for occupancy and 0.43 (95% CI = 0.35–0.52) for distance sampling. Although all sampling methods have limitations, occupancy estimation offers a promising alternative for monitoring populations of rare vertebrates, including tortoises in the Sonoran Desert.     

Estimating Abundance of an Unmarked,Low-Density Species using Cameras

Estimating abundance of wildlife populations can be challenging and costly, especially for species that are difficult to detect and that live at low densities, such as cougars (Puma concolor). Remote, motion-sensitive cameras are a relatively efficient monitoring tool, but most abundance estimation techniques using remote cameras rely on some or all of the population being uniquely identifiable. Recently developed methods estimate abundance from encounter rates with remote cameras and do not require identifiable individuals. We used 2 methods, the time-to-event and space-to-event models, to estimate the density of 2 cougar populations in Idaho, USA, over 3 winters from 2016–2019. We concurrently estimated cougar density using the random encounter model (REM), an existing camera-based method for unmarked populations, and genetic spatial capture recapture (SCR), an established method for monitoring cougar populations. In surveys for which we successfully estimated density using the SCR model, the time-to-event estimates were more precise and showed comparable variation between survey years. The space-to-event estimates were less precise than the SCR estimates and were more variable between survey years. Compared to REM, time-to-event was more precise and consistent, and space-to-event was less precise and consistent. Low sample sizes made the space-to-event and SCR models inconsistent from survey to survey, and non-random camera placement may have biased both of the camera-based estimators high. We show that camera-based estimators can perform comparably to existing methods for estimating abundance in unmarked species that live at low densities. With the time- and space-to-event models, managers could use remote cameras to monitor populations of multiple species at broader spatial and temporal scales than existing methods allow. © 2020 The Wildlife Society.     

Improving removal-based estimates of abundance by sampling a population of spatially distinct subpopulations

A statistical modeling framework is described for estimating the abundances of spatially distinct subpopulations of animals surveyed using removal sampling. To illustrate this framework, hierarchical models are developed using the Poisson and negative-binomial distributions to model variation in abundance among subpopulations and using the beta distribution to model variation in capture probabilities. These models are fitted to the removal counts observed in a survey of a federally endangered fish species. The resulting estimates of abundance have similar or better precision than those computed using the conventional approach of analyzing the removal counts of each subpopulation separately. Extension of the hierarchical models to include spatial covariates of abundance is straightforward and may be used to identify important features of an animal's habitat or to predict the abundance of animals at unsampled locations.     

Data quality

A methodology is presented that enables incorporating expert judgment regarding the variability of input data for environmental life cycle assessment (LCA) modeling. The quality of input data in the life-cycle inventory (LCI) phase is evaluated by LCA practitioners using data quality indicators developed for this application. These indicators are incorporated into the traditional LCA inventory models that produce non-varying point estimate results (i.e., deterministic models) to develop LCA inventory models that produce results in the form of random variables that can be characterized by probability distributions (i.e., stochastic models). The outputs of these probabilistic LCA models are analyzed using classical statistical methods for better decision and policy making information. This methodology is applied to real-world beverage delivery system LCA inventory models. The inventory study results for five beverage delivery system alternatives are compared using statistical methods that account for the variance in the model output values for each alternative. Sensitivity analyses are also performed that indicate model output value variance increases as input data uncertainty increases (i.e., input data quality degrades). Concluding remarks point out the strengths of this approach as an alternative to providing the traditional qualitative assessment of LCA inventory study input data with no efficient means of examining the combined effects on the model results. Data quality assessments can now be captured quantitatively within the LCA inventory model structure. The approach produces inventory study results that are variables reflecting the uncertainty associated with the input data. These results can be analyzed using statistical methods that make efficient quantitative comparisons of inventory study alternatives possible. Recommendations for future research are also provided that include the screening of LCA inventory model inputs for significance and the application of selection and ranking techniques to the model outputs.     

虎豹及有蹄类猎物种群数量监测方法概述

虎(Panthera tigris)和豹(P. pardus)及有蹄类猎物的种群数量监测是虎豹保护的核心任务, 也是制定有效管理、保护和恢复措施的基础。近年来, 国内外用于虎豹种群数量监测的方法主要有: 信息网络收集法、基于标志重捕模型的红外相机调查法和非损伤采样粪便DNA分析技术; 有蹄类猎物的监测方法主要有: 样线法、样带法、大样方法、红外相机调查技术和非损伤性遗传标志重捕法。每种监测方法基于的假设前提和生态学原理不同, 监测结果的准确度也不同。由于监测物种的生物学特征、种群分布状况、监测目标和空间尺度或环境因素各异, 每种方法的适用性也不同。本文从野外调查设计、数据收集、处理分析等方面对虎豹及其有蹄类猎物数量监测方法的应用过程和统计原理进行了介绍, 分析了各种监测方法的优缺点, 并针对在虎豹监测中相机布设密度过大可能造成的伪重复抽样, 以及应用虎豹监测设计的自动相机监测替代猎物种群监测数量的评估等不科学的方面进行了探讨和建议。     

Population Indices Versus Correlated Density Estimates of Black-Footed Ferret Abundance

ABSTRACT Estimating abundance of carnivore populations is problematic because individuals typically are elusive, nocturnal, and dispersed across the landscape. Rare or endangered carnivore populations are even more difficult to estimate because of small sample sizes. Considering behavioral ecology of the target species can drastically improve survey efficiency and effectiveness. Previously, abundance of the black-footed ferret (Mustela nigripes) was monitored by spotlighting and generating indices of relative abundance because reintroduced populations were slow to establish. Indices, however, lack variance estimates and are costly to generate for the black-footed ferret. We therefore used spotlight surveys and live-trapping in conjunction with a robust mark-recapture estimator to improve abundance monitoring for the black-footed ferret, one of North America's most endangered carnivores. We estimated abundance of the black-footed ferret at Shirley Basin, Wyoming, USA, using correlated density estimates and Program MARK. We compared our results to 2 indices of relative abundance, minimum number alive and predicted number of ferrets from litter counts. The correlated density estimate for the black-footed ferret (N̂_R = 229; 95% CI = 161–298) was similar to minimum number alive (N̂_R = 192) and predicted number of ferrets from litter counts (N̂_R= 235). The efficiency and effectiveness of survey methods we used for the black-footed ferret were high by carnivoran standards. Our results suggest that the sampling approach we utilized can be implemented for a fraction of the cost and effort required to generate 2 indices of relative abundance for the black-footed ferret. Although we recommend managers implement a similar survey approach to monitor abundance of reintroduced populations of the black-footed ferret, analysis with sparse data sets will be problematic. Until the black-footed ferret becomes widespread and abundant at a reintroduction site, spotlighting will remain preferable as a means to generate indices of distribution and relative abundance for the black-footed ferret.     

Developing indices of relative abundance for monitoring cave and ground wētā (Orthoptera) in southern beech forest,New Zealand

We sampled populations of forest-floor dwelling cave and ground wētā using footprint tracking tunnels and spotlight transect counts in southern beech forest, New Zealand. Samples were compared to estimates of wētā density based on mark–recapture estimates from 25?m² enclosures. Both activity indices captured variability in cave wētā in time and space, were strongly correlated with each other, and have the potential for monitoring cave wētā activity levels. Comparisons between indices and cave wētā density estimates were equivocal, as recapture rates were too low to calculate high-resolution density estimates. We also found that cave wētā counts had a curved relationship increasing with temperature, and a negative relationship with increasing shrub and woody debris cover. Based on these preliminary results, tracking tunnels could be a viable method of monitoring cave wētā as they appear more efficient than transect counts and are relatively inexpensive. However, further calibration trials are needed to determine if indices mirror robust population density estimates.     

Accuracy and precision of skink counts from artificial retreats

Index counts are commonly used to detect spatial and temporal changes in the size of wildlife populations. For indices to be valid there must be a constant (usually linear) relationship between the index and population size. In a study conducted in the Eglinton Valley (Fiordland, South Island, New Zealand), single-day index counts of common skinks (Oligosoma polychroma) from artificial retreats were compared with capture?mark?recapture (CMR) estimates of population size (N?) obtained by pitfall trapping. Generalised linear models revealed that skink counts from artificial retreats provided a reasonably accurate (P??1, which was high compared with other common skink populations. We recommend: (1) long-term monitoring of common skinks in the Eglinton Valley, using the index method described herein; (2) calibration of index counts against population size estimates collected from other habitats and species.     

Linking monitoring and modelling: can long-term datasets be used more effectively as a basis for large-scale prediction?

Data from long-term monitoring sites are vital for biogeochemical process understanding, and for model development. Implicitly or explicitly, information provided by both monitoring and modelling must be extrapolated in order to have wider scientific and policy utility. In many cases, large-scale modelling utilises little of the data available from long-term monitoring, instead relying on simplified models and limited, often highly uncertain, data for parameterisation. Here, we propose a new approach whereby outputs from model applications to long-term monitoring sites are upscaled to the wider landscape using a simple statistical method. For the 22 lakes and streams of the UK Acid Waters Monitoring Network (AWMN), standardised concentrations (Z scores) for Acid Neutralising Capacity (ANC), dissolved organic carbon, nitrate and sulphate show high temporal coherence among sites. This coherence permits annual mean solute concentrations at a new site to be predicted by back-transforming Z scores derived from observations or model applications at other sites. The approach requires limited observational data for the new site, such as annual mean estimates from two synoptic surveys. Several illustrative applications of the method suggest that it is effective at predicting long-term ANC change in upland surface waters, and may have wider application. Because it is possible to parameterise and constrain more sophisticated models with data from intensively monitored sites, the extrapolation of model outputs to policy relevant scales using this approach could provide a more robust, and less computationally demanding, alternative to the application of simple generalised models using extrapolated input data.     

Spatial and temporal modeling of daily pollen concentrations

Accurate assessments of pollen counts are valuable to allergy sufferers, the medical industry, and health researchers; however, monitoring stations do not exist in most areas. In addition, the degree of spatial reliability provided by the limited number of monitoring stations is poorly understood. We developed and compared spatial models to estimate pollen concentrations in locations without monitoring stations. Daily Acer, Quercus, and overall tree, grass, and weed pollen counts, in grains/m³, were obtained from 14 aeroallergen monitoring stations located in the northeastern and mid-Atlantic region of the United States from 2003 to 2006. Pollen counts were spatially interpolated using ordinary kriging. Mixed effects and generalized estimating equations incorporating daily and seasonal weather characteristics, pollen season characteristics and land-cover information were also developed to estimate daily pollen concentrations. We then compared observed values from a monitoring station to model estimates for that location. Observed counts and kriging estimates for tree pollen differed (p = 0.04), but not when peak periods were removed (p = 0.29). No differences between observed and kriging estimates of Acer (p = 0.46), Quercus (p = 0.24), grass (p = 0.31) or weed pollen (p = 0.29) were found. Estimates from longitudinal models also demonstrated good agreement with observed counts, except for the extremes of pollen distributions. Our results demonstrate that spatial interpolation techniques as well as regression methods incorporating both weather and land-cover characteristics can provide reliable estimates of daily pollen concentrations in areas where monitors do not exist for all but periods of extremely high pollen.     

Survey of predators and sampling method comparison in sweet corn

Natural predation is an important component of integrated pest management that is often overlooked because it is difficult to quantify and perceived to be unreliable. To begin incorporating natural predation into sweet corn, Zea mays L., pest management, a predator survey was conducted and then three sampling methods were compared for their ability to accurately monitor the most abundant predators. A predator survey on sweet corn foliage in New York between 1999 and 2001 identified 13 species. Orius insidiosus (Say), Coleomegilla maculata (De Geer), and Harmonia axyridis (Pallas) were the most numerous predators in all years. To determine the best method for sampling adult and immature stages of these predators, comparisons were made among nondestructive field counts, destructive counts, and yellow sticky cards. Field counts were correlated with destructive counts for all populations, but field counts of small insects were biased. Sticky cards underrepresented immature populations. Yellow sticky cards were more attractive to C. maculata adults than H. axyridis adults, especially before pollen shed, making coccinellid population estimates based on sticky cards unreliable. Field counts were the most precise method for monitoring adult and immature stages of the three major predators. Future research on predicting predation of pests in sweet corn should be based on field counts of predators because these counts are accurate, have no associated supply costs, and can be made quickly.     

Seasonal variation in detectability of butterflies surveyed with Pollard walks

Monitoring protocols should be designed to maximize the probability of detecting target species with limited resources. Most species are imperfectly detected, hence, they will often be overlooked at sites where they actually occur, resulting in false-negative errors (i.e. false absences). Uncertain detection of target species has profound implications for conservation, but can be dealt with by using adequate survey designs and statistical models. Butterflies often are monitored with repeated, fixed-route transect counts (Pollard walks). Even though this survey method is widely used in temperate regions, its efficiency in terms of detection probability has never been rigorously assessed in part owing to a lack of suitable analysis methods. Here, I use site-occupancy models to explore the seasonal patterns in detection probability of four California butterflies using Pollard walks. In an effort to inventory the butterfly fauna in two natural areas in the eastern foothills of the Santa Cruz mountains (California), I surveyed twelve 250 m long transects weekly for 22 weeks. I estimated the detection probability (the probability of recording a species during a single transect walk, given it is present) of four species. The probability of detecting each species depended mostly on the monitoring week. Average detection probability across the season was 64% for Cercyonis pegala, 56% for Limenitis lorquini, 76% for Euphydryas chalcedona, and 50% for Lycaena arota. Based on the mean detection probability, I then inferred the number of visits necessary to be statistically confident that a given species was indeed absent from a transect where it was not observed (i.e. obtaining a false absence rate <5%). Knowledge of detection probabilities is fundamental to the optimal design of monitoring programs and the interpretation of their results. The methods applied in this study provide an efficient and evidence-based method to optimally allocate butterfly monitoring resources across space (number of transects) and time (number and timing of visits).     

Evaluating abundance estimates and evidence of breeding for Bobolinks from transect and point-count surveys

Estimating the abundance and breeding success of territorial songbirds is challenging. Various types of surveys and analyses are available, but all receive some criticism in the literature, and most methods are rarely compared with results obtained using intensive monitoring efforts. We assessed the efficacy of transect and point-count surveys to estimate the abundance of male Bobolinks (Dolichonyx oryzivorus) and detect evidence of nesting and fledging by comparing the results of those surveys to results from more intensive monitoring (i.e., spot mapping and nest monitoring). We monitored 36 fields (254 ha) of late-harvest hay, restored grassland, and fallow fields in the Luther Marsh Wildlife Management Area and on four farms in southern Ontario, Canada, in 2018. Compared to the number of territories identified based on spot mapping (197), distance sampling analysis of transect survey data provided a more accurate estimate of the abundance of male Bobolinks (230, 95% CI: 187, 282) than N-mixture models of transect (668, 95% CI: 332, 1342) and point-count (337, 95% CI: 203, 559) data. Three visits to survey transects and five to point counts did not effectively detect evidence of Bobolink breeding (i.e., nesting or fledging) in fields compared to spot mapping and nest monitoring. Distance sampling analysis of transect data appears promising for estimating the number of Bobolink territories in an area, e.g., those impacted by conservation programs. If estimates of the number of nesting Bobolinks and frequency of fledging are of interest, spot mapping and nest monitoring could be implemented at a subset of sampled fields. Our results suggest that additional studies to evaluate model-based estimates of abundance with the best available information (e.g., from spot mapping of marked or unmarked populations and nest monitoring) would be useful to ensure that robust estimates are provided to support population estimates and conservation actions.     

Effect of detection heterogeneity in occupancy‐detection models: an experimental test of time‐to‐first‐detection methods

Imperfect detection can bias estimates of site occupancy in ecological surveys but can be corrected by estimating detection probability. Time‐to‐first‐detection (TTD) occupancy models have been proposed as a cost–effective survey method that allows detection probability to be estimated from single site visits. Nevertheless, few studies have validated the performance of occupancy‐detection models by creating a situation where occupancy is known, and model outputs can be compared with the truth. We tested the performance of TTD occupancy models in the face of detection heterogeneity using an experiment based on standard survey methods to monitor koala Phascolarctos cinereus populations in Australia. Known numbers of koala faecal pellets were placed under trees, and observers, uninformed as to which trees had pellets under them, carried out a TTD survey. We fitted five TTD occupancy models to the survey data, each making different assumptions about detectability, to evaluate how well each estimated the true occupancy status. Relative to the truth, all five models produced strongly biased estimates, overestimating detection probability and underestimating the number of occupied trees. Despite this, goodness‐of‐fit tests indicated that some models fitted the data well, with no evidence of model misfit. Hence, TTD occupancy models that appear to perform well with respect to the available data may be performing poorly. The reason for poor model performance was unaccounted for heterogeneity in detection probability, which is known to bias occupancy‐detection models. This poses a problem because unaccounted for heterogeneity could not be detected using goodness‐of‐fit tests and was only revealed because we knew the experimentally determined outcome. A challenge for occupancy‐detection models is to find ways to identify and mitigate the impacts of unobserved heterogeneity, which could unknowingly bias many models.     

Robustness and uncertainty in estimates of butterfly abundance from transect counts

Many butterfly populations are monitored by counting the number of butterflies observed while walking transects during the butterfly’s flight season. Methods for estimating population abundance from these transect counts are appealing because they allow rare populations to be monitored without capture–recapture studies that could harm fragile individuals. An increasingly popular method for estimating abundance from transect counts relies on strong assumptions about the counting process and the processes that govern butterfly population dynamics. Here, we study the statistical performance of this method when underlying model assumptions are violated. We find that estimates of population size are robust to departures from underlying model assumptions, but that the uncertainty in these estimates (i.e., confidence intervals) is substantially underestimated. Alternative bootstrap and Bayesian methods provide better measures of the uncertainty in estimated population size, but are conditional upon knowledge of butterfly detectability. Because of these requirements, a mixed approach that combines data from small capture–recapture studies with transect counts strikes the best balance between accurate monitoring and minimal injury to individuals. Our study is motivated by monitoring studies for St. Francis satyr (Neonympha mitchelli francisci), a rare and relatively immobile butterfly occurring only in the sandhills region of south-central North Carolina, USA.     

Optimal Stimulus Coding by Neural Populations Using Rate Codes

We create a framework based on Fisher information for determining the most effective population coding scheme for representing a continuous-valued stimulus attribute over its entire range. Using this scheme, we derive optimal single- and multi-neuron rate codes for homogeneous populations using several statistical models frequently used to describe neural data. We show that each neuron's discharge rate should increase quadratically with the stimulus and that statistically independent neural outputs provides optimal coding. Only cooperative populations can achieve this condition in an informationally effective way.     

Spatial Modeling of Air Pollution in Studies of Its Short‐Term Health Effects

Summary In studies that estimate the short‐term effects of air pollution on health, daily measurements of pollution concentrations are often available from a number of monitoring locations within the study area. However, the health data are typically only available in the form of daily counts for the entire area, meaning that a corresponding single daily measure of pollution is required. The standard approach is to average the observed measurements at the monitoring locations, and use this in a log‐linear health model. However, as the pollution surface is spatially variable this simple summary is unlikely to be an accurate estimate of the average pollution concentration across the region, which may lead to bias in the resulting health effects. In this article, we propose an alternative approach that jointly models the pollution concentrations and their relationship with the health data using a Bayesian spatio‐temporal model. We compare this approach with the simple spatial average using a simulation study, by investigating the impact of spatial variation, monitor placement, and measurement error in the pollution data. An epidemiological study from Greater London is then presented, which estimates the relationship between respiratory mortality and four different pollutants.     

Assessing the performance of index calibration survey methods to monitor populations of wide‐ranging low‐density carnivores

Apex carnivores are wide‐ranging, low‐density, hard to detect, and declining throughout most of their range, making population monitoring both critical and challenging. Rapid and inexpensive index calibration survey (ICS) methods have been developed to monitor large African carnivores. ICS methods assume constant detection probability and a predictable relationship between the index and the actual population of interest. The precision and utility of the resulting estimates from ICS methods have been questioned. We assessed the performance of one ICS method for large carnivores—track counts—with data from two long‐term studies of African lion populations. We conducted Monte Carlo simulation of intersections between transects (road segments) and lion movement paths (from GPS collar data) at varying survey intensities. Then, using the track count method we estimated population size and its confidence limits. We found that estimates either overstate precision or are too imprecise to be meaningful. Overstated precision stemmed from discarding the variance from population estimates when developing the method and from treating the conversion from tracks counts to population density as a back‐transformation, rather than applying the equation for the variance of a linear function. To effectively assess the status of species, the IUCN has set guidelines, and these should be integrated in survey designs. We propose reporting the half relative confidence interval width (HRCIW) as an easily calculable and interpretable measure of precision. We show that track counts do not adhere to IUCN criteria, and we argue that ICS methods for wide‐ranging low‐density species are unlikely to meet those criteria. Established, intensive methods lead to precise estimates, but some new approaches, like short, intensive, (spatial) capture–mark–recapture (CMR/SECR) studies, aided by camera trapping and/or genetic identification of individuals, hold promise. A handbook of best practices in monitoring populations of apex carnivores is strongly recommended.