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.     

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.     

Absent or undetected? Effects of non-detection of species occurrence on wildlife-habitat models

Presence-absence data are used widely in analysis of wildlife-habitat relationships. Failure to detect a species’ presence in an occupied habitat patch is a common sampling problem when the population size is small, individuals are difficult to sample, or sampling effort is limited. In this paper, the influence of non-detection of occurrence on parameter estimates of logistic regression models of wildlife-habitat relationships was assessed using analytical analysis and simulations. Two patterns of non-detection were investigated: (1) a random distribution of non-detection among occupied patches; and (2) a non-random distribution of non-detection in which the probability of detecting a species in an occupied patch covaried with measurable habitat variables. Our results showed that logistic regression models of wildlife-habitat relationships were sensitive to even low levels of non-detection in occupancy data. Both analytic and simulation studies show that non-detection yields bias in parameter estimation of logistic regression models. More importantly, the direction of bias was affected by the underlying pattern of non-detection and whether the habitat variable was positively or negatively related to occupancy. For a positive habitat coefficient, a random distribution of non-detection yielded negative bias in estimation, whereas linkage of the probability of non-detection to habitat covariates produced positive bias. For a negative habitat coefficient, the pattern was reversed, with a random distribution of non-detection leading to positive bias in estimation. A release-recapture livetrapping study of small mammals in central Indiana, USA, was used to illustrate the magnitude of non-detection in a typical field sampling protocol with varying levels of sampling intensity. Estimates of non-detection error ranged from 0 to 23% for seven species after 5 days of sampling. We suggest that for many sampling situations, relationships between probability of detection and habitat covariates need to be established to correctly interpret results of wildlife-habitat models.     

空间自相关性对冬小麦种植面积空间抽样效率的影响

空间抽样是实现区域农作物面积高效估算的重要手段,农作物分布受自然条件等因素影响普遍存在空间自相关性,但以往针对空间相关性对农作物面积抽样效率的影响研究明显不足。该研究选取安徽省凤台县为研究区,通过2017年4月4景GF-1全色多光谱影像(Panchromatic and Multispectral, PMS)与Google Earth高空间分辨率影像相结合提取研究区冬小麦。设计10种抽样单元尺度、3种抽样外推方法、2种相对允许误差和5种样本布局方式,构建多种冬小麦面积空间抽样方案。利用全局莫兰指数(global Moran’s index)评价不种尺度下抽样单元内冬小麦面积比的空间自相关强度,分析空间自相关性对冬小麦面积抽样效率(抽样误差、样本容量和空间布局)的影响。研究结果表明,抽样单元内冬小麦面积比的空间自相关强度随单元尺度的增大而减小,全局莫兰指数相应地由0.75降至0.50。无论在何种尺度下抽样单元内冬小麦面积比都呈显著的空间正相关性;抽样外推冬小麦面积总体的误差随空间自相关强度的减小呈先减小后明显增大的趋势。在10种抽样单元尺度中,当抽样单元尺度为2000m且抽样比为5%时,无论采用何种抽样方法外推总体的误差均为最小(简单随机抽样、系统和分层抽样外推总体的相对误差分别为17.94%、9.48%和1.82%);当相对允许误差设计为5%时,简单随机抽样外推总体所需样本容量随空间自相关强度的降低从660降至56。而分层抽样的样本容量不受空间自相关性的影响;5种样本布局方式中,采用分层随机抽样方式外推冬小麦面积总体的平均相对误差、平均变异系数和均方根误差最小,分别为1.82%、3.19%和0.11×108 m2。该研究可为有空间自相关存在下的农作物面积空间抽样方案合理设计提供参考依据。     

Hierarchical models for estimating herd prevalence and test accuracy in the absence of a gold standard

A common assumption made in studies involving two or more binary diagnostic tests in the absence of a gold standard is one of conditional independence among tests given disease status. Although reasonable in some cases, often this assumption is untenable or untested and may lead to biased results. We proposed a class of hierarchical models for the purpose of estimating the herd-level prevalence distribution and the accuracies of two tests in the absence of a gold standard when several exchangeable populations with differing disease prevalence are available for sampling, relaxing the assumption of conditional independence between tests. The models are used to estimate the prevalence of bovine brucellosis in Mexican cow herds and to estimate the error rates of two tests for the detection of swine pneumonia.     

Soil Contamination Interpretation by the Use of Monitoring Data Analysis

The presented study deals with the interpretation of soil quality monitoring data using hierarchical cluster analysis (HCA) and principal components analysis (PCA). Both statistical methods contributed to the correct data classification and projection of the surface (0–20 cm) and subsurface (20–40 cm) soil layers of 36 sampling sites in the region of Burgas, Bulgaria. Clustering of the variables led to formation of four significant clusters corresponding to possible sources defining the soil quality like agricultural activity, industrial impact, fertilizing, etc. Two major clusters were found to explain the sampling site locations according to soil composition—one cluster for coastal and mountain sites and another—for typical rural and industrial sites. Analogous results were obtained by the use of PCA. The advantage of the latter was the opportunity to offer more quantitative interpretation of the role of identified soil quality sources by the level of explained total variance. The score plots and the dendrogram of the sampling sites indicated a relative spatial homogeneity according to geographical location and soil layer depth. The high-risk areas and pollution profiles were detected and visualized using surface maps based on Kriging algorithm.     

A resource selection model for analyzing pseudoreplicated data due to grouping behavior of animals

Quantifying resource selection is of primary interest in animal ecology. Many analyses of resource selection assume spatial and temporal independence of the sampling unit. Autocorrelation between observations, which is a general property of ecological variables, causes difficulties for most standard statistical procedures of resource selection because autocorrelated data violate the assumption of independence. To overcome this problem, we develop a mixed-effects model to estimate resource selection functions from data that are autocorrelated because of unobserved grouping behavior by animals. In the application of the expectation-maximization (EM) algorithm, the computation of the conditional expectation of the complete-data log-likelihood function does not have a closed-form solution requiring numerical integration. A Monte Carlo EM algorithm with Gibbs sampling can be used effectively in such situations to find exact maximum likelihood estimates. We propose a simple automated Monte Carlo EM algorithm with multiple sequences in which the Monte Carlo sample size is increased when the EM step is swamped by Monte Carlo errors.We demonstrate that the model can detect inherent autocorrelation and provide reasonable variance estimates when applied to nocturnal bird migration data. This approach could also be applied to ecological processes with various types of spatially and temporally autocorrelated data, circumventing serious problems caused by dangerous pseudoreplication.     

Assessing the Impacts of Time-to-Detection Distribution Assumptions on Detection Probability Estimation

Abundance estimates from animal point-count surveys require accurate estimates of detection probabilities. The standard model for estimating detection from removal-sampled point-count surveys assumes that organisms at a survey site are detected at a constant rate; however, this assumption can often lead to biased estimates. We consider a class of N-mixture models that allows for detection heterogeneity over time through a flexibly defined time-to-detection distribution (TTDD) and allows for fixed and random effects for both abundance and detection. Our model is thus a combination of survival time-to-event analysis with unknown-N, unknown-p abundance estimation. We specifically explore two-parameter families of TTDDs, e.g., gamma, that can additionally include a mixture component to model increased probability of detection in the initial observation period. Based on simulation analyses, we find that modeling a TTDD by using a two-parameter family is necessary when data have a chance of arising from a distribution of this nature. In addition, models with a mixture component can outperform non-mixture models even when the truth is non-mixture. Finally, we analyze an Ovenbird data set from the Chippewa National Forest using mixed effect models for both abundance and detection. We demonstrate that the effects of explanatory variables on abundance and detection are consistent across mixture TTDDs but that flexible TTDDs result in lower estimated probabilities of detection and therefore higher estimates of abundance.Supplementary materials accompanying this paper appear on-line.     

Effects of tropical forest fragmentation on aerial insectivorous bats in a land-bridge island system

Habitat fragmentation causes drastic changes in the biota and it is crucial to understand these modifications to mitigate its consequences. While studies on Neotropical bats have mainly targeted phyllostomid bats, impacts of fragmentation on the equally important aerial insectivores remain largely unexplored. We studied species richness, composition, count abundance and feeding activity of aerial insectivorous bats in a system of land-bridge islands in Panama with acoustic sampling. We predicted negative effects of fragmentation on forest species while bats foraging in open space should remain essentially unaffected. Rarefaction analyses indicated higher species richness for islands than mainland sites. For forest species, multivariate analyses suggested compositional differences between sites due to effects of isolation, area and vegetation structure. Contrary to our expectations, count abundance of forest species was similar across site categories. Feeding activity, however, was curtailed on far islands compared to near islands. As expected, bats hunting in open space did not reveal negative responses to fragmentation. Interestingly, they even displayed higher abundance counts on far and small islands. On the species level, two forest bats responded negatively to size reduction or site isolation, respectively, while a forest bat and a bat hunting in open space were more abundant on islands, irrespectively of island isolation or size. Our findings suggest that small forest remnants are of considerable conservation value as many aerial insectivores intensively use them. Hence high conservation priority should be given to retain or re-establish a high degree of forest integrity and low levels of isolation.     

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.     

Mark-recapture with occasion and individual effects: Abundance estimation through Bayesian model selection in a fixed dimensional parameter space

We present a Bayesian mark-recapture method for explicitly communicating uncertainty about the size of a closed population where capture probabilities vary across both individuals and sampling occasions. Heterogeneity is modeled hierarchically using a continuous logistic-Normal model to specify the capture probabilities for both individuals that are captured on at least one occasion and individuals that are never captured and so remain undetected. Inference about how many undetected individuals to include in the model is accomplished through a Bayesian model selection procedure using MCMC, applied to a product space of possible models for different numbers of undetected individuals. Setting the estimation problem in a fixed dimensional parameter space enables the model selection procedure to be performed using the freely available WinBUGS software. The outcome of inference is a full “posterior” probability distribution for the population size parameter. We demonstrate this method through an example involving real mark-recapture data.     

Accounting for Lack of Independence and Partial Overlap of Observation Zones in Line-Transect Mark-Recapture Distance Sampling

Line-transect mark-recapture distance sampling methods can be used to estimate abundance when at least two observers sight and record distances to detected groups of individuals within the survey area. However, a lack of independence between the observer’s detections will cause biased abundance estimates. Studies are also typically designed such that there is complete overlap of the regions searched by the two observers, but that may not always be possible. Here we detail an intuitive approach for line-transect distance sampling applications based upon logistic regression to account for a potential lack of independence by using the detections of one observer as a covariate in the detection function of the second observer. Partial overlap of the observer survey regions can be addressed by constraining detection probability to equal 0 for the respective observer outside of the overlap zone. We show via simulation that the method provides reliable estimates of abundance and is not affected by random unmodeled heterogeneity in detection probability. The method is illustrated by estimating abundance within the covered region of an aerial line-transect survey for New Zealand’s endemic Hector’s dolphin (Cephalorhynchus hectori hectori) conducted in the austral summer of 2013, the motivating application for this work. Supplementary materials accompanying this paper appear on-line.     

Brown hyaenas on roads: Estimating carnivore occupancy and abundance using spatially auto-correlated sign survey replicates

Carnivore survey protocols that properly address spatial sampling and detectability issues are seldom feasible at a landscape-scale. This limits knowledge of large-scale patterns in distribution, abundance and their underlying determinants, hindering conservation of globally threatened carnivore populations. Occupancy analysis of data from logistically efficient sign surveys along consecutive road segments (spatially auto-correlated replicates) offers a potential solution. We adapted and applied this newly-developed method over 62,979 km² of human-modified land in South Africa. Our aims were to (1) generate unbiased estimates of brown hyaena occupancy and abundance (2) investigate two suspected determinants of occupancy using a combination of biological and socio-economic sampling techniques, and (3) use simulations to evaluate the effort required for abundance and occupancy estimates with acceptable bias, precision and power. Brown hyaena occupancy was estimated at 0.748 (±SE 0.1), and estimated overall density in agricultural land (0.15/100 km², ±SE 0.08) was an order of magnitude lower than in protected areas. Positive attitudes to carnivores and presence of wildlife farms exerted strong positive effects on occupancy, so changes in these factors may well exert monotonic impacts on local metapopulation status. Producing reliable occupancy and abundance estimates would require ?6 replicates and ?12 replicates per site respectively. Detecting 50% and 30% declines in brown hyaena occupancy with adequate power would require five annual surveys at ?65 sites and ?125 sites respectively. Our results suggest that protocols based on spatially auto-correlated sign survey replicates could be used to monitor carnivore populations at large, and possibly even country-wide spatial scales.     

Assessment of cropping‐system impact on soil organic matter levels in short‐term field experiments

It has been suggested that short‐term field experiments are not suitable for the quantitative assessment of cropping‐systems impact on soil organic matter (SOM) levels in arable soils, as expectable temporal changes are very small compared to a large spatial variation of SOM background levels. However, applying an optimized sampling design based on repeated sampling in small plots, we were able to detect soil total carbon (STC) and nitrogen (STN) changes in the magnitude of ≈ 1% (STC) and ≈ 2% (STN) of background levels with only four replications, respectively. Gradually enlarging the sample size up to n = 24 did not considerably improve change detectability with STC, but with STN (n = 15 allowing for the dection of ≈ 1% change of background levels). The common calculation of minimum detectable differences (MDD) based on a state analysis of SOM levels instead of repeated measurements considerably underestimated change detectability.     

Estimating Distance Sampling Detection Functions When Distances Are Measured With Errors

Distance sampling methods assume that distances are known but in practice there are often errors in measuring them. These can have substantial impact on the bias and precision of distance sampling estimators. In this paper we develop methods that accommodate both systematic and stochastic measurement errors. We use the methods to estimate detection probability in two surveys with substantial measurement error. The first is a shipboard line transect survey in the North Sea in which information on measurement error comes from photographically measured distances to a subset of detections. The second is an aerial cue-counting survey off Iceland in which information on measurement error comes from pairs of independently estimated distances to a subset of detections. Different methods are required for measurement error estimation in the two cases. We investigate by simulation the properties of the new estimators and compare them to conventional estimators. They are found to perform better than conventional estimators in the presence of measurement error, more so in the case of cue-counting and point transect estimators than line transect estimators. An appendix on the asymptotic distributions of conditional and full likelihood estimators is available online.     

Two-stage sequential sampling: A neighborhood-free adaptive sampling procedure

Designing an efficient sampling scheme for a rare and clustered population is a challenging area of research. Adaptive cluster sampling, which has been shown to be viable for such a population, is based on sampling a neighborhood of units around a unit that meets a specified condition. However, the edge units produced by sampling neighborhoods have proven to limit the efficiency and applicability of adaptive cluster sampling. We propose a sampling design that is adaptive in the sense that the final sample depends on observed values, but it avoids the use of neighborhoods and the sampling of edge units. Unbiased estimators of population total and its variance are derived using Murthy’s estimator. The modified two-stage sampling design is easy to implement and can be applied to a wider range of populations than adaptive cluster sampling. We evaluate the proposed sampling design by simulating sampling of two real biological populations and an artificial population for which the variable of interest took the value either 0 or 1 (e.g., indicating presence and absence of a rare event). We show that the proposed sampling design is more efficient than conventional sampling in nearly all cases. The approach used to derive estimators (Murthy’s estimator) opens the door for unbiased estimators to be found for similar sequential sampling designs.     

Post-fire succession affects abundance and survival but not detectability in a knob-tailed gecko

Altered fire regimes threaten the persistence of many animal species globally, thus understanding how fire affects demographic processes is critical for conservation. Using 2 years of mark-recapture data from the Australian gecko Nephrurus stellatus, we investigated the effect of fire on (i) detectability to reliably measure post-fire changes in abundance, and (ii) survival and reproductive rates to investigate the mechanisms of successional change. Data were collected from two conservation reserves each with three different fire categories based on time since the last fire. “Early”, “medium” and “late” sites had 2–3, 7–9 and 42–48 years since fire, respectively. A robust design modelling framework was used to estimate the effect of fire category on abundance, survival and capture probability while also examining the influence of temperature and behaviour on detectability. Geckos showed trap-shy behaviour and detectability increased significantly with increasing temperature but was not affected by time since fire. Accounting for detectability, geckos were more abundant in the medium than the early sites, and were rare in the late sites. Although trends in survival are more difficult to address with short-term data, our results showed lower monthly survival rates, but higher fecundity in the early than the medium sites. These results were possibly related to successional changes in predation, the thermal environment, and food availability. We demonstrated how mark-recapture analysis can show the causes of animal fire responses while realistically accounting for detectability. Such information is necessary to provide a predictive framework to guide fire management for biodiversity.     

Accounting for Data Architecture on Structural Equation Modeling of Feedlot Cattle Performance

Structural equation models (SEM) are a type of multi-trait model increasingly being used for inferring functional relationships between multiple outcomes using operational data from livestock production systems. These data often present a hierarchical architecture given by clustering of observations at multiple levels including animals, cohorts and farms. A hierarchical data architecture introduces correlation patterns that, if ignored, can have detrimental effects on parameter estimation and inference. Here, we evaluate the inferential implications of accounting for, or conversely, misspecifying data architecture in the context of SEM. Motivated by beef cattle feedlot data, we designed simulation scenarios consisting of multiple responses in a clustered architecture. Competing fitted SEMs differed in their model specification so that data architecture was explicitly accounted for (M1; true model) or misspecified due to disregarding either the cluster-level correlation between responses (M2) or the correlation between observations of a response within a cluster (M3), or ignored all together (M4). Model fit was increasingly impaired when data architecture was misspecified or ignored. Both accuracy and precision of estimation were also negatively affected when data architecture was disregarded. Our findings are further illustrated using data from feedlot operations from the US Great Plains. Standing statistical recommendations that call for proper model specification capturing relevant hierarchical levels in data structure extend to the multivariate context of structural equation modeling.Supplementary materials accompanying this paper appear on-line.     

Distribution of large soil invertebrates as related to soil parameters

The study of three types of forest soils has shown virtually no reliable relationships between the distribution of large soil invertebrates and the soil parameters (the stone content, pH, litter thickness, etc.) when the sample area has a size of 76 cm². However, an increase in the size of the observation plots by two to four times (depending on the particular soil type) makes it possible to find statistically significant coefficients of correlation between the studied parameters. Thus, the size of the sample area influences our assessment of the relationships between the abundance of large invertebrates and the soil parameters. In each of the studied types of forest soils, the heterogeneity of the soil structure is manifested at different scales. A correct forecast of the effect of the factors of the soil on the population of large invertebrates depends on the spatial distribution of these factors.     

数据驱动的农作物遥感分类地面样本点布设

地面样本点是农作物遥感分类模型训练的基础，样本点数量和质量是影响模型分类精度的2个主要因素。该研究构建了数据驱动的样本点布设方法，利用待分类影像的光谱、植被指数等特征构造分层抽样底图，结合分层随机抽样方法进行地面样本点布设，并分析不同抽样策略对农作物遥感分类结果的影响。采取基于k-means聚类分析的数据驱动方法，考虑6景哨兵2号影像提取的共78个分类特征，生成同一个最优k的聚类结果图；设计等量分配和按面积比分配2种样本量分配方式，样本点数量为25、49、100、169、225的5个总样本量；基于不同抽样策略获取地面样本点信息，利用同一个支持向量机模型对待分类影像进行监督分类，并通过与139个样本点的理论总样本量和400个样本点的传统方式总样本量对比分析，定量解析不同抽样策略对分类精度的影响。结果表明：1）在数据驱动非监督聚类生成的底图上进行抽样（按面积比分层抽样法、等量分层抽样法）获得的样本点质量和分类精度明显优于没有该底图的抽样策略（简单随机抽样法、系统抽样法）；2）当总样本量低于理论总样本量时，等量分层抽样法能获取比按面积比分层抽样法更高的分类精度。例如，当理论样本量为139时，...