A practical sampling design for acoustic surveys of bats

Acoustic surveys are widely used for describing bat occurrence and activity patterns and are increasingly important for addressing concerns for habitat management, wind energy, and disease on bat populations. Designing these surveys presents unique challenges, particularly when a probabilistic sample is required for drawing inference to unsampled areas. Sampling frame errors and other logistical constraints often require survey sites to be dropped from the sample and new sites added. Maintaining spatial balance and representativeness of the sample when these changes are made can be problematic. Spatially balanced sampling designs recently developed to support aquatic surveys along rivers provide solutions to a number of practical challenges faced by bat researchers and allow for sample site additions and deletions, support unequal-probability selection of sites, and provide an approximately unbiased local neighborhood-weighted variance estimator that is efficient for spatially structured populations such as is typical for bats. We implemented a spatially balanced design to survey canyon bat (Parastrellus hesperus) activity along a stream network. The spatially balanced design accommodated typical logistical challenges and yielded a 25% smaller estimated standard error for the mean activity level than the usual simple random sampling estimator. Spatially balanced designs have broad application to bat research and monitoring programs and will improve studies relying on model-based inference (e.g., occupancy models) by providing flexibility and protection against violations of the independence assumption, even if design-based estimators are not used. Our approach is scalable and can be used for pre- and post-construction surveys along wind turbine arrays and for regional monitoring programs. © 2011 The Wildlife Society.     

Evaluating sampling designs by computer simulation: a case study with the Missouri bladderpod

To effectively manage rare populations, accurate monitoring data are critical. Yet many monitoring programs are initiated without careful consideration of whether chosen sampling designs will provide accurate estimates of population parameters. Obtaining accurate estimates is especially difficult when natural variability is high, or limited budgets determine that only a small fraction of the population can be sampled. The Missouri bladderpod, Lesquerella filiformis Rollins, is a federally threatened winter annual that has an aggregated distribution pattern and exhibits dramatic interannual population fluctuations. Using the simulation program SAMPLE, we evaluated five candidate sampling designs appropriate for rare populations, based on 4 years of field data: (1) simple random sampling, (2) adaptive simple random sampling, (3) grid-based systematic sampling, (4) adaptive grid-based systematic sampling, and (5) GIS-based adaptive sampling. We compared the designs based on the precision of density estimates for fixed sample size, cost, and distance traveled. Sampling fraction and cost were the most important factors determining precision of density estimates, and relative design performance changed across the range of sampling fractions. Adaptive designs did not provide uniformly more precise estimates than conventional designs, in part because the spatial distribution of L. filiformis was relatively widespread within the study site. Adaptive designs tended to perform better as sampling fraction increased and when sampling costs, particularly distance traveled, were taken into account. The rate that units occupied by L. filiformis were encountered was higher for adaptive than for conventional designs. Overall, grid-based systematic designs were more efficient and practically implemented than the others. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Searching for weeds – a GIS tool

Sampling for rare events, such as a new weed incursion, can be surprisingly efficient when adaptive, unequal probability survey designs are used. Spatially explicit habitat models and expert knowledge of weedy species can be used to identify areas of varied survey intensity. We introduce a GIS-based tool that can be used for designing such a survey. The user-friendly tool interfaces (behind the scenes) with the US Environmental Protection Agency’s spatially balanced sampling design functions in R. The functions ensure that the location of the sample points are spatially balanced while at the same time, allowing the user to specify survey intensity in area of special interest (preferred habitats, areas of high conservation value, areas of high public use, etc). We discuss the use of the GIS tool in a case study where we designed a 5-year weed monitoring plan for a local authority in New Zealand. The plan includes ‘over sample’ sites to replace any original sample sites that were impractical or costly to visit. Initial results include estimates of what proportion of the total region has weeds present and an estimate of weed density. More detailed results are produced for specified known weed hot spots, such as areas adjacent to roads and rivers. These estimates are available for all weed species, and for individual species. Because the system is GIS-based, spatial information is stored. Over time, as the weed surveillance and monitoring progresses, regional changes in weed distribution can be tracked, and species and locations that require more targeted weed management can be identified. Further results of such a probability-based design can be used to develop habitat models for predicting future distributions.     

Prospective studies of diagnostic test accuracy when disease prevalence is low

Prospective studies of diagnostic test accuracy have important advantages over retrospective designs. Yet, when the disease being detected by the diagnostic test(s) has a low prevalence rate, a prospective design can require an enormous sample of patients. We consider two strategies to reduce the costs of prospective studies of binary diagnostic tests: stratification and two-phase sampling. Utilizing neither, one, or both of these strategies provides us with four study design options: (1) the conventional design involving a simple random sample (SRS) of patients from the clinical population; (2) a stratified design where patients from higher-prevalence subpopulations are more heavily sampled; (3) a simple two-phase design using a SRS in the first phase and selection for the second phase based on the test results from the first; and (4) a two-phase design with stratification in the first phase. We describe estimators for sensitivity and specificity and their variances for each design, along with sample size estimation. We offer some recommendations for choosing among the various designs. We illustrate the study designs with two examples.     

Bayesian Estimation Using Ranked Set Sampling

Bayesian Estimation of the parameter of a distribution is considered using Ranked set sampling (RSS). It is shown that for at least one RSS plan, the Bayes estimator has smaller Bayes risk than the Bayes estimator using simple random sampling (SRS). Furthermore, for exponential family with conjugate prior, the Bayes estimator of the mean using balanced RSS dominates, in terms of its Bayes risk, the Bayes estimator of the mean using SRS. This procedure is used to estimate the average Milk yield of four hundreds and two sheep. The empirical efficiency supports the theoretical findings.     

Spatially balanced sampling and ground‐level imagery for vegetation monitoring on reclaimed well pads

Land reclamation associated with natural gas development has become increasingly important to mitigate land surface disturbance in western North America. Since well pads occur on sites with multiple land use and ownership, the progress and outcomes of these efforts are of interest to multiple stakeholders including industry, practitioners and consultants, regulatory agents, private landowners, and the scientific community. Reclamation success criteria often vary within, and among, government agencies and across land ownership type. Typically, reclamation success of a well pad is judged by comparing vegetation cover from a single transect on the pad to a single transect in an adjacent reference site and data are collected by a large number of technicians with various field monitoring skills. We utilized “SamplePoint” image analysis software and a spatially balanced sampling design, called balanced acceptance sampling, to demonstrate how spatially explicit quantitative data can be used to determine if sites are meeting various reclamation success criteria and used chi‐square tests to show how sites in vegetation percent cover differ from a statistical standpoint. This method collects field data faster than traditional methods. We demonstrate how quantitative and spatially explicit data can be utilized by multiple stakeholders, how it can improve upon current reference site selection, how it can satisfy reclamation monitoring requirements for multiple regulatory agencies, how it may help improve future seed mix selection, and discuss how it may reduce costs for operations responsible for reclamation and how it may reduce observer bias.     

Simulations inform design of regional occupancy‐based monitoring for a sparsely distributed,territorial species

Sparsely distributed species attract conservation concern, but insufficient information on population trends challenges conservation and funding prioritization. Occupancy‐based monitoring is attractive for these species, but appropriate sampling design and inference depend on particulars of the study system. We employed spatially explicit simulations to identify minimum levels of sampling effort for a regional occupancy monitoring study design, using white‐headed woodpeckers (Picoides albolvartus), a sparsely distributed, territorial species threatened by habitat decline and degradation, as a case study. We compared the original design with commonly proposed alternatives with varying targets of inference (i.e., species range, space use, or abundance) and spatial extent of sampling. Sampling effort needed to achieve adequate power to observe a long‐term population trend (≥80% chance to observe a 2% yearly decline over 20 years) with the previously used study design consisted of annually monitoring ≥120 transects using a single‐survey approach or ≥90 transects surveyed twice per year using a repeat‐survey approach. Designs that shifted inference toward finer‐resolution trends in abundance and extended the spatial extent of sampling by shortening transects, employing a single‐survey approach to monitoring, and incorporating a panel design (33% of units surveyed per year) improved power and reduced error in estimating abundance trends. In contrast, efforts to monitor coarse‐scale trends in species range or space use with repeat surveys provided extremely limited statistical power. Synthesis and applications. Sampling resolutions that approximate home range size, spatially extensive sampling, and designs that target inference of abundance trends rather than range dynamics are probably best suited and most feasible for broad‐scale occupancy‐based monitoring of sparsely distributed territorial animal species.     

Spatio-temporal heterogeneity in river sounds: Disentangling micro- and macro-variation in a chain of waterholes

1. Passive acoustic monitoring is gaining momentum as a viable alternative method to surveying freshwater ecosystems. As part of an emerging field, the spatio-temporal replication levels of these sampling methods need to be standardised. However, in shallow waters, acoustic spatio-temporal patchiness remains virtually unexplored.
2. In this paper, we specifically investigate the spatial heterogeneity in underwater sounds observed within and between waterholes of an ephemeral river at different times of the day and how it could affect sampling in passive acoustic monitoring.
3. We recorded in the Einasleigh River, Queensland in August 2016, using a linear transect of hydrophones mounted on frames. We recorded four times a day: at dawn, midday, dusk, and midnight. To measure different temporal and spectral attributes of the recorded sound, we investigated the mean frequency spectrum and computed acoustic indices.
4. Both mean frequency spectrum and index analyses revealed that the site and diel activity patterns significantly influenced the sounds recorded, even for adjacent sites with similar characteristics along a single river. We found that most of the variation was due to temporal patterns, followed by between-site differences, while within-site differences had limited influence.
5. This study demonstrates high spatio-temporal acoustic variability in freshwater environments, linked to different species or species groups. Decisions about sampling design are vital to obtain adequate representation. This study thus emphasises the need to tailor spatio-temporal settings of a sampling design to the aim of the study, the species and the habitat.

     

Cost considerations for long-term ecological monitoring

For an ecological monitoring program to be successful over the long-term, the perceived benefits of the information must justify the cost. Financial limitations will always restrict the scope of a monitoring program, hence the program’s focus must be carefully prioritized. Clearly identifying the costs and benefits of a program will assist in this prioritization process, but this is easier said than done. Frequently, the true costs of monitoring are not recognized and are, therefore, underestimated. Benefits are rarely evaluated, because they are difficult to quantify. The intent of this review is to assist the designers and managers of long-term ecological monitoring programs by providing a general framework for building and operating a cost-effective program. Previous considerations of monitoring costs have focused on sampling design optimization. We present cost considerations of monitoring in a broader context. We explore monitoring costs, including both budgetary costs, what dollars are spent on, and economic costs, which include opportunity costs. Often, the largest portion of a monitoring program budget is spent on data collection, and other, critical aspects of the program, such as scientific oversight, training, data management, quality assurance, and reporting, are neglected. Recognizing and budgeting for all program costs is therefore a key factor in a program’s longevity. The close relationship between statistical issues and cost is discussed, highlighting the importance of sampling design, replication and power, and comparing the costs of alternative designs through pilot studies and simulation modeling. A monitoring program development process that includes explicit checkpoints for considering costs is presented. The first checkpoint occurs during the setting of objectives and during sampling design optimization. The last checkpoint occurs once the basic shape of the program is known, and the costs and benefits, or alternatively the cost-effectiveness, of each program element can be evaluated. Moving into the implementation phase without careful evaluation of costs and benefits is risky because if costs are later found to exceed benefits, the program will fail. The costs of development, which can be quite high, will have been largely wasted. Realistic expectations of costs and benefits will help ensure that monitoring programs survive the early, turbulent stages of development and the challenges posed by fluctuating budgets during implementation.     

Dealing with clustered samples for assessing map accuracy by cross-validation

Mapping of environmental variables often relies on map accuracy assessment through cross-validation with the data used for calibrating the underlying mapping model. When the data points are spatially clustered, conventional cross-validation leads to optimistically biased estimates of map accuracy. Several papers have promoted spatial cross-validation as a means to tackle this over-optimism. Many of these papers blame spatial autocorrelation as the cause of the bias and propagate the widespread misconception that spatial proximity of calibration points to validation points invalidates classical statistical validation of maps. We present and evaluate alternative cross-validation approaches for assessing map accuracy from clustered sample data. The first method uses inverse sampling-intensity weighting to correct for selection bias. Sampling-intensity is estimated by a two-dimensional kernel approach. The two other approaches are model-based methods rooted in geostatistics, where the first assumes homogeneity of residual variance over the study area whilst the second accounts for heteroscedasticity as a function of the sampling intensity. The methods were tested and compared against conventional k-fold cross-validation and blocked spatial cross-validation to estimate map accuracy metrics of above-ground biomass and soil organic carbon stock maps covering western Europe. Results acquired over 100 realizations of five sampling designs ranging from non-clustered to strongly clustered confirmed that inverse sampling-intensity weighting and the heteroscedastic model-based method had smaller bias than conventional and spatial cross-validation for all but the most strongly clustered design. For the strongly clustered design where large portions of the maps were predicted by extrapolation, blocked spatial cross-validation was closest to the reference map accuracy metrics, but still biased. For such cases, extrapolation is best avoided by additional sampling or limitation of the prediction area. Weighted cross-validation is recommended for moderately clustered samples, while conventional random cross-validation suits fairly regularly spread samples.     

Accounting for cluster sampling in constructing enumerative sequential sampling plans

Green's sequential sampling plan is widely used in applied entomology. Green's equation can be used to construct sampling stop charts, and a crop can then be surveyed using a simple random sampling (SRS) approach. In practice, however, crops are rarely surveyed according to SRS. Rather, some type of hierarchical design is usually used, such as cluster sampling, where sampling units form distinct groups. This article explains how to make adjustments to sampling plans that intend to use cluster sampling, a commonly used hierarchical design, rather than SRS. The methodologies are illustrated using diamondback moth, Plutella xylostella (L.), a pest of Brassica crops, as an example.     

An improved survey method for monitoring population trends of Golden‐winged Warblers and other patchily distributed birds

Conventional surveys designed to monitor common and widespread species may fail to adequately track population changes of rare or patchily distributed species that are often of high conservation concern. We evaluated the performance of a new monitoring approach that employs both a spatially balanced sampling design and a targeted survey protocol designed to estimate population trends of one such patchily distributed species, the Golden‐winged Warbler (Vermivora chrysoptera), in the Appalachian Mountains Bird Conservation Region (BCR 28), USA. Our spatially balanced survey consisted of 105 sample quads (one‐quarter Delorme Atlas pages) across the current range of Golden‐winged Warblers within BCR 28, each with five sample points located in early successional habitat. From 2009 to 2013, collaborators visited each sample point once per year during the peak breeding season and conducted a 17‐min survey consisting of passive observation and playback of conspecific songs and mobbing vocalizations. We used multi‐season, single‐species occupancy models to estimate probability of quad occupancy, detection probability, and occupancy dynamics for Golden‐winged Warblers and closely related Blue‐winged Warblers (Vermivora cyanoptera). Our survey protocol resulted in high estimates of detection probability for Golden‐winged (92%) and Blue‐winged (79%) warblers, with 47% and 56% of quads estimated to be initially occupied, respectively. Derived population trend estimates (λ) indicated an average decline in population of 6% for Golden‐winged Warblers and 7% for Blue‐winged Warblers, resulting in estimated 21% and 22% declines, respectively, in quad occupancy after 5 yr. Our results demonstrate that coupling a spatially balanced survey design in appropriate habitat with a playback protocol to increase detection rates is a viable strategy for tracking populations of Golden‐winged Warblers in the Appalachian Mountains BCR. Similar survey methods should be considered for other rare, declining, or patchily distributed bird species that require targeted monitoring.     

Efficiency of balanced treatment allocation for survival analysis

We assess the efficiency of balanced treatment allocation methods in clinical trials for comparing treatments with respect to survival. We compare optimal designs for each of three standard survival analysis techniques (maximum partial likelihood estimation, log-rank test, exponential regression) with balanced designs, over a range of hypothetical trials. Although balanced designs are not optimal, we find them to be very efficient. In view of the high efficiency demonstrated in this and in a previous paper (Begg and Kalish, 1984, Biometrics 40, 409-420), and practical difficulties in implementing an optimal design, we recommend the use of balanced allocation methods in practice.     

Contrasting patterns of population connectivity between regions in a commercially important mollusc Haliotis rubra: integrating population genetics,genomics and marine LiDAR data

Estimating contemporary genetic structure and population connectivity in marine species is challenging, often compromised by genetic markers that lack adequate sensitivity, and unstructured sampling regimes. We show how these limitations can be overcome via the integration of modern genotyping methods and sampling designs guided by LiDAR and SONAR data sets. Here we explore patterns of gene flow and local genetic structure in a commercially harvested abalone species (Haliotis rubra) from southeastern Australia, where the viability of fishing stocks is believed to be dictated by recruitment from local sources. Using a panel of microsatellite and genomewide SNP markers, we compare allele frequencies across a replicated hierarchical sampling area guided by bathymetric LiDAR imagery. Results indicate high levels of gene flow and no significant genetic structure within or between benthic reef habitats across 1400 km of coastline. These findings differ to those reported for other regions of the fishery indicating that larval supply is likely to be spatially variable, with implications for management and long‐term recovery from stock depletion. The study highlights the utility of suitably designed genetic markers and spatially informed sampling strategies for gaining insights into recruitment patterns in benthic marine species, assisting in conservation planning and sustainable management of fisheries.     

Stability of the spatio-temporal distribution and niche overlap in neotropical earthworm assemblages

The spatial distribution of soil invertebrates is aggregated with high-density patches alternating with low-density zones. A high degree of spatio-temporal organization generally exists with identified patches of specific species assemblages, in which species coexist according to assembly rules related to competitive mechanisms for spatial and trophic resources occur. However, these issues have seldom been addressed. The spatio-temporal structure of a native earthworm community in a natural savanna and a grass–legume pasture in the Colombian “Llanos” was studied during a 2-year-period. A spatially explicit sampling design (regular grid) was used to discern the distribution pattern of species assemblages in both systems. Earthworms were collected from small soil pits at three different sampling dates. Data collected from 1 m² soil monoliths were also used in the present study. Data were analyzed with the partial triadic analysis (PTA) and correlograms, while niche overlap was computed with the Pianka index. The PTA and correlogram analysis revealed that earthworm communities displayed a similar stable spatial structure in both systems during the 2-year study period. An alternation of population patches where different species' assemblages dominated was common to all sampling dates. The medium-sized Andiodrilus sp. and Glossodrilus sp. exhibited a clear spatial opposition in natural savanna and the grass–legume pasture for the duration of the study. The Pianka index showed a high degree of niche overlapping in several dimensions (vertical distribution, seasonality of population density) between both species. The inclusion of space-time data analysis tools as the PTA and the use of classical ecological indices (Pianka) in soil ecology studies may improve our knowledge of earthworm assemblages' dynamics.     

Stability of the spatio-temporal distribution and niche overlap in neotropical earthworm assemblages

The spatial distribution of soil invertebrates is aggregated with high-density patches alternating with low-density zones. A high degree of spatio-temporal organization generally exists with identified patches of specific species assemblages, in which species coexist according to assembly rules related to competitive mechanisms for spatial and trophic resources occur. However, these issues have seldom been addressed. The spatio-temporal structure of a native earthworm community in a natural savanna and a grass–legume pasture in the Colombian “Llanos” was studied during a 2-year-period. A spatially explicit sampling design (regular grid) was used to discern the distribution pattern of species assemblages in both systems. Earthworms were collected from small soil pits at three different sampling dates. Data collected from 1 m² soil monoliths were also used in the present study. Data were analyzed with the partial triadic analysis (PTA) and correlograms, while niche overlap was computed with the Pianka index. The PTA and correlogram analysis revealed that earthworm communities displayed a similar stable spatial structure in both systems during the 2-year study period. An alternation of population patches where different species' assemblages dominated was common to all sampling dates. The medium-sized Andiodrilus sp. and Glossodrilus sp. exhibited a clear spatial opposition in natural savanna and the grass–legume pasture for the duration of the study. The Pianka index showed a high degree of niche overlapping in several dimensions (vertical distribution, seasonality of population density) between both species. The inclusion of space-time data analysis tools as the PTA and the use of classical ecological indices (Pianka) in soil ecology studies may improve our knowledge of earthworm assemblages' dynamics.     

Design of validation studies for estimating the odds ratio of exposure-disease relationships when exposure is misclassified

We compared several validation study designs for estimating the odds ratio of disease with misclassified exposure. We assumed that the outcome and misclassified binary covariate are available and that the error-free binary covariate is measured in a subsample, the validation sample. We considered designs in which the total size of the validation sample is fixed and the probability of selection into the validation sample may depend on outcome and misclassified covariate values. Design comparisons were conducted for rare and common disease scenarios, where the optimal design is the one that minimizes the variance of the maximum likelihood estimator of the true log odds ratio relating the outcome to the exposure of interest. Misclassification rates were assumed to be independent of the outcome. We used a sensitivity analysis to assess the effect of misspecifying the misclassification rates. Under the scenarios considered, our results suggested that a balanced design, which allocates equal numbers of validation subjects into each of the four outcome/mismeasured covariate categories, is preferable for its simplicity and good performance. A user-friendly Fortran program is available from the second author, which calculates the optimal sampling fractions for all designs considered and the efficiencies of these designs relative to the optimal hybrid design for any scenario of interest.     

Monitoring temporal trends in spatially structured populations: how should sampling effort be allocated between space and time?

Estimating temporal trends in spatially structured populations has a critical role to play in understanding regional changes in biological populations and developing management strategies. Designing effective monitoring programmes to estimate these trends requires important decisions to be made about how to allocate sampling effort among spatial replicates (i.e. number of sites) and temporal replicates (i.e. how often to survey) to minimise uncertainty in trend estimates. In particular, the optimal mix of spatial and temporal replicates is likely to depend upon the spatial and temporal correlations in population dynamics. Although there has been considerable interest in the ecological literature on understanding spatial and temporal correlations in species’ population dynamics, little attention has been paid to its consequences for monitoring design. We address this issue using model‐based survey design to identify the optimal allocation of sampling effort among spatial and temporal replicates for estimating population trends under different levels of spatial and temporal correlation. Based on linear trends, we show that how we should allocate sampling effort among spatial and temporal replicates depends crucially on the spatial and temporal correlations in population dynamics, environmental variation, observation error and the spatial variation in temporal trends. When spatial correlation is low and temporal correlation is high, the best option is likely to be to sample many sites infrequently, particularly when observation error and/or spatial variation in temporal trends are high. When spatial correlation is high and temporal correlation is low, the best option is likely to be to sample few sites frequently, particularly when observation error and/or spatial variation in temporal trends are low. When abundances are spatially independent, it is always preferable to maximise spatial replication. This provides important insights into how spatio‐temporal monitoring programmes should be designed to estimate temporal trends in spatially structured populations.     

Improved procedures for estimation of disease prevalence using ranked set sampling

Ranked set sampling (RSS) is a sampling procedure that can be considerably more efficient than simple random sampling (SRS). When the variable of interest is binary, ranking of the sample observations can be implemented using the estimated probabilities of success obtained from a logistic regression model developed for the binary variable. The main objective of this study is to use substantial data sets to investigate the application of RSS to estimation of a proportion for a population that is different from the one that provides the logistic regression. Our results indicate that precision in estimation of a population proportion is improved through the use of logistic regression to carry out the RSS ranking and, hence, the sample size required to achieve a desired precision is reduced. Further, the choice and the distribution of covariates in the logistic regression model are not overly crucial for the performance of a balanced RSS procedure.     

Optimizing sampling design to infer the number of marine turtles nesting on low and high density sea turtle rookeries using convolution of negative binomial distribution

Reliable monitoring of wildlife populations represents a non-negligible cost, and in a limited-resource world, resources allocated to monitoring are not devoted to actions to solve identified problems.I explore resource efficient survey designs based on a negative binomial distribution including variable survey intervals for marine turtles using track counts as an index of female activity. In the modified procedure, all new tracks between two monitoring patrols are recorded. These data are analyzed by statistical models that take advantage of the statistical properties of the sum of counts.The outputs of models with different lagged monitoring dates (3–10 days) are compared with the outputs of daily surveys using extrapolations from high and low density populations. Results show that the quality of the estimates is similar when total time series analysis is compared with situations in which only a fourth, a seventh, or a tenth of monitoring daily during the season are used.This solution permits the reallocation of funds from monitoring to other conservation activities. Furthermore, the efficient sampling design and the statistical methods allow getting similar information with less effort.