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.     

Atlantic bluefin tuna in the Gulf of Maine,II: precision of sampling designs in estimating seasonal abundance accounting for tuna behaviour

A primary challenge of animal surveys is to understand how to reliably sample populations exhibiting strong spatial heterogeneity. Building upon recent findings from survey, tracking and tagging data, we investigate spatial sampling of a seasonally resident population of Atlantic bluefin tuna in the Gulf of Maine, Northwestern Atlantic Ocean. We incorporate empirical estimates to parameterize a stochastic population model and simulate measurement designs to examine survey efficiency and precision under variation in tuna behaviour. We compare results for random, systematic, stratified, adaptive and spotter-search survey designs, with spotter-search comprising irregular transects that target surfacing schools and known aggregation locations (i.e., areas of expected high population density) based on a priori knowledge. Results obtained show how survey precision is expected to vary on average with sampling effort, in agreement with general sampling theory and provide uncertainty ranges based on simulated variance in tuna behaviour. Simulation results indicate that spotter-search provides the highest level of precision, however, measurable bias in observer-school encounter rate contributes substantial uncertainty. Considering survey bias, precision, efficiency and anticipated operational costs, we propose that an adaptive-stratified sampling alone or a combination of adaptive-stratification and spotter-search (a mixed-layer design whereby a priori information on the location and size of school aggregations is provided by sequential spotter-search sampling) may provide the best approach for reducing uncertainty in seasonal abundance estimates.

Variance estimation for systematic designs in spatial surveys

Summary In spatial surveys for estimating the density of objects in a survey region, systematic designs will generally yield lower variance than random designs. However, estimating the systematic variance is well known to be a difficult problem. Existing methods tend to overestimate the variance, so although the variance is genuinely reduced, it is over‐reported, and the gain from the more efficient design is lost. The current approaches to estimating a systematic variance for spatial surveys are to approximate the systematic design by a random design, or approximate it by a stratified design. Previous work has shown that approximation by a random design can perform very poorly, while approximation by a stratified design is an improvement but can still be severely biased in some situations. We develop a new estimator based on modeling the encounter process over space. The new “striplet” estimator has negligible bias and excellent precision in a wide range of simulation scenarios, including strip‐sampling, distance‐sampling, and quadrat‐sampling surveys, and including populations that are highly trended or have strong aggregation of objects. We apply the new estimator to survey data for the spotted hyena (Crocuta crocuta) in the Serengeti National Park, Tanzania, and find that the reported coefficient of variation for estimated density is 20% using approximation by a random design, 17% using approximation by a stratified design, and 11% using the new striplet estimator. This large reduction in reported variance is verified by simulation.     

Sampling Considerations for Disease Surveillance in Wildlife Populations

Abstract Disease surveillance in wildlife populations involves detecting the presence of a disease, characterizing its prevalence and spread, and subsequent monitoring. A probability sample of animals selected from the population and corresponding estimators of disease prevalence and detection provide estimates with quantifiable statistical properties, but this approach is rarely used. Although wildlife scientists often assume probability sampling and random disease distributions to calculate sample sizes, convenience samples (i.e., samples of readily available animals) are typically used, and disease distributions are rarely random. We demonstrate how landscape-based simulation can be used to explore properties of estimators from convenience samples in relation to probability samples. We used simulation methods to model what is known about the habitat preferences of the wildlife population, the disease distribution, and the potential biases of the convenience-sample approach. Using chronic wasting disease in free-ranging deer (Odocoileus virginianus) as a simple illustration, we show that using probability sample designs with appropriate estimators provides unbiased surveillance parameter estimates but that the selection bias and coverage errors associated with convenience samples can lead to biased and misleading results. We also suggest practical alternatives to convenience samples that mix probability and convenience sampling. For example, a sample of land areas can be selected using a probability design that oversamples areas with larger animal populations, followed by harvesting of individual animals within sampled areas using a convenience sampling method.     

Sampling designs, field techniques and analytical methods for systematic plant population surveys

Summary Intense pressures on the use and management of land underscore the need for reliable and up-to-date information on the status of native species. The outcomes of the most recent plant population surveys commissioned by agencies are generally limited by faults or omissions in survey design. There is little guidance on how to design and implement field surveys of plant populations in ways that address the most pertinent gaps in our current knowledge and provide answers of known reliability. In this paper, I used the International Union for the Conservation of Nature (IUCN) Red List criteria as a framework to define the data required from surveys to assess the conservation status of potentially threatened species. The criteria address the location and geographical range of extant populations, aspects of species' life history, the size and structure of extant populations and rates of change in abundance and range. I have described survey designs and sampling techniques for estimating these parameters. Choices of appropriate methods that consider trade-offs between desired levels of precision and rigour and sampling effort are illustrated using surveys of 13 Tasmanian Epacris species as examples. Key elements of the approach are: (i) systematic approaches to field searches and recording both positive and negative search outcomes; (ii) construction and testing of intuitive or quantitative distribution models in an explicit experimental framework; (iii) rigorous cost-effective sampling designs, systematic field methodologies and simple analytical techniques to estimate both the magnitude and uncertainty of distribution and abundance; (iv) assessment of the merits and limitations of alternative sampling options; and (v) inference of changes in distribution and abundance by judicious use of historical data and field evidence of recent population processes.     

Improving inference for aerial surveys of bears: The importance of assumptions and the cost of unnecessary complexity

Obtaining useful estimates of wildlife abundance or density requires thoughtful attention to potential sources of bias and precision, and it is widely understood that addressing incomplete detection is critical to appropriate inference. When the underlying assumptions of sampling approaches are violated, both increased bias and reduced precision of the population estimator may result. Bear (Ursus spp.) populations can be difficult to sample and are often monitored using mark‐recapture distance sampling (MRDS) methods, although obtaining adequate sample sizes can be cost prohibitive. With the goal of improving inference, we examined the underlying methodological assumptions and estimator efficiency of three datasets collected under an MRDS protocol designed specifically for bears. We analyzed these data using MRDS, conventional distance sampling (CDS), and open‐distance sampling approaches to evaluate the apparent bias‐precision tradeoff relative to the assumptions inherent under each approach. We also evaluated the incorporation of informative priors on detection parameters within a Bayesian context. We found that the CDS estimator had low apparent bias and was more efficient than the more complex MRDS estimator. When combined with informative priors on the detection process, precision was increased by >50% compared to the MRDS approach with little apparent bias. In addition, open‐distance sampling models revealed a serious violation of the assumption that all bears were available to be sampled. Inference is directly related to the underlying assumptions of the survey design and the analytical tools employed. We show that for aerial surveys of bears, avoidance of unnecessary model complexity, use of prior information, and the application of open population models can be used to greatly improve estimator performance and simplify field protocols. Although we focused on distance sampling‐based aerial surveys for bears, the general concepts we addressed apply to a variety of wildlife survey contexts.     

Variance of Stratified Survey Estimators With Probability of Detection Adjustments

Abstract: Estimates of wildlife population sizes are frequently constructed by combining counts of observed animals from a stratified survey of aerial sampling units with an estimated probability of detecting animals. Unlike traditional stratified survey designs, stratum-specific estimates of population size will be correlated if a common detection model is used to adjust counts for undetected animals in all strata. We illustrate this concept in the context of aerial surveys, considering 2 cases: 1) a single-detection parameter is estimated under the assumption of constant detection probabilities, and 2) a logistic-regression model is used to estimate heterogeneous detection probabilities. Naïve estimates of variance formed by summing stratum-specific estimates of variance may result in significant bias, particularly if there are a large number of strata, if detection probabilities are small, or if estimates of detection probabilities are imprecise. (JOURNAL OF WILDLIFE MANAGEMENT 72(3):837–844; 2008)     

Inverse Adaptive Cluster Sampling

Consider a population in which the variable of interest tends to be at or near zero for many of the population units but a subgroup exhibits values distinctly different from zero. Such a population can be described as rare in the sense that the proportion of elements having nonzero values is very small. Obtaining an estimate of a population parameter such as the mean or total that is nonzero is difficult under classical fixed sample-size designs since there is a reasonable probability that a fixed sample size will yield all zeroes. We consider inverse sampling designs that use stopping rules based on the number of rare units observed in the sample. We look at two stopping rules in detail and derive unbiased estimators of the population total. The estimators do not rely on knowing what proportion of the population exhibit the rare trait but instead use an estimated value. Hence, the estimators are similar to those developed for poststratification sampling designs. We also incorporate adaptive cluster sampling into the sampling design to allow for the case where the rare elements tend to cluster within the population in some manner. The formulas for the variances of the estimators do not allow direct analytic comparison of the efficiency of the various designs and stopping rules, so we provide the results of a small simulation study to obtain some insight into the differences among the stopping rules and sampling approaches. The results indicate that a modified stopping rule that incorporates an adaptive sampling component and utilizes an initial random sample of fixed size is the best in the sense of having the smallest variance.     

Improving species occupancy estimation when sampling violates the closure assumption

Site occupancy models that account for imperfect detection of species are increasingly utilized in ecological research and wildlife monitoring. Occupancy models require replicate surveys to estimate detection probability over a time period where the occupancy status at sampled sites is assumed closed. Unlike mark–recapture models, few studies have examined how violations of closure can bias occupancy estimates. Our study design allowed us to differentiate among two processes that violate the closure assumption during a sampling season: 1) repeated destructive sampling events that result in either short‐ or long‐term site avoidance by the target species and 2) sampling occurring over a time period during which non‐random movements of the target species result in variable occupancy status. We used dynamic occupancy models to quantify the potential bias in occupancy estimation associated with these processes for a terrestrial salamander system. Our results provide strong evidence of a systematic decrease in salamander occupancy within a field season. Chronic disturbance due to repeated searches of natural cover objects accelerated natural declines in species occurrence on the forest surface as summer progressed. We also observed a strong but temporary disturbance effect on salamander detection probability associated with repeated sampling within a 24‐h. period. We generalized our findings by conducting a simulation to evaluate how violations of closure can bias occupancy estimates when local extinction occurs within a sampling season. Our simulation study revealed general sensitivity of estimates from single‐season occupancy models to violations of closure, with the strength and direction of bias varying between scenarios. Bias was minimal when extinction proba bility or the number of sample occasions was relatively low. Our research highlights the importance of addressing closure in occupancy studies and we provide multiple solutions, using both design‐ and model‐based frameworks, for minimizing bias associated with non‐random changes in occupancy and repeated sampling disturbances.     

Integrating distance sampling with minimum counts to improve monitoring

Minimum counts are commonly used to estimate population size and trend for wildlife conservation and management; however, the scope of inference based on such data is limited by untestable assumptions regarding the detection process. Alternative approaches, such as distance sampling, occupancy surveys, and repeated counts, can be employed to produce detection-corrected estimates of population parameters. Unfortunately, these approaches can be more complicated and costly to implement, potentially limiting their use. We explored a conceptual framework linking datasets collected at different spatial scales under different survey designs, with the goal of improving inference. Specifically, we link landscape-scale distance sampling surveys with local-scale minimum counts in an integrated modeling framework to estimate mountain goat (Oreamnos americanus) abundance at both the local and regional scale in south-central Alaska, USA, and provide an estimate of detection probability (i.e., sightability) for the minimum counts. Estimated sightability for the minimum count surveys was 0.67 (95% credible interval [CrI] = 0.52–0.83) and abundance for the entire area was 5,600 goats (CV = 9%), both in broad agreement with estimates from previous studies. Abundance estimates at the local scale (i.e., individual min. count unit) were reasonably precise ( = 18%), suggesting the integrated approach can increase the amount of information produced at both spatial scales by linking minimum count approaches with more rigorous survey designs. We propose that our integrated approach may be implemented in the context of a modified split-panel monitoring design by altering survey protocols to include frequent minimum counts within local count units and intermittent but more rigorous survey designs with inference to the entire study area or population of interest. Doing so would provide estimates of abundance with appropriate measures of uncertainty at multiple spatial scales, thereby improving inference for population monitoring and management. © 2019 The Wildlife Society.     

Toward reliable population density estimates of partially marked populations using spatially explicit mark–resight methods

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Multiple sensitive estimation and optimal sample size allocation in the item sum technique

For surveys of sensitive issues in life sciences, statistical procedures can be used to reduce nonresponse and social desirability response bias. Both of these phenomena provoke nonsampling errors that are difficult to deal with and can seriously flaw the validity of the analyses. The item sum technique (IST) is a very recent indirect questioning method derived from the item count technique that seeks to procure more reliable responses on quantitative items than direct questioning while preserving respondents' anonymity. This article addresses two important questions concerning the IST: (i) its implementation when two or more sensitive variables are investigated and efficient estimates of their unknown population means are required; (ii) the determination of the optimal sample size to achieve minimum variance estimates. These aspects are of great relevance for survey practitioners engaged in sensitive research and, to the best of our knowledge, were not studied so far. In this article, theoretical results for multiple estimation and optimal allocation are obtained under a generic sampling design and then particularized to simple random sampling and stratified sampling designs. Theoretical considerations are integrated with a number of simulation studies based on data from two real surveys and conducted to ascertain the efficiency gain derived from optimal allocation in different situations. One of the surveys concerns cannabis consumption among university students. Our findings highlight some methodological advances that can be obtained in life sciences IST surveys when optimal allocation is achieved.     

Adaptive line transect sampling

Adaptive line transect sampling offers the potential of improved population density estimation efficiency over conventional line transect sampling when populations are spatially clustered. In adaptive sampling, survey effort is increased when areas of high animal density are located, thereby increasing the number of observations. Its disadvantage is that the survey effort required is not known in advance. We develop an adaptive line transect methodology that, by varying the degree of adaptation, allows total effort to be fixed at the design stage. Relative to conventional line transect surveys, it also provides better survey coverage in the event of disruption in survey effort, e.g., due to poor weather. In analysis, sightings from the adaptive sections are downweighted in proportion to the increase in effort. We evaluate the methodology by simulation and report on surveys of harbor porpoise in the Gulf of Maine, in which the approach was compared with conventional line transect sampling.     

Using distance sampling techniques to estimate bottlenose dolphin (Tursiops truncatus) abundance at Turneffe Atoll,Belize

Reliable abundance estimates are critical for management and conservation of coastal small cetaceans. This is particularly important in developing countries where coastal human populations are increasing, the impacts of anthropogenic activities are often unknown, and the resources necessary to assess coastal cetaceans are limited. We adapted ship‐based line transect methods to small‐boat surveys to estimate the abundance of bottlenose dolphins (Tursiops truncatus) at Turneffe Atoll, Belize. Using a systematic survey design with random start and uniform coverage, 34 dolphin clusters were sighted during small‐boat line transect surveys conducted in 2005–2006. Distance sampling methods estimated abundance at 216 individuals (CV = 27.7%, 95% CI = 126–370). Due to species rarity in the Atoll, small sample size, and potential violations in line transect assumptions, the estimate should be considered preliminary. Nevertheless, it provides up‐to‐date information on the status of a regional population in an area under increasing threat of habitat loss and prey depletion via uncontrolled development and unsustainable fishing. This information will be useful as Belize develops a new conservation initiative to create a comprehensive and resilient marine protected area system. Our study illustrates the application of distance sampling methods to small‐boat surveys to obtain abundance estimates of coastal cetaceans in a region lacking resources.     

Sampling strategy optimization to increase statistical power in landscape genomics: A simulation‐based approach

An increasing number of studies are using landscape genomics to investigate local adaptation in wild and domestic populations. Implementation of this approach requires the sampling phase to consider the complexity of environmental settings and the burden of logistical constraints. These important aspects are often underestimated in the literature dedicated to sampling strategies. In this study, we computed simulated genomic data sets to run against actual environmental data in order to trial landscape genomics experiments under distinct sampling strategies. These strategies differed by design approach (to enhance environmental and/or geographical representativeness at study sites), number of sampling locations and sample sizes. We then evaluated how these elements affected statistical performances (power and false discoveries) under two antithetical demographic scenarios. Our results highlight the importance of selecting an appropriate sample size, which should be modified based on the demographic characteristics of the studied population. For species with limited dispersal, sample sizes above 200 units are generally sufficient to detect most adaptive signals, while in random mating populations this threshold should be increased to 400 units. Furthermore, we describe a design approach that maximizes both environmental and geographical representativeness of sampling sites and show how it systematically outperforms random or regular sampling schemes. Finally, we show that although having more sampling locations (between 40 and 50 sites) increase statistical power and reduce false discovery rate, similar results can be achieved with a moderate number of sites (20 sites). Overall, this study provides valuable guidelines for optimizing sampling strategies for landscape genomics experiments.     

Bayesian methods for multiple capture-recapture surveys

To estimate the total size of a closed population, a multiple capture-recapture sampling design can be used. This sampling design has been used traditionally to estimate the size of wildlife populations and is becoming more widely used to estimate the size of hard-to-count human populations. This paper presents Bayesian methods for obtaining point and interval estimates from data gathered from capture-recapture surveys. A numerical example involving the estimation of the size of a fish population is given to illustrate the methods.     

Raising the bar for the next generation of biological atlases: using existing data to inform the design and implementation of atlas monitoring

Selecting a sampling design to monitor multiple species across a broad geographical region can be a daunting task and often involves tradeoffs between limited resources and the accurate estimation of population abundance and occurrence. Since the 1950s, biological atlases have been implemented in various regions to document the occurrence of plant and animal species. As next‐generation atlases repeat original surveys, investigators often seek to raise the rigour of atlases by incorporating species abundances. We present a repeatable framework that incorporates existing monitoring data, hierarchical modelling and sampling simulations to augment existing atlas occurrence and breeding status maps with a secondary sampling of species abundances. Using existing information on three bird species with varying abundance and detectability, we evaluated several sampling scenarios for the 2nd Wisconsin Breeding Bird Atlas. In general, we found that most sampling schemes produced accurate mean statewide abundance estimates for species with medium to high abundance and detection probability, but estimates varied significantly for species with low abundance and low detection probability. Our approach provided a statewide point‐count sampling design that: provided precise and unbiased abundance estimates for species of varied prevalence and detectability; ensured suitable spatial coverage across the state and its habitats; and reduced spending on total survey costs. Our framework could benefit investigators conducting atlases and other broad‐scale avian surveys that seek to add systematic, multi‐species sampling for estimating density and abundance across broad geographical regions.     

Evaluation of Bear Rub Surveys to Monitor Grizzly Bear Population Trends

Abstract: Wildlife managers need reliable estimates of population size, trend, and distribution to make informed decisions about how to recover at-risk populations, yet obtaining these estimates is costly and often imprecise. The grizzly bear (Ursus arctos) population in northwestern Montana, USA, has been managed for recovery since being listed under the United States Endangered Species Act in 1975, yet no rigorous data were available to evaluate the program's success. We used encounter data from 379 grizzly bears identified through bear rub surveys to parameterize a series of Pradel model simulations in Program MARK to assess the ability of noninvasive genetic sampling to estimate population growth rates. We evaluated model performance in terms of 1) power to detect gender-specific and population-wide declines in population abundance, 2) precision and relative bias of growth rate estimates, and 3) sampling effort required to achieve 80% power to detect a decline within 10 years. Simulations indicated that ecosystem-wide, annual bear rub surveys would exceed 80% power to detect a 3% annual decline within 6 years. Robust-design models with 2 simulated surveys per year provided precise and unbiased annual estimates of trend, abundance, and apparent survival. Designs incorporating one survey per year require less sampling effort but only yield trend and apparent survival estimates. Our results suggest that systematic, annual bear rub surveys may provide a viable complement or alternative to telemetry-based methods for monitoring trends in grizzly bear populations.     

Application of photographic capture–recapture modelling to estimate demographic parameters for male Asian elephants

In addition to the threats of habitat loss and degradation, adult males of the Asian elephant Elephas maximus also face greater threats from ivory poaching and conflict with humans. To understand the impact of these threats, conservationists need robust estimates of abundance and vital rates specifically for the adult male segment of elephant populations. By integrating the identification of individual male elephants in a population from distinct morphology and natural markings, with modern capture–recapture (CR) sampling designs, it is possible to estimate various demographic parameters that are otherwise difficult to obtain from this long-lived and wide-ranging megaherbivore. In this study, we developed systematic individual identification protocols and integrated them into CR sampling designs to obtain capture histories and thereby estimate the abundance of adult bull elephants in a globally important population in southern India. We validated these estimates against those obtained from an independent method combining line-transect density estimates with age–sex composition data for elephants. The sampled population was open to gains and losses between sampling occasions. The abundance of adult males in the 176 km² study area was (SÊ ) = 134(14.20) and they comprised 14% (±1%) of the total elephant population. Time-specific abundance estimates for each sampling occasion showed a distinct increase in adult male numbers over the sampling period, explained by seasonal patterns of local migration. CR-based estimates for adult male abundance closely matched estimates from distance-based methods. Thus, while providing abundance data of comparable rigour and precision, photographic CR methods permit estimation of demographic parameters for the Asian elephant that are both urgently needed and difficult to obtain.