Desirable design characteristics for long-term monitoring of ecological variables

Long-term environmental monitoring places a set of demands on a sampling strategy not present in a survey designed for a single time period. The inevitability that a sample will become out of date must be a dominant consideration in planning a long-term monitoring programme. The sampling strategy must be able to accommodate periodic frame update and sample restructuring in order to address changes in the composition of the universe and changes in the perception of issues leading to new questions and concerns. The sampling strategy must be capable of adapting to such changes while maintaining its identification as a probability sample and its capacity to detect trends that span the update occasions. These issues are examined with respect to sub-population estimation, post-stratification via conditioning, and sample enlargement and reduction. Design features that involve complex sample structure create potentially serious difficulties, whereas an equal probability design permits greater adaptability and flexibility. Structure should be employed sparingly and in awareness of its undesirable effects.     

Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data

The mean of a balanced ranked set sample is more efficient than the mean of a simple random sample of equal size and the precision of ranked set sampling may be increased by using an unbalanced allocation when the population distribution is highly skewed. The aim of this paper is to show the practical benefits of the unequal allocation in estimating simultaneously the means of more skewed variables through real data. In particular, the allocation rule suggested in the literature for a single skewed distribution may be easily applied when more than one skewed variable are of interest and an auxiliary variable correlated with them is available. This method can lead to substantial gains in precision for all the study variables with respect to the simple random sampling, and to the balanced ranked set sampling too.     

Using forest inventory data to assess fisher resting habitat suitability in California.

The fisher (Martes pennanti) is a forest-dwelling carnivore whose current distribution and association with late-seral forest conditions make it vulnerable to stand-altering human activities or natural disturbances. Fishers select a variety of structures for daily resting bouts. These habitat elements, together with foraging and reproductive (denning) habitat, constitute the habitat requirements of fishers. We develop a model capable of predicting the suitability of fisher resting habitat using standard forest vegetation inventory data. The inventory data were derived from Forest Inventory and Analysis (FIA), a nationwide probability-based sample used to estimate forest characteristics. We developed the model by comparing vegetation and topographic data at 75 randomly selected fisher resting structures in the southern Sierra Nevada with 232 forest inventory plots. We collected vegetation data at fisher resting locations using the FIA vegetation sampling protocol and centering the 1-ha FIA plot on the resting structure. To distinguish used and available inventory plots, we used nonparametric logistic regression to evaluate a set of a priori biological models. The top model represented a dominant portion of the Akaike weights (0.87), explained 31.5% of the deviance, and included the following variables: average canopy closure, basal area of trees <51 cm diameter breast height (dbh), average hardwood dbh, maximum tree dbh, percentage slope, and the dbh of the largest conifer snag. Our use of routinely collected forest inventory data allows the assessment and monitoring of change in fisher resting habitat suitability over large regions with no additional sampling effort. Although models were constrained to include only variables available from the list of those measured using the FIA protocol, we did not find this to be a shortcoming. The model makes it possible to compare average resting habitat suitability values before and after forest management treatments, among administrative units, across regions and over time. Considering hundreds of plot estimates as a sample of habitat conditions over large spatial scales can bring a broad perspective, at high resolution, and efficiency to the assessment and monitoring of wildlife habitat.     

Triangulation based inclusion probabilities: a design-unbiased sampling approach

A probabilistic sampling approach for design-unbiased estimation of area-related quantitative characteristics of spatially dispersed population units is proposed. The developed field protocol includes a fixed number of 3 units per sampling location and is based on partial triangulations over their natural neighbors to derive the individual inclusion probabilities. The performance of the proposed design is tested in comparison to fixed area sample plots in a simulation with two forest stands. Evaluation is based on a general approach for areal sampling in which all characteristics of the resulting population of possible samples is derived analytically by means of a complete tessellation of the areal sampling frame. The example simulation shows promising results. Expected errors under this design are comparable to sample plots including a much greater number of trees per plot.     

Asymptotics in adaptive cluster sampling

In this article we consider asymptotic properties of the Horvitz-Thompson and Hansen-Hurwitz types of estimators under the adaptive cluster sampling variants obtained by selecting the initial sample by simple random sampling without replacement and by unequal probability sampling with replacement. We develop an asymptotic framework, which basically assumes that the number of units in the initial sample, as well as the number of units and networks in the population tend to infinity, but that the network sizes are bounded. Using this framework we prove that under each of the two variants of adaptive sampling above mentioned, both the Horvitz-Thompson and Hansen-Hurwitz types of estimators are design-consistent and asymptotically normally distributed. In addition we show that the ordinary estimators of their variances are also design-consistent estimators.     

A framework for adapting survey design through time for wildlife population assessment

Sampling strategies for monitoring the status and trends in wildlife populations are often determined before the first survey is undertaken. However, there may be little information about the distribution of the population and so the sample design may be inefficient. Through time, as data are collected, more information about the distribution of animals in the survey region is obtained but it can be difficult to incorporate this information in the survey design. This paper introduces a framework for monitoring motile wildlife populations within which the design of future surveys can be adapted using data from past surveys whilst ensuring consistency in design-based estimates of status and trends through time. In each survey, part of the sample is selected from the previous survey sample using simple random sampling. The rest is selected with inclusion probability proportional to predicted abundance. Abundance is predicted using a model constructed from previous survey data and covariates for the whole survey region. Unbiased design-based estimators of status and trends and their variances are derived from two-phase sampling theory. Simulations over the short and long-term indicate that in general more precise estimates of status and trends are obtained using this mixed strategy than a strategy in which all of the sample is retained or all selected with probability proportional to predicted abundance. Furthermore the mixed strategy is robust to poor predictions of abundance. Estimates of status are more precise than those obtained from a rotating panel design.     

Halton iterative partitioning: spatially balanced sampling via partitioning

A new spatially balanced sampling design for environmental surveys is introduced, called Halton iterative partitioning (HIP). The design draws sample locations that are well spread over the study area. Spatially balanced designs are known to be efficient when surveying natural resources because nearby locations tend to be similar. The HIP design uses structural properties of the Halton sequence to partition a resource into nested boxes. Sample locations are then drawn from specific boxes in the partition to ensure spatial diversity. The method is conceptually simple and computationally efficient, draws spatially balanced samples in two or more dimensions and uses standard design-based estimators. Furthermore, HIP samples have an implicit ordering that can be used to define spatially balanced over-samples. This feature is particularly useful when sampling natural resources because we can dynamically add spatially balanced units from the over-sample to the sample as non-target or inaccessible units are discovered. We use several populations to show that HIP sampling draws spatially balanced samples and gives precise estimates of population totals.     

Network inclusion probabilities and Horvitz-Thompson estimation for adaptive simple Latin square sampling

Consider a survey of a plant or animal species in which abundance or presence/absence will be recorded. Further assume that the presence of the plant or animal is rare and tends to cluster. A sampling design will be implemented to determine which units to sample within the study region. Adaptive cluster sampling designs Thompson (1990) are sampling designs that are implemented by first selecting a sample of units according to some conventional probability sampling design. Then, whenever a specified criterion is satisfied upon measuring the variable of interest, additional units are adaptively sampled in neighborhoods of those units satisfying the criterion. The success of these adaptive designs depends on the probabilities of finding the rare clustered events, called networks. This research uses combinatorial generating functions to calculate network inclusion probabilities associated with a simple Latin square sample. It will be shown that, in general, adaptive simple Latin square sampling when compared to adaptive simple random sampling will (i) yield higher network inclusion probabilities and (ii) provide Horvitz-Thompson estimators with smaller variability.     

Restricted adaptive cluster sampling

Adaptive cluster sampling can be a useful design for sampling rare and patchy populations. With this design the initial sample size is fixed but the size of the final sample (and total sampling effort) cannot be predicted prior to sampling. For some populations the final sample size can be quite variable depending on the level of patchiness. Restricted adaptive cluster sampling is a proposed modification where a limit is placed on the sample size prior to sampling and quadrats are selected sequentially for the initial sample size. As a result there is less variation in the final sample size and the total sampling effort can be predicted with some certainty, which is impor- tant for many ecological studies. Estimates of density are biased with the restricted design but under some circumstances the bias can be estimated well by bootstrapping. © Rapid Science 1998     

Estimating the number of active and successful bald eagle nests:an application of the dual frame method

Monitoring the number of animals in a wildlife population is an important task. In this paper, we estimate the number of active and successful bald eagle nests in a specific region using dual frame sampling techniques. The dual frame method combines independent samples from an incomplete list frame and an area frame that is assumed to be complete. Hartley's screening estimator is used to combine sample information from both frames. This methodology will be useful for monitoring any wildlife population where the breeding individuals have highly visible nesting territories which tend to be stable over many years.     

Antipoaching standards in onshore hydrocarbon concessions drawn from a Central African case study

Unsustainable hunting outside protected areas is threatening tropical biodiversity worldwide and requires conservationists to engage increasingly in antipoaching activities. Following the example of ecocertified logging companies, we argue that other extractive industries managing large concessions should engage in antipoaching activities as part of their environmental management plans. Onshore hydrocarbon concessions should also adopt antipoaching protocols as a standard because they represent a biodiversity threat comparable to logging. We examined the spatiotemporal patterns of small‐ and large‐mammal poaching in an onshore oil concession in Gabon, Central Africa, with a Bayesian occupancy model based on signs of poaching collected from 2010 to 2015 on antipoaching patrols. Patrol locations were initially determined based on local intelligence and past patrol successes (adaptive management) and subsequently with a systematic sampling of the concession. We generated maps of poaching probability in the concession and determined the temporal trends of this threat over 5 years. The spatiotemporal patterns of large‐ and small‐mammal poaching differed throughout the concession, and likely these groups will need different management strategies. By elucidating the relationship between site‐specific sampling effort and detection probability, the Bayesian method allowed us to set goals for future antipoaching patrols. Our results indicate that a combination of systematic sampling and adaptive management data is necessary to infer spatiotemporal patterns with the statistical method we used. On the basis of our case study, we recommend hydrocarbon companies interested in implementing efficient antipoaching activities in their onshore concessions to lay the foundation of long‐needed industry standards by: adequately measuring antipoaching effort; mixing adaptive management and balanced sampling; setting goals for antipoaching effort; pairing patrols with large‐mammal monitoring; supporting antipoaching patrols across the landscape; restricting access to their concessions; performing random searches for bushmeat and mammal products at points of entry; controlling urban and agricultural expansion; supporting bushmeat alternatives; and supporting land‐use planning.     

Improving effectiveness of systematic conservation planning with density data

Systematic conservation planning aims to design networks of protected areas that meet conservation goals across large landscapes. The optimal design of these conservation networks is most frequently based on the modeled habitat suitability or probability of occurrence of species, despite evidence that model predictions may not be highly correlated with species density. We hypothesized that conservation networks designed using species density distributions more efficiently conserve populations of all species considered than networks designed using probability of occurrence models. To test this hypothesis, we used the Zonation conservation prioritization algorithm to evaluate conservation network designs based on probability of occurrence versus density models for 26 land bird species in the U.S. Pacific Northwest. We assessed the efficacy of each conservation network based on predicted species densities and predicted species diversity. High‐density model Zonation rankings protected more individuals per species when networks protected the highest priority 10‐40% of the landscape. Compared with density‐based models, the occurrence‐based models protected more individuals in the lowest 50% priority areas of the landscape. The 2 approaches conserved species diversity in similar ways: predicted diversity was higher in higher priority locations in both conservation networks. We conclude that both density and probability of occurrence models can be useful for setting conservation priorities but that density‐based models are best suited for identifying the highest priority areas. Developing methods to aggregate species count data from unrelated monitoring efforts and making these data widely available through ecoinformatics portals such as the Avian Knowledge Network will enable species count data to be more widely incorporated into systematic conservation planning efforts.     

Two neighborhood-free plot designs for adaptive sampling of forests

Adaptive cluster sampling (ACS) has the potential of being superior for sampling rare and geographically clustered populations. However, setting up an efficient ACS design is challenging. In this study, two adaptive plot designs are proposed as alternatives: one for fixed-area plot sampling and the other for relascope sampling (also known as variable radius plot sampling). Neither includes a neighborhood search which makes them much easier to execute. They do, however, include a conditional plot expansion: at a sample point where a predefined condition is satisfied, sampling is extended to a predefined larger cluster-plot or a larger relascope plot. Design-unbiased estimators of population total and its variance are derived for each proposed design, and they are applied to ten artificial and one real tree position maps to estimate density (number of trees per ha) and basal area (the cross-sectional area of a tree stem at breast height) per hectare. The performances—in terms of relative standard error (SE%)—of the proposed designs and their non-adaptive alternatives are compared. The adaptive plot designs were superior for the clustered populations in all cases of equal sample sizes and in some cases of equal area of sample plots. However, the improvement depends on: (1) the plot size factor; (2) the critical value (the minimum number of trees triggering an expansion); (3) the subplot distance for the adapted cluster-plots, and (4) the spatial arrangement of the sampled population. For some spatial arrangements, the improvement is relatively small. The adaptive designs may be particularly attractive for sampling in rare and compactly clustered populations with critical value of 1, subplot distance equal to the diameter of initial circular plots, or plot size factor of 2.5 for an initial basal area factor of 2.     

Effects of site-selection bias on estimates of biodiversity change

Estimates of biodiversity change are essential for the management and conservation of ecosystems. Accurate estimates rely on selecting representative sites, but monitoring often focuses on sites of special interest. How such site-selection biases influence estimates of biodiversity change is largely unknown. Site-selection bias potentially occurs across four major sources of biodiversity data, decreasing in likelihood from citizen science, museums, national park monitoring, and academic research. We defined site-selection bias as a preference for sites that are either densely populated (i.e., abundance bias) or species rich (i.e., richness bias). We simulated biodiversity change in a virtual landscape and tracked the observed biodiversity at a sampled site. The site was selected either randomly or with a site-selection bias. We used a simple spatially resolved, individual-based model to predict the movement or dispersal of individuals in and out of the chosen sampling site. Site-selection bias exaggerated estimates of biodiversity loss in sites selected with a bias by on average 300–400% compared with randomly selected sites. Based on our simulations, site-selection bias resulted in positive trends being estimated as negative trends: richness increase was estimated as 0.1 in randomly selected sites, whereas sites selected with a bias showed a richness change of −0.1 to −0.2 on average. Thus, site-selection bias may falsely indicate decreases in biodiversity. We varied sampling design and characteristics of the species and found that site-selection biases were strongest in short time series, for small grains, organisms with low dispersal ability, large regional species pools, and strong spatial aggregation. Based on these findings, to minimize site-selection bias, we recommend use of systematic site-selection schemes; maximizing sampling area; calculating biodiversity measures cumulatively across plots; and use of biodiversity measures that are less sensitive to rare species, such as the effective number of species. Awareness of the potential impact of site-selection bias is needed for biodiversity monitoring, the design of new studies on biodiversity change, and the interpretation of existing data.     

Two-stage estimation of ungulate abundance in Mediterranean areas using pellet group count

A design-based strategy for estimating wildlife ungulate abundance in a Mediterranean protected area (Maremma Regional Park) is considered. The estimation is based on pellet group count (clearance count technique) in a set of plots, whose size and number is established on the basis of practical considerations and available resources. The sampling scheme involves a preliminary stratification and subsequent two-stage sampling. In the first stage, large strata (defined through habitat features) are partitioned into spatial units and a sample of units is selected by means of a sampling scheme ensuring inclusion probabilities proportional to unit size, but avoiding the selection of contiguous units. Then, the abundances of the selected units are estimated in a second stage, in which plots are located using a random scheme ensuring an even coverage of the units. In small strata, only the second stage is performed. Unbiased estimators of abundance and conservative estimators of their variances are derived for each strata and for the whole study area. The proposed strategy has been applied since the Summer of 2006 and the estimation results reveal substantial improvement with respect to the previous results obtained by means of an alternative strategy.     

Nonparametric estimation of Shannon’s index of diversity when there are unseen species in sample

A biological community usually has a large number of species with relatively small abundances. When a random sample of individuals is selected and each individual is classified according to species identity, some rare species may not be discovered. This paper is concerned with the estimation of Shannons index of diversity when the number of species and the species abundances are unknown. The traditional estimator that ignores the missing species underestimates when there is a non-negligible number of unseen species. We provide a different approach based on unequal probability sampling theory because species have different probabilities of being discovered in the sample. No parametric forms are assumed for the species abundances. The proposed estimation procedure combines the Horvitz–Thompson (1952) adjustment for missing species and the concept of sample coverage, which is used to properly estimate the relative abundances of species discovered in the sample. Simulation results show that the proposed estimator works well under various abundance models even when a relatively large fraction of the species is missing. Three real data sets, two from biology and the other one from numismatics, are given for illustration.     

Sampling design trade-offs in occupancy studies with imperfect detection: examples and software.

Researchers have used occupancy, or probability of occupancy, as a response or state variable in a variety of studies (e.g., habitat modeling), and occupancy is increasingly favored by numerous state, federal, and international agencies engaged in monitoring programs. Recent advances in estimation methods have emphasized that reliable inferences can be made from these types of studies if detection and occupancy probabilities are simultaneously estimated. The need for temporal replication at sampled sites to estimate detection probability creates a trade-off between spatial replication (number of sample sites distributed within the area of interest/inference) and temporal replication (number of repeated surveys at each site). Here, we discuss a suite of questions commonly encountered during the design phase of occupancy studies, and we describe software (program GENPRES) developed to allow investigators to easily explore design trade-offs focused on particularities of their study system and sampling limitations. We illustrate the utility of program GENPRES using an amphibian example from Greater Yellowstone National Park, U.S.A.     

Optimal spatial sampling schemes for environmental surveys

A practical problem in spatial statistics is that of constructing spatial sampling designs for environmental monitoring network. This paper presents a fractal-based criterion for the construction of coverage designs to optimize the location of sampling points. The algorithm does not depend on the covariance structure of the process and provides desirable results for situations in which a poor prior knowledge is available. The statistical characteristics of the method are explored by a simulation study while a design exercise concerning the Pescara area monitoring network is used to demonstrate potential designs under realistic assumptions.     

Mark-recapture estimators for dual frame population size of prominent nesting structures: the effect of uncertain detection probability

The combined mark-recapture and line transect sampling methodology proposed by Alpizar-Jara and Pollock [Journal of Environmental and Ecological Statistics, 3(4), 311–327, 1996; In Marine Mammal Survey and Assessment Methods Symposium. G.W. Garner, S.C. Amstrup, J.L. Laake, B.F.J. Manly, L.L. McDonald, and D.C. Robertson (Eds.), A.A. Balkema, Rotterdam, Netherlands, pp. 99–114, 1999] is used to illustrate the estimation of population size for populations with prominent nesting structures (i.e., bald eagle nests). In the context of a bald eagle population, the number of nests in a list frame corresponds to a pre-marked sample of nests, and an area frame corresponds to a set of transect strips that could be regularly monitored. Unlike previous methods based on dual frame methodology using the screening estimator [Haines and Pollock (Journal of Environmental and Ecological Statistics, 5, 245–256, 1998a; Survey Methodology, 24(1), 79–88, 1998b)], we no longer need to assume that the area frame is complete (i.e., all the nests in the sampled sites do not need to be seen). One may use line transect sampling to estimate the probability of detection in a sampled area. Combining information from list and area frames provides more efficient estimators than those obtained by using data from only one frame. We derive an estimator for detection probability and generalize the screening estimator. A simulation study is carried out to compare the performance of the Chapman modification of the Lincoln–Petersen estimator to the screening estimator. Simulation results show that although the Chapman estimator is generally less precise than the screening estimator, the latter can be severely biased in presence of uncertain detection. The screening estimator outperforms the Chapman estimator in terms of mean squared error when detection probability is near 1 wheareas the Chapman estimator outperforms the screening estimator when detection probability is lower than a certain threshold value depending on particular scenarios.