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

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

Estimating Abundances of Interacting Species Using Morphological Traits,Foraging Guilds,and Habitat

We developed a statistical model to estimate the abundances of potentially interacting species encountered while conducting point-count surveys at a set of ecologically relevant locations – as in a metacommunity of species. In the model we assume that abundances of species with similar traits (e.g., body size) are potentially correlated and that these correlations, when present, may exist among all species or only among functionally related species (such as members of the same foraging guild). We also assume that species-specific abundances vary among locations owing to systematic and stochastic sources of heterogeneity. For example, if abundances differ among locations due to differences in habitat, then measures of habitat may be included in the model as covariates. Naturally, the quantitative effects of these covariates are assumed to differ among species. Our model also accounts for the effects of detectability on the observed counts of each species. This aspect of the model is especially important for rare or uncommon species that may be difficult to detect in community-level surveys. Estimating the detectability of each species requires sampling locations to be surveyed repeatedly using different observers or different visits of a single observer. As an illustration, we fitted models to species-specific counts of birds obtained while sampling an avian community during the breeding season. In the analysis we examined whether species abundances appeared to be correlated due to similarities in morphological measures (body mass, beak length, tarsus length, wing length, tail length) and whether these correlations existed among all species or only among species of the same foraging guild. We also used the model to estimate the effects of forested area on species abundances and the effects of sound power output (as measured by body size) on species detection probabilities.     

Converting visual census data into absolute abundance estimates: a method for calibrating timed counts of a sedentary insect population

Abstract.  1. Visual surveys for small organisms on complex substrates often yield serious underestimates of true counts. When both visual counts (relative estimates of abundance) and absolute counts can be obtained from the same sample, however, the visual counts can be calibrated such that absolute estimates can be obtained in the future from visual surveys alone.
2. A method is presented for converting quick, timed, visual counts of a sedentary insect on a shrub into absolute estimates of abundance.
3. Analogies were drawn from simple, well-known predation theories to develop a two-parameter non-linear model. Parameter estimates were obtained by both inverse prediction and direct estimation methods; the latter were found to yield more accurate predictions of absolute abundance.
4. The calibration model is mechanistic in its approach, and thus has potential for application in other systems in which all individuals are visible, but able to be missed during timed counts.     

Empirically simulated study to compare and validate sampling methods used in aerial surveys of wildlife populations

This paper compares the distribution, sampling and estimation of abundance for two animal species in an African ecosystem by means of an intensive simulation of the sampling process under a geographical information system (GIS) environment. It focuses on systematic and random sampling designs, commonly used in wildlife surveys, comparing their performance to an adaptive design at three increasing sampling intensities, using the root mean square errors (RMSE). It further assesses the impact of sampling designs and intensities on estimates of population parameters. The simulation is based on data collected during a prior survey, in which geographical locations of all observed animals were recorded. This provides more detailed data than that usually available from transect surveys. The results show precision of estimates to increase with increasing sampling intensity, while no significant differences are observed between estimates obtained under random and systematic designs. An increase in precision is observed for the adaptive design, thereby validating the use of this design for sampling clustered populations. The study illustrates the benefits of combining statistical methods with GIS techniques to increase insight into wildlife population dynamics.     

A statistical theory for sampling species abundances

The pattern of species abundances is central to ecology. But direct measurements of species abundances at ecologically relevant scales are typically unfeasible. This limitation has motivated a long-standing interest in the relationship between the abundance distribution in a large, regional community and the distribution observed in a small sample from the community. Here, we develop a statistical sampling theory to describe how observed patterns of species abundances are influenced by the spatial distributions of populations. For a wide range of regional-scale abundance distributions we derive exact expressions for the sampled abundance distributions, as a function of sample size and the degree of conspecific spatial aggregation. We show that if populations are randomly distributed in space then the sampled and regional-scale species-abundance distribution typically have the same functional form: sampling can be expressed by a simple scaling relationship. In the case of aggregated spatial distributions, however, the shape of a sampled species-abundance distribution diverges from the regional-scale distribution. Conspecific aggregation results in sampled distributions that are skewed towards both rare and common species. We discuss our findings in light of recent results from neutral community theory, and in the context of estimating biodiversity.     

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.     

Mixture models for estimating the size of a closed population when capture rates vary among individuals

We develop a parameterization of the beta-binomial mixture that provides sensible inferences about the size of a closed population when probabilities of capture or detection vary among individuals. Three classes of mixture models (beta-binomial, logistic-normal, and latent-class) are fitted to recaptures of snowshoe hares for estimating abundance and to counts of bird species for estimating species richness. In both sets of data, rates of detection appear to vary more among individuals (animals or species) than among sampling occasions or locations. The estimates of population size and species richness are sensitive to model-specific assumptions about the latent distribution of individual rates of detection. We demonstrate using simulation experiments that conventional diagnostics for assessing model adequacy, such as deviance, cannot be relied on for selecting classes of mixture models that produce valid inferences about population size. Prior knowledge about sources of individual heterogeneity in detection rates, if available, should be used to help select among classes of mixture models that are to be used for inference.     

Assessment of species diversity from species abundance distributions at different localities

We show how the spatial structure of species diversity can be analyzed using the correlation between the log abundances of the species in the communities, assuming that two communities at different localities can be described by a bivariate lognormal species abundance distribution. A useful property of this approach is that the log abundances of the species at two localities can be considered as samples from a bivariate normal distribution defined by only five parameters. The variances and the correlation can be estimated by maximum likelihood methods even if there is no information about the sampling intensity and the number of unobserved species. This method also enables estimation of over-dispersion in the sampling relative to a Poisson distribution that allows sampling adjustment of the estimate of β-diversity. Furthermore, we also obtain a partitioning of species diversity into additive components of α-, β- and γ-diversity. For instance, if the correlation between the log abundances of the species is close to one, the same species will be common and rare in the two communities and the β-diversity will be low. We illustrate this approach by analysing similarities of communities of rare and endangered species of oak-living beetles in south-eastern Norway. The number of recorded species was estimated to be only 48.1% of the total number of species actually present in these communities. The correlations among communities dropped rather quickly with distance with a scaling of order 200 km. This illustrates large spatial heterogeneity in species composition, which should be accounted for in the design of schemes of such devices for assessing species diversity in these habitat-types.     

Multiple modes in a coral species abundance distribution

Species abundance distributions are an important measure of biodiversity and community structure. These distributions are affected by sampling, and alternative species-abundance models often make similar predictions for small sample sizes. Very large samples reveal the relative abundances of rare species, and thus provide information about species relative abundances that small samples cannot. Here, we present the species-abundance distribution for a sample of > 40,000 coral colonies at a single site, exceeding existing samples of coral local assemblages by over an order of magnitude. This abundance distribution is multimodal when examined on a logarithmic scale. Four different model selection procedures all indicate that the underlying community abundance distribution has at least three modes. We show that the multiple modes are not caused by mixtures of species with different habitat preferences. However, spatial aggregation partially explains our results. We inspect published work on species abundance distributions, and suggest that multimodality may be a common feature of large samples.     

Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors

Summary .  A variety of flexible approaches have been proposed for functional data analysis, allowing both the mean curve and the distribution about the mean to be unknown. Such methods are most useful when there is limited prior information. Motivated by applications to modeling of temperature curves in the menstrual cycle, this article proposes a flexible approach for incorporating prior information in semiparametric Bayesian analyses of hierarchical functional data. The proposed approach is based on specifying the distribution of functions as a mixture of a parametric hierarchical model and a nonparametric contamination. The parametric component is chosen based on prior knowledge, while the contamination is characterized as a functional Dirichlet process. In the motivating application, the contamination component allows unanticipated curve shapes in unhealthy menstrual cycles. Methods are developed for posterior computation, and the approach is applied to data from a European fecundability study.     

Sampling tiger ungulate prey by the distance method: lessons learned in Bardia National Park, Nepal

Because tiger Panthera tigris numbers are regulated by their prey base, prey abundance needs to monitored and estimated reliably. Recently, distance sampling has been adopted as the most appropriate method and is now becoming the standard monitoring protocol in all tiger range countries in south Asia. However, the accuracy of the density estimates generated by this method has not been assessed. From total counts within habitat blocks, we obtained accurate density estimates of ungulates within three main habitats in Bardia National Park, Nepal. We then applied the distance sampling method in the same habitats and compared the results. Distance sampling on foot in dense habitats (riverine forest and tallgrass floodplain) violated method assumptions, and sampling from vehicle along roads gave biased estimates. Sampling from elephant back worked well in all habitat types, but owing to their behaviour, the density of barking deer Muntiacus muntjak was underestimated. The accuracy of the estimates varied with sampling effort; for the very abundant chital deer Axis axis , estimates varied markedly at <200 animal observations, but converged at larger sample sizes to a similar point estimate as intensive block counts when approaching 300 observations. For the less abundant species, with <20 observations along >100 km of transect lines, the confidence intervals were quite high, and, hence, of limited value for detecting short-term populations trends. It is therefore difficult to obtain accurate density estimates of rare species by the distance method. In areas consisting of dense habitats, we recommend that the food base of tiger be estimated by distance sampling from elephant back, not on foot, directed at the main and most abundant prey species. For rare species, encounter rates obtained simultaneously may then serve as indices of relative abundances.     

Assessing the Status of Wild Felids in a Highly-Disturbed Commercial Forest Reserve in Borneo and the Implications for Camera Trap Survey Design

The proliferation of camera-trapping studies has led to a spate of extensions in the known distributions of many wild cat species, not least in Borneo. However, we still do not have a clear picture of the spatial patterns of felid abundance in Southeast Asia, particularly with respect to the large areas of highly-disturbed habitat. An important obstacle to increasing the usefulness of camera trap data is the widespread practice of setting cameras at non-random locations. Non-random deployment interacts with non-random space-use by animals, causing biases in our inferences about relative abundance from detection frequencies alone. This may be a particular problem if surveys do not adequately sample the full range of habitat features present in a study region. Using camera-trapping records and incidental sightings from the Kalabakan Forest Reserve, Sabah, Malaysian Borneo, we aimed to assess the relative abundance of felid species in highly-disturbed forest, as well as investigate felid space-use and the potential for biases resulting from non-random sampling. Although the area has been intensively logged over three decades, it was found to still retain the full complement of Bornean felids, including the bay cat Pardofelis badia, a poorly known Bornean endemic. Camera-trapping using strictly random locations detected four of the five Bornean felid species and revealed inter- and intra-specific differences in space-use. We compare our results with an extensive dataset of >1,200 felid records from previous camera-trapping studies and show that the relative abundance of the bay cat, in particular, may have previously been underestimated due to the use of non-random survey locations. Further surveys for this species using random locations will be crucial in determining its conservation status. We advocate the more wide-spread use of random survey locations in future camera-trapping surveys in order to increase the robustness and generality of inferences that can be made.     

Combining counts and incidence data: an efficient approach for estimating the log-normal species abundance distribution and diversity indices

Obtaining accurate estimates of diversity indices is difficult because the number of species encountered in a sample increases with sampling intensity. We introduce a novel method that requires that the presence of species in a sample to be assessed while the counts of the number of individuals per species are only required for just a small part of the sample. To account for species included as incidence data in the species abundance distribution, we modify the likelihood function of the classical Poisson log-normal distribution. Using simulated community assemblages, we contrast diversity estimates based on a community sample, a subsample randomly extracted from the community sample, and a mixture sample where incidence data are added to a subsample. We show that the mixture sampling approach provides more accurate estimates than the subsample and at little extra cost. Diversity indices estimated from a freshwater zooplankton community sampled using the mixture approach show the same pattern of results as the simulation study. Our method efficiently increases the accuracy of diversity estimates and comprehension of the left tail of the species abundance distribution. We show how to choose the scale of sample size needed for a compromise between information gained, accuracy of the estimates and cost expended when assessing biological diversity. The sample size estimates are obtained from key community characteristics, such as the expected number of species in the community, the expected number of individuals in a sample and the evenness of the community.     

Estimation and Correction of Visibility Bias in Aerial Surveys of Wintering Ducks

Abstract: Incomplete detection of all individuals leading to negative bias in abundance estimates is a pervasive source of error in aerial surveys of wildlife, and correcting that bias is a critical step in improving surveys. We conducted experiments using duck decoys as surrogates for live ducks to estimate bias associated with surveys of wintering ducks in Mississippi, USA. We found detection of decoy groups was related to wetland cover type (open vs. forested), group size (1–100 decoys), and interaction of these variables. Observers who detected decoy groups reported counts that averaged 78% of the decoys actually present, and this counting bias was not influenced by either covariate cited above. We integrated this sightability model into estimation procedures for our sample surveys with weight adjustments derived from probabilities of group detection (estimated by logistic regression) and count bias. To estimate variances of abundance estimates, we used bootstrap resampling of transects included in aerial surveys and data from the bias-correction experiment. When we implemented bias correction procedures on data from a field survey conducted in January 2004, we found bias-corrected estimates of abundance increased 36–42%, and associated standard errors increased 38–55%, depending on species or group estimated. We deemed our method successful for integrating correction of visibility bias in an existing sample survey design for wintering ducks in Mississippi, and we believe this procedure could be implemented in a variety of sampling problems for other locations and species. (JOURNAL OF WILDLIFE MANAGEMENT 72(3):808–813; 2008)     

New methods and technologies for regional-scale abundance estimation of land-breeding marine animals: application to Adélie penguin populations in East Antarctica

Land-breeding marine animals such as penguins, flying seabirds and pinnipeds are important components of marine ecosystems, and their abundance has been used extensively as an indication of ecosystem status and change. Until recently, many efforts to measure and monitor abundance of these species’ groups have focussed on smaller populations and spatial scales, and efforts to account for perception bias and availability bias have been variable and often ad hoc. We describe a suite of new methods, technologies and estimation procedures for cost-effective, large-scale abundance estimation within a general estimation framework and illustrate their application on large Adélie penguin populations in two regions of East Antarctica. The methods include photographic sample counts, automated cameras for collecting availability data, and bootstrap estimation to adjust counts for the sampling fraction, perception bias, and availability bias, and are applicable for a range of land-breeding marine species. The methods will improve our ability to obtain population data over large spatial and population scales within tight logistic, environmental and time constraints. This first application of the methods has given new insights into the biases and uncertainties in abundance estimation for penguins and other land-breeding marine species. We provide guidelines for applying the methods in future surveys.     

Determining the effective sample size of a parametric prior

Summary .   We present a definition for the effective sample size of a parametric prior distribution in a Bayesian model, and propose methods for computing the effective sample size in a variety of settings. Our approach first constructs a prior chosen to be vague in a suitable sense, and updates this prior to obtain a sequence of posteriors corresponding to each of a range of sample sizes. We then compute a distance between each posterior and the parametric prior, defined in terms of the curvature of the logarithm of each distribution, and the posterior minimizing the distance defines the effective sample size of the prior. For cases where the distance cannot be computed analytically, we provide a numerical approximation based on Monte Carlo simulation. We provide general guidelines for application, illustrate the method in several standard cases where the answer seems obvious, and then apply it to some nonstandard settings.     

Predicting the Geographic Distribution of a Species from Presence‐Only Data Subject to Detection Errors

Summary Several models have been developed to predict the geographic distribution of a species by combining measurements of covariates of occurrence at locations where the species is known to be present with measurements of the same covariates at other locations where species occurrence status (presence or absence) is unknown. In the absence of species detection errors, spatial point‐process models and binary‐regression models for case‐augmented surveys provide consistent estimators of a species’ geographic distribution without prior knowledge of species prevalence. In addition, these regression models can be modified to produce estimators of species abundance that are asymptotically equivalent to those of the spatial point‐process models. However, if species presence locations are subject to detection errors, neither class of models provides a consistent estimator of covariate effects unless the covariates of species abundance are distinct and independently distributed from the covariates of species detection probability. These analytical results are illustrated using simulation studies of data sets that contain a wide range of presence‐only sample sizes. Analyses of presence‐only data of three avian species observed in a survey of landbirds in western Montana and northern Idaho are compared with site‐occupancy analyses of detections and nondetections of these species.     

Accounting for preferential sampling in species distribution models

Species distribution models (SDMs) are now being widely used in ecology for management and conservation purposes across terrestrial, freshwater, and marine realms. The increasing interest in SDMs has drawn the attention of ecologists to spatial models and, in particular, to geostatistical models, which are used to associate observations of species occurrence or abundance with environmental covariates in a finite number of locations in order to predict where (and how much of) a species is likely to be present in unsampled locations. Standard geostatistical methodology assumes that the choice of sampling locations is independent of the values of the variable of interest. However, in natural environments, due to practical limitations related to time and financial constraints, this theoretical assumption is often violated. In fact, data commonly derive from opportunistic sampling (e.g., whale or bird watching), in which observers tend to look for a specific species in areas where they expect to find it. These are examples of what is referred to as preferential sampling, which can lead to biased predictions of the distribution of the species. The aim of this study is to discuss a SDM that addresses this problem and that it is more computationally efficient than existing MCMC methods. From a statistical point of view, we interpret the data as a marked point pattern, where the sampling locations form a point pattern and the measurements taken in those locations (i.e., species abundance or occurrence) are the associated marks. Inference and prediction of species distribution is performed using a Bayesian approach, and integrated nested Laplace approximation (INLA) methodology and software are used for model fitting to minimize the computational burden. We show that abundance is highly overestimated at low abundance locations when preferential sampling effects not accounted for, in both a simulated example and a practical application using fishery data. This highlights that ecologists should be aware of the potential bias resulting from preferential sampling and account for it in a model when a survey is based on non‐randomized and/or non‐systematic sampling.     

Analytical evidence for scale-invariance in the shape of species abundance distributions

The distribution of species abundances within an ecological community provides a window into ecological processes and has important applications in conservation biology as an indicator of disturbance. Previous work indicates that species abundance distributions might be independent of the scales at which they are measured which has implications for data interpretation. Here we formulate an analytically tractable model for the species abundance distribution at different scales and discuss the biological relevance of its assumptions. Our model shows that as scale increases, the shape of the species abundance distribution converges to a particular shape given uniquely by the Jaccard index of spatial species turnover and by a parameter for the spatial correlation of abundances. Our model indicates that the shape of the species abundance distribution is taxon specific but does not depend on sample area, provided this area is large. We conclude that the species abundance distribution may indeed serve as an indicator of disturbances affecting species spatial turnover and that the assumption of conservation of energy in ecosystems, which is part of the Maximum Entropy approach, should be re-evaluated.     

Abundance estimates to inform butterfly management: double-observer versus distance sampling

Abundance estimates are used to establish baselines, set recovery targets, and assess management actions, all of which are essential aspects of evidence-based natural resource management. For many rare butterflies, these estimates do not exist, and conservation decisions rely instead on expert opinion. Using Bartram’s scrub-hairstreak (Strymon acis bartrami, US Endangered) as a case study, we present a novel comparison of two methods that permit the incorporation of detection probabilities into abundance estimates, distance sampling and double-observer surveys. Additionally we provide a framework for establishing a systematic sampling scheme for monitoring very rare butterflies. We surveyed butterflies monthly in 2013, increasing intensity to weekly when butterflies were detected. We conducted 19 complete, island-wide surveys on Big Pine Key in the Florida Keys, detecting a total of 59 Bartram’s scrub-hairstreaks across all surveys. Peak daily abundances were similar as estimated with distance sampling, 156 butterflies (95 % CI 65–247), and double-observer, 169 butterflies (95 % CI 65–269). Selecting a method for estimating abundance of rare species involves evaluating trade-offs between methods. Distance sampling requires at least 40 detections, but only one observer, while double-observer requires only 10 detections, but two observers. Double-observer abundance estimates agreed with distance sampling estimates, which suggests that double-observer is a reasonable alternative method to use for estimating detection probability and abundance for rare species that cannot be surveyed with other, more commonly used methods.