The use of replicated plot,line and point sampling for estimating species abundance and ecological diversity

The paper deals with the problem of estimating diversity indexes for an ecological community. First the species abundances are unbiasedly and consistently estimated using designs based on n random and independent selections of plots, points or lines over the study area. The problem of sampling elusive populations is also considered. Finally, the diversity index estimates are obtained as functions of the abundance estimates. The resulting estimators turn out to be asymptotically (n large) unbiased, even if a considerable bias may occur for a small n. Accordingly, the method of jackknifing is made use of in order to reduce bias.     

Line transect sampling of Karner blue butterflies ( Lycaeides melissa samuelis)

Line transect sampling is an effective survey method for estimating butterfly densities because it provides unbiased estimates of site-density (provided key assumptions are met), and estimates are comparable among sites. For monitoring Karner blue butterflies in Wisconsin, USA, comparable estimates are required because each year a different selection of sites will be monitored. Annual state-wide indices of species abundance can be derived from the site-surveys and compared to previous year's indices to monitor trends. We advocate that line transect sampling is preferable to Pollard-Yates transects as a survey technique for monitoring Karner blue butter- flies. The Pollard-Yates surveys do not adjust for diferences in site detectability. As a consequence, estimates of among-site from Pollard-Yates surveys can be biased. © Rapid Science 1998     

Randomly selected order statistics in ranked set sampling: A less expensive comparable alternative to simple random sampling

Rank-based sampling designs are powerful alternatives to simple random sampling (SRS) and often provide large improvements in the precision of estimators. In many environmental, ecological, agricultural, industrial and/or medical applications the interest lies in sampling designs that are cheaper than SRS and provide comparable estimates. In this paper, we propose a new variation of ranked set sampling (RSS) for estimating the population mean based on the random selection technique to measure a smaller number of observations than RSS design. We study the properties of the population mean estimator using the proposed design and provide conditions under which the mean estimator performs better than SRS and some existing rank-based sampling designs. Theoretical results are augmented with some numerical studies and a real-life example, where we also study the performance of our proposed design under perfect and imperfect ranking situations.     

Integrating habitat-masked range maps with quantifications of prevalence to estimate area of occupancy in IUCN assessments

Estimates of species geographic ranges constitute critical input for biodiversity assessments, including those for the International Union for the Conservation of Nature (IUCN) Red List of Threatened Species. Area of occupancy (AOO) is one metric that IUCN uses to quantify a species’ range, but data limitations typically lead to either under- or overestimates (and unnecessarily wide bounds of uncertainty). Fortunately, existing methods in which range maps and land-cover data are used to estimate the area currently holding habitat for a species can be extended to yield an unbiased range of plausible estimates for AOO. Doing so requires estimating the proportion of sites (currently containing habitat) that a species occupies within its range (i.e., prevalence). Multiplying a quantification of habitat area by prevalence yields an estimate of what the species inhabits (i.e., AOO). For species with intense sampling at many sites, presence–absence data sets or occupancy modeling allow calculation of prevalence. For other species, primary biodiversity data (records of a species’ presence at a point in space and time) from citizen-science initiatives and research collections of natural history museums and herbaria could be used. In such cases, estimates of sample prevalence should be corrected by dividing by the species’ detectability. To estimate detectability from these data sources, extensions of inventory-completeness analyses merit development. With investments to increase the quality and availability of online biodiversity data, consideration of prevalence should lead to tighter and more realistic bounds of AOO for many taxonomic groups and geographic regions. By leading to more realistic and representative characterizations of biodiversity, integrating maps of current habitat with estimates of prevalence should empower conservation practitioners and decision makers and thus guide actions and policy worldwide.     

Evaluating growth of larval walleye pollock, Theragra chalcogramma, using cell cycle analysis

Cell cycle analysis of muscle cell division rates offers a new and efficient technique to analyze growth of larval fish. Using this approach, growth of larval walleye pollock was estimated by determining cell proliferation rates, reasoning that growth during early life stages is probably attributed to increases in cell number rather than to increases in cell size. Characteristic patterns of brain and muscle cell division rates were produced in larval walleye pollock by manipulating their diet in the laboratory. The fraction of dividing muscle cells and, to a lesser extent, the fraction of dividing brain cells were direct indicators of fast and slow growth. A model was produced to estimate average growth rate from the fraction of dividing muscle cells. We developed a simple method for preparing and storing the muscle tissue that ensures nucleic acid stability for subsequent analyses and permits sampling in the field. We envision that the cell cycle methodology will have on-site applications, presenting an opportunity to attain real-time estimates of larval fish growth at sea. Determining the proportion of first-feeding larvae with a high fraction of dividing muscle cells may yield a means for predicting the proportion of fast-growing fish, i.e., the potential survivors.     

Spatial statistics for modeling of abundance and distribution of wildlife species in the Masai Mara ecosystem, Kenya

This study illustrates the use of modern statistical procedures for better wildlife management by addressing three key issues: determination of abundance, modeling of animal distributions and variability of diversity in space and time. Prior information in Markov Chain Monte Carlo (MCMC) methods is used to improve estimates of abundance. Measures of autocorrelation are included when modeling distributions of animal counts, and a diversity index to indicate species abundance and richness for large herbivores is developed. Data from the Masai Mara ecosystem in Kenya are used to develop and demonstrate these procedures. The new abundance estimates are up to 35% more accurate than those obtained by existing methods. Significant temporal changes in spatial patterns are found from a space-time analysis of elephant counts over a 20-year period, with strong interactions over 5 km and 6 months space and time separations, respectively. The new diversity index is sensitive to both high abundance and species richness and is also able to capture year to year variation. It indicates an overall marginal decrease in diversity for large herbivores in the Mara ecosystem. The space-time analyses and diversity index can easily be computed thereby providing tools for rapid decision making.     

Estimating nonlinear interaction strengths: an observation-based method for species-rich food webs

Efforts to estimate the strength of species interactions in species-rich, reticulate food webs have been hampered by the multitude of direct and indirect interactions such systems exhibit and have been limited by an assumption that pairwise interactions display linear functional forms. Here we present a new method for directly measuring, on a per capita basis, the nonlinear strength of trophic species interactions within such food webs. This is an observation-based method, requiring three pieces of information: (1) species abundances, (2) predator and prey-specific handling times, and (3) data from predator-specific feeding surveys in which the number of individuals observed feeding on each of the predator's prey species has been tallied. The method offers a straightforward way to assess the completeness of one's sampling effort in accurately estimating interaction strengths through the construction of predator-specific prey accumulation curves. The method should be applicable to a variety of systems in which empirical estimates of direct interaction strengths have thus far remained elusive.     

Application of adaptive cluster sampling to low-density populations of freshwater mussels

Freshwater mussels appear to be promising candidates for adaptive cluster sampling because they are benthic macroinvertebrates that cluster spatially and are frequently found at low densities. We applied adaptive cluster sampling to estimate density of freshwater mussels at 24 sites along the Cacapon River, WV, where a preliminary timed search indicated that mussels were present at low density. Adaptive cluster sampling increased yield of individual mussels and detection of uncommon species; however, it did not improve precision of density estimates. Because finding uncommon species, collecting individuals of those species, and estimating their densities are important conservation activities, additional research is warranted on application of adaptive cluster sampling to freshwater mussels. However, at this time we do not recommend routine application of adaptive cluster sampling to freshwater mussel populations. The ultimate, and currently unanswered, question is how to tell when adaptive cluster sampling should be used, i.e., when is a population sufficiently rare and clustered for adaptive cluster sampling to be efficient and practical? A cost-effective procedure needs to be developed to identify biological populations for which adaptive cluster sampling is appropriate.     

Population Status of the Razorback Sucker in the Middle Green River (U.S.A.)

The razorback sucker, Xyrauchen texanus , in the middle Green River (U.S.A.) has been described as a static population consisting of old individuals that will eventually disappear through attrition. Capture data between 1980 and 1992 indicated a constant length frequency despite a slow but positive growth rate of individual fish. Abundance and survival estimates indicated that the population of razorback sucker in the middle Green River is precariously low but dynamic. Although high variation existed among survival estimates, no significant decrease in the population between 1982 and 1992 could be detected. The low level of recruitment occurring in the razorback sucker population of the middle Green River was related to high-flow years, indicating that floodplain habitats may be necessary for survival of the species.     

Evident but context-dependent mortality of fish passing hydroelectric turbines

Globally, policies aiming for conservation of species, free-flowing rivers, and promotion of hydroelectricity as renewable energy and as a means to decarbonize energy systems generate trade-offs between protecting freshwater fauna and development of hydropower. Hydroelectric turbines put fish at risk of severe injury during passage. Therefore, comprehensive, reliable analyses of turbine-induced fish mortality are pivotal to support an informed debate on the sustainability of hydropower (i.e., how much a society is willing to pay in terms of costs incurred on rivers and their biota). We compiled and examined a comprehensive, global data set of turbine fish-mortality assessments involving >275,000 individual fish of 75 species to estimate mortality across turbine types and fish species. Average fish mortality from hydroelectric turbines was 22.3% (95% CI 17.5–26.7%) when accounting for common uncertainties related to empirical estimates (e.g., handling- or catch-related effects). Mortality estimates were highly variable among and within different turbine types, study methods, and taxa. Technical configurations of hydroelectric turbines that successfully reduce fish mortality and fish-protective hydropower operation as a global standard could balance the need for renewable energy with protection of fish biodiversity.     

Hierarchical demographic approaches for assessing invasion dynamics of non-indigenous species: An example using northern snakehead (Channa argus)

Models of species’ demographic features are commonly used to understand population dynamics and inform management tactics. Hierarchical demographic models are ideal for the assessment of non-indigenous species because our knowledge of non-indigenous populations is usually limited, data on demographic traits often come from a species’ native range, these traits vary among populations, and traits are likely to vary considerably over time as species adapt to new environments. Hierarchical models readily incorporate this spatiotemporal variation in species’ demographic traits by representing demographic parameters as multi-level hierarchies. As is done for traditional non-hierarchical matrix models, sensitivity and elasticity analyses are used to evaluate the contributions of different life stages and parameters to estimates of population growth rate. We applied a hierarchical model to northern snakehead (Channa argus), a fish currently invading the eastern United States. We used a Monte Carlo approach to simulate uncertainties in the sensitivity and elasticity analyses and to project future population persistence under selected management tactics. We gathered key biological information on northern snakehead natural mortality, maturity and recruitment in its native Asian environment. We compared the model performance with and without hierarchy of parameters. Our results suggest that ignoring the hierarchy of parameters in demographic models may result in poor estimates of population size and growth and may lead to erroneous management advice. In our case, the hierarchy used multi-level distributions to simulate the heterogeneity of demographic parameters across different locations or situations. The probability that the northern snakehead population will increase and harm the native fauna is considerable. Our elasticity and prognostic analyses showed that intensive control efforts immediately prior to spawning and/or juvenile-dispersal periods would be more effective (and probably require less effort) than year-round control efforts. Our study demonstrates the importance of considering the hierarchy of parameters in estimating population growth rate and evaluating different management strategies for non-indigenous invasive species.     

Multi-lag cluster designs for estimating the semivariogram for sediments affected by effluent discharges offshore in San Diego

Maps are useful tools for understanding, managing, and protecting the marine environment, yet few useful and statistically defensible maps of environmental quality and aquatic resources have been developed in near-coastal regions. Current environmental management efforts, such as ocean monitoring by sewage dischargers, routinely sample areas of potential impact using sparse sampling grids. Heterogeneous oceanic conditions often make extrapolation from these grids to non-sampled locations questionable. Although rarely applied in coastal monitoring, kriging offers a more rigorous statistical approach to mapping and allows confidence intervals to be calculated for predictions. Its usefulness relies on accurate models of the spatial variability through estimating the semivariogram. Many optimal designs for estimating the semivariogram have been proposed, but these designs are often difficult to implement in practice. In this paper, we present simple design strategies for augmenting existing monitoring designs with the goal of estimating the semivariogram. In particular, we investigate a multi-lag cluster design strategy, where clusters of sites, spaced at various lag distances, are placed around fixed stations on an existing sampling grid. We find that these multi-lag cluster designs provide improved accuracy in estimating the parameters of the semivariogram. Based on simulation study findings, we apply a multi-lag cluster enhancement to the monitoring grid for the City of San Diego’s Point Loma Wastewater Treatment Plant as part of a special study to map chemical contaminants in sediments around its sewage outfall.     

Estimating trend precision and power to detect trends across grouped count data

Ecologists commonly use grouped or clustered count data to estimate temporal trends in counts, abundance indices, or abundance. For example, the U.S. Breeding Bird Survey data represent multiple counts of birds from within each of multiple, spatially defined routes. Despite a reliance on grouped counts, analytical methods for prospectively estimating precision of trend estimates or statistical power to detect trends that explicitly acknowledge the characteristics of grouped count data are undescribed. These characteristics include the fact that the sampling variance is an increasing function of the mean, and that sampling and group-level variance estimates are generally estimated on different scales (the sampling and log scales, respectively). We address these issues for repeated sampling of a single population using an analytical approach that has the flavor of a generalized linear mixed model, specifically that of a negative binomial-distributed count variable with random group effects. The count mean, including grand intercept, trend, and random group effects, is modeled linearly on the log scale, while sampling variance of the mean is estimated on the log scale via the delta method. Results compared favorably with those derived using Monte Carlo simulations. For example, at trend = 5% per temporal unit, differences in standard errors and in power were modest relative to those estimated by simulation (< or = /11/% and < or = /16/%, respectively), with relative differences among power estimates decreasing to < or = /7/% when power estimated by simulations was > or = 0.50. Similar findings were obtained using data from nine surveys of fingernail clams in the Mississippi River. The proposed method is suggested (1) where simulations are not practical and relative precision or power is desired, or (2) when multiple precision or power calculations are required and where the accuracy of a fraction of those calculations will be confirmed using simulations.     

Estimating species richness and accumulation by modeling species occurrence and detectability

A statistical model is developed for estimating species richness and accumulation by formulating these community-level attributes as functions of model-based estimators of species occurrence while accounting for imperfect detection of individual species. The model requires a sampling protocol wherein repeated observations are made at a collection of sample locations selected to be representative of the community. This temporal replication provides the data needed to resolve the ambiguity between species absence and nondetection when species are unobserved at sample locations. Estimates of species richness and accumulation are computed for two communities, an avian community and a butterfly community. Our model-based estimates suggest that detection failures in many bird species were attributed to low rates of occurrence, as opposed to simply low rates of detection. We estimate that the avian community contains a substantial number of uncommon species and that species richness greatly exceeds the number of species actually observed in the sample. In fact, predictions of species accumulation suggest that even doubling the number of sample locations would not have revealed all of the species in the community. In contrast, our analysis of the butterfly community suggests that many species are relatively common and that the estimated richness of species in the community is nearly equal to the number of species actually detected in the sample. Our predictions of species accumulation suggest that the number of sample locations actually used in the butterfly survey could have been cut in half and the asymptotic richness of species still would have been attained. Our approach of developing occurrence-based summaries of communities while allowing for imperfect detection of species is broadly applicable and should prove useful in the design and analysis of surveys of biodiversity.     

Multiple data sources improve DNA-based mark-recapture population estimates of grizzly bears.

A fundamental challenge to estimating population size with mark-recapture methods is heterogeneous capture probabilities and subsequent bias of population estimates. Confronting this problem usually requires substantial sampling effort that can be difficult to achieve for some species, such as carnivores. We developed a methodology that uses two data sources to deal with heterogeneity and applied this to DNA mark-recapture data from grizzly bears (Ursus arctos). We improved population estimates by incorporating additional DNA "captures" of grizzly bears obtained by collecting hair from unbaited bear rub trees concurrently with baited, grid-based, hair snag sampling. We consider a Lincoln-Petersen estimator with hair snag captures as the initial session and rub tree captures as the recapture session and develop an estimator in program MARK that treats hair snag and rub tree samples as successive sessions. Using empirical data from a large-scale project in the greater Glacier National Park, Montana, USA, area and simulation modeling we evaluate these methods and compare the results to hair-snag-only estimates. Empirical results indicate that, compared with hair-snag-only data, the joint hair-snag-rub-tree methods produce similar but more precise estimates if capture and recapture rates are reasonably high for both methods. Simulation results suggest that estimators are potentially affected by correlation of capture probabilities between sample types in the presence of heterogeneity. Overall, closed population Huggins-Pledger estimators showed the highest precision and were most robust to sparse data, heterogeneity, and capture probability correlation among sampling types. Results also indicate that these estimators can be used when a segment of the population has zero capture probability for one of the methods. We propose that this general methodology may be useful for other species in which mark-recapture data are available from multiple sources.     

Using the bootstrap and fast Fourier transform to estimate confidence intervals of 2D kernel densities

Kernel density estimators are often used to estimate the utilization distributions (UDs) of animals. Kernel UD estimates have a strong theoretical basis and perform well, but are usually reported without estimates of error or uncertainty. It is intuitively and theoretically appealing to estimate the sampling error in kernel UD estimates using bootstrapping. However, standard equations for kernel density estimates are complicated and computationally expensive. Bootstrapping requires computing hundreds or thousands of probability densities and is impractical when the number of observations, or the area of interest is large. We used the fast Fourier transform (FFT) and discrete convolution theorem to create a bootstrapping algorithm fast enough to run on commonly available desktop or laptop computers. Application of the FFT method to a large (n>20,000) set of radio telemetry data would provide a 99.6% reduction in computation time (i.e., 1.6 as opposed to 444 hours) for 1000 bootstrap UD estimates. Bootstrap error contours were computed using data from a radio-collared polar bear (Ursus maritimus) in the Beaufort Sea north of Alaska.     

Rareness and specialization in plant-pollinator networks

Most rare species appear to be specialists in plant-pollinator networks. This observation could result either from real ecological processes or from sampling artifacts. Several methods have been proposed to overcome these artifacts, but they have the limitation of being based on visitation data, causing interactions involving rare visitor species to remain undersampled. We propose the analysis of food composition in bee trap nests to assess the reliability of network specialization estimates. We compared data from a plant-pollinator network in the Monte Desert of Villavicencio Nature Reserve, Argentina, sampled by visit observation, and data from trap nests sampled at the same time and location. Our study shows that trap nest sampling was good for estimating rare species degree. The rare species in the networks appear to be more specialized than they really are, and the bias in the estimation of the species degree increases with the rareness. The low species degree of these rare species in the visitation networks results from insufficient sampling of the rare interactions, which could have important consequences for network structure.     

Detecting conservation benefits in spatially protected fish populations with meta-analysis of long-term monitoring data

Marine protected areas (MPA) produce a positive effect on fish populations, but this may be difficult to identify due to the high temporal variability of populations. Meta-analysis is an option for analysing data from different sources and sampling designs and it can address problems related to temporal and spatial variability in fish populations. We analysed fish abundance data from visual counts conducted in summer, from 1996 to 2002, in the MPA of Tabarca (Alicante, Spain). The results showed an overall positive effect of protection at the species and family levels. Overall abundance of fishes inside the reserve was, on average, 1.22 times higher than outside the reserve boundaries. Positive effect of protection was found for Boops boops, Diplodus annularis, Diplodus cervinus, Epinephelus marginatus, Epinephelus costae and Epinephelus aenus. Species of Labrids were not affected by protection, except for Thalassoma pavo and Symphodus ocellatus. Meta-analysis of temporal data allows evaluation of the protection MPA provide and is particularly useful when data sources have different experimental designs or sampling programs. The Tabarca MPA has benefited fish populations by increasing their abundance and we suggest that meta-analysis is a complementary tool for the management of MPAs.     

On the Estimation of Dispersal Kernels from Individual Mark-Recapture Data

We present a new method for estimating a distribution of dispersal displacements (a dispersal kernel) from mark-recapture data. One conventional method of calculating the dispersal kernel assumes that the distribution of displacements are Gaussian (e.g. resulting from a diffusion process) and that individuals remain within sampled areas. The first assumption prohibits an analysis of dispersal data that do not exhibit the Gaussian distribution (a common situation); the second assumption leads to underestimation of dispersal distance because individuals that disperse outside of sampling areas are never recaptured. Our method eliminates these two assumptions. In addition, the method can also accommodate mortality during a sampling period. This new method uses integrodifference equations to express the probability of spatial mark-recapture data; associated dispersal, survival, and recapture parameters are then estimated using a maximum likelihood method. We examined the accuracy of the estimators by applying the method to simulated data sets. Our method suggests designs for future mark-recapture experiments. Received: January 2004 / Revised: July 2005