The Reliability of Using Population Viability Analysis for Risk Classification of Species

I examine whether or not it is appropriate to use extinction probabilities generated by population viability analyses, based on best estimates for model parameters, as criteria for listing species in Red Data Book categories as recently proposed by the World Conservation Union. Such extinction probabilities are influenced by how accurately model parameters are estimated and by how accurately the models depict actual population dynamics. I evaluate the effect of uncertainty in parameter estimation through simulations. Simulations based on Steller sea lions were used to evaluate bias and precision in estimates of probability of extinction and to consider the performance of two proposed classification schemes. Extinction time estimates were biased (because of violation of the assumption of stable age distribution) and underestimated the variability of probability of extinction for a given time (primarily because of uncertainty in parameter estimation). Bias and precision in extinction probabilities are important when these probabilities are used to compare the risk of extinction between species. Suggestions are given for population viability analysis techniques that incorporate parameter uncertainty. I conclude that testing classification schemes with simulations using quantitative performance objectives should precede adoption of quantitative listing criteria.     

Simultaneous-count models to estimate abundance from counts of unmarked individuals with imperfect detection

We developed a method to estimate population abundance from simultaneous counts of unmarked individuals over multiple sites. We considered that at each sampling occasion, individuals in a population could be detected at 1 of the survey sites or remain undetected and used either multinomial or binomial simultaneous-count models to estimate abundance, the latter being equivalent to an N-mixture model with one site. We tested model performance with simulations over a range of detection probabilities, population sizes, growth rates, number of years, sampling occasions, and sites. We then applied our method to 3 critically endangered vulture species in Cambodia to demonstrate the real-world applicability of the model and to provide the first abundance estimates for these species in Cambodia. Our new approach works best when existing methods are expected to perform poorly (i.e., few sites and large variation in abundance among sites) and if individuals may move among sites between sampling occasions. The approach performed better when there were >8 sampling occasions and net probability of detection was high (>0.5). We believe our approach will be useful in particular for simultaneous surveys at aggregation sites, such as roosts. The method complements existing approaches for estimating abundance of unmarked individuals and is the first method designed specifically for simultaneous counts.     

Estimation of population parameters from aerial counts of North American mallards: a cautionary tale.

The accuracy of population estimates strongly interferes with our ability to obtain unbiased estimates of population parameters based on analyses of time series of population fluctuations. Here we use long-term data on fluctuations in the size of Mallard populations collected as part of the May Breeding Waterfowl Survey covering a large section of North America. We assume a log-linear model of density dependence and use a hierarchical Bayesian state-space approach in which all parameters are assumed to be realizations from a common underlying distribution. Thus, parameters for different populations are not allowed to vary independently of each other. We then simulated independent time series of aerial counts, using the estimated parameters and adding various levels of observation error. These simulations showed that the estimates of stochastic population growth rate and strength of density dependence were biased even when moderate sampling errors were present. In contrast, the estimates of the environmental stochasticity and the carrying capacity were unbiased even for short time series and large observation error. Our results underline the importance of reducing the magnitude of sampling error in the design of large-scale monitoring programs of population fluctuations.     

Measuring and modeling the seasonal changes of an urban Green Treefrog (Hyla cinerea) population

Green Treefrogs (Hyla cinerea) were captured, marked, measured and released at an urban study site in Lafayette, LA, during the 2004 and 2005 breeding seasons. A statistical method based on a generalization of the hypergeometric distribution was used to derive weekly time-series estimates of the population sizes. To describe the population dynamics, a stage structured mathematical model was developed and compared to time-series obtained from the weekly population estimates study using a least-squares approach. Two fitting experiments were done: (1) Using uniform distribution for the birth rate during the breeding season; (2) Using a birth rate distributed according to weekly data on frog calling intensity. Although both model-to-data fits look very promising during the years 2004 and 2005 and result in similar inherent survivorship rates for the tadpoles, juvenile and adult frogs, the fit that uses the calling data predicts a lower number of tadpoles and frogs in the long term than the one that uses uniform birth distribution. The parameter estimates resulting from these fitting experiments are used in the context of stochastic simulations to derive extinction and persistence probabilities for this population. Due to the oscillatory dynamics (with high amplitude) evidenced by the capture-recapture data and corroborated by the model, it is suggested that anuran monitoring efforts should take into account the natural intra-annual variation in population size.     

Determining Optimal Population Monitoring for Rare Butterflies

Abstract: Determining population viability of rare insects depends on precise, unbiased estimates of population size and other demographic parameters. We used data on the endangered St. Francis' satyr butterfly (Neonympha mitchellii francisci) to evaluate 2 approaches (mark–recapture and transect counts) for population analysis of rare butterflies. Mark–recapture analysis provided by far the greatest amount of demographic information, including estimates (and standard errors) of population size, detection, survival, and recruitment probabilities. Mark–recapture analysis can also be used to estimate dispersal and temporal variation in rates, although we did not do this here. Models of seasonal flight phenologies derived from transect counts (Insect Count Analyzer) provided an index of population size and estimates of survival and statistical uncertainty. Pollard–Yates population indices derived from transect counts did not provide estimates of demographic parameters. This index may be highly biased if detection and survival probabilities vary spatially and temporally. In terms of statistical performance, mark–recapture and Pollard–Yates indices were least variable. Mark–recapture estimates were less likely to fail than Insect Count Analyzer, but mark–recapture estimates became less precise as sampling intensity decreased. In general, count‐based approaches are less costly and less likely to cause harm to rare insects than mark–recapture. The optimal monitoring approach must reconcile these trade‐offs. Thus, mark–recapture should be favored when demographic estimates are needed, when financial resources enable frequent sampling, and when marking does not harm the insect populations. The optimal sampling strategy may use 2 sampling methods together in 1 overall sampling plan: limited mark–recapture sampling to estimate survival and detection probabilities and frequent but less expensive transect counts.     

Including model uncertainty in estimating variances in multiple capture studies

We present bootstrap-based methods which incorporate model uncertainty in estimating variances in multiple capture studies. Each of our three methods has a specific set of properties, and we discuss when each method should be used. Our first method can be used in any multiple capture setting, but it gives an estimate of the variance conditional on the number of observed animals. Our other two methods yield estimates of the unconditional variance; they require good estimates of part or all of the specific probability model, respectively. Smoothed estimated cell probabilities are utilized by the latter method. We contrast the three methods on a real-life data set, and then conduct simulations for a simple setting. Finally, we detail the use of our methodology for specific settings and discuss adaptations for tag-return studies.     

Estimating Population Size with Noninvasive Capture-Mark-Recapture Data

Abstract:  Estimating population size of elusive and rare species is challenging. The difficulties in catching such species has triggered the use of samples collected noninvasively, such as feces or hair, from which genetic analysis yields data similar to capture-mark-recapture (CMR) data. There are, however, two differences between classical CMR and noninvasive CMR. First, capture and recapture data are gathered over multiple sampling sessions in classical CMR, whereas in noninvasive CMR they can be obtained from a single sampling session. Second, because of genotyping errors and unlike classical CMR, there is no simple relationship between (genetic) marks and individuals in noninvasive CMR. We evaluated, through simulations, the reliability of population size estimates based on noninvasive CMR. For equal sampling efforts, we compared estimates of population size N obtained from accumulation curves, a maximum likelihood, and a Bayesian estimator. For a closed population and without sampling heterogeneity, estimates obtained from noninvasive CMR were as reliable as estimates from classical CMR. The sampling structure (single or multiple session) did not alter the results, the Bayesian estimator in the case of a single sampling session presented the best compromise between low mean squared error and a 95% confidence interval encompassing the parametric value of N in most simulations. Finally, when suitable field and lab protocols were used, genotyping errors did not substantially bias population size estimates (bias < 3.5% in all simulations). The ability to reliably estimate population size from noninvasive samples taken during a single session offers a new and useful technique for the management and conservation of elusive and rare species.     

Logistic regression and fuzzy logic as a classification method for feral fish sampling sites

This study presents a classification method combining logistic regression and fuzzy logic in the determination of sampling sites for feral fish, Nile Tilapia (Tilapia rendalli). This method statistically analyzes the variable domains involved in the problem, by using a logistic regression model. This in turn generates the knowledge necessary to construct the rule base and fuzzy clusters of the fuzzy inference system (FIS) variables. The proposed hybrid method was validated using three fish stress indices; the Fulton Condition Factor (FCF) and the gonadossomatic and hepatossomatic indices (GSI and HSI, respectively), from fish sampled at 3 different locations in the Rio de Janeiro State. A multinomial logistic regression allowed for the FIS construction of the proposed method and both statistical approaches, when combined, complemented each other satisfactorily, allowing for the construction of an efficient classification method regarding feral fish sampling sites that, in turn, has great value regarding fish captures and fishery resource management.     

A novel statistical method for classifying habitat generalists and specialists

We develop a novel statistical approach for classifying generalists and specialists in two distinct habitats. Using a multinomial model based on estimated species relative abundance in two habitats, our method minimizes bias due to differences in sampling intensities between two habitat types as well as bias due to insufficient sampling within each habitat. The method permits a robust statistical classification of habitat specialists and generalists, without excluding rare species a priori. Based on a user-defined specialization threshold, the model classifies species into one of four groups: (1) generalist; (2) habitat A specialist; (3) habitat B specialist; and (4) too rare to classify with confidence. We illustrate our multinomial classification method using two contrasting data sets: (1) bird abundance in woodland and heath habitats in southeastern Australia and (2) tree abundance in second-growth (SG) and old-growth (OG) rain forests in the Caribbean lowlands of northeastern Costa Rica. We evaluate the multinomial model in detail for the tree data set. Our results for birds were highly concordant with a previous nonstatistical classification, but our method classified a higher fraction (57.7%) of bird species with statistical confidence. Based on a conservative specialization threshold and adjustment for multiple comparisons, 64.4% of tree species in the full sample were too rare to classify with confidence. Among the species classified, OG specialists constituted the largest class (40.6%), followed by generalist tree species (36.7%) and SG specialists (22.7%). The multinomial model was more sensitive than indicator value analysis or abundance-based phi coefficient indices in detecting habitat specialists and also detects generalists statistically. Classification of specialists and generalists based on rarefied subsamples was highly consistent with classification based on the full sample, even for sampling percentages as low as 20%. Major advantages of the new method are (1) its ability to distinguish habitat generalists (species with no significant habitat affinity) from species that are simply too rare to classify and (2) applicability to a single representative sample or a single pooled set of representative samples from each of two habitat types. The method as currently developed can be applied to no more than two habitats at a time.     

Zooplankton proportion estimates from non-uniform sample volumes

The relative abundance of organisms from different taxa provides information about ecosystem health and diversity. When the numbers of sampled organisms are modelled as Poisson counts, and the sample volumes are not uniform, variance for the proportion attributable to each taxon is difficult to compute. We present a method for computing approximate variances for this situation. The point estimates and their standard errors reduce to the standard multinomial maximum likelihood results when sample volumes are uniform. Further, given initial estimates of population densities for the taxa of interest, optimal sample volumes can be computed. The methods are illustrated for zooplankton counts from Andrus Lake, Michigan.     

Occupancy estimation and modeling with multiple states and state uncertainty

The distribution of a species over space is of central interest in ecology, but species occurrence does not provide all of the information needed to characterize either the well-being of a population or the suitability of occupied habitat. Recent methodological development has focused on drawing inferences about species occurrence in the face of imperfect detection. Here we extend those methods by characterizing occupied locations by some additional state variable (e.g., as producing young or not). Our modeling approach deals with both detection probabilities <1 and uncertainty in state classification. We then use the approach with occupancy and reproductive rate data from California Spotted Owls (Strix occidentalis occidentalis) collected in the central Sierra Nevada during the breeding season of 2004 to illustrate the utility of the modeling approach. Estimates of owl reproductive rate were larger than na?ve estimates, indicating the importance of appropriately accounting for uncertainty in detection and state classification.     

Multiple sources of predictive uncertainty in modeled estimates of net ecosystem CO2 exchange

Net ecosystem CO₂ exchange (NEE) is typically measured directly by eddy covariance towers or is estimated by ecosystem process models, yet comparisons between the data obtained by these two methods can show poor correspondence. There are three potential explanations for this discrepancy. First, estimates of NEE as measured by the eddy-covariance technique are laden with uncertainty and can potentially provide a poor baseline for models to be tested against. Second, there could be fundamental problems in model structure that prevent an accurate simulation of NEE. Third, ecosystem process models are dependent on ecophysiological parameter sets derived from field measurements in which a single parameter for a given species can vary considerably. The latter problem suggests that with such broad variation among multiple inputs, any ecosystem modeling scheme must account for the possibility that many combinations of apparently feasible parameter values might not allow the model to emulate the observed NEE dynamics of a terrestrial ecosystem, as well as the possibility that there may be many parameter sets within a particular model structure that can successfully reproduce the observed data. We examined the extent to which these three issues influence estimates of NEE in a widely used ecosystem process model, Biome-BGC, by adapting the generalized likelihood uncertainty estimation (GLUE) methodology. This procedure involved 400,000 model runs, each with randomly generated parameter values from a uniform distribution based on published parameter ranges, resulting in estimates of NEE that were compared to daily NEE data from young and mature Ponderosa pine stands at Metolius, Oregon. Of the 400,000 simulations run with different parameter sets for each age class (800,000 total), over 99% of the simulations underestimated the magnitude of net ecosystem CO₂ exchange, with only 4.07% and 0.045% of all simulations providing satisfactory simulations of the field data for the young and mature stands, even when uncertainties in eddy-covariance measurements are accounted for. Results indicate fundamental shortcomings in the ability of this model to produce realistic carbon flux data over the course of forest development, and we suspect that much of the mismatch derives from an inability to realistically model ecosystem respiration. However, difficulties in estimating historic climate data are also a cause for model-data mismatch, particularly in a highly ecotonal region such as central Oregon. This latter difficulty may be less prevalent in other ecosystems, but it nonetheless highlights a challenge in trying to develop a dynamic representation of the terrestrial biosphere.     

Toward estimation of map accuracy without a probability test sample

The time and effort required of probability sampling for accuracy assessment of large-scale land cover maps often means that probability test samples are not collected. Yet, map usefulness is substantially reduced without reliable accuracy estimates. In this article, we introduce a method of estimating the accuracy of a classified map that does not utilize a test sample in the usual sense, but instead estimates the probability of correct classification for each map unit using only the classification rule and the map unit covariates. We argue that the method is an improvement over conventional estimators, though it does not eliminate the need for probability sampling. The method also provides a new and simple method of constructing accuracy maps. We illustrate some of problems associated with accuracy assessment of broad-scale land cover maps, and our method, with a set of nine Landsat Thematic Mapper satellite image-based land cover maps from Montana and Wyoming, USA.     

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.     

Optimization of capture–recapture monitoring of elusive species illustrated with a threatened grasshopper

Information on population sizes and trends of threatened species is essential for their conservation, but obtaining reliable estimates can be challenging. We devised a method to improve the precision of estimates of population size obtained from capture–recapture studies for species with low capture and recapture probabilities and short seasonal activity, illustrated with population data of an elusive grasshopper (Prionotropis rhodanica). We used data from 5 capture–recapture studies to identify methodological and environmental factors affecting capture and recapture probabilities and estimates of population size. In a simulation, we used the population size and capture and recapture probability estimates obtained from the field studies to identify the minimum number of sampling occasions needed to obtain unbiased and robust estimates of population size. Based on these results we optimized the capture–recapture design, implemented it in 2 additional studies, and compared their precision with those of the nonoptimized studies. Additionally, we simulated scenarios based on thresholds of population size in criteria C and D of the International Union for Conservation of Nature (IUCN) Red List to investigate whether estimates of population size for elusive species can reliably inform red-list assessments. Identifying parameters that affect capture and recapture probabilities (for the grasshopper time since emergence of first adults) and optimizing field protocols based on this information reduced study effort (−6% to −27% sampling occasions) and provided more precise estimates of population size (reduced coefficient of variation) compared with nonoptimized studies. Estimates of population size from the scenarios based on the IUCN thresholds were mostly unbiased and robust (only the combination of very small populations and little study effort produced unreliable estimates), suggesting capture–recapture can be considered reliable for informing red-list assessments. Although capture–recapture remains difficult and costly for elusive species, our optimization procedure can help determine efficient protocols to increase data quality and minimize monitoring effort.     

Direct calculation of likelihood-based benchmark dose levels for quantitative responses

A benchmark dose (BMD) for quantitative responses is a lower confidence limit (LCL) on the effective dose corresponding to a specified risk level r. A commonly adopted method for calculating the BMD is to obtain a pointwise upper confidence curve U(d) on the risk function and then invert this relationship by solving the equation U(d)=r. The solution d is taken to be the BMD. Sciullo et al. (2000) have shown that the coverage achieved by this inversion method is at least as great as the coverage achieved by U (·) but that there is otherwise no general relationship between the two coverage probabilities. The present paper develops a method for direct calculation of the BMD based on the asymptotic distribution of the likelihood ratio statistic. It is further shown that the direct method and the inversion method are equivalent when U (·) is also based on the likelihood ratio. Since the direct method is known to be asymptotically correct, it follows that the LR-based inversion method is also asymptotically correct. However, the direct method is computationally faster and easier to program. Finally, some simulation studies are conducted to assess the small sample coverage probabilities of the direct method when responses follow either a normal or a gamma distribution.     

Continuous-time capture-recapture population estimation when capture probabilities vary over time

Closed capture-recapture (CR) estimators have been used extensively to estimate population size. Most closed CR approaches have been developed and evaluated for discrete-time models, but there has been little effort to evaluate their continuous-time counterparts. Continuous-time estimators — developed using maximum likelihood theory by Craig (1953) and Darroch (1958), and martingale theory by Becker (1984) — that allow capture probabilities to vary over time were evaluated using Monte Carlo simulation. Overall, the ML estimators had a smaller MSE. The estimators performed well when model assumptions were upheld, and were somewhat robust to heterogeneity in capture probabilities. However, the estimators were not robust to behavioural effects in the capture probabilities. Time lag effects (periods when animals might be unavailable for immediate recapture) on continuous-time estimates were also investigated and results indicated a positive bias which was greater for smaller populations. There was no gain in performance when using a continuous-time estimator versus a discrete-time estimator on the same simulated data. Usefulness of the continuous-time approach may be limited to study designs where animals are easier to sample using continuous-time methodology.     

Habitat selection models to account for seasonal persistence in radio telemetry data

Models for the analysis of habitat selection data incorporate covariates in an independent multinomial selections model (McCracken et al. 1998) Ramsey and Usner 2003 and an extension of that model to include a persistence parameter (2003). In both cases, all parameters are assumed to be fixed through time. Radio telemetry data collected for habitat selection studies typically consist of animal relocations through time, suggesting the need for an extension to these models. We use a Bayesian approach that allows for the habitat selection probabilities, persistence parameter, or both, to change with season. These extensions are particularly important when movement patterns are expected to differ seasonally and/or when availabilities of habitats change throughout the study period due to weather or migration. We implement and compare the models using radio telemetry data for westslope cutthroat trout in two streams in eastern Oregon.     

Variability in Population Abundance and the Classification of Extinction Risk

Abstract: Classifying species according to their risk of extinction is a common practice and underpins much conservation activity. The reliability of such classifications rests on the accuracy of threat categorizations, but very little is known about the magnitude and types of errors that might be expected. The process of risk classification involves combining information from many sources, and understanding the quality of each source is critical to evaluating the overall status of the species. One common criterion used to classify extinction risk is a decline in abundance. Because abundance is a direct measure of conservation status, counts of individuals are generally the preferred method of evaluating whether populations are declining. Using the thresholds from criterion A of the International Union for Conservation of Nature (IUCN) Red List (critically endangered, decline in abundance of >80% over 10 years or 3 generations; endangered, decline in abundance of 50–80%; vulnerable, decline in abundance of 30–50%; least concern or near threatened, decline in abundance of 0–30%), we assessed 3 methods used to detect declines solely from estimates of abundance: use of just 2 estimates of abundance; use of linear regression on a time series of abundance; and use of state‐space models on a time series of abundance. We generated simulation data from empirical estimates of the typical variability in abundance and assessed the 3 methods for classification errors. The estimates of the proportion of falsely detected declines for linear regression and the state‐space models were low (maximum 3–14%), but 33–75% of small declines (30–50% over 15 years) were not detected. Ignoring uncertainty in estimates of abundance (with just 2 estimates of abundance) allowed more power to detect small declines (95%), but there was a high percentage (50%) of false detections. For all 3 methods, the proportion of declines estimated to be >80% was higher than the true proportion. Use of abundance data to detect species at risk of extinction may either fail to detect initial declines in abundance or have a high error rate.     

Estimating Population Size of Elusive Animals with DNA from Hunter-Collected Feces: Four Methods for Brown Bears

Abstract:  Noninvasive genetic methods can be used to estimate animal abundances and offer several advantages over conventional methods. Few attempts have been made, however, to evaluate the accuracy and precision of the estimates. We compared four methods of estimating population size based on fecal sampling. Two methods used rarefaction indices and two were based on capture-mark-recapture (CMR) estimators, one combining genetic and field data. Volunteer hunters and others collected 1904 fecal samples over 2 consecutive years in a large area containing a well-studied population of brown bears ( Ursus arctos ). On our 49,000-km² study area in south-central Sweden, population size estimates ranged from 378 to 572 bears in 2001 and 273 to 433 bears in 2002, depending on the method of estimation used. The estimates from the best model in the program MARK appeared to be the most accurate, based on the minimum population size estimate from radio-marked bears in a subsection of our sampling area. In addition, MARK models included heterogeneity and temporal variation in detection probabilities, which appeared to be present in our samples. All methods, though, incorrectly suggested a biased sex ratio, probably because of sex differences in detection probabilities and low overall detection probabilities. The population size of elusive animals can be estimated reliably over large areas with noninvasive genetic methods, but we stress the importance of an adequate and well-distributed sampling effort. In cases of biased sampling, calibration with independent estimates may be necessary. We recommend that this noninvasive genetic approach, using the MARK models, be used in the future in areas where sufficient numbers of volunteers can be mobilized.