Null model analysis of species associations using abundance data

The influence of negative species interactions has dominated much of the literature on community assembly rules. Patterns of negative covariation among species are typically documented through null model analyses of binary presence/absence matrices in which rows designate species, columns designate sites, and the matrix entries indicate the presence (1) or absence (0) of a particular species in a particular site. However, the outcome of species interactions ultimately depends on population-level processes. Therefore, patterns of species segregation and aggregation might be more clearly expressed in abundance matrices, in which the matrix entries indicate the abundance or density of a species in a particular site. We conducted a series of benchmark tests to evaluate the performance of 14 candidate null model algorithms and six covariation metrics that can be used with abundance matrices. We first created a series of random test matrices by sampling a metacommunity from a lognormal species abundance distribution. We also created a series of structured matrices by altering the random matrices to incorporate patterns of pairwise species segregation and aggregation. We next screened each algorithm-index combination with the random and structured matrices to determine which tests had low Type I error rates and good power for detecting segregated and aggregated species distributions. In our benchmark tests, the best-performing null model does not constrain species richness, but assigns individuals to matrix cells proportional to the observed row and column marginal distributions until, for each row and column, total abundances are reached. Using this null model algorithm with a set of four covariance metrics, we tested for patterns of species segregation and aggregation in a collection of 149 empirical abundance matrices and 36 interaction matrices collated from published papers and posted data sets. More than 80% of the matrices were significantly segregated, which reinforces a previous meta-analysis of presence/absence matrices. However, using two of the metrics we detected a significant pattern of aggregation for plants and for the interaction matrices (which include plant-pollinator data sets). These results suggest that abundance matrices, analyzed with an appropriate null model, may be a powerful tool for quantifying patterns of species segregation and aggregation.     

Experimental investigation of false positive errors in auditory species occurrence surveys

False positive errors are a significant component of many ecological data sets, which in combination with false negative errors, can lead to severe biases in conclusions about ecological systems. We present results of a field experiment where observers recorded observations for known combinations of electronically broadcast calling anurans under conditions mimicking field surveys to determine species occurrence. Our objectives were to characterize false positive error probabilities for auditory methods based on a large number of observers, to determine if targeted instruction could be used to reduce false positive error rates, and to establish useful predictors of among-observer and among-species differences in error rates. We recruited 31 observers, ranging in abilities from novice to expert, who recorded detections for 12 species during 180 calling trials (66,960 total observations). All observers made multiple false positive errors, and on average 8.1% of recorded detections in the experiment were false positive errors. Additional instruction had only minor effects on error rates. After instruction, false positive error probabilities decreased by 16% for treatment individuals compared to controls with broad confidence interval overlap of 0 (95% CI:--46 to 30%). This coincided with an increase in false negative errors due to the treatment (26%;--3 to 61%). Differences among observers in false positive and in false negative error rates were best predicted by scores from an online test and a self-assessment of observer ability completed prior to the field experiment. In contrast, years of experience conducting call surveys was a weak predictor of error rates. False positive errors were also more common for species that were played more frequently but were not related to the dominant spectral frequency of the call. Our results corroborate other work that demonstrates false positives are a significant component of species occurrence data collected by auditory methods. Instructing observers to only report detections they are completely certain are correct is not sufficient to eliminate errors. As a result, analytical methods that account for false positive errors will be needed, and independent testing of observer ability is a useful predictor for among-observer variation in observation error rates.     

Analyzing Variability and the Rate of Decline of Migratory Shorebirds in Moreton Bay,Australia

Abstract: Estimating the abundance of migratory species is difficult because sources of variability differ substantially among species and populations. Recently developed state‐space models address this variability issue by directly modeling both environmental and measurement error, although their efficacy in detecting declines is relatively untested for empirical data. We applied state‐space modeling, generalized least squares (with autoregression error structure), and standard linear regression to data on abundance of wetland birds (shorebirds and terns) at Moreton Bay in southeast Queensland, Australia. There are internationally significant numbers of 8 species of waterbirds in the bay, and it is a major terminus of the large East Asian‐Australasian Flyway. In our analyses, we considered 22 migrant and 8 resident species. State‐space models identified abundances of 7 species of migrants as significantly declining and abundance of one species as significantly increasing. Declines in migrant abundance over 15 years were 43–79%. Generalized least squares with an autoregressive error structure showed abundance changes in 11 species, and standard linear regression showed abundance changes in 15 species. The higher power of the regression models meant they detected more declines, but they also were associated with a higher rate of false detections. If the declines in Moreton Bay are consistent with trends from other sites across the flyway as a whole, then a large number of species are in significant decline.     

Debt-for-nature swaps: an overview

SUMMARY

The debt crisis of developing countries in the early 1980s has been linked with environmental degradation. In order to combat the debt and environmental crisis, debt-for-nature swap transactions were proposed by Lovejoy in 1984. They involve a mechanism of exchange in which a certain amount of the debtor's foreign debt is cancelled or forgiven, in return for local currency from the debtor government to be invested in a domestic environmental protection project. The swaps may involve two governments, and in most cases, are aided by an International Non-Governmental Organization (INGO), who must have a local contact with a domestic NGO. The first swap (1987), between Bolivia and Conservation International (US-INGO) involved cancellation of $650 000 Bolivian foreign debt for exchange of $100 000 worth of local currency to be used towards the Beni Biosphere Reserve. Since 1987, swaps have resulted in an excess of US$1.5 billion in transactions. Debt-for-nature swaps may not provide debt relief of significant magnitude nor solve the world's environmental or conservation problems, they have enabled provision of additional funding to ailing environmental organizations (more than $100 million), raised a sense of awareness about environmental protection, and some environments especially in Costa Rica are benefiting from the process.     

Determining Decision Thresholds and Evaluating Indicators when Conservation Status is Measured as a Continuum

Categorization of the status of populations, species, and ecosystems underpins most conservation activities. Status is often based on how a system's current indicator value (e.g., change in abundance) relates to some threshold of conservation concern. Receiver operating characteristic (ROC) curves can be used to quantify the statistical reliability of indicators of conservation status and evaluate trade‐offs between correct (true positive) and incorrect (false positive) classifications across a range of decision thresholds. However, ROC curves assume a discrete, binary relationship between an indicator and the conservation status it is meant to track, which is a simplification of the more realistic continuum of conservation status, and may limit the applicability of ROC curves in conservation science. We describe a modified ROC curve that treats conservation status as a continuum rather than a discrete state. We explored the influence of this continuum and typical sources of variation in abundance that can lead to classification errors (i.e., random variation and measurement error) on the true and false positive rates corresponding to varying decision thresholds and the reliability of change in abundance as an indicator of conservation status, respectively. We applied our modified ROC approach to an indicator of endangerment in Pacific salmon (Oncorhynchus nerka) (i.e., percent decline in geometric mean abundance) and an indicator of marine ecosystem structure and function (i.e., detritivore biomass). Failure to treat conservation status as a continuum when choosing thresholds for indicators resulted in the misidentification of trade‐offs between true and false positive rates and the overestimation of an indicator's reliability. We argue for treating conservation status as a continuum when ROC curves are used to evaluate decision thresholds in indicators for the assessment of conservation status. Determinación de Umbrales de Decisiones y Evaluación delos Indicadores cuando se Mide el Estado de de Conservación como un Continuo     

Performance of a Bayesian state-space model of semelparous species for stock-recruitment data subject to measurement error

Measurement errors in spawner abundance create problems for fish stock assessment scientists. To deal with measurement error, we develop a Bayesian state-space model for stock-recruitment data that contain measurement error in spawner abundance, process error in recruitment, and time series bias. Through extensive simulations across numerous scenarios, we compare the statistical performance of the Bayesian state-space model with that of standard regression for a traditional stock-recruitment model that only considers process error. Performance varies depending on the information content in data, as determined by stock productivity, types of harvest situations, and amount of measurement error. Overall, in terms of estimating optimal spawner abundance S_MSY, the Ricker density-dependence parameter β, and optimal harvest rate h_MSY, the Bayesian state-space model works best for informative data from low and variable harvest rate situations for high-productivity salmon stocks. The traditional stock-recruitment model (TSR) may be used for estimating α and h_MSY for low-productivity stocks from variable and high harvest rate situations. However, TSR can severely overestimate S_MSY when spawner abundance is measured with large error in low and variable harvest rate situations. We also found that there is substantial merit in using h_MSY (or benchmarks derived from it) instead of S_MSY as a management target.     

Effects of Patch Size and Type of Coffee Matrix on Ithomiine Butterfly Diversity and Dispersal in Cloud-Forest Fragments

Abstract: Determining the permeability of different types of landscape matrices to animal movement is essential for conserving populations in fragmented landscapes. We evaluated the effects of habitat patch size and matrix type on diversity, isolation, and dispersal of ithomiine butterflies in forest fragments surrounded by coffee agroecosystems in the Colombian Andes. Because ithomiines prefer a shaded understory, we expected the highest diversity and abundance in large fragments surrounded by shade coffee and the lowest in small fragments surrounded by sun coffee. We also thought shade coffee would favor butterfly dispersal and immigration into forest patches. We marked 9675 butterflies of 39 species in 12 forest patches over a year. Microclimate conditions were more similar to the forest interior in the shade‐coffee matrix than in the sun‐coffee matrix, but patch size and matrix type did not affect species richness and abundance in forest fragments. Furthermore, age structure and temporal recruitment patterns of the butterfly community were similar in all fragments, independent of patch size or matrix type. There were no differences in the numbers of butterflies flying in the matrices at two distances from the forest patch, but their behavior differed. Flight in the sun‐coffee matrix was rapid and directional, whereas butterflies in shade‐coffee matrix flew slowly. Seven out of 130 recaptured butterflies immigrated into patches in the shade‐coffee matrix, and one immigrated into a patch surrounded by sun coffee. Although the shade‐coffee matrix facilitated movement in the landscape, sun‐coffee matrix was not impermeable to butterflies. Ithomiines exhibited behavioral plasticity in habitat use and high mobility. These traits favor their persistence in heterogeneous landscapes, opening opportunities for their conservation. Understanding the dynamics and resource requirements of different organisms in rural landscapes is critical for identifying management options that address both animals’ and farmers’ needs.     

Effects of uncertainty and variability on population declines and IUCN Red List classifications

The International Union for Conservation of Nature (IUCN) Red List Categories and Criteria is a quantitative framework for classifying species according to extinction risk. Population models may be used to estimate extinction risk or population declines. Uncertainty and variability arise in threat classifications through measurement and process error in empirical data and uncertainty in the models used to estimate extinction risk and population declines. Furthermore, species traits are known to affect extinction risk. We investigated the effects of measurement and process error, model type, population growth rate, and age at first reproduction on the reliability of risk classifications based on projected population declines on IUCN Red List classifications. We used an age‐structured population model to simulate true population trajectories with different growth rates, reproductive ages and levels of variation, and subjected them to measurement error. We evaluated the ability of scalar and matrix models parameterized with these simulated time series to accurately capture the IUCN Red List classification generated with true population declines. Under all levels of measurement error tested and low process error, classifications were reasonably accurate; scalar and matrix models yielded roughly the same rate of misclassifications, but the distribution of errors differed; matrix models led to greater overestimation of extinction risk than underestimations; process error tended to contribute to misclassifications to a greater extent than measurement error; and more misclassifications occurred for fast, rather than slow, life histories. These results indicate that classifications of highly threatened taxa (i.e., taxa with low growth rates) under criterion A are more likely to be reliable than for less threatened taxa when assessed with population models. Greater scrutiny needs to be placed on data used to parameterize population models for species with high growth rates, particularly when available evidence indicates a potential transition to higher risk categories.     

Spatial error propagation when computing linear combinations of spectral bands: The case of vegetation indices

The collection of accurate and timely information on land use, crops, forest and vegetation are increasingly based on remote sensing spectral measurements produced by satellites. The most recent spacecrafts like the Earth Observing 1 (EO-1) produce a rich source of information being endowed with hyperspectral sensors that can provide up to 200 or more channels. In many instances such a multivariate signal has to be reduced to just one single value per pixel representing a particular characteristic of land. Linear combinations of bands are the general form of many indices. Since each individual image used to construct indices contains errors, when combined they produce a propagation of errors, a process that can distort a final output map. In this paper we measure the extent of error propagation when building linear vegetation indices. We consider three types of indices: the difference vegetation index (DVI), selected Kauth-Thomas indices (SBI, GVI and WET), and principal components, using benchmarking examples taken from the remote sensing literature. The main implication emerging from these examples is that the SBI and the first principal component are the indices more prone to error propagation. The formalization presented here allows a user to derive measures of error propagation in cases where technical characteristics of a sensor and physical characteristics of a landscape are known. These results can help a user to choose between alternative vegetation indices, and to associate a measure of reliability with such indices.     

Indirect effects of large herbivores on snakes in an African savanna

Many large mammal species are declining in African savannas, yet we understand relatively little about how these declines influence other species. Previous studies have shown that the removal of large herbivorous mammals from large-scale, replicated experimental plots results in a dramatic increase in the density of small mammals, an increase that has been attributed to the relaxation of competition between rodents and large herbivores for food resources. To assess whether the removal of large herbivores also influenced a predator of small mammals, we measured the abundance of the locally common olive hissing snake, Psammophis mossambicus, over a 19-mo period in plots with and without large herbivores. Psammophis mossambicus was significantly more abundant in plots where large herbivores were removed and rodent numbers were high. Based on results from raptor surveys and measurements of vegetative cover, differences in snake density do not appear to be driven by differences in rates of predation on snakes. Instead, snakes appear to be responding numerically to greater abundances of small-mammal prey in areas from which large herbivores have been excluded. This is the first empirical demonstration of the indirect effects of large herbivores on snake abundance and presents an interesting example of how the influence of dominant and keystone species can move through a food web.     

Traditional occupancy–abundance models are inadequate for zero-inflated ecological count data

Traditional occupancy–abundance and abundance–variance–occupancy models do not take into account zero-inflation, which occurs when sampling rare species or in correlated counts arising from repeated measures. In this paper we propose a novel approach extending occupancy–abundance relationships to zero-inflated count data. This approach involves three steps: (1) selecting distributional assumptions and parsimonious models for the count data, (2) estimating abundance, occupancy and variance parameters as functions of site- and/or time-specific covariates, and (3) modelling the occupancy–abundance relationship using the parameters estimated in step 2. Five count datasets were used for comparing standard Poisson and negative binomial distribution (NBD) occupancy–abundance models. Zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) occupancy–abundance models were introduced for the first time, and these were compared with the Poisson, NBD, He and Gaston's and Wilson and Room's abundance–variance–occupancy models. The percentage of zero counts ranged from 45 to 80% in the datasets analysed. For most of the datasets, the ZINB occupancy–abundance model performed better than the traditional Poisson, NBD and Wilson and Room's model. He and Gaston's model performed better than the ZINB in two out of the five datasets. However, the occupancy predicted by all models increased faster than the observed as density increased resulting in significant mismatch at the highest densities. Limitations of the various models are discussed, and the need for careful choice of count distributions and predictors in estimating abundance and occupancy parameter are indicated.     

Despotic, high-impact species and the subcontinental scale control of avian assemblage structure

Some species have disproportionate influence on assemblage structure, given their numbers or biomass. Most examples of such "strong interactors" come from small-scale experiments or from observations of the effects of invasive species. There is evidence that entire avian assemblages in open woodlands can be influenced strongly by individual species over very large areas in eastern Australia, with small-bodied species (< 50 g) being adversely affected. We used data from repeated surveys in 371 sites in seven districts across a region from Victoria to Queensland (> 2000 km). A series of linked Bayesian models was used to identify large-bodied (> or = 50 g) bird species that were associated with changes in occurrence and abundance of small-bodied species. One native species, the Noisy Miner (Manorina melanocephala; family Meliphagidae), was objectively identified as the sole large-bodied species having similar detrimental effects in all districts, depressing occurrence of 57 of 71 small-bodied species. Adverse effects on abundances of small-bodied species were profound when the Noisy Miner occurred with mean site abundances > or = 1.6 birds/2 ha. The Noisy Miner may be the first species to have been shown to influence whole-of-avifauna assemblage structure through despotic aggressiveness over subcontinental scales. These substantial shifts in occurrence rates and abundances of small-bodied species flow on to alter species abundance distributions of entire assemblages over much of eastern Australia.     

Will Observation Error and Biases Ruin the Use of Simple Extinction Models?

Abstract: Estimating the risk of extinction for populations of endangered species is an important component of conservation biology. These estimates must be made from data that contain both environmental noise in the year-to-year transitions in population size (so-called "process error"), random errors in sampling, and possible biases in sampling ( both forms of observation errors). To determine how much faith to place in estimated extinction rates, it is important to know how sensitive they are to observation error. We used three simple, commonly employed models of population dynamics to generate simulated population time series. We then combined random observation error or systematic biases with those data, fit models to the time series data, and observed how close the extinction dynamics of the fitted models compared with the dynamics of the underlying models. We found that systematic biases in sampling rarely affected estimates of extinction risk. We also found that even moderate levels of random observation error do not significantly affect extinction estimates except over a small range of process errors, corresponding to the region where extinction risk is most uncertain. With more substantial sampling error, estimates of extinction risk degraded rapidly. Field census techniques for a variety of taxa often involve observation errors within ±32% of actual population sizes. For typical time series used in conservation, therefore, we often may not need to be overly concerned about observation errors as an extra source of imperfection in our estimated extinction rates.     

Variations in mortality of a coral-reef fish: links with predator abundance

The mortality rates of a pomacentrid Acanthochromis polyacanthus were examined in relation to the abundance of large predatory fish (>200 mm total length, TL) at two spatial scales. Survivorship was negatively related to patterns of predator abundance at a large spatial scale (hundreds of metres) over 3 yr, but not at a small spatial scale (tens of metres) over 2 yr. On the large scale, mortality was consistently greater (14 to 30%) in locations where there were greater numbers of predators, and lower in locations where predators occurred in smaller numbers. Among these locations, spatial differences in rank abundance of surviving juveniles were primarily due to mortality, whereas temporal differences in rank abundance were primarily due to initial juvenile abundance. These data suggest that impacts of large predatory fish were likely to have been greater in space than time and at the large spatial scale than the small spatial scale.     

Chilean Blue Whales as a Case Study to Illustrate Methods to Estimate Abundance and Evaluate Conservation Status of Rare Species

Abstract: Often abundance of rare species cannot be estimated with conventional design‐based methods, so we illustrate with a population of blue whales (Balaenoptera musculus) a spatial model‐based method to estimate abundance. We analyzed data from line‐transect surveys of blue whales off the coast of Chile, where the population was hunted to low levels. Field protocols allowed deviation from planned track lines to collect identification photographs and tissue samples for genetic analyses, which resulted in an ad hoc sampling design with increased effort in areas of higher densities. Thus, we used spatial modeling methods to estimate abundance. Spatial models are increasingly being used to analyze data from surveys of marine, aquatic, and terrestrial species, but estimation of uncertainty from such models is often problematic. We developed a new, broadly applicable variance estimator that showed there were likely 303 whales (95% CI 176–625) in the study area. The survey did not span the whales' entire range, so this is a minimum estimate. We estimated current minimum abundance relative to pre‐exploitation abundance (i.e., status) with a population dynamics model that incorporated our minimum abundance estimate, likely population growth rates from a meta‐analysis of rates of increase in large baleen whales, and two alternative assumptions about historic catches. From this model, we estimated that the population was at a minimum of 9.5% (95% CI 4.9–18.0%) of pre‐exploitation levels in 1998 under one catch assumption and 7.2% (CI 3.7–13.7%) of pre‐exploitation levels under the other. Thus, although Chilean blue whales are probably still at a small fraction of pre‐exploitation abundance, even these minimum abundance estimates demonstrate that their status is better than that of Antarctic blue whales, which are still <1% of pre‐exploitation population size. We anticipate our methods will be broadly applicable in aquatic and terrestrial surveys for rarely encountered species, especially when the surveys are intended to maximize encounter rates and estimate abundance.     

Null model analysis of species nestedness patterns

Nestedness is a common biogeographic pattern in which small communities form proper subsets of large communities. However, the detection of nestedness in binary presence-absence matrices will be affected by both the metric used to quantify nestedness and the reference null distribution. In this study, we assessed the statistical performance of eight nestedness metrics and six null model algorithms. The metrics and algorithms were tested against a benchmark set of 200 random matrices and 200 nested matrices that were created by passive sampling. Many algorithms that have been used in nestedness studies are vulnerable to type I errors (falsely rejecting a true null hypothesis). The best-performing algorithm maintains fixed row and fixed column totals, but it is conservative and may not always detect nestedness when it is present. Among the eight indices, the popular matrix temperature metric did not have good statistical properties. Instead, the Brualdi and Sanderson discrepancy index and Cutler's index of unexpected presences performed best. When used with the fixed-fixed algorithm, these indices provide a conservative test for nestedness. Although previous studies have revealed a high frequency of nestedness, a reanalysis of 288 empirical matrices suggests that the true frequency of nested matrices is between 10% and 40%.     

Generalized site occupancy models allowing for false positive and false negative errors

Site occupancy models have been developed that allow for imperfect species detection or "false negative" observations. Such models have become widely adopted in surveys of many taxa. The most fundamental assumption underlying these models is that "false positive" errors are not possible. That is, one cannot detect a species where it does not occur. However, such errors are possible in many sampling situations for a number of reasons, and even low false positive error rates can induce extreme bias in estimates of site occupancy when they are not accounted for. In this paper, we develop a model for site occupancy that allows for both false negative and false positive error rates. This model can be represented as a two-component finite mixture model and can be easily fitted using freely available software. We provide an analysis of avian survey data using the proposed model and present results of a brief simulation study evaluating the performance of the maximum-likelihood estimator and the naive estimator in the presence of false positive errors.     

Increasing accuracy of dispersal kernels in grid-based population models

Dispersal kernels in grid-based population models specify the proportion, distance and direction of movements within the model landscape. Spatial errors in dispersal kernels can have large compounding effects on model accuracy. Circular Gaussian and Laplacian dispersal kernels at a range of spatial resolutions were investigated, and methods for minimizing errors caused by the discretizing process were explored. Kernels of progressively smaller sizes relative to the landscape grid size were calculated using cell-integration and cell-center methods. These kernels were convolved repeatedly, and the final distribution was compared with a reference analytical solution. For large Gaussian kernels (σ > 10 cells), the total kernel error was <10⁻¹¹ compared to analytical results. Using an invasion model that tracked the time a population took to reach a defined goal, the discrete model results were comparable to the analytical reference. With Gaussian kernels that had σ ≤ 0.12 using the cell integration method, or σ ≤ 0.22 using the cell center method, the kernel error was greater than 10%, which resulted in invasion times that were orders of magnitude different than theoretical results. A goal-seeking routine was developed to adjust the kernels to minimize overall error. With this, corrections for small kernels were found that decreased overall kernel error to <10⁻¹¹ and invasion time error to <5%.     

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.     

Assessing conservation status with extensive but low-resolution data: Application of frequentist and Bayesian models to endangered Athabasca River rainbow trout

Use of extensive but low-resolution abundance data is common in the assessment of species at-risk status based on quantitative decline criteria under International Union for Conservation of Nature (IUCN) and national endangered species legislation. Such data can be problematic for 3 reasons. First, statistical power to reject the null hypothesis of no change is often low because of small sample size and high sampling uncertainty leading to a high frequency of type II errors. Second, range-wide assessments composed of multiple site-specific observations do not effectively weight site-specific trends into global trends. Third, uncertainty in site-specific temporal trends and relative abundance are not propagated at the appropriate spatial scale. A common result is the propensity to underestimate the magnitude of declines and therefore fail to identify the appropriate at-risk status for a species. We used 3 statistical approaches, from simple to more complex, to estimate temporal decline rates for a designatable unit (DU) of rainbow trout in the Athabasca River watershed in western Canada. This DU is considered a native species for purposes of listing because of its genetic composition characterized as >0.95 indigenous origin in the face of continuing introgressive hybridization with introduced populations in the watershed. Analysis of abundance trends from 57 time series with a fixed-effects model identified 33 sites with negative trends, but only 2 were statistically significant. By contrast, a hierarchical linear mixed model weighted by site-specific abundance provided a DU-wide decline estimate of 16.4% per year and a 3-generation decline of 93.2%. A hierarchical Bayesian mixed model yielded a similar 3-generation decline trend of 91.3% and the posterior distribution showed that the estimate had a >99% probability of exceeding thresholds for an endangered listing. We conclude that the Bayesian approach was the most useful because it provided a probabilistic statement of threshold exceedance in support of an at-risk status recommendation.