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.     

Reliability of Absolute and Relative Predictions of Population Persistence Based on Time Series

Abstract:  Conventional population viability analysis (PVA) is often impractical because data are scarce for many threatened species. For this reason, simple count-based models are being advocated. The simplest of these models requires nothing more than a time series of abundance estimates, from which variance and autocorrelation in growth rate are estimated and predictions of population persistence are generated. What remains unclear, however, is how many years of data are needed to generate reliable estimates of these parameters and hence reliable predictions of persistence. By analyzing published and simulated time series, we show that several decades of data are needed. Predictions based on short time series were very unreliable mainly because limited data yielded biased, unreliable estimates of variance in growth rate, especially when growth rate was strongly autocorrelated. More optimistically, our results suggest that count-based PVA is sometimes useful for relative risk assessment (i.e., for ranking populations by extinction risk), even when time series are only a decade long. However, some conditions consistently lead to backward rankings. We explored the limited conditions under which simple count-based PVA may be useful for relative risk assessment.     

Population level effects of reduced fecundity in the fish species perch (Perca fluviatilis) and the implications for environmental monitoring

A 40% reduction in relative gonad size in perch (Perca fluviatilis) has been observed over that past two decades at the Swedish national reference site Kvädöfjärden. This biomarker response could be interpreted as a reduction in fecundity and increased risk of local extinction. However, abundance estimates from the same area has not provided any evidence of a reduction in population size. In the present study, a matrix population model was developed to investigate if a reduction in fecundity can be expected to have long term effects on population viability for perch and to evaluate the probability to detect such effects through abundance estimates. The model was parameterized from 17 years of population data from Kvädöfjärden as well as from other studies on perch. The model included density dependence and environmental stochasticity. The results indicated that a reduction in fecundity that is in level with the observed reduction in relative gonad size in Kvädöfjärden will cause a substantial risk for local extinction. The risk that the population will fall below 20% of the carrying capacity within 50 years is 44% when the fecundity is reduced by 40%. However, due to variability in abundance measurements it will take some time before a reduction in gonad size leads to statistically significant effects on the population. If the fecundity is reduced by 40% successively over a 10-year period, the probability to detect this through abundance estimates within 10 years is less than 50%. The results of the present study clearly show that relevant biomarkers have an important role in environmental monitoring as early warning signals, preferably in combination with measurements at higher levels of biological organization.     

Reconstructibility of Density Dependence and the Conservative Assessment of Extinction Risks

Abstract: The probability of extinction is sensitive to the presence and character of density dependence controlling the dynamics of a population. This means that our capacity to estimate a population's risks of extinction under varying environmental conditions or competing management regimes is linked to our ability to reconstruct from data the density-dependence relationships governing the natural dynamics, especially when data do not reveal a trend of population growth or decline. In an example using Gadus morhua , we show that even 10- or 20-year data sets are too short to make precise estimates of these risks. We also observe, however, that under moderate or weak density dependence, the computed risks are lower than when density dependence is not included in the model. We propose, therefore, that when available data sets are insufficient for reconstructing reliable measurements of density dependence, conservative estimates of extinction probabilities can be made from models that simply omit density dependence.     

Predicting [corrected] extinction risk in spite of predator-prey oscillations.

Most population viability analyses (PVA) assume that the effects of species interactions are subsumed by population-level parameters. We examine how robust five commonly used PVA models are to violations of this assumption. We develop a stochastic, stage-structured predator-prey model and simulate prey population vital rates and abundance. We then use simulated data to parameterize and estimate risk for three demographic models (static projection matrix, stochastic projection matrix, stochastic vital rate matrix) and two time series models (diffusion approximation [DA], corrupted diffusion approximation [CDA]). Model bias is measured as the absolute deviation between estimated and observed quasi-extinction risk. Our results highlight three generalities about the application of single-species models to multi-species conservation problems. First, our collective model results suggest that most single-species PVA models overestimate extinction risk when species interactions cause periodic variation in abundance. Second, the DA model produces the most (conservatively) biased risk forecasts. Finally, the CDA model is the most robust PVA to population cycles caused by species interactions. CDA models produce virtually unbiased and relatively precise risk estimates even when populations cycle strongly. High performance of simple time series models like the CDA owes to their ability to effectively partition stochastic and deterministic sources of variation in population abundance.     

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.     

Mapping shifts in spatial synchrony in grassland birds to inform conservation planning

Spatial synchrony, defined as the correlated fluctuations in abundance of spatially separated populations, can be caused by regional fluctuations in natural and anthropogenic environmental population drivers. Investigations into the geography of synchrony can provide useful insight to inform conservation planning efforts by revealing regions of common population drivers and metapopulation extinction vulnerability. We examined the geography of spatial synchrony and decadal changes in these patterns for grassland birds in the United States and Canada, which are experiencing widespread and persistent population declines. We used Bayesian hierarchical models and over 50 years of abundance data from the North American Breeding Bird Survey to generate population indices within a 2° latitude by 2° longitude grid. We computed and mapped mean local spatial synchrony for each cell (mean detrended correlation of the index among neighboring cells), along with associated uncertainty, for 19 species in 2, 26-year periods, 1968–1993 and 1994–2019. Grassland birds were predicted to increase in spatial synchrony where agricultural intensification, climate change, or interactions between the 2 increased. We found no evidence of an overall increase in synchrony among grassland bird species. However, based on the geography of these changes, there was considerable spatial heterogeneity within species. Averaging across species, we identified clusters of increasing spatial synchrony in the Prairie Pothole and Shortgrass Prairie regions and a region of decreasing spatial synchrony in the eastern United States. Our approach has the potential to inform continental-scale conservation planning by adding an additional layer of relevant information to species status assessments and spatial prioritization of policy and management actions. Our work adds to a growing literature suggesting that global change may result in shifting patterns of spatial synchrony in population dynamics across taxa with broad implications for biodiversity conservation.     

The Threat of Disease Increases as Species Move Toward Extinction

At local scales, infectious disease is a common driver of population declines, but globally it is an infrequent contributor to species extinction and endangerment. For species at risk of extinction from disease important questions remain unanswered, including when does disease become a threat to species and does it co‐occur, predictably, with other threats? Using newly compiled data from the International Union for Conservation of Nature (IUCN) Red List, we examined the relative role and co‐occurrence of threats associated with amphibians, birds, and mammals at 6 levels of extinction risk (i.e., Red List status categories: least concern, near threatened, vulnerable, endangered, critically endangered, and extinct in the wild/extinct). We tested the null hypothesis that the proportion of species threatened by disease is the same in all 6 Red List status categories. Our approach revealed a new method for determining when disease most frequently threatens species at risk of extinction. The proportion of species threatened by disease varied significantly between IUCN status categories and linearly increased for amphibians, birds, and all species combined as these taxa move from move from least concern to critically endangered. Disease was infrequently the single contributing threat. However, when a species was negatively affected by a major threat other than disease (e.g., invasive species, land‐use change) that species was more likely to be simultaneously threatened by disease than species that had no other threats. Potential drivers of these trends include ecological factors, clustering of phylogenetically related species in Red List status categories, discovery bias among species at greater risk of extinction, and availability of data. We echo earlier calls for baseline data on the presence of parasites and pathogens in species when they show the first signs of extinction risk and arguably before. La Amenaza de Enfermedades Incrementa a Medida que las Especies se Aproximan a la Extinción     

Transient population dynamics in periodic matrix models: methodology and effects of cyclic permutations

Many biological populations are subject to periodically changing environments such as years with or without fire, or rotation of crop types. The dynamics and management options for such populations are frequently investigated using periodic matrix models. However the analysis is usually limited to long-term results (asymptotic population growth rate and its sensitivity to perturbations of vital rates). In non-periodic matrix models it has been shown that long-term results may be misleading as populations are rarely in their stable structure. We therefore develop methods to analyze transient dynamics of periodic matrix models. In particular, we show how to calculate the effects of perturbations on population size within and at the end of environmental cycles. Using a model of a weed population subject to a crop rotation, we show that different cyclic permutations produce different patterns of sensitivity of population size and different population sizes. By examining how the starting environment interacts with the initial conditions, we explain how different patterns arise. Such understanding is critical to developing effective management and monitoring strategies for populations subject to periodically recurring environments.     

A Behaviorally Explicit Demographic Model Integrating Habitat Selection and Population Dynamics in California Sea Lions

Abstract: Although there has been a call for the integration of behavioral ecology and conservation biology, there are few tools currently available to achieve this integration. Explicitly including information about behavioral strategies in population viability analyses may enhance the ability of conservation biologists to understand and estimate patterns of extinction risk. Nevertheless, most behavioral‐based PVA approaches require detailed individual‐based data that are rarely available for imperiled species. We present a mechanistic approach that incorporates spatial and demographic consequences of behavioral strategies into population models used for conservation. We developed a stage‐structured matrix model that includes the costs and benefits of movement associated with 2 habitat‐selection strategies (philopatry and direct assessment). Using a life table for California sea lions (Zalophus californianus), we explored the sensitivity of model predictions to the inclusion of these behavioral parameters. Including behavioral information dramatically changed predicted population sizes, model dynamics, and the expected distribution of individuals among sites. Estimated population sizes projected in 100 years diverged up to 1 order of magnitude among scenarios that assumed different movement behavior. Scenarios also exhibited different model dynamics that ranged from stable equilibria to cycles or extinction. These results suggest that inclusion of behavioral data in viability models may improve estimates of extinction risk for imperiled species. Our approach provides a simple method for incorporating spatial and demographic consequences of behavioral strategies into population models and may be easily extended to other species and behaviors to understand the mechanisms of population dynamics for imperiled populations.     

Value of protected areas to avian persistence across 20 years of climate and land-use change

Establishing protected areas, where human activities and land cover changes are restricted, is among the most widely used strategies for biodiversity conservation. This practice is based on the assumption that protected areas buffer species from processes that drive extinction. However, protected areas can maintain biodiversity in the face of climate change and subsequent shifts in distributions have been questioned. We evaluated the degree to which protected areas influenced colonization and extinction patterns of 97 avian species over 20 years in the northeastern United States. We fitted single-visit dynamic occupancy models to data from Breeding Bird Atlases to quantify the magnitude of the effect of drivers of local colonization and extinction (e.g., climate, land cover, and amount of protected area) in heterogeneous landscapes that varied in the amount of area under protection. Colonization and extinction probabilities improved as the amount of protected area increased, but these effects were conditional on landscape context and species characteristics. In this forest-dominated region, benefits of additional land protection were greatest when both forest cover in a grid square and amount of protected area in neighboring grid squares were low. Effects did not vary with species’ migratory habit or conservation status. Increasing the amounts of land protection benefitted the range margins species but not the core range species. The greatest improvements in colonization and extinction rates accrued for forest birds relative to open-habitat or generalist species. Overall, protected areas stemmed extinction more than they promoted colonization. Our results indicate that land protection remains a viable conservation strategy despite changing habitat and climate, as protected areas both reduce the risk of local extinction and facilitate movement into new areas. Our findings suggest conservation in the face of climate change favors creation of new protected areas over enlarging existing ones as the optimal strategy to reduce extinction and provide stepping stones for the greatest number of species.     

Modelling with uncertainty: Introducing a probabilistic framework to predict animal population dynamics

Predictive population models designed to assist managers and policy makers require an explicit treatment of inherent uncertainty and variability. These are particular concerns when modelling non-native and reintroduced species, when data have been collected within one geographical or ecological context but predictions are required for another, or when extending models to predict the consequences of environmental change (e.g., climate or land-use). We present an aspatial, probabilistic framework of hierarchical process models for predicting population growth even when data are sparse or of poor quality. Insight into the factors affecting population dynamics in real landscapes can be provided and Kullback–Leibler distances are used to compare the relative output of models. This flexible yet robust framework gives easily interpretable results, allowing managers as well as modellers to invalidate anomalous models and apply others to real-life scenarios.We illustrate the framework’s power with a meta-analysis of European wild boar (Sus scrofa) data. We test hypotheses about the effect of geographic region, hunting and mast years on wild boar population growth, to build models of wild boar dynamics for the UK. The framework quantifies the importance of hunting pressure as a driver of population growth, and confirms that reproductive success is greatly decreased in poor mast years, suggesting that the key to predicting wild boar dynamics is to ascertain local hunting pressure and to better understand changing food availability. Geography had no significant effect, indicating that it is not a good proxy for modelling the impact of change in climate or land-use on wild boar populations at the European scale. We use the framework to predict population abundance 9 years after an isolated population of wild boar established in the UK; in a comparison with the only field data and two independent modelling exercises, our framework provides the most robust and informative results.     

Ability of Matrix Models to Explain the Past and Predict the Future of Plant Populations

Uncertainty associated with ecological forecasts has long been recognized, but forecast accuracy is rarely quantified. We evaluated how well data on 82 populations of 20 species of plants spanning 3 continents explained and predicted plant population dynamics. We parameterized stage‐based matrix models with demographic data from individually marked plants and determined how well these models forecast population sizes observed at least 5 years into the future. Simple demographic models forecasted population dynamics poorly; only 40% of observed population sizes fell within our forecasts’ 95% confidence limits. However, these models explained population dynamics during the years in which data were collected; observed changes in population size during the data‐collection period were strongly positively correlated with population growth rate. Thus, these models are at least a sound way to quantify population status. Poor forecasts were not associated with the number of individual plants or years of data. We tested whether vital rates were density dependent and found both positive and negative density dependence. However, density dependence was not associated with forecast error. Forecast error was significantly associated with environmental differences between the data collection and forecast periods. To forecast population fates, more detailed models, such as those that project how environments are likely to change and how these changes will affect population dynamics, may be needed. Such detailed models are not always feasible. Thus, it may be wiser to make risk‐averse decisions than to expect precise forecasts from models. Habilidad de los Modelos Matriciales para Explicar el Pasado y Predecir el Futuro de las Poblaciones de Plantas     

Extinction Rate Estimates for Plant Populations in Revisitation Studies: Importance of Detectability

Abstract:  Many researchers have obtained extinction-rate estimates for plant populations by comparing historical and current records of occurrence. A population that is no longer found is assumed to have gone extinct. Extinction can then be related to characteristics of these populations, such as habitat type, size, or species, to test ideas about what factors may affect extinction. Such studies neglect the fact that a population may be overlooked, however, which may bias estimates of extinction rates upward. In addition, if populations are unequally detectable across groups to be compared, such as habitat type or population size, comparisons become distorted to an unknown degree. To illustrate the problem, I simulated two data sets, assuming a constant extinction rate, in which populations occurred in different habitats or habitats of different size and these factors affected their detectability. The conventional analysis implicitly assumed that detectability equalled 1 and used logistic regression to estimate extinction rates. It wrongly identified habitat and population size as factors affecting extinction risk. In contrast, with capture-recapture methods, unbiased estimates of extinction rates were recovered. I argue that capture-recapture methods should be considered more often in estimations of demographic parameters in plant populations and communities.     

Effects of Recent Environmental Change on Accuracy of Inferences of Extinction Status

Correctly classifying a species as extinct or extant is of critical importance if current rates of biodiversity loss are to be accurately quantified. Observing an extinction event is rare, so in many cases extinction status is inferred using methods based on the analysis of records of historic sighting events. The accuracy of such methods is difficult to test. However, results of recent experiments with microcosm communities suggest that the rate at which a population declines to extinction, potentially driven by varying environmental conditions, may alter one's ability accurately to infer extinction status. We tested how the rate of population decline, driven by historic environmental change, alters the accuracy of 6 commonly applied sighting‐based methods used to infer extinction. We used data from small‐scale experimental communities and recorded wild population extirpations. We assessed how accuracy of the different methods was affected by rate of population decline, search effort, and number of sighting events recorded. Rate of population decline and historic population size of the species affected the accuracy of inferred extinction dates; however, faster declines produced more accurate inferred dates of extinction, but only when population sizes were higher. Optimal linear estimation (OLE) offered the most reliable and robust estimates, though no single method performed best in all situations, and it may be appropriate to use a different method if information regarding historic search efforts is available. OLE provided the most accurate estimates of extinction when the number of sighting events used was >10, and future use of this method should take this into account. Data from experimental populations provide added insight into testing techniques to discern wild extirpation events. Care should be taken designing such experiments so that they mirror closely the abundance dynamics of populations affected by real‐world extirpation events. Efectos del Cambio Ambiental Reciente sobre la Precisión de las Inferencias sobre el Estado de Extinción     

Predicting Extinction Risk of Brazilian Atlantic Forest Angiosperms

Understanding how plant life history affects species vulnerability to anthropogenic disturbances and environmental change is a major ecological challenge. We examined how vegetation type, growth form, and geographic range size relate to extinction risk throughout the Brazilian Atlantic Forest domain. We used a database containing species‐level information of 6,929 angiosperms within 112 families and a molecular‐based working phylogeny. We used decision trees, standard regression, and phylogenetic regression to explore the relationships between species attributes and extinction risk. We found a significant phylogenetic signal in extinction risk. Vegetation type, growth form, and geographic range size were related to species extinction risk, but the effect of growth form was not evident after phylogeny was controlled for. Species restricted to either rocky outcrops or scrub vegetation on sandy coastal plains exhibited the highest extinction risk among vegetation types, a finding that supports the hypothesis that species adapted to resource‐limited environments are more vulnerable to extinction. Among growth forms, epiphytes were associated with the highest extinction risk in non‐phylogenetic regression models, followed by trees, whereas shrubs and climbers were associated with lower extinction risk. However, the higher extinction risk of epiphytes was not significant after correcting for phylogenetic relatedness. Our findings provide new indicators of extinction risk and insights into the mechanisms governing plant vulnerability to extinction in a highly diverse flora where human disturbances are both frequent and widespread. Predicción del Riesgo de Extinción de Angiospermas del Bosque Atlántico Brasileño     

The unified neutral theory of biodiversity: do the numbers add up?

Hubbell's unified neutral theory is a zero-sum ecological drift model in which population sizes change at random in a process resembling genetic drift, eventually leading to extinction. Diversity is maintained within the community by speciation. Hubbell's model makes predictions about the distribution of species abundances within communities and the turnover of species from place to place (beta diversity). However, ecological drift cannot be tested adequately against these predictions without independent estimates of speciation rates, population sizes, and dispersal distances. A more practical prediction from ecological drift is that time to extinction of a population of size N is approximately 2N generations. I test this prediction here using data for passerine birds (Passeriformes). Waiting times to speciation and extinction were estimated from genetic divergence between sister populations and a lineage-through-time plot for endemic South American suboscine passerines. Population sizes were estimated from local counts of birds in two large forest plots extrapolated to the area of wet tropical forest in South America and from atlas data on European passerines. Waiting times to extinction (ca. 2 Ma) are much less than twice the product of average population size (4.0 and 14.4 x 10(6) individuals in South America and Europe) and generation length (five and three years) for songbirds, that is, 40 and 86 Ma, respectively. Thus, drift is too slow to account for turnover in regional avifaunas. Presumably, other processes, involving external drivers, such as climate and physiographic change, and internal drivers, such as evolutionary change in antagonistic interactions, predominate. Hubbell's model is historical and geographic, and his perspective importantly links local and regional process and pattern. Ecological reality can be added to the mix while retaining Hubbell's concept of continuity of communities in space and time.     

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.     

Demographic stochasticity reduces the synchronizing effect of dispersal in predator-prey metapopulations

Dispersal may affect predator-prey metapopulations by rescuing local sink populations from extinction or by synchronizing population dynamics across the metapopulation, increasing the risk of regional extinction. Dispersal is likely influenced by demographic stochasticity, however, particularly because dispersal rates are often very low in metapopulations. Yet the effects of demographic stochasticity on predator-prey metapopulations are not well known. To that end, I constructed three models of a two-patch predator-prey system. The models constitute a hierarchy of complexity, allowing direct comparisons. Two models included demographic stochasticity (pure jump process [PJP] and stochastic differential equations [SDE]), and the third was deterministic (ordinary differential equations [ODE]). One stochastic model (PJP) treated population sizes as discrete, while the other (SDE) allowed population sizes to change continuously. Both stochastic models only produced synchronized predator-prey dynamics when dispersal was high for both trophic levels. Frequent dispersal by only predators or prey in the PJP and SDE spatially decoupled the trophic interaction, reducing synchrony of the non-dispersive species. Conversely, the ODE generated synchronized predator-prey dynamics across all dispersal rates, except when initial conditions produced anti-phase transients. These results indicate that demographic stochasticity strongly reduces the synchronizing effect of dispersal, which is ironic because demographic stochasticity is often invoked post hoc as a driver of extinctions in synchronized metapopulations.     

Demographic Characteristics of Extinction in a Small, Insular Population of House Sparrows in Northern Norway

Abstract:  In conservation ecology there is an urgent need for indicators that can be used to predict the risk of extinction of populations. Identifying extinction-prone populations has been difficult because few data sets on the demographic characteristics of the final stage to extinction are available and because of problems in separating out stochastic effects from changes in the expected dynamics. We documented the demographic changes that occurred during the period prior to extinction of a small island population of House Sparrows ( Passer domesticus ) after the end of permanent human settlement. A mark-recapture analysis revealed that this decline to extinction was mainly due to increased mortality after closure of the last farm that resulted in a negative long-term-specific growth rate. No change occurred in either the structural composition (breeding sex ratio and age distribution) of the population or in female recruitment. No male, however, recruits were produced on the island after the farm closure. Based on a simple, stochastic, density-dependent model we constructed a population prediction interval (PPI) to estimate the time to extinction. The 95% PPI slightly overestimated the time to extinction with large uncertainty in predictions, especially due to the influence of demographic stochasticity and parameter drift. Our results strongly emphasize the importance of access to data on temporal variation that can be used to parameterize simple population models that allow estimation of critical parameters for credible prediction of time to extinction.