We describe a discrete-time, stochastic population model with density dependence, environmental-type process noise, and lognormal observation or sampling error. The model, a stochastic version of the Gompertz model, can be transformed into a linear Gaussian state-space model (Kalman filter) for convenient fitting to time series data. The model has a multivariate normal likelihood function and is simple enough for a variety of uses ranging from theoretical study of parameter estimation issues to routine data analyses in population monitoring. A special case of the model is the discrete-time, stochastic exponential growth model (density independence) with environmental-type process error and lognormal observation error.We describe two methods for estimating parameters in the Gompertz state-space model, and we compare the statistical qualities of the methods with computer simulations. The methods are maximum likelihood based on observations and restricted maximum likelihood based on first differences. Both offer adequate statistical properties. Because the likelihood function is identical to a repeated-measures analysis of variance model with a random time effect, parameter estimates can be calculated using PROC MIXED of SAS.We use the model to analyze a data set from the Breeding Bird Survey. The fitted model suggests that over 70% of the noise in the population's growth rate is due to observation error. The model describes the autocovariance properties of the data especially well.While observation error and process noise variance parameters can both be estimated from one time series, multimodal likelihood functions can and do occur. For data arising from the model, the statistically consistent parameter estimates do not necessarily correspond to the global maximum in the likelihood function. Maximization, simulation, and bootstrapping programs must accommodate the phenomenon of multimodal likelihood functions to produce statistically valid results.

Time series of population abundance estimates often are the only data available for evaluating the prospects for persistence of a species of concern. With such data, it is possible to perform a population viability analysis (PVA) with diffusion approximation methods using estimates of the mean population trend and the variance of the trend, the so‐called process variation. Sampling error in the data, however, may bias estimators of process variation derived by simple methods. We develop a restricted maximum likelihood (REML)‐based method for estimating trend, process variation, and sampling error from a single time series based on a discrete‐time model of density‐independent growth coupled with a model of the sampling process. Transformation of the data yields a conventional linear mixed model, in which the variance components are functions of the process variation and sampling error. Simulation results show essentially unbiased estimators of trend, process variation, and sampling error over a range of process variation/sampling error combinations. Example data analyses are provided for the Whooping Crane (Grus americana), grizzly bear (Ursus arctos horribilis), California Condor (Gymnogyps californianus), and Puerto Rican Parrot (Amazona vittata). This REML‐based method is useful for PVA methods that depend on accurate estimation of process variation from time‐series data.

Despite the widespread use of redd counts to monitor trends in salmonid populations, few studies have evaluated the uncertainties in observed counts. We assessed the variability in redd counts for migratory bull trout Salvelinus confluentus among experienced observers in Lion and Goat creeks, which are tributaries to the Swan River, Montana. We documented substantially lower observer variability in bull trout redd counts than did previous studies. Observer counts ranged from 78% to 107% of our best estimates of true redd numbers in Lion Creek and from 90% to 130% of our best estimates in Goat Creek. Observers made both errors of omission and errors of false identification, and we modeled this combination by use of a binomial probability of detection and a Poisson count distribution of false identifications. Redd detection probabilities were high (mean ¼ 83%) and exhibited no significant variation among observers (SD ¼ 8%). We applied this error structure to annual redd counts in the Swan River basin to correct for observer error and thus derived more accurate estimates of redd numbers and associated confidence intervals. Our results indicate that bias in redd counts can be reduced if experienced observers are used to conduct annual redd counts. Future studies should assess both sources of observer error to increase the validity of using redd counts for inferring true redd numbers in different basins. This information will help fisheries biologists to more precisely monitor population trends, identify recovery and extinction thresholds for conservation and recovery programs, ascertain and predict how management actions influence distribution and abundance, and examine effects of recovery and restoration activities.

The risk of mercury (Hg) exposure to humans and wildlife from fish consumption has driven extensive mercury analysis throughout the Great Lakes Region since the 1970s. This study compiled fish-Hg data from multiple sources in the region and assessed spatiotemporal trends of Hg concentrations in two representative top predator fish species. Walleye (Sander vitreus) and largemouth bass (Micropterus salmoides) were chosen for the trend analysis because they had more Hg records (63,872) than other fish species that had been sampled from waters throughout the region. Waterbody types were inland lakes (70%), the Great Lakes, impoundments, and rivers. The compiled datasets were analyzed with a mixed effects statistical model having random effects of station, year, and fish length; and fixed effects of year, tissue type, fish length, habitat, and season. The results showed a generally declining temporal trend in fish-Hg for the region (1970-2009), with spatial trends of increasing Hg concentration from south to north and from west to east across the region. Nonlinearity was evident in the general downward trends of Ontario walleye, with a shift to an upward trend beginning in the 1990s. Only ongoing monitoring can reveal if this upward shift is an oscillation in a long-term decline, a statistical anomaly, or a sustained declining temporal trend in regional fish-Hg concentrations.

We describe risk-based viable population monitoring, in which the monitoring indicator is a yearly prediction of the probability that, within a given timeframe, the population abundance will decline below a prespecified level. Common abundance-based monitoring strategies usually have low power to detect declines in threatened and endangered species and are largely reactive to declines. Comparisons of the population's estimated risk of decline over time will help determine status in a more defensible manner than current monitoring methods. Monitoring risk is a more proactive approach; critical changes in the population's status are more likely to be demonstrated before a devastating decline than with abundance-based monitoring methods. In this framework, recovery is defined not as a single evaluation of long-term viability but as maintaining low risk of decline for the next several generations. Effects of errors in risk prediction techniques are mitigated through shorter prediction intervals, setting threshold abundances near current abundance, and explicitly incorporating uncertainty in risk estimates. Viable population monitoring also intrinsically adjusts monitoring effort relative to the population's true status and exhibits considerable robustness to model misspecification. We present simulations showing that risk predictions made with a simple exponential growth model can be effective monitoring indicators for population dynamics ranging from random walk to density dependence with stable, decreasing, or increasing equilibrium. In analyses of time-series data for five species, risk-based monitoring warned of future declines and demonstrated secure status more effectively than statistical tests for trend.Resumen: Describimos el monitoreo de poblaciones viables basado en riesgos, en el que el indicador del monitoreo es la probabilidad de que la abundancia de la población decline, en un período de tiempo determinado, por debajo de un nivel predefinido. Las estrategias comunes de monitoreo basadas en la abundancia generalmente tienen poco poder para detectar declinaciones de especies amenazadas y en peligro y son ampliamente reactivas a las declinaciones. Las comparaciones del riesgo de declinación estimado a lo largo del tiempo ayudarán a determinar el estatus de una manera más defendible que con los métodos de monitoreo actuales. El monitoreo de riesgo es un método más preventivo; es más probable que los cambios críticos en el estatus de una población sean evidentes antes de una declinación devastadora que con métodos de monitoreo basados en la abundancia. En este marco, la recuperación está definida como el mantenimiento de un bajo riesgo de declinación para varias generaciones futuras y no solo como una evaluación de la viabilidad a largo plazo. Los efectos de los errores de las técnicas de predicción de riesgos son mitigados mediante intervalos de predicción más cortos, el ajuste de umbrales de abundancia cerca de la abundancia actual y la incorporación explícita de la incertidumbre en las estimaciones de ri...