Assessing tiger population dynamics using photographic capture-recapture sampling

Although wide-ranging, elusive, large carnivore species, such as the tiger, are of scientific and conservation interest, rigorous inferences about their population dynamics are scarce because of methodological problems of sampling populations at the required spatial and temporal scales. We report the application of a rigorous, noninvasive method for assessing tiger population dynamics to test model-based predictions about population viability. We obtained photographic capture histories for 74 individual tigers during a nine-year study involving 5725 trap-nights of effort. These data were modeled under a likelihood-based, "robust design" capture-recapture analytic framework. We explicitly modeled and estimated ecological parameters such as time-specific abundance, density, survival, recruitment, temporary emigration, and transience, using models that incorporated effects of factors such as individual heterogeneity, trap-response, and time on probabilities of photo-capturing tigers. The model estimated a random temporary emigration parameter of gamma" = gamma' = 0.10 +/- 0.069 (values are estimated mean +/- SE). When scaled to an annual basis, tiger survival rates were estimated at S = 0.77 +/- 0.051, and the estimated probability that a newly caught animal was a transient was tau = 0.18 +/- 0.11. During the period when the sampled area was of constant size, the estimated population size N(t) varied from 17 +/- 1.7 to 31 +/- 2.1 tigers, with a geometric mean rate of annual population change estimated as lambda = 1.03 +/- 0.020, representing a 3% annual increase. The estimated recruitment of new animals, B(t), varied from 0 +/- 3.0 to 14 +/- 2.9 tigers. Population density estimates, D, ranged from 7.33 +/- 0.8 tigers/100 km2 to 21.73 +/- 1.7 tigers/100 km2 during the study. Thus, despite substantial annual losses and temporal variation in recruitment, the tiger density remained at relatively high levels in Nagarahole. Our results are consistent with the hypothesis that protected wild tiger populations can remain healthy despite heavy mortalities because of their inherently high reproductive potential. The ability to model the entire photographic capture history data set and incorporate reduced-parameter models led to estimates of mean annual population change that were sufficiently precise to be useful. This efficient, noninvasive sampling approach can be used to rigorously investigate the population dynamics of tigers and other elusive, rare, wide-ranging animal species in which individuals can be identified from photographs or other means.     

Sensitivity analysis of North American bird population estimates

The Partners in Flight North American Landbird Conservation Plan provided estimates of population sizes for 448 landbird species using a multiplicative model. Input parameters in this calculation included the area of state × Bird Conservation Region polygons, area-specific mean Breeding Bird Survey counts circa 1995, and adjustment factors for the distance over which species may presumably be correctly counted, the assumed pairing of singing males with non-singing females, and variability in the propensity of birds to sing over the course of the survey day. I assessed the sensitivity of this population calculation to changes in the input parameters. I assessed both local and global sensitivity of the model to changes in the parameters with Monte Carlo one-at-a-time simulations and the Fourier amplitude sensitivity test (FAST). Monte Carlo simulations were an estimate of local model sensitivity whereas FAST estimated global model sensitivity, accommodating the potential shared variance between model parameters. Monte Carlo simulations suggested population estimates were 39% more sensitive to changes in the detection distance adjustment than to the other parameters; the other parameters were nearly equal in their contribution to model sensitivity. Conversely, FAST analysis determined that each of the input variables aside from the pair adjustment provided roughly equal contributions to variability in population estimates. The most efficient means for improving continental population estimates for birds surveyed by the Breeding Bird Survey will be through increased scrutiny of the species-specific distance detection and time-of-day adjustments and improved understanding in the spatial and temporal variability in the mean Breeding Bird Survey count.     

A comparison of sensitivity analysis and error analysis based on a stream ecosystem model

When individual model parameters must be measured in field or laboratory experiments, the provision of feedback information for allocation of research efforts is an important function of modeling. Both sensitivity analysis and Monte Carlo error analysis can be used to determine which parameters require intensified measurement effort. When both methods are applied to a stream ecosystem model, the assumptions of sensitivity analysis are violated if reasonable estimates of measurement errors on parameters are used. Sensitivity analysis estimates a linear relationship between a state variable and a parameter and largely ignores higher order effects.In the model investigated in this study, higher-order effects dominate prediction error, and the results of sensitivity analysis are misleading. It is suggested that the simple correlation coefficient derived from analysis of Monte Carlo simulations is a more reasonable way to rank model parameters according to their contribution to prediction uncertainty. For the stream model used in this study, halving variance on the four parameters, indicated as most important by sensitivity analysis, reduces prediction errors by only 2–6%. Halving variance on the four, completely different, parameters with the largest simple correlation coefficients reduces prediction errors by 17–31%.     

On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

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

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

Determining patterns of variability in ecological communities: time lag analysis revisited

All ecological communities experience change over time. One method to quantify temporal variation in the patterns of relative abundance of communities is time lag analysis (TLA). It uses a distance-based approach to study temporal community dynamics by regressing community dissimilarity over increasing time lags (one-unit lags, two-unit lags, three-unit lags). Here, we suggest some modifications to the method and revaluate its potential for detecting patterns of community change. We apply Hellinger distance based TLA to artificial data simulating communities with different levels of directional and stochastic dynamics and analyse their effects on the slope and its statistical significance. We conclude that statistical significance of the TLA slope (obtained by a Monte Carlo permutation procedure) is a valid criterion to discriminate between (i) communities with directional change in species composition, regardless whether it is caused by directional abundance change of the species or by stochastic change according to a Markov process, and (ii) communities that are composed of species with population sizes oscillating around a constant mean or communities whose species abundances are governed by a white noise process. TLA slopes range between 0.02 and 0.25, depending on the proportions of species with different dynamics; higher proportions of species with constant means imply shallower slopes; and higher proportions of species with stochastic dynamics or directional change imply steeper slopes. These values are broadly in line with TLA slopes from real world data. Caution must be exercised when TLA is used for the comparison of community time series with different lengths since the slope depends on time series length and tends to decrease non-linearly with it.     

Uncertainty analyses for calibrating a soil carbon balance model to agricultural field trial data in Sweden and Kenya

How do additional data of the same and/or different type contribute to reducing model parameter and predictive uncertainties? Most modeling applications of soil organic carbon (SOC) time series in agricultural field trial datasets have been conducted without accounting for model parameter uncertainty. There have been recent advances with Monte Carlo-based uncertainty analyses in the field of hydrological modeling that are applicable, relevant and potentially valuable in modeling the dynamics of SOC. Here we employed a Monte Carlo method with threshold screening known as Generalized Likelihood Uncertainty Estimation (GLUE) to calibrate the Introductory Carbon Balance Model (ICBM) to long-term field trail data from Ultuna, Sweden and Machang’a, Kenya. Calibration results are presented in terms of parameter distributions and credibility bands on time series simulations for a number of case studies. Using these methods, we demonstrate that widely uncertain model parameters, as well as strong covariance between inert pool size and rate constant parameters, exist when root mean square simulation errors were within uncertainties in input estimations and data observations. We show that even rough estimates of the inert pool (perhaps from chemical analysis) can be quite valuable to reduce uncertainties in model parameters. In fact, such estimates were more effective at reducing parameter and predictive uncertainty than an additional 16 years time series data at Ultuna. We also demonstrate an effective method to jointly, simultaneously and in principle more robustly calibrate model parameters to multiple datasets across different climatic regions within an uncertainty framework. These methods and approaches should have benefits for use with other SOC models and datasets as well.     

Assessing plausible rates of population growth in humpback whales from life-history data

The rate of growth of any population is a quantity of interest in conservation and management and is constrained by biological factors. In this study, recent data on life-history parameters influencing rates of population growth in humpback whales, including survival, age at first parturition and calving rate are reviewed. Monte Carlo simulations are used to compute a distribution of rates of increase (ROIs) taking into account uncertainty in biological parameter estimates. Two approaches for computing juvenile survival are proposed, which taken into account along with other life-history data, resulted in the following estimates of the rate of population growth: Approach A: mean of 7.3%/year (95% CI = 3.5–10.5%/year) and Approach B: mean of 8.6%/year (95% CI = 5.0–11.4%/year). It is proposed that the upper 99% quantile of the resulting distribution of the ROI for Approach B (11.8%/year) be established as the maximum plausible ROI for humpback whales and be used in population assessment of the species. Possible sources of positive and negative biases in the present estimates are presented and include measurement error in estimation of life-history parameters, changes in the environment within the period these quantities are measured, density dependence or other natural factors. However, it is difficult to evaluate potential biases without additional data. The methods presented in this study can be applied to other species for which life-history parameters are available and are useful in assessing plausibility in the estimation of population growth rates from time series of abundance estimates.     

Cross-correlation bias in lag analysis of aquatic time series

Cross-correlation analysis is the most valuable and widely used statistical tool for evaluating the strength and direction of time-lagged relationships between ecological variables. Although it is well understood that temporal autocorrelation can inflate estimates of cross correlations and cause high rates of incorrectly concluding that lags exist among time series (i.e. type I error), in this study we show that a problem we term intra-multiplicity can cause substantial bias in cross-correlation analysis even in the absence of autocorrelation. Intra-multiplicity refers to the numerous time lags examined and cross-correlation coefficients computed within a pair of time series during cross-correlation analysis. We show using Monte Carlo simulations that intra-multiplicity can spuriously inflate estimates of cross correlations by identifying incorrect time lags. Further, unlike autocorrelation, which generally identifies lags close to the true lag, intra-multiplicity can erroneously identify lags anywhere in the time series and commonly results in a direction change of the correlation (i.e. positive or negative). Using Monte Carlo simulations we develop formulas that quantify the bias introduced by intra-multiplicity as a function of sample size, true cross correlation between the series, and the number of time lags examined. A priori these formulas enable researchers to determine the sample size needed to minimize the biases introduced by intra-multiplicity. A posteriori the formulas can be used to predict the expected bias and type I error rate associated with the data at hand, as well as the maximum number of time lags that can be analyzed to minimize the effects of intra-multiplicity. We examine the relationship between commercial catch of chum salmon and surface temperatures of the North Pacific (1925–1992) to illustrate the problems of intra-multiplicity in fisheries studies and the application of our formulas. These analyses provide a more robust framework to assess the temporal relationships between ecological variables. Received: 28 July 2000 / Accepted: 6 December 2000     

Adjusting age and stage distributions for misclassification errors

Ecologists often use samples from the age or stage structure of a population to make inferences about population-level processes and to parameterize matrix models. Typically, researchers make a simplifying assumption that age and stage classes are determined without error, when in fact some level of misclassification often can be expected. If unaccounted for, misclassification will lead to overly optimistic levels of precision and can cause biased estimates of age or stage structure. Although several studies have used information from known-age individuals to quantify errors in age or stage distribution, the problem of estimating the age or stage structure in face of such errors has received comparably little attention. In this paper, we describe a general statistical framework for estimating the true stage distribution of a sample when misclassification rates can be estimated. The estimation process requires auxiliary information on misclassification rates, such as data from individuals of known age. We analyze age-structured harvest records from black bears in Pennsylvania to illustrate how incorporating misclassification errors leads to changes in point estimates and provides a measure of precision.     

An Age-Structured Demographic Model for the Endangered Stephens' Kangaroo Rat

Effective conservation of endangered species often is hampered by inadequate knowledge of demography. We extracted information on survival and fecundity from an 18-month, live-trapping study of Dipodomys stephensi , and from this we developed an age-structured demographic model to assess population viability. Adult Stephens' kangaroo rats persisted longer than juveniles, and adult females persisted longer than adult males. Disappearance rates were high in the first months after initial capture. Thereafter, the fraction of animals persisting decreased slowly and in an approximately linear fashion on a semilogarithmic scale, suggesting age-independent mortality factors such as predation. Juvenile persistence did not differ substantially between two years of strikingly different rainfall. Onset of breeding followed the start of winter rains. Length of the breeding season, average number of litters per female, and the fraction of first-year females breeding were much greater in the year of higher rainfall. We propose a birth-pulse demographic model for D. stephensi that distinguishes juvenile and adult age classes. Temporal environmental variation can be modeled adequately with a constant survivorship schedule and variable fecundity determined by yearly precipitation. Several issues should be resolved, however, before conservation decisions are based on the model. Better estimates of juvenile survivorship are critical, the quantitative relationship between precipitation and fecundity must be determined, and the potential for density dependence and source-sink population dynamics must be evaluated.     

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.     

Designs with a priori information for nonmarket valuation with choice experiments: A Monte Carlo study

Good practice in experimental design is essential for choice experiments used in nonmarket valuation. We review the practice of experimental design for choice experiments in environmental economics and we compare it with advances in experimental design. We then evaluate the statistical efficiency of four different designs by means of Monte Carlo experiments. Correct and incorrect specifications are investigated with gradually more precise information on the true parameter values. The data generating process (DGP) is based on estimates from data of a real study. Results indicate that D-efficient designs are promising, especially when based on Bayesian algorithms with informative prior. However, if good quality a priori information is lacking, and if there is strong uncertainty about the real DGP—conditions which are quite common in environmental valuation—then practitioners might be better off with shifted designs built from conventional fractional factorial designs for linear models.     

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

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

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

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

Random versus stratified location of transects or points in distance sampling: theoretical results and practical considerations

A composite approach mixing design-based and model-based inference is considered for analyzing line-transect or point-transect data. In this setting, the properties of the animal abundance estimator stem from the sampling scheme adopted to locate transects or points on the study region, as well as from the modeled detection probabilities. Moreover, the abundance estimation can be viewed as a “generalized” version of Monte Carlo integration. This approach permits to prove the superiority of the stratified placement of transects or points (based on a regular tessellation of the study region) over the uniform random placement. Even if the result was already established for the fixed-area sampling, i.e., when a perfect detection takes place, it was lacking in distance sampling. Comparisons with other widely-applied schemes pursuing an even placement of transects or points are also considered.     

State-specific detection probabilities and disease prevalence.

Investigations of disease dynamics in wild animal populations often use estimated prevalence or incidence as a measure of true disease frequency. Such indices, almost always based solely on raw counts of infected and uninfected individuals, are often used as the basis for analysis of temporal and spatial dynamics of diseases. Generally, such studies do not account for potential differences in observer detection probabilities of host individuals stratified by biotic and/or abiotic factors. We demonstrate the potential effects of heterogeneity in state-specific detection probabilities on estimated disease prevalence using mark-recapture data from previous work in a House Finch (Carpodacus mexicanus) and Mycoplasma gallisepticum system. In this system, detection probabilities of uninfected finches were generally higher than infected individuals. We show that the magnitude and seasonal pattern of variation in estimated prevalence, corrected for differences in detection probabilities, differed markedly from uncorrected (apparent) prevalence. When the detection probability of uninfected individuals is higher than infected individuals (as in our study), apparent prevalence is negatively biased, and vice versa. In situations where state-specific detection probabilities strongly interact over time, we show that the magnitude and pattern of apparent prevalence can change dramatically; in such cases, observed variations in prevalence may be completely spurious artifacts of variation in detection probability, rather than changes in underlying disease dynamics. Accounting for differential detection probabilities in estimates of disease frequency removes a potentially confounding factor in studies seeking to identify biotic and/or abiotic drivers of disease dynamics. Given that detection probabilities of different groups of individuals are likely to change temporally and spatially in most field studies, our results underscore the importance of estimating and incorporating detection probabilities in estimated disease prevalence (specifically), and more generally, any ecological index used to estimate some parameter of interest. While a mark-recapture approach makes it possible to estimate detection probabilities, it is not always practical, especially at large scales. We discuss several alternative approaches and categorize the assumptions under which analysis of uncorrected prevalence may be acceptable.     

Comparing model averaging with other model selection strategies for benchmark dose estimation

Model averaging (MA) has been proposed as a method of accommodating model uncertainty when estimating risk. Although the use of MA is inherently appealing, little is known about its performance using general modeling conditions. We investigate the use of MA for estimating excess risk using a Monte Carlo simulation. Dichotomous response data are simulated under various assumed underlying dose–response curves, and nine dose–response models (from the USEPA Benchmark dose model suite) are fit to obtain both model specific and MA risk estimates. The benchmark dose estimates (BMDs) from the MA method, as well as estimates from other commonly selected models, e.g., best fitting model or the model resulting in the smallest BMD, are compared to the true benchmark dose value to better understand both bias and coverage behavior in the estimation procedure. The MA method has a small bias when estimating the BMD that is similar to the bias of BMD estimates derived from the assumed model. Further, when a broader range of models are included in the family of models considered in the MA process, the lower bound estimate provided coverage close to the nominal level, which is superior to the other strategies considered. This approach provides an alternative method for risk managers to estimate risk while incorporating model uncertainty.

Are network indices robust indicators of food web functioning? A Monte Carlo approach

Indices based on network theory are often used to describe food web functioning. These indices take as input food web flows that are estimated based on merging of (scarce) data with linear inverse methods (LIMs). Due to under sampling, most food webs are highly uncertain and can only be quantified within a specific uncertainty range. The linear inverse method (LIM) can estimate food web flows using a variety of techniques, e.g. the parsimonious or minimum norm (MN) solution, which selects one food web, based on a quadratic minimization technique or the Monte Carlo solution where a finitely many random solutions are generated which are then averaged. We use the Monte Carlo approach (MCA) to estimate the values of several indices from four published food webs, the Gulf of Riga for the autumn, summer and spring seasons, and the Takapoto atoll system. We first show that network indices are much better constrained than the uncertain food webs from which they are calculated. Therefore, even in the face of food web uncertainty, they are robust estimators of food web functioning. We then use the MCA-derived network indices to generate cumulative density functions for each index. These serve to compute the probabilities of the MN indices estimates being an extreme solution as compared to the median values. Our findings show that 82% of the MN solutions are smaller than the MCA solutions, and 63% of the network indices are significantly under-estimated.     

Population growth in snow geese: a modeling approach integrating demographic and survey information

There are few analytic tools available to formally integrate information coming from population surveys and demographic studies. The Kalman filter is a procedure that facilitates such integration. Based on a state-space model, we can obtain a likelihood function for the survey data using a Kalman filter, which we may then combine with a likelihood for the demographic data. In this paper, we used this combined approach to analyze the population dynamics of a hunted species, the Greater Snow Goose (Chen caerulescens atlantica), and to examine the extent to which it can improve previous demographic population models. The state equation of the state-space model was a matrix population model with fecundity and regression parameters relating adult survival and harvest rate estimated in a previous capture-recapture study. The observation equation combined the output from this model with estimates from an annual spring photographic survey of the population. The maximum likelihood estimates of the regression parameters from the combined analysis differed little from the values of the original capture-recapture analysis, though their precision improved. The model output was found to be insensitive to a wide range of coefficient of variation (CV) in fecundity parameters. We found a close match between the surveyed and smoothed population size estimates generated by the Kalman filter over an 18-year period, and the estimated CV of the survey (0.078-0.150) was quite compatible with its assumed value (approximately 0.10). When we used the updated parameter values to predict future population size, the model underestimated the surveyed population size by 18% over a three-year period. However, this could be explained by a concurrent change in the survey method. We conclude that the Kalman filter is a promising approach to forecast population change because it incorporates survey information in a formal way compared with ad hoc approaches that either neglect this information or require some parameter or model tuning.