A comparison of state-space approaches for population viability analysis with short time series

Background/Question/Methods

Population viability analysis (PVA) tools are critically important component of status assessments for endangered and threatened species, as exemplified by the revised IUCN Red List criteria. Unfortunately, census data on endangered species are often plagued by problems that make quantitative assessments a challenge, such as short time series, unknown sampling error, and unknown density-dependence. State-space models can explicitly account for population dynamics, process error and sampling error, and are thus an ideal modeling approach for PVA. However, such models often perform poorly with short time series because of complex and multi-modal likelihood surfaces. To deal with this problem we developed a Bayesian Kalman filter using sampling importance re-sampling. We compared the performance of this Bayesian Kalman method with two other state-space estimation techniques: 1) Kalman MLE: maximum likelihood estimates using a Kalman filter, and 2) Cloning MLE: maximum likelihood estimates using the recently developed ‘data-cloning’ method.

Results/Conclusions

 All three methods were unbiased based on fits to 1,000 artificial data sets. However, the Kalman MLE process variance and observation variance were often alternatively estimated at ~0 for short time series’ of data. Both the Cloning MLE and Bayesian Kalman methods avoided the 0-error problem, and thus provided more accurate estimates of extinction risk. Unlike the Cloning MLE method, the Bayesian Kalman method required the specification of prior distributions for parameters, which may be subjective in practice. On the other hand, the Bayesian Kalman method gave explicit descriptions of parameter uncertainty that were easily translated into confidence intervals for extinction risk estimates, an important but typically overlooked component of PVA.  Given that PVA models are often confronted with short time series data, methods for fitting state-space models that are robust to limited data, such as the Cloning MLE and Bayesian Kalman methods, would undoubtedly improve PVA risk estimates.