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.     

Dynamics of a low‐density tiger population in Southeast Asia in the context of improved law enforcement

Recovering small populations of threatened species is an important global conservation strategy. Monitoring the anticipated recovery, however, often relies on uncertain abundance indices rather than on rigorous demographic estimates. To counter the severe threat from poaching of wild tigers (Panthera tigris), the Government of Thailand established an intensive patrolling system in 2005 to protect and recover its largest source population in Huai Kha Khaeng Wildlife Sanctuary. Concurrently, we assessed the dynamics of this tiger population over the next 8 years with rigorous photographic capture‐recapture methods. From 2006 to 2012, we sampled across 624–1026 km² with 137–200 camera traps. Cameras deployed for 21,359 trap days yielded photographic records of 90 distinct individuals. We used closed model Bayesian spatial capture‐recapture methods to estimate tiger abundances annually. Abundance estimates were integrated with likelihood‐based open model analyses to estimate rates of annual and overall rates of survival, recruitment, and changes in abundance. Estimates of demographic parameters fluctuated widely: annual density ranged from 1.25 to 2.01 tigers/100 km², abundance from 35 to 58 tigers, survival from 79.6% to 95.5%, and annual recruitment from 0 to 25 tigers. The number of distinct individuals photographed demonstrates the value of photographic capture–recapture methods for assessments of population dynamics in rare and elusive species that are identifiable from natural markings. Possibly because of poaching pressure, overall tiger densities at Huai Kha Khaeng were 82–90% lower than in ecologically comparable sites in India. However, intensified patrolling after 2006 appeared to reduce poaching and was correlated with marginal improvement in tiger survival and recruitment. Our results suggest that population recovery of low‐density tiger populations may be slower than anticipated by current global strategies aimed at doubling the number of wild tigers in a decade.