Fitting complex population models by combining particle filters with Markov chain Monte Carlo

Area of Science:

• Ecology
• Computational Statistics
• Population Dynamics

Background:

• State-space models are crucial for understanding population dynamics.
• Markov Chain Monte Carlo (MCMC) and Particle Filters (PF) are powerful but have limitations when used alone.
• Combining MCMC and PF offers a synergistic approach to model estimation.

Purpose of the Study:

• To present and exemplify the Particle Filter Markov Chain Monte Carlo (PFMCMC) framework for estimating population state-space models.
• To analyze red kangaroo (Macropus rufus) population time-series data from New South Wales, Australia.
• To compare the performance of three distinct population models: logistic diffusion, exponential growth, and random-walk.

Main Methods:

• Utilized a hybrid PFMCMC approach, leveraging particle filters for hidden state exploration and MCMC for parameter estimation.
• Employed an adaptive Metropolis-Hastings algorithm within the MCMC component.
• Fitted three population models to red kangaroo data, including density-dependent and stochastic growth models.

Main Results:

• Bayes factors and posterior model probabilities indicated minimal support for density dependence in the red kangaroo population.
• The random-walk model emerged as the most parsimonious and best-fitting model for the analyzed data.
• PFMCMC proved effective for fitting complex population models, with straightforward implementation.

Conclusions:

• The PFMCMC framework offers a robust and accessible method for fitting complex ecological models.
• For the studied red kangaroo population, environmental stochasticity and random fluctuations appear more influential than density-dependent regulation.
• Future improvements in PFMCMC efficiency can be achieved through parallelization to mitigate computational costs.