A Bayesian space-time model for discrete spread processes on a lattice.

Area of Science:

• Ecology
• Epidemiology
• Computational Biology

Background:

• Environmental spread processes, such as infectious diseases and biological invasions, exhibit complex dispersal patterns.
• Understanding these patterns requires models that account for both local diffusion and long-distance dispersal mechanisms.

Purpose of the Study:

• To develop and validate a Bayesian Markov model for investigating environmental spread processes.
• To model the probabilistic function of local diffusion and random-jump dispersal in heterogeneous landscapes over time.

Main Methods:

• Formulation of a Bayesian Markov model incorporating local diffusion and random-jump dispersal.
• Demonstration of model properties through a simulation experiment.
• Application to an empirical case study: the spread of mountain pine beetle in western Canada (1999-2009).
• Inclusion of spatial covariates (elevation, forest cover) and refined jump-dispersal definition for the case study.
• Validation using posterior predictive checking.

Main Results:

• The model performed well in simulations, with goodness-of-fit statistics falling within 95% credible intervals in over 97% of cases.
• The mountain pine beetle case study showed the model's fit improved with spatial covariates and refined dispersal definitions.
• Posterior predictive checks for the beetle model indicated good fit for 8 out of 10 years.

Conclusions:

• The developed Bayesian Markov model is robust and flexible for analyzing a wide range of environmental spread processes.
• The model accurately captures the dual mechanisms of local and long-distance spread observed in epidemiology and ecology.
• The study validates the model's utility in both simulated environments and real-world ecological scenarios.