Dating and localizing an invasion from post-introduction data and a coupled reaction-diffusion-absorption model.

Area of Science:

• Ecology
• Mathematical Biology
• Biomathematics

Background:

• Invasive species pose significant environmental and health risks.
• Mathematical modeling is crucial for understanding and predicting species invasions.
• Partial differential equations provide a robust framework for invasion dynamics.

Purpose of the Study:

• To develop a method for dating and localizing the introduction of invasive organisms.
• To apply a mechanistic-statistical approach to invasion analysis.
• To estimate initial conditions and model parameters for invasion dynamics.

Main Methods:

• Utilized a coupled reaction-diffusion-absorption model.
• Employed a mechanistic-statistical approach.
• Integrated Bayesian inference with an adaptive importance sampling algorithm.
• Jointly estimated initial conditions (date and site) and model parameters.

Main Results:

• Successfully applied the framework to the invasion of Xylella fastidiosa.
• Demonstrated the ability to estimate introduction date and location.
• Provided insights into the spread dynamics of the bacterium.

Conclusions:

• The developed modeling framework is effective for pinpointing invasion origins.
• This approach aids in managing and controlling invasive species.
• Accurate dating and localization are vital for effective biosecurity measures.