Probability, Parameters, and Duration of Immigration and Extinction in Microbial Communities

Area of Science:

• Microbial Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Estimating microbial immigration and extinction is crucial for understanding community stability.
• Existing models often lack simple, mechanistic frameworks for these processes.

Purpose of the Study:

• To develop simple equations for estimating microbial immigration and extinction probabilities and durations.
• To apply these equations to various ecological and pathogenic scenarios.

Main Methods:

• Utilized the gambler's ruin equation to model population abundance changes.
• Estimated immigration (m) and death-to-birth ratios (q/p) from empirical data.
• Applied models to Vibrio cholerae infections and wastewater treatment plant microbial communities.

Main Results:

• Demonstrated the gambler's ruin equation's utility in predicting microbial population dynamics.
• Calculated a low probability (10^-43) for a specific bacterial inoculum to reach high abundance.
• Showed that stable microbial communities have a long-term average q/p ratio near 1, with q/p ≥1 leading to extinction without migration.

Conclusions:

• Simple mechanistic models based on the gambler's ruin equation can accurately estimate microbial immigration and extinction.
• These models have practical applications in bioaugmentation, infection dynamics, and microbial community management.
• Extinction in stable microbial communities (q/p ≥1) is probable without migration, with long durations required for even small populations.