Invasion thresholds for fungicide resistance: deterministic and stochastic analyses

Area of Science:

• Agricultural Science
• Mathematical Biology
• Ecology

Background:

• Fungicide resistance poses a significant challenge in agriculture, yet population-level understanding remains limited.
• Existing knowledge gaps hinder effective management strategies for preventing widespread resistance.
• The dynamics of host-parasite interactions and chemical control are complex and require robust modeling.

Purpose of the Study:

• To develop a mathematical model for analyzing fungicide resistance risk in botanical epidemics.
• To incorporate host-parasite dynamics, demographic stochasticity, and fungicide application parameters.
• To identify thresholds for the invasion of fungicide-resistant strains.

Main Methods:

• Introduction of a simple nonlinear model for fungicide resistance.
• Inclusion of fungicide dynamics (amount, longevity, frequency) and host population parameters.
• Analysis of demographic stochasticity in host-parasite interactions.

Main Results:

• The model reveals critical thresholds for resistant strain invasion, dependent on relative fitness and control effectiveness.
• Below the threshold, resistant strains are eliminated; above it, invasion probability increases.
• Fungicide decay rate, application amount, and frequency significantly influence control effectiveness and resistance development timelines.

Conclusions:

• The developed model provides a quantitative framework for assessing fungicide resistance risk.
• Grower-controlled parameters like fungicide application can influence resistance development.
• The model's principles are applicable to other forms of chemical resistance, including herbicides and antibiotics.