Multiple attractors in host-parasitoid interactions: coexistence and extinction

Area of Science:

• Ecology
• Population Dynamics
• Mathematical Biology

Background:

• Host-parasitoid interactions are fundamental to ecological systems.
• Discrete-time models are crucial for understanding population dynamics.
• Bistability, or multiple stable states, can significantly impact species persistence.

Purpose of the Study:

• To analyze the dynamical behavior of a two-dimensional discrete-time host-parasitoid model.
• To identify and characterize the attractors of the model.
• To investigate the prevalence and implications of bistability in host-parasitoid systems.

Main Methods:

• Development of a two-dimensional discrete-time mathematical model.
• Analysis of model attractors, including fixed points and limit cycles.
• Application of Liapunov exponent calculations to confirm stability properties.

Main Results:

• The model exhibits two distinct attractors: a stable fixed point (coexistence) and a stable boundary cycle (parasitoid absence).
• Liapunov exponent analysis confirms the presence of bistability, indicating multiple possible long-term outcomes.
• The findings suggest bistability is a common feature in host-parasitoid interactions.

Conclusions:

• Host-parasitoid systems can exhibit bistability, leading to alternative stable states.
• The absence of parasitoids can be a stable long-term outcome.
• Understanding bistability is critical for predicting the persistence and dynamics of interacting species.