Modeling mixotroph-bacterium dynamics: Spatial homogeneity vs heterogeneity

Area of Science:

• Aquatic Ecology
• Mathematical Biology
• Microbial Ecology

Background:

• Mixotrophs, organisms capable of both photosynthesis and heterotrophy, play crucial roles in aquatic ecosystems.
• Understanding the dynamics of mixotroph-bacterium interactions is vital for comprehending nutrient cycling and food web structures in eutrophic waters.
• Previous models often simplify environmental conditions, limiting their applicability to complex, heterogeneous aquatic systems.

Purpose of the Study:

• To investigate mixotroph-bacterium interaction dynamics using two distinct mathematical models representing different aquatic environments.
• To analyze the influence of environmental factors like light availability, turbulent diffusion, and advection on population dynamics.
• To develop ecological indices for characterizing invasion potentials of mixotrophs and bacteria.

Main Methods:

• Development and analysis of a spatially homogeneous ordinary differential equation model for well-mixed aquatic environments.
• Development and analysis of a spatially heterogeneous reaction-diffusion-advection model for poorly-mixed aquatic environments.
• Investigation of model properties including dissipativity, equilibria, steady states, uniform persistence, and ecological reproductive indices.
• Numerical simulations to explore population dynamics and stability.

Main Results:

• Both models exhibit bistability, indicating multiple possible stable states for the interacting populations.
• Sufficient light availability and a high proportion of autotrophic behavior in mixotrophs promote the coexistence of mixotrophs and bacteria.
• Turbulent diffusion and advection significantly impact population dynamics in heterogeneous environments.

Conclusions:

• The study highlights the importance of environmental heterogeneity and specific biological traits (light, autotrophy) in shaping mixotroph-bacterium interactions.
• Mathematical modeling provides valuable insights into the complex dynamics governing these crucial ecological relationships.
• Findings suggest that environmental conditions favoring mixotrophic strategies can lead to stable, coexisting populations.