Predator-prey equations with constant harvesting and planting

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• The Lotka-Volterra model is a foundational ecological model for predator-prey interactions.
• Existing models often incorporate complex functional responses to capture population dynamics.
• The role of simple constant terms in these dynamics is less explored.

Purpose of the Study:

• To investigate the impact of small constant terms on Lotka-Volterra predator-prey equations.
• To determine if these constants can model ecological phenomena like harvesting, Allee effects, planting, or external influx.
• To compare the dynamics generated by these modified equations with those of more complex models.

Main Methods:

• Modified the standard Lotka-Volterra equations by adding small constant terms.
• Focused exclusively on the Lotka-Volterra functional responses to isolate the effect of the constants.
• Analyzed the resulting system for dynamic and static patterns.

Main Results:

• A negative constant term effectively models harvesting or the Allee effect.
• A positive constant term can represent planting or external influx.
• The modified Lotka-Volterra equations with constant terms reproduce a wide range of dynamic and static patterns observed in other complex predator-prey models.

Conclusions:

• Simple constant terms in Lotka-Volterra equations are sufficient to generate diverse ecological dynamics.
• These modified equations offer a parsimonious approach to modeling complex population interactions.
• The findings suggest that basic ecological processes can be effectively represented by simple mathematical additions.