Modelling the dynamics of traits involved in fighting-predators-prey system.

Area of Science:

• Ecology and Evolutionary Biology
• Mathematical Biology
• Game Theory

Background:

• Predator-prey systems are fundamental to ecological dynamics.
• Intra-specific competition, such as fighting for prey, adds complexity to predator behavior.
• Understanding predator strategy evolution is crucial for predicting population dynamics.

Purpose of the Study:

• To model predator fighting behavior using hawk-dove game dynamics within a predator-prey system.
• To compare the outcomes of two adaptation models: replicator dynamics (RD) and adaptive dynamics (AD).
• To investigate how these models affect predator trait evolution and population structure.

Main Methods:

• Developed a predator-prey model incorporating continuous-time hawk-dove game dynamics for predator fighting.
• Quantified predator strategy by the proportion of individuals employing hawk tactics.
• Analyzed trait dynamics using both replicator dynamics and adaptive dynamics approaches.

Main Results:

• Both RD and AD models converge to a neutral singular strategy in equilibrium systems.
• In oscillating systems, AD can lead to a continuously evolving singular strategy, which is non-invasible.
• Predator population structure (monomorphic or dimorphic) depends on fighting costs and prey carrying capacity.

Conclusions:

• The choice of adaptation model (RD vs. AD) significantly impacts predator-prey system dynamics, especially in oscillating scenarios.
• Intra-specific trait dynamics, influenced by fighting costs, are critical for determining predator population structure (e.g., hawks vs. doves).
• This study highlights the importance of considering the nuances of evolutionary adaptation mechanisms in ecological modeling.