Bistability in a size-structured population model of cannibalistic fish--a continuation study

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Cannibalism is a significant factor influencing population dynamics.
• Size-structured models are crucial for understanding species with size-dependent interactions.
• Previous models often simplified the complex size-dependent nature of cannibalism.

Purpose of the Study:

• To investigate bistability in a size-structured cannibalistic fish population model.
• To explore the role of size-dependent cannibalism in population dynamics.
• To introduce a novel ecological mechanism driving population bistability.

Main Methods:

• Numerical continuation of equilibria for an infinite-dimensional dynamical system.
• Application of existing methods for physiologically structured population models.
• Analysis of size-dependent cannibalistic interactions based on length ratios.

Main Results:

• Cannibalism can induce bistability, leading to a fold (saddle-node) bifurcation.
• Two stable population states were identified: 'stunted' and 'piscivorous'.
• A new mechanism, the 'Hansel and Gretel' effect, explains bistability via size-dependent prey consumption and energy gain.

Conclusions:

• Equilibrium continuation provides deeper insights into size-structured population dynamics than simulations alone.
• The 'Hansel and Gretel' effect highlights the importance of population size distribution in ecological interactions.
• Size-dependent cannibalism can fundamentally alter population structure and stability.