Long-time behavior and Darwinian optimality for an asymmetric size-structured branching process

Area of Science:

• Mathematical Biology
• Dynamical Systems
• Population Dynamics

Background:

• Cellular processes involve growth and division, influencing population dynamics.
• Asymmetry in cell division (physiological and morphological) is a key biological factor.
• Understanding long-term population behavior requires advanced mathematical modeling.

Purpose of the Study:

• To analyze the long-term behavior of an asymmetric size-structured branching process.
• To investigate Malthusian growth and trait distribution convergence in cell populations.
• To explore the impact of asymmetry on population growth rates and evolutionary fitness.

Main Methods:

• Developed an asymmetric size-structured measure-valued growth-fragmentation branching process model.
• Employed generalized Lyapunov function techniques for non-conservative semi-groups.
• Analyzed fluctuations in growth rate concerning asymmetry parameters.

Main Results:

• Demonstrated exponential population size growth (Malthusian behavior).
• Showed convergence of individual trait distributions to a stable state.
• Identified that symmetric division can be sub-optimal in a Darwinian sense under specific conditions.

Conclusions:

• The studied branching process exhibits predictable long-term population dynamics.
• Asymmetry in cell division plays a crucial role in population growth and evolutionary strategy.
• Mathematical frameworks can reveal evolutionary advantages of biological processes like asymmetric division.