Evolution models with extremal dynamics.

Area of Science:

• Theoretical Biology
• Complex Systems
• Evolutionary Dynamics

Background:

• The Bak-Sneppen (BS) model and random replicator models are used to study biological evolution.
• These models often exhibit self-organization to a critical state under certain conditions.

Purpose of the Study:

• To reproduce and analyze the random-neighbor BS model and an analogous random replicator model.
• To investigate the impact of topology changes and speciation-extinction dynamics on self-organization.
• To determine if biological macroevolution can be characterized as a self-organized critical system.

Main Methods:

• Reproduced the random-neighbor Bak-Sneppen (BS) model.
• Developed and analyzed an analogous random replicator model, including scenarios with and without topology changes.
• Introduced a replicator model incorporating speciation to observe its effects on system dynamics.

Main Results:

• In the absence of topology changes, both BS and replicator models self-organize to a critical state.
• Species extinctions in the replicator system and vanishing species interactions in the BS model lead to a random walk, disrupting self-organization.
• A replicator model with speciation exhibited dramatic topology changes and a variety of emergent features, but rarely self-organized to a critical state.

Conclusions:

• Speciation and extinction dynamics significantly interfere with self-organization in evolutionary models.
• Biological macroevolution is unlikely to be a self-organized critical system due to the disruptive effects of speciation-extinction dynamics.