Emerging diversity in a population of evolving intransitive dice

Area of Science:

• Theoretical Biology
• Evolutionary Dynamics
• Mathematical Modeling

Background:

• Intransitive dice provide a novel mathematical framework for studying complex systems.
• Understanding the emergence of species diversity and coevolutionary dynamics is a key challenge in biology.

Purpose of the Study:

• To develop a theoretical model for coevolution inspired by intransitive dice.
• To investigate the relationship between genome dynamics, competitive advantage, and species diversity.
• To explore the emergence of sympatric speciation within a closed system.

Main Methods:

• A theoretical model simulating evolving agents with genomes interpreted as dice.
• Analysis of competitive interactions and mutation dynamics within a closed system.
• Investigation of free mutations in both genomes and mutation rates.

Main Results:

• The model demonstrates sympatric speciation, where new species arise within existing populations.
• A metastable state emerged, characterized by finite mutation rates and stable species diversity.
• Competitive advantage and mutation dynamics were shown to arise directly from the genome structure.

Conclusions:

• The intransitive dice model offers a new perspective on coevolutionary processes and species diversification.
• The findings suggest that complex evolutionary patterns can emerge from simple, non-hierarchical rules.
• The study highlights the potential for stable coexistence of mutation and diversity in evolutionary systems.