Emerging Diversity in a Population of Evolving Intransitive Dice

TL;DR

This paper introduces a theoretical model of co-evolution using intransitive dice, demonstrating how species diversity and sympatric speciation can emerge from competitive interactions and mutations.

Contribution

It presents a novel intransitive dice-based model capturing co-evolution dynamics and species diversity emergence in a closed ecosystem.

Findings

Emergence of a metastable state with finite mutation rate and diversity.

Sympatric speciation occurs from existing species in contact.

Diversity persists under free mutation rates.

Abstract

Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a set of evolving agents that interact competitively in a closed system, in which both the dynamics of mutations and competitive advantage emerge directly from interpreting a genome as the sides of a die. The model demonstrates sympatric speciation where new species evolve from existing ones while in contact with the entire ecosystem. Allowing free mutations both in the genomes and the mutation rates, we find, in contrast to hierarchical models of fitness, the emergence of a metastable state of finite mutation rate and diversity.