Phase Transition in an Exactly Solvable Extinction Model

TL;DR

This paper presents an exactly solvable model of biological evolution that exhibits a phase transition to extinction, characterized by unique critical behavior, and offers insights into fossil data trends.

Contribution

The paper introduces a novel, exactly solvable evolution model with a unique phase transition and critical exponent, enhancing understanding of extinction dynamics.

Findings

Identifies a phase transition to extinction driven by environmental stress and mutation rate.

Characterizes the critical behavior with a dynamic exponent z=1/3.

Applicable to fossil data trend analysis.

Abstract

We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective stress level is greater than their individual fitness. The model exhibits a phase transition to a completely extinct phase as the environmental stress or the mutation rate is varied. We discuss the generic conditions for which this transition is continuous. The model is exactly solvable and the critical behavior is characterized by an unusual dynamic exponent z=1/3. Apart from predicting large scale evolution, the model can be applied to understand the trends in the available fossil data.