Polymer-population mapping and localization in the space of phenotypes

Area of Science:

• Statistical mechanics
• Theoretical population dynamics
• Biophysics

Background:

• Heteropolymers exhibit phase transitions influenced by external fields.
• Population dynamics are complex, especially in fluctuating environments.
• Understanding adaptation requires modeling phenotypic variation and environmental changes.

Purpose of the Study:

• To establish a theoretical link between heteropolymer thermodynamics and population dynamics.
• To develop a path integral formulation for structured populations.
• To predict a biological phase transition analogous to heteropolymer localization.

Main Methods:

• We established a mapping between heteropolymer thermodynamics and population dynamics.
• A population model with individuals adopting different phenotypes was employed.
• A path integral formulation was developed for population dynamics.

Main Results:

• A direct correspondence was found between heteropolymer behavior and population dynamics.
• The study predicts a biological phase transition mirroring heteropolymer localization.
• The path integral formulation provides a novel tool for population modeling.

Conclusions:

• The established mapping offers a new perspective on population adaptation in fluctuating environments.
• The predicted biological phase transition has significant implications for evolutionary biology.
• This work bridges concepts from statistical physics and population genetics.