Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell...

Area of Science:

• Evolutionary biology
• Mathematical modeling
• Population dynamics

Background:

• Deterministic continuum models analyze asexual species adaptation to fluctuating environments.
• These models lack stochastic variability of individual evolutionary paths.
• Stochastic individual-based models are needed to capture microevolutionary processes.

Purpose of the Study:

• Develop a stochastic individual-based model for coevolving, phenotype-structured cell populations.
• Investigate the impact of phenotypic variation and environmental fluctuations on population dynamics.
• Compare predictions with deterministic continuum models.

Main Methods:

• Developed a discrete-time branching random walk for individual cell evolution.
• Modeled nutrient levels with a difference equation including a consumption sink term.
• Formally derived the deterministic continuum counterpart (nonlocal PDEs and ODE).
• Compared individual-based and continuum models under varying conditions.

Main Results:

• Identified conditions where individual-based and continuum models diverge.
• Bottleneck effects, driven by low phenotypic variation probability, cause divergence.
• Lower initial fitness and heterogeneity exacerbate bottleneck effects.
• Initial population proportions influence the emergence of these effects.

Conclusions:

• Stochastic individual-based models capture crucial adaptive phenomena missed by continuum models.
• Bottleneck effects significantly alter population dynamics and model agreement.
• Findings are relevant for understanding early metastatic colonization and other evolutionary processes.