Fitness response relation of a multi-type age-structured population dynamics

TL;DR

This paper develops a mathematical framework for multi-type age-structured populations, linking individual cell dynamics to overall population growth, and providing tools for prediction and control based on lineage data.

Contribution

It introduces a variational representation of the population growth rate and a response relation connecting lineage statistics to growth, advancing understanding of structured population dynamics.

Findings

Derived a variational formula for growth rate

Established a response relation using lineage data

Linked individual dynamics to population-level outcomes

Abstract

We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a trade-off relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the stationary population growth rate, in which statistics on a retrospective history work as the response coefficients. These results contribute to predicting and controlling growing populations based on experimentally observed cell-lineage information.