Fitness is a macroscopic quantity that characterizes the potential success of a growing population of organisms and cells.

Fitness is also a major target or objective for controlling growth and expansion of pathological bacteria and tumors by perturbing properties of individual cells such as replication rate, death rate, and so on.

Better understanding of the nature of growing populations and the controllability over them requires us to clarify the relation how the fitness is determined by these single-cell or single-organism level properties.

To this end, we investigate a multi-type age-structured population model in which the inter-division interval and phenotypic states of cells are explicitly accounted.

By using a path integral formulation of the model and its contraction onto an empirical triplet over a path, we derive a response relation of the fitness to the change in the several single-cell-level parameters.

This work is an extension of our previous work with Dr. Yuki Sughiyama [1]:

[1] Y.Sughiyama, T.J. Kobayashi, et al., Pathwise thermodynamic structure in population dynamics, Phys. Rev. E. 2015.