Fluctuation relations and universal constraints on divisions, growth and fitness in lineage trees

We construct a pathwise formulation of a growing population of cells, based on two samplings of the lineages within the population, namely the forward and backward samplings. We show that a general symmetry relation, called fluctuation relation and similar to Crooks fluctuation theorem in Stochastic Thermodynamics,
relates these two samplings independently of the model used to generate divisions and growth in the population. This symmetry implies general
inequalities between the mean number of divisions and the growth rate of the population, and in the long time limit, between the mean generation time and the population doubling time [1,2].
This relation also leads to various universal inequalities constraining the fluctuations in lineage trees of a phenotypic trait of interest or of its fitness, which quantifies the correlations between the trait and the number of divisions.
We illustrate our results with numerical simulations of growing cell populations and with data from time-lapse video-microscopy experiments of bacteria colonies.

[1] Garcia-Garcia et al., Phys. Rev. E, 042413 (2019)
[2] A. Genthon et al., Sci. Rep. 10, 11889 (2020)