Universal constraints on selection strength in lineage trees
Abstract
We obtain general inequalities constraining the difference between the average of an arbitrary function of
a phenotypic trait, which includes the fitness landscape of the trait itself, in the presence or in the absence of
natural selection. These inequalities imply bounds on the strength of selection, which can be measured from
the statistics of trait values and divisions along lineages. The upper bound is related to recent generalizations of
linear response relations in stochastic thermodynamics, and shares common features with Fisher’s fundamental
theorem of natural selection, and with its generalization by Price, although they define different measures of
selection. The lower bound follows from recent improvements on Jensen’s inequality, and both bounds depend
on the variability of the fitness landscape. We illustrate our results using numerical simulations of growing cell
colonies and with experimental data of time-lapse microscopy experiments of bacteria cell colonies.