Universal constraints on selection strength in lineage trees

TL;DR

This paper derives universal inequalities that bound the strength of natural selection in lineage trees, linking statistical trait data to fundamental evolutionary principles and thermodynamics.

Contribution

It introduces general inequalities constraining selection strength based on lineage trait statistics, connecting evolutionary biology with stochastic thermodynamics.

Findings

Bounds on selection strength can be measured from lineage data.

Upper bounds relate to thermodynamic response relations.

Validated with simulations and bacterial microscopy data.

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.