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.
Highlights
Quantifying the strength of selection in populations is an essential step in any description of evolution
The general idea of comparing the response of a system in the presence of a perturbation to its fluctuations in the absence of the perturbation lies at the heart of the fluctuationdissipation theorem, which has a long history in physics, with some applications to evolution [1,28]
The present framework with forward and backward dynamics can be conveniently applied to population dynamics without having to perform additional experiments, since both probabilities can be calculated with the same lineage tree
Summary
Quantifying the strength of selection in populations is an essential step in any description of evolution. An alternate method to infer selection in evolution focuses on dynamical trajectories of frequency distributions [6,7] In these works, Mustonen et al introduced the notion of fitness flux to characterize the adaptation of a population by taking inspiration from stochastic thermodynamics. Ideas from stochastic thermodynamics can be applied directly at the level of individual cell trajectories [8] By following this kind of approach, we have derived general constraints on dynamical quantities characterizing the cell cycle such as the average number of divisions or the mean generation time [9,10]. We derive universal constraints for the average value of a function of a trait, and for its selection strength, by exploiting a set of recent results known under the name of thermodynamic uncertainty relations (TUR). Several Appendices (Appendix A to G) present the details of the calculations, supplementary figures, and numerical comparisons between our results and results previously published
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