Controlling the speed and trajectory of evolution with counterdiabatic driving


The pace and unpredictability of evolution are critically relevant in a variety of modern challenges, such as combating drug resistance in pathogens and cancer, understanding how species respond to environmental perturbations like climate change and developing artificial selection approaches for agriculture. Great progress has been made in quantitative modelling of evolution using fitness landscapes, allowing a degree of prediction for future evolutionary histories. Yet fine-grained control of the speed and distributions of these trajectories remains elusive. We propose an approach to achieve this using ideas originally developed in a completely different context—counterdiabatic driving to control the behaviour of quantum states for applications like quantum computing and manipulating ultracold atoms. Implementing these ideas for the first time in a biological context, we show how a set of external control parameters (that is, varying drug concentrations and types, temperature and nutrients) can guide the probability distribution of genotypes in a population along a specified path and time interval. This level of control, allowing empirical optimization of evolutionary speed and trajectories, has myriad potential applications, from enhancing adaptive therapies for diseases to the development of thermotolerant crops in preparation for climate change, to accelerating bioengineering methods built on evolutionary models, like directed evolution of biomolecules.

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Fig. 1: Schematic overview of counterdiabatic driving for evolutionary systems.
Fig. 2: Counterdiabatic driving results for two genotypes.
Fig. 3: CD driving eliminates evolutionary lag in a 16-genotype simulation.

Data availability

The raw numerical data for the figures in the main text and Supplementary Information, as well as the code to generate the figures, are available via GitHub at Source Data are provided with this paper.

Code availability

The code to perform the numerical simulations and the specific driving protocols is available via GitHub at


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M.H. thanks the US National Science Foundation for support through a CAREER grant (BIO/MCB 1651560). J.G.S. thanks the NIH Loan Repayment Program for their generous support and the Paul Calabresi Career Development Award for Clinical Oncology (NIH K12CA076917). S.D. acknowledges support from the US National Science Foundation under grant no. CHE-1648973. E.I. acknowledges support from Labex CelTisPhyBio (ANR-11-LABX-0038, ANR-10-IDEX-0001-02).

Author information




S.I. and J.P. performed mathematical analysis, wrote the two-allele code, peformed simulations, analysed the data and wrote the manuscript. J.C., E.I., O.G., B.K.-S. performed mathematical analysis, analysed the data and wrote the manuscript. E.D. and N.K. wrote the multidimensional ABM code, performed the simulations, analysed data and wrote the manuscript. J.G.S. analysed the data and wrote the manuscript. M.H. performed the mathematical analysis and simulations, wrote code, analysed the data and wrote the manuscript. S.D. wrote the manuscript, and S.D., E.I., J.G.S. and M.H. contributed to developing the overall theoretical framework.

Corresponding authors

Correspondence to Jacob G. Scott or Michael Hinczewski.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Ken Funo and Daniel Weinreich for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 CD driving for an altered 16-genotype pyrimethamine seascape.

This is the same seascape as in main text Fig. 3, using the experimental data of Ref. 2, except that genotype 0110 has been modified to have a 5% larger base growth rate under no drug conditions. a,b, Sample simulation trajectories (solid lines) versus IE expectation (dashed lines) for the fraction of 4 representative genotypes without a and with b CD driving. The CD driving is implemented approximately through the drug dosage protocol (green curve) shown in panel c with cutoff 10−2 M. The original protocol (blue curve) is shown for comparison. d, Kullback–Leibler divergence between actual and IE distributions versus time, with and without CD driving. Source data

Extended Data Fig. 2 CD driving for a 16-genotype cycloguanil seascape.

This is the same 16-genotype system as in the examples of main text Fig. 3 and Extended Data Fig. 1, except using the antimalarial drug cycloguanil instead of pyrimethamine. The seascape is based on the experimental data of Ref. 2, without any modifications. a,b, Sample simulation trajectories (solid lines) versus IE expectation (dashed lines) for the fraction of 4 representative genotypes without a and with b CD driving. The CD driving is implemented approximately through the drug dosage protocol (green curve) shown in panel c. The original protocol (blue curve) is shown for comparison. d, Kullback–Leibler divergence between actual and IE distributions versus time, with and without CD driving. Source data

Supplementary information

Supplementary Information

Supplementary Discussion and Figs. 1–4.

Source data

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Iram, S., Dolson, E., Chiel, J. et al. Controlling the speed and trajectory of evolution with counterdiabatic driving. Nat. Phys. (2020).

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