Metabolic trade-offs and the maintenance of the fittest and the flattest

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How is diversity maintained? Environmental heterogeneity is considered to be important1, yet diversity in seemingly homogeneous environments is nonetheless observed2. This, it is assumed, must either be owing to weak selection, mutational input or a fitness advantage to genotypes when rare1. Here we demonstrate the possibility of a new general mechanism of stable diversity maintenance, one that stems from metabolic and physiological trade-offs3. The model requires that such trade-offs translate into a fitness landscape in which the most fit has unfit near-mutational neighbours, and a lower fitness peak also exists that is more mutationally robust. The ‘survival of the fittest’ applies at low mutation rates, giving way to ‘survival of the flattest’4, 5, 6 at high mutation rates. However, as a consequence of quasispecies-level negative frequency-dependent selection and differences in mutational robustness we observe a transition zone in which both fittest and flattest coexist. Although diversity maintenance is possible for simple organisms in simple environments, the more trade-offs there are, the wider the maintenance zone becomes. The principle may be applied to lineages within a species or species within a community, potentially explaining why competitive exclusion need not be observed in homogeneous environments. This principle predicts the enigmatic richness of metabolic strategies in clonal bacteria7 and questions the safety of lethal mutagenesis8, 9 as an antimicrobial treatment.

At a glance


  1. Maintenance of the fittest and flattest with known parameter values.
    Figure 1: Maintenance of the fittest and flattest with known parameter values.

    a, Using a parameterization of the MSC equation with rate-affinity and rate-yield trade-off data from empirical studies of S.cerevisiae (see Supplementary Fig. 5), the diagram shows the locus of steady-state densities for different mutation rates. b, The cited multimodality index is the ratio of biomass supported under each quasispecies. c, Normal distributions have been fitted to each quasispecies to provide a guide.

  2. The maintenance of the fittest and the flattest is not a simple mutation-selection equilibrium.
    Figure 2: The maintenance of the fittest and the flattest is not a simple mutation–selection equilibrium.

    A single type (number 25) seeded a clonal population subject to rate-yield and rate-affinity trade-offs that diverged into two lineages of quasispecies of efficient and inefficient generalists. For the trade-offs see Supplementary Fig. 17; for further details see Supplementary Information section 7.3.

  3. Quasispecies negative frequency-dependent selection.
    Figure 3: Quasispecies negative frequency-dependent selection.

    a, Sugar dynamics after altering cloud frequencies. The MSC equation maintains distinct quasispecies though negative frequency-dependent selection mediated by the abiotic environment. Shown are typical responses in resource concentration resulting from changes in the frequency of fit quasispecies (high uptake) and flat quasispecies (high yield). Removing ‘fit cells’ momentarily decreases sugar concentration; removing ‘flat cells’ increases it. b, This results in negative frequency dependence at the level of quasispecies. Ten tests of the MSC model for negative frequency dependence are shown. For trade-offs see Supplementary Fig. 8b. The grey line indicates the line of equal fitness.


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Author information

  1. These authors contributed equally to this work.

    • Robert E. Beardmore &
    • Ivana Gudelj


  1. Department of Mathematics, Imperial College London, Huxley Building, 180 Queen’s Gate, London SW7 2A7, UK

    • Robert E. Beardmore &
    • Ivana Gudelj
  2. Department of Biology, San Diego State University, San Diego, California 92182-4614, USA

    • David A. Lipson
  3. Department of Biochemistry and Biology, University of Bath, Claverton Down, Bath, BA2 7AY, UK

    • Laurence D. Hurst
  4. Present address: Biosciences, Geoffrey Pope Building, Streatham Campus, University of Exeter, Exeter, Devon, EX4 4SB, UK.

    • Robert E. Beardmore &
    • Ivana Gudelj


R.E.B. and I.G. wrote the paper, conceived the paper, designed analyses and performed analysis, D.A.L. wrote the paper and performed analysis, L.D.H. wrote the paper, conceived the paper and designed analyses.

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The authors declare no competing financial interests.

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Supplementary information

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  1. Supplementary Information (1.4M)

    This file contains Supplementary Text and Data, Supplementary Figures 1-26 with legends and additional references. See Table of Contents on page 1 for full details.

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