Long-term experimental evolution in Escherichia coli. XI. Rejection of non-transitive interactions as cause of declining rate of adaptation

Abstract

Background: Experimental populations of Escherichia coli have evolved for 20,000 generations in a uniform environment. Their rate of improvement, as measured in competitions with the ancestor in that environment, has declined substantially over this period. This deceleration has been interpreted as the bacteria approaching a peak or plateau in a fitness landscape. Alternatively, this deceleration might be caused by non-transitive competitive interactions, in particular such that the measured advantage of later genotypes relative to earlier ones would be greater if they competed directly.

Results: To distinguish these two hypotheses, we performed a large set of competitions using one of the evolved lines. Twenty-one samples obtained at 1,000-generation intervals each competed against five genetically marked clones isolated at 5,000-generation intervals, with three-fold replication. The pattern of relative fitness values for these 315 pairwise competitions was compared with expectations under transitive and non-transitive models, the latter structured to produce the observed deceleration in fitness relative to the ancestor. In general, the relative fitness of later and earlier generations measured by direct competition agrees well with the fitness inferred from separately competing each against the ancestor. These data thus support the transitive model.

Conclusion: Non-transitive competitive interactions were not a major feature of evolution in this population. Instead, the pronounced deceleration in its rate of fitness improvement indicates that the population early on incorporated most of those mutations that provided the greatest gains, and subsequently relied on beneficial mutations that were fewer in number, smaller in effect, or both.

Figure 1

Long-term E. coli populations show decelerating improvement. Each point shows the mean fitness (averaged over 12 replicate populations) measured relative to the common ancestor. Error bars are 95% confidence intervals calculated from the 12 population estimates. The hyperbolic curve was fit to the data. Data from Cooper and Lenski [3].

Figure 2

Transitive and non-transitive models. Both models could, in principle, account for the declining rate of fitness improvement relative to the ancestor. In competition with the ancestor, both models yield identical results, and were parameterized to match the data in Figure 1 (see Additional file 1). However, the two models make different predictions about fitness measured relative to clones isolated from later generations. (A) Transitive model. (B) Transitive model, ln-transformed. (C) Non-transitive model. (D) Non-transitive model, ln-transformed.

Figure 3

Cumulative fitness gains under two models. The two models depicted in Figure 2 differ most strikingly in their cumulative fitness gains, here shown ln-transformed. The transitive model shows cumulative gains that are identical to fitness measured relative to the common ancestor. The non-transitive model predicts cumulative gains that increase indefinitely at a constant rate.

Figure 4

Fitness trajectory measured relative to clones from five time-points. (A) Each line shows the fitness trajectory of the Ara-1 population measured relative to one of five clones bearing a neutral marker. The clones are the ancestor and isolates from generations 5,000, 10,000, 15,000 and 20,000. Each competition was replicated three-fold, and error bars are standard errors. (B) The same data ln-transformed.

Figure 5

Cumulative fitness gains measured and compared with two models. Test of the two model predictions shown in Figure 3 using cumulative ln-transformed fitness gains, as explained in the text. Error bars are 95% confidence intervals. A: Cumulative gains predicted by the transitive model. B: Cumulative gains observed over the four 5,000-generation intervals. C: Cumulative gains predicted by the non-transitive model. Both the A and B confidence intervals reciprocally overlap the A and B means, indicating that the prediction of the transitive model is consistent with the independently measured cumulative gains. By contrast, neither the B nor C confidence interval includes the reciprocal mean, and thus the non-transitive model is strongly rejected by the data.