This is the *second* in a series of posts where I summarize what I think are the most important findings and discoveries from the LTEE.

**Number 2.** An exciting new twist on the dynamics of adaptation by natural selection is the discovery that fitness can increase “forever” – or at least for a very long time – even in a constant environment.

A power-law model, which has no upper bound, gives a significantly better fit to the mean-fitness trajectories measured in the LTEE populations than does a model with an asymptote.

Moreover, the power law *predicts* the trajectory of fitness evolution with much greater accuracy. That is, if we reduce the data so that it includes only the first 20,000 generations, the power law trajectory that fits this truncated dataset accurately predicts fitness out to 50,000 generations (blue trajectory in the figure below). By contrast, the same procedure with the asymptotic model consistently underestimates the future fitness gains (red trajectory in the figure below).

Also, a dynamical model that incorporates clonal interference (competition between different beneficial mutations) and diminishing-returns epistasis (where the marginal effect of a beneficial mutation declines with increasing fitness) produces trajectories that have the same power-law form. That, in turn, facilitates estimation of important population-genetic parameters including the rate of beneficial mutations and the average strength of the diminishing-returns epistasis.

The figure below shows the grand-mean fitness data (symbols with error bars) over 50,000 generations of the LTEE. It also shows the trajectories predicted by the power law (blue curve) and by a model with an asymptote (red curve) using only the first 20,000 generations of data. The figure comes from Wiser *et al.*, 2013, *Science*; it is shown here under the doctrine of fair use.

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Big fan of LTEE, and unfortunately cannot access the full referenced paper for a proper read. I am slightly confused as to what the precise claim about fitness increase is. Relative fitness also increases “forever” under the asymptotic model. If there is no asymptote, do you suggest there is no limit to relative fitness, and doubling time can get arbitrarily close to zero?

In general, how much do you trust the predictions of the mathematical model – would you take a $100 1:1 odds bet for average relative fitness of generation 60,000 from your model prediction to be within 0.01, say? What about generation 75,000, or 100,000? What about multiple restarts from 0 to follow the fit from this model? The reason I am asking is that confidence in the model output implies that you believe all the main contributors to the fitness are included in the model, and that the effects of the selected mutations that accumulate are in some sense independent, with little scope for major deviations from small fitness improvements. This kind of predictability would of course be great, but also counterintuitive given how hard it is to predict life in general.

Best to read the paper regarding statistical issues. Send me a request to my MSU address, and I’ll send p/reprint.

Yes, we’re saying there’s no upper bound, unlike the asymptotic model. However, the power law does not make “crazy” predictions even very far into the future. You can read more about that aspect in my recent post called Fifty-Thousand Squared, as well as in the paper itself.

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