Analysis of morphological evolution in a long-term experiment with Escherichia coli

Great attentions are still paid to the morphological evolution, such as the waiting time to the morphological stability in constant environment, the contributions of different evolutionary forces to the morphological evolution and so on, despite considerable progress. To investigate these issues, some biologists seek to carry out evolution experiments owing to the incompleteness and uncontrollability of the fossil record and the natural populations. We analyze the morphology (cell size) evolution observed from a long-term evolution experiment with Escherichia coli by Lenski et al. and explore these questions more rigorously. We adopt a population genetics model, the Wright-Fisher model, to describe this morphological evolution and calculate the estimates of the waiting time until the ultimate stasis (near stasis) in morphology (cell size) in the long-term experiment by simulations. These calculations have been verified to be in good accordance with the experimental data, which demonstrates the effectiveness of our model. We have shown how the per-locus mutation rate, the average selection advantage per mutation and the population size devote to the morphology (cell size) evolution. Our results indicate that the selective advantage plays a powerful effect on this morphological evolution. By comparison, the mutation rate and population size have a weaker influence.