Evolutionary dynamics of morphological stability in a long-term experiment with Escherichia coli

To investigate the questions in morphological evolution, some biologists seek to carry out evolution experiments owing to the incompleteness and uncontrollability of the fossil record and natural populations. To quantitatively analyse the morphology (cell size) evolution observed from a long-term experiment with Escherichia coli, the authors present three mathematical approximations to the Wright-Fisher model of the morphological evolution. They firstly use a deterministic approximation, which fails to predict evolutionary dynamics of cell size and proves the importance of stochasticity in large populations. Then, they develop a stochastic approximation and derive an analytic expression for the anticipated waiting time to reach the stability of cell size. The results show that the calculation of this waiting time is in good agreement with the experimental data and that the selective advantage plays a prominent role in cell size evolution, with mutation rate and population size having less impact. Finally, they employ a multistep process to approximate the Wright-Fisher model of cell size evolution and acquire an analytical formula for the median waiting time until the stability of cell size. This median time supports the idea that the selective advantage is the dominant force for the morphological evolution in the long-term experiment.