Most prokaryotes divide by binary fission in which that undergo cell division to produce two daughter cells identical to the parent cell. .one bacterium divides into two, these two produce four, and then eight, and so on..
Thank you for your reply, Christina. So, remembering how mutant bacterial cells appear, I can conclude that they retain their "individuality" only until the next fission step and no "mother" cell can be distinguished, while in eukaryotic cells such a "mother" cell, bearing specific hallmarks, can give origin to several "daughters", even though the cells resulting after division look identical (under a microscope).
The question was slightly related to eukaryogenesis, to the factors that could underly such a transition between developmental strategies between prokaryotes and eukaryotes.
Actually, there is a paper that covers this very specific question. basically, you should not look at just one division but at least two. When E coli divides, each daughter has an old pole and a new pole. When one of this daughter divides, a daughter of the second generation has the old pole and a new pole while the other has the new pole from before and a new pole and is thus "younger". The paper shows that bacteria with old poles proliferate slower: in a sense they "age"