  We propose a purely probabilistic model to explain the evolution path of a
population maximum fitness. We show that after $n$ births in the population
there are about $\ln n$ upwards jumps. This is true for any mutation
probability and any fitness distribution and therefore suggests a general law
for the number of upwards jumps. Simulations of our model show that a typical
evolution path has first a steep rise followed by long plateaux. Moreover,
independent runs show parallel paths. This is consistent with what was observed
by Lenski and Travisano (1994) in their bacteria experiments.
