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

Can evolution paths be explained by chance alone?