  In a series of recent papers and in a book, this author put forward a
mathematical model capable of embracing the search for extra-terrestrial
intelligence (SETI), Darwinian Evolution and Human History into a single,
unified statistical picture, concisely called Evo-SETI. The relevant
mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic
process representing evolution as the stochastic increase of the number of
species living on Earth over the last 3.5 billion years. This GBM is well known
in the mathematics of finances (Black-Sholes models). (2) The probability
distributions known as b-lognormals, i.e. lognormals starting at a certain
positive instant b>0 rather than at the origin. In the framework of Darwinian
Evolution, the resulting mathematical construction was shown to be what
evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such
b-lognormals is then seen to represent the 'degree of progress' reached by each
living organism or by each big set of living organisms, like historic human
civilizations. (4) All these results also match with SETI in that the
statistical Drake equation (generalization of the ordinary Drake equation to
encompass statistics) leads just to the lognormal distribution as the
probability distribution for the number of extra-terrestrial civilizations
existing in the Galaxy. (5) The well-known 'Molecular Clock of Evolution',
namely the 'constant rate of Evolution at the molecular level' as shown by
Kimura's Neutral Theory of Molecular Evolution, identifies with growth rate of
the entropy of our Evo-SETI model. (6) Furthermore, we apply our Evo-SETI model
to lognormal stochastic processes other than GBMs. For instance, we provide two
models for the mass extinctions that occurred in the past. (7) Finally, we show
that the Markov & Korotayev model for Darwinian Evolution identifies with an
Evo-SETI model.
