title: Evo-SETI: A Mathematical Tool for Cladistics, Evolution, and SETI.
abstract: The discovery of new exoplanets makes us wonderwhereeach new exoplanetstandsalong its way to develop life as we know it on Earth. Our Evo-SETI Theory is a mathematical way to face this problem. We describe cladistics and evolution by virtue of a few statistical equations based on lognormal probability density functions (pdf)in the time. We callb-lognormal a lognormal pdf starting at instantb(birth). Then, the lifetime of any living being becomes a suitableb-lognormalin the time. Next, our"Peak-Locus Theorem" translates cladistics: each species created by evolution is ab-lognormal whose peak lies on theexponentially growingnumber of living species. This exponential is themean value of a stochastic processcalled "Geometric Brownian Motion" (GBM). Past mass extinctions were all-lows of this GBM. In addition, the Shannon Entropy (with a reversed sign) of eachb-lognormal is the measure of how evolved that species is, and we call it EvoEntropy. The "molecular clock" is re-interpreted as the EvoEntropy straight line in the time whenever the mean value is exactly the GBM exponential. We were also able to extend the Peak-Locus Theorem to any mean value other than the exponential. For example, we derive in this paper for the first time the EvoEntropy corresponding to the Markov-Korotayev (2007) "cubic" evolution: a curve of logarithmic increase.
authors.affiliation: International Academy of Astronautics (IAA) and IAA SETI Permanent Committee; IAA, 6 Rue Galilée, 75016 Paris, France. clmaccon@libero.it.|Istituto Nazionale di Astrofisica (INAF), Via Martorelli 43, 10155 Torino (TO), Italy. clmaccon@libero.it.
authors.forename: Claudio
authors.initials: C
authors.lastname: Maccone
keywords: Darwinian evolution; SETI; cladistics; entropy; molecular clock