Evo-SETI: A Mathematical Tool for Cladistics, Evolution, and SETI

TL;DR

Evo-SETI introduces a mathematical framework using statistical equations and cladistics to analyze the evolution of species and their potential for developing life, with applications to exoplanet studies.

Contribution

It presents a novel mathematical model based on lognormal distributions and stochastic processes to describe cladistics, evolution, and species diversity in the context of SETI.

Findings

Derived the Peak-Locus Theorem relating species creation to exponential growth.

Introduced EvoEntropy as a measure of species evolution.

Extended the theorem to non-exponential evolutionary models.

Abstract

The discovery of new exoplanets makes us wonder where each new exoplanet stands along 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 call b-lognormal a lognormal pdf starting at instant b (birth). Then, the lifetime of any living being becomes a suitable b-lognormal in the time. Next, our "Peak-Locus Theorem" translates cladistics: each species created by evolution is a b-lognormal whose peak lies on the exponentially growing number of living species. This exponential is the mean value of a stochastic process called "Geometric Brownian Motion" (GBM). Past mass extinctions were all-lows of this GBM. In addition, the Shannon Entropy (with a reversed sign) of each b-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.