Universal statistics of selected values

TL;DR

This paper introduces a universal probabilistic framework for understanding selection, showing that selected values follow universal limiting distributions influenced by the tail properties of the underlying variables, with evidence from diverse fields.

Contribution

It provides the first general theory of selection distributions, linking tail behavior to universal classes of limiting distributions, supported by empirical data.

Findings

Selected values follow universal limiting distributions.

Universality classes depend on tail thickness.

Empirical data from biology, agriculture, and sports support the theory.

Abstract

Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social phenomena. Yet a general theory of selection, analogous to the Fisher-Tippett-Gnedenko theory of extreme events, is lacking. Here we introduce a probabilistic definition of selection and show that selected values are attracted to a universal family of limiting distributions. The universality classes and scaling exponents are determined by the tail thickness of the random variable under selection. Our results are supported by data from molecular biology, agriculture and sport.