Volume 117, Number 5, March 2017
|Number of page(s)||6|
|Published online||02 May 2017|
Universal statistics of selected values
1 Perimeter Institute for Theoretical Physics - 31 Caroline St. N., Waterloo ON N2L 2Y5, Canada
2 LD - Research - Pappelallee 78/79, 10437 Berlin, Germany
Received: 4 January 2017
Accepted: 7 April 2017
Selection, the tendency of some traits to become more frequent than others 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 which generalize the log-normal distribution. The universality classes and scaling exponents are determined by the tail thickness of the random variable under selection. Our results provide a possible explanation for skewed distributions observed in diverse contexts where selection plays a key role, from molecular biology to agriculture and sport.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 87.10.-e – General theory and mathematical aspects / 87.23.Kg – Dynamics of evolution
© EPLA, 2017
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