The Birth-Death-Mutation process: a new paradigm for fat tailed distributions

TL;DR

This paper introduces the birth-death-mutation (BDM) process as a neutral model that explains fat-tailed distributions across complex systems, emphasizing luck over inherent qualities.

Contribution

It presents the BDM process as a comprehensive neutral model that accurately fits entire distributions, not just tails, challenging traditional fitness-based explanations.

Findings

BDM process fits empirical fat-tailed distributions well

The model explains entire distributions, not just tails

Deviations from BDM indicate effects of fitness or selection

Abstract

Fat tailed statistics and power-laws are ubiquitous in many complex systems. Usually the appearance of of a few anomalously successful individuals (bio-species, investors, websites) is interpreted as reflecting some inherent "quality" (fitness, talent, giftedness) as in Darwin's theory of natural selection. Here we adopt the opposite, "neutral", outlook, suggesting that the main factor explaining success is merely luck. The statistics emerging from the neutral birth-death-mutation (BDM) process is shown to fit marvelously many empirical distributions. While previous neutral theories have focused on the power-law tail, our theory economically and accurately explains the entire distribution. We thus suggest the BDM distribution as a standard neutral model: effects of fitness and selection are to be identified by substantial deviations from it.