The cause of universality in growth fluctuations

TL;DR

This paper explains the universal patterns in growth fluctuations across diverse systems using a simple additive model and network dynamics, showing that heavy-tailed replication leads to Levy distributions and scaling laws.

Contribution

It introduces a simple additive replication model with heavy-tailed distributions and demonstrates its ability to reproduce universal growth fluctuation patterns across various systems.

Findings

Model predicts Levy distributed growth fluctuations.

Data collapse onto a universal curve is improved.

Standard deviation scales with size as predicted.

Abstract

Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth fluctuations. The fluctuations display characteristic features, including double exponential scaling in the body of the distribution and power law scaling of the standard deviation as a function of size. To explain this we propose a remarkably simple additive replication model: At each step each individual is replaced by a new number of individuals drawn from the same replication distribution. If the replication distribution is sufficiently heavy tailed then the growth fluctuations are Levy distributed. We analyze the data from bird populations, firms, and mutual funds and show that our predictions match the data well, in several respects: Our theory results in a much better collapse of the individual distributions onto a single curve and also correctly predicts the scaling of the standard deviation with size. To illustrate how this can emerge from a collective microscopic dynamics we propose a model based on stochastic influence dynamics over a scale-free contact network and show that it produces results similar to those observed. We also extend the model to deal with correlations between individual elements. Our main conclusion is that the universality of growth fluctuations is driven by the additivity of growth processes and the action of the generalized central limit theorem.