Fluctuation scaling in L\'evy-stable recruitment of marine fishes in randomly varying environments

TL;DR

This study investigates the fluctuation scaling of marine fish recruitment in variable environments, demonstrating that a Le9vy-stable distribution better models recruitment variability than traditional models, revealing potential universality in ecological data.

Contribution

It introduces the Le9vy-stable model as a superior framework for describing recruitment fluctuations, highlighting the role of infinite variance processes in marine population dynamics.

Findings

Recruitment fluctuations follow a proportional standard deviation-mean relationship.

Le9vy-stable distribution outperforms log-normal in modeling recruitment data.

Scaling behavior suggests a universal distribution across different stocks.

Abstract

This paper studies the scaling properties of recruitment fluctuations in randomly varying environments, for abundant marine species with extreme reproductive behavior. Fisheries stock-recruitment data from the North Atlantic display fluctuation scaling, a proportionality between the standard deviation and the average recruitment among stocks. The proportionality covers over five orders of magnitude in the range studied. A linear-scaling behavior can be a sign of a universal distribution of the normalized data across stocks. In light of this conjecture, it is demonstrated that the L\'evy-stable model offers a better effective description of the recruitment distribution than the log-normal model. Care is devoted to the problem of random sums of random variables. Recruitment is calculated by summing random offspring numbers with infinite variance, where the number of summands (i.e. spawning population size) is also a random process with infinite variance.