The thermodynamics of reproduction constrain species ranking dynamics and diversity

Abstract

Iniguez, Pineda, Gershenson, and Barabasi proposed that complex systems can be simplified and analyzed in terms of the dynamics of ordered lists. For social, economic, and infrastructural systems, they succeeded in modeling the dynamics of ranking with two mechanisms, namely displacement (i.e., shuffling of ranks among existing elements) and replacement of elements by new elements. A general pattern is that, for open systems with influx and outflux of elements, e.g., a list with a subset of elements, only the top of the list is stable; for closed systems, top and bottom are stable. This model was fitted to empirical data, resulting in a universal curve in which displacement and replacement parameters are inversely related, which implies that a single parameter could regulate both. Our aim is twofold: First, we demonstrate that the pattern generalizes to ranking of biological species, based on FishBase records of fish taxonomy and life history traits. Second, we propose a candidate for a unified mechanism, based on a recent model of the thermodynamics of self-replication.