On The Universal Scaling Relations In Food Webs

TL;DR

This paper investigates the universal scaling relation in food webs, showing that the efficiency exponent approaches 1 as the number of species increases, challenging previous claims of a universal value.

Contribution

The study derives bounds and analytical expressions for the energy transport exponent in food webs, demonstrating its dependence on species number and levels, and clarifying finite size effects.

Findings

Exponent $ta$ approaches 1 for large species number

Finite size effects explain previous universal value $ta=1.13$

Food webs are highly efficient resource transport systems

Abstract

In the last three decades, researchers have tried to establish universal patterns about the structure of food webs. Recently was proposed that the exponent $\eta$ characterizing the efficiency of the energy transportation of the food web had a universal value ($\eta=1.13$). Here we establish a lower bound and an upper one for this exponent in a general spanning tree with the number of trophic species and the trophic levels fixed. When the number of species is large the lower and upper bounds are equal to 1, implying that the result $\eta=1.13$ is due to finite size effects. We also evaluate analytically and numerically the exponent $\eta$ for hierarchical and random networks. In all cases the exponent $\eta$ depends on the number of trophic species $K$ and when $K$ is large we have that $\eta\to 1$. Moreover, this result holds for any number $M$ of trophic levels. This means that food webs are very efficient resource transportation systems.