Filippo Simini — University of Bristol#
Scaling laws and optimisation principles in ecological systems: from river basins to tropical forests and cities.#
The finite-size scaling method was originally developed to analyse the properties of physical systems near phase transitions, allowing to compute the values of the critical exponents and their relations, and to precisely define the notion of universality.

Allometric relationships have also been found in many biological and ecological systems, and scaling laws have been successfully used to provide a unified description to seemingly unrelated empirical patterns.
The most famous scaling relationship in biology is probably Kleiber's law that relates an organism's metabolic rate with its mass: for animals and plants spanning more than ten orders of magnitude in body size, the metabolic rate scales approximately as the mass to the power 3/4. Quarter power scaling with body mass is also observed for many characteristic times and rates, such as life times and heart rates.
The universality of these exponents suggests that there might be a general explanation for them that only relies on few fundamental features common to such a diverse range of systems.
In this talk I will present a framework based on finite-size scaling and optimisation principles that can provide a general explanation to Kleiber's law and a consistent description of the structure of many biological and ecological systems, focusing in particular on river basins and tropical forests.
I will also discuss the possibility to use a similar framework to describe the patterns of population distribution observed in urban systems.