Scaling laws and stochastic constraints in the functional architecture of genomes and ecosystems

Advances in genomic sequencing have opened the way to quantify the functional organization of life across unprecedented scales, from single genomes to entire ecosystems. This talk presents a statistical-physics perspective on how stochastic gene-level dynamics give rise to large-scale regularities in functional composition. Using global metagenomic and metatranscriptomic data from the Tara Oceans expedition, we show that the abundance and expression of marine phytoplankton genes follow universal scaling laws that vary systematically with temperature.

These macroscopic regularities suggest that high-dimensional functional data can be effectively described by low-dimensional stochastic processes constrained by a few emergent variables. To test whether similar principles apply across species, we analyze cross-genome relationships between genome length and gene copy numbers, revealing power-law patterns that point to intrinsic dimensional constraints on genome architecture. By comparing these null expectations with observed metagenomic distributions, we propose a framework to identify biological and ecological signals emerging from deviations from stochastic predictions.