🚨 NEW PREPRINT 🚨 Happy to share our work with @ada_altieri & @SamirSuweis! We inferred the parameters of the Disordered Generalized Lotka-Volterra (dgLV) model to compare healthy and chronically inflamed gut microbiomes. 🧵A thread 🧵 arxiv.org/abs/2406.07465

We combined gathered metagenomic data from various experiments, e.g. the human microbiome project with plenty of metadata to distinguish heathy and diseased individuals. Secondly, we obtained all the taxonomic profiles. What about the theory? [1/n]

Lotka-Volterra model is a cornerstone of theoretical ecology, describing how the abundances of a local pool of species (S) evolve in time. However, it is typically unfeasible to fit all the O(S^2) parameters, especially with metagenomic data. What's the problem? [2/n]

Metagenomic data lack time resolution, so it is reasonable to assume that, at available sampling resolution, what we see is the dynamics at stationarity. This allows us to set dN/dt=0. The other key assumption is on the interactions. [3/n]

Inspired by Robert May's approach, we draw the interactions from a normal distribution choosing carefully the scaling of the mean and the variance with S. Albeit crude, this assumption leads to a dramatic reduction of the parameters to infer from O(S^2) to just O(1)! [4/n]

To link the theory and data, we rely on previous results. Using the magic of replica-trick formalism the theory admits a mean-field Hamiltonian formulation. This formalism allows us to trade complexity (S species) with one species with random potential (here's \zeta!)

Similarly to the magnetization of the Ising model, we have some order parameters, describing some coarse-grained statistics of the community (e.g. mean abundance) and require to average both over the species and over the disorder. Here's the key intuition of our work... [6/n]

We propose an analogy between the theory's disorder average and the data's sample average. At the end of the day, each gut microbiome can be idealised as and independent realization of the disorder, allowing us to estimate the order parameters from the data! [7/n]