🚨 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]

That's halfway. In self-consistency equations, both the order parameters (OPs) and the model parameters appear. We build a cost function as a relative error on the self-consistency equations that we minimize to find the best parameters matching the data. Now, the results! [8/n]

How do healthy (blue) and diseased (red) microbiomes look like, when we consider the inferred parameters? There's a lot to say, but stay with me, and consider the following plot [9/n]

We consider the stability of such communities. We can do a harmonic expansion of the obtained free energy (with a global attractor/replica symm. guess) and study its convexity. When it hits zero (we track it with a quantity known as Replicon), multiple equilibria emerge [10/n]

As shown in our preprint, diseased microbiomes are closer to the edge of stability of the single attractor phase, while the healthy ones are really stable. We can introduce other interesting quantities, like the "mass" and the niche/neutral ratio. [11/n]

The mass is the quadratic coefficient of the Hamiltonian I showed you before. When it hits zero, the system enters into a pathological phase of abundance unbounded growth. The right panel shows that the diseased microbiomes are closer than the healthy ones to that phase. [12/n]