So this becomes a directed bipartitie network, but if you want you can also think of it as a multilayer net or hypergraph. What fascinates me is the algebraic structure: Bacteria in the system need ALL their requirements to be met, whereas metabolites need ONE of their producers to be present... - ThreadSky

thilogross.bsky.social • 46 days ago

So this becomes a directed bipartitie network, but if you want you can also think of it as a multilayer net or hypergraph.

What fascinates me is the algebraic structure: Bacteria in the system need ALL their requirements to be met, whereas metabolites need ONE of their producers to be present...

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thilogross.bsky.social•46 days ago

So this becomes a percolation problem. The whole setup is captured by two nice eqs. Here c* is num of bacteria chance m^* is num of metabolites, and C, M, are the GFs for number of requirements, number of producers per metabolite ...

thilogross.bsky.social•46 days ago

For reasonable choices of parameters this system exhibits tipping points between a low and high diversity state ...

thilogross.bsky.social•46 days ago

Of course this is the classic two-folds scenario of tipping, so when we vary a second parameter (e.g. mean number of producers per metabolite), we find a nice Cusp bifurcation. This shows that the transition from high diversity to low diversity can occur by tipping/gradually depending on params...

thilogross.bsky.social•46 days ago

Why is this interesting: First, it shows why diversity tends to collapse in small samples. By missing some of the producers of metabolites we can cross the tipping point. In the equations we can model this effect of sampling as an attack on the network: We replace M(x)->M(A(x)).

thilogross.bsky.social•46 days ago

In the lab we then supply the community with growth media which supply some of the metabolites. This effectively removes these metabolites as limiting requirements. So this can be also modelled as an attack: C(x)->C(B(x)), where B describes the medium.
...

thilogross.bsky.social•46 days ago

There is another reason why this is interesting. Presently there is a debate whether or when biodiversity in diverse systems can actually tip. See for example this paper by @hillebr1.bsky.social et al.

https://www.nature.com/articles/s41559-020-1256-9

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