Sup­pose you held in your hands a bunch of indi­vid­uals from dif­ferent species, sort of like a minia­ture Jumanji set. You have some cows, some bac­teria, some plants, some bugs, and a whole bunch of other living things. You throw the lot up in the air and let them land where they will, ran­domly posi­tioning them­selves next to one another.

Like a social net­work, links between the indi­vid­uals will form based simply on who’s nearby. One cow takes a bite of grass; another cow eats a bug. A bac­terium sets up shop on a bug’s back, so now it’s in a cow’s stomach, and so on. Not all of these inter­ac­tions will be the most ideal for a species’ sur­vival. But a few, called mutu­al­istic inter­ac­tions, will be great for everyone involved.

Species select their mutu­al­istic part­ners to max­i­mize their pop­u­la­tion,” said Fil­ippo Simini, a post­doc­toral research asso­ciate in Northeastern’s Center for Com­plex Net­work Research. While on its own this fact isn’t all that sur­prising, its impli­ca­tions have puz­zled ecol­o­gists and net­work sci­en­tists like Simini for some time.

Here’s the conun­drum: As random net­works become pro­gres­sively more orga­nized, with less favor­able inter­ac­tions being cast aside for more favor­able ones, the com­mu­nity becomes less resilient while simul­ta­ne­ously becoming more stable. That’s because the net­work topology that emerges from this kind of opti­miza­tion is less capable of bouncing back after small per­tur­ba­tions, like dis­ease or a storm or short drought.

So why does it happen at all?

In a paper recently released in the journal Nature, Simini and his col­leagues Samir Suweis and Amos Mar­itan of the Uni­ver­sity of Padova and Jayanth Banavar of the Uni­ver­sity of Mary­land present a so-​​called “vari­a­tional prin­ciple” to explain the unex­pected, though com­monly observed, topology of mutu­al­istic networks.

Called “nest­ed­ness,” this type of archi­tec­ture looks like a set of Russian Matryoshka dolls. The smallest doll com­prises the most spe­cial­ized species—for instance, the bac­teria that can only sur­vive inside a cow’s stomach, where it pays rent by keep the cow’s gut clean and healthy. The rest of the net­work, the out­er­most dolls, are made up of the links between more gen­er­alist species—the cows, the grass, and the bugs that can interact with each other plus a host of other species in the ecosystem.

By ana­lyzing the­o­ret­ical mutu­al­istic net­works via com­pu­ta­tional mod­eling, the researchers were able to show that com­mu­ni­ties with strong mutu­al­istic inter­ac­tions tended to be less nested, and thus more resilient. “When inter­ac­tion strengths are weak, it becomes cru­cial for the com­mu­nity to orga­nize into a highly nested archi­tec­ture in order to max­i­mize its pop­u­la­tion,” said first author Suweis.

In mutu­ally ben­e­fi­cial inter­ac­tions, everyone wins. So, if a process max­i­mizes one species’ abun­dance, the community’s total pop­u­la­tion will increase and thus tend fur­ther toward this nested architecture.

The system becomes more stable overall, but in the face of dis­tress, it will take more time to return to normal. The system’s resilience, according to the team’s find­ings, is ulti­mately deter­mined by the pop­u­la­tion of the rarest species: “The lower the pop­u­la­tion of the rarest species,” said Simini, “the longer the time to recovery.”

It turns out mutu­al­istic net­works don’t just show up in the nat­ural world. Other exam­ples include cred­i­tors and debtors, aca­d­emic col­lab­o­ra­tions, and even man­u­fac­turing net­works. Regard­less of their set­ting, be it a marine ecosystem or a finan­cial board­room, mutu­al­istic net­works will tend toward nest­ed­ness and Simini’s work could go a long way toward explaining that phe­nom­enon and its impli­ca­tions in a variety of settings.