Ecologists have long searched for the rules that govern how individual species join together to form a community. Whether forest or desert, the problem is complex. Myriad factors influence a community’s composition and stability —from how strongly species compete to how often new species migrate into a community.

Now, physicist Guy Bunin of the Technion-Israel Institute of Technology in Israel has combined tools from ecology and physics to develop a new method for identifying the key drivers of community assembly, findings recently reported in Physical Review E.

Bunin studies what’s known as the physics of disordered systems, or as he calls them “dirty, messy systems.” Take a pile of sand, for example. “Every pair of sand grains push each other slightly differently,” he explains, “because each grain is shaped differently, and some are wet and some are dry.” Physicists develop mathematical tools to understand how these complex systems take shape. Bunin says that species in a natural community are a lot like those grains of sand in a pile. “For every pair of species, you expect them to interact in at least a slightly different way.”

Bunin started with a version of a classic ecological model known as the Lotka-Volterra equation, first devised in the 1920s and 1930s by Alfred J. Lotka and Vito Volterra. By plugging in information about how quickly individual species multiply and how much competition reduces population growth, ecologists use the equation to make predictions about which species will become abundant and which will decline or die out.

For the results reported in the present study, Bunin started by tweaking the model by allowing species to migrate into the modeled community at random, a common ecological modeling technique that Bunin says dates back decades. Combined, these classic tools of ecology can predict an ultimate community composition, but they can’t explain exactly why the community forms a certain way.

Using mathematics borrowed from the physics of disordered systems, Bunin then explored the complex network of interacting species in this model to identify which ecological factors are important drivers of the results predicted by the model.

He identified three main factors—how strongly pairs of species facilitate or compete with one another on average, how widely those interactions differ across pairs of species, and whether those interactions are symmetric, meaning that both species in a pair have equally strong effects on one another. Together, these factors determine how abundant each species will be and whether species in a community fit together the same way every time. For example, Bunin found that when mean competition is low and the variation in competition is also low, the species in the community will always assemble the same way, regardless of which arrives first. But when the strength of competition varies greatly across species pairs, which could happen if some species in the community facilitate rather than compete with species from the pool of possible migrants, the ultimate community composition will depend on the order that the species arrive, and may even continue to fluctuate indefinitely.

This idea, that facilitation could affect whether community assembly has a fixed outcome or multiple possible outcomes, is not a new idea, says ecologist Tadashi Fukami of Stanford University, who was not involved in the study. “But the value of this paper is that it was mathematically confirmed in a rigorous way,” says Fukami. “Sometimes intuitive thoughts can be wrong.”

Fukami says that making correct predictions about how ecological communities assemble is important in many branches of ecology—from restoration ecologists who want to know what will happen to a forest when they swap an invasive species for a native one, to medical ecologists who want to know how the composition of the gut microbiome will change if they add or remove a bacterial species.

Bunin finds his results satisfying in their simplicity, a complex system boiled down to a few driving factors. “At the end, I have very few nobs that I can change and that really matter,” he says. “I can change them in a small way and voilà, something very different comes out.”