Quanta Magazine

https://www.quantamagazine.org/how-nature-defies-math-in-keeping-ecosystems-stable-20180926/ September 26, 2018

How Nature Defies Math in Keeping EcosystemsStableParadoxically, the abundance of tight interactions among living species usually leads to disasters inecological models. New analyses hint at how nature seemingly defies the math.

By Veronique Greenwood

Maxim Usik for Quanta Magazine

Diverse, complex ecosystems in nature are generally stabilized by the abundant interactions among the speciesthey hold. Yet in simulations, model ecosystems typically become less stable as the interactions become strongerand more numerous. Researchers are beginning to understand what’s behind the discrepancy.

Behind the beautiful facade of a rainforest, a savanna or a placid lake is a world teeming withcontests and partnerships. Species are competing for space, consuming one another for resources,taking advantage of one another’s talents, and brokering trades of nutrients. But there’s somethingfunny about this picture. When ecologists try to model ecosystems using math, they tend to find that

Quanta Magazine

https://www.quantamagazine.org/how-nature-defies-math-in-keeping-ecosystems-stable-20180926/ September 26, 2018

the more interactions there are among species, the more unstable the system. For a simpleecosystem model to be stable, all the interactions among its species must be in perfect harmony.Maintaining that balancing act gets much harder, however, as the number of coupled species andthe strengths of their interactions rise: Any disturbance or imbalance for one couple ripples outwardand sows chaos throughout the network.

Bring in mutualisms, relationships in which species contribute directly to each other’s survival, andthings can really fly off the handle. Pairs of organisms that live off each other sometimes do so wellin the mathematical simulations — thriving exponentially in extreme cases, in what Robert May, thetheoretical ecology pioneer, once called “an orgy of mutual benefaction” — that everything else cango extinct.

It seems unlikely that real ecosystems are quite this flimsy. In a new paper in NatureCommunications, a pair of theoretical ecologists at the University of Illinois explored more preciselyhow the give-and-take in mutualism affects ecosystem stability and how, under the right conditions,it might contribute to it. Their result joins previous work in suggesting how real-world communitiesmanage to be more resilient than the models imply.

While researchers have learned how to work around the inconsistencies to get more realisticoutcomes in their modeling studies, lately the problem of mutualism has taken on new urgency,according to James O’Dwyer, a theoretical ecologist and associate professor at the University ofIllinois at Urbana-Champaign, who co-authored the paper with Stacey Butler, one of his doctoralstudents. Growing knowledge of how common communities of microbes are and how important theyare for health makes it more pressing to find out how to model them.

Quanta Magazine

https://www.quantamagazine.org/how-nature-defies-math-in-keeping-ecosystems-stable-20180926/ September 26, 2018

Courtesy of James O’Dwyer

James O’Dwyer, a theoretical ecologist at the University of Illinois at Urbana-Champaign, has investigated howprecise levels of reciprocal interactions, or mutualism, between pairs of species affect the stability of the largerecosystem.

“Large microbial communities with a lot of cross-feeding interactions where there’s exchange ofresources should have a lot of strong mutualistic interactions,” he said. In traditional models, thiswould make for a very unstable system, and yet stability is considered a hallmark of thesecommunities. Gut microbiomes are notably stable during periods of health, and fluctuations coincidewith illness.

For their study, O’Dwyer and Butler first built a model in which organisms are born, reproduce anddie while consuming and competing for resources that arrive from elsewhere, in a representation ofthe flow of nutrients into a microbial ecosystem. The researchers specified the preferences theorganisms had for different kinds of resources. “You can imagine that this bacterium grows betteron this carbon source but a little worse on another carbon source, so it would prefer the former,”explained Stefano Allesina, a theoretical ecologist at the University of Chicago who was not involvedin the research but reviewed it for publication. For certain values of nutrient influxes and deathrates, a stable ecosystem emerged.

Then O’Dwyer and Butler introduced mutualism by directing that the organisms feed not only onexternal resources but on each other’s byproducts — and they were very specific about who gotwhat from whom. As expected, the mutualisms had a destabilizing effect on the system. But animportant exception was if the researchers specified that the mutualism had to be symmetric — ifeach party in the partnership gave the same amount that it took. In that case, the system returned tostability.

What makes this finding interesting, according to Allesina, is that in previous studies, mutualisms inwhich the two parties didn’t benefit equally were generally thought to be more stabilizing becausethey would not drive the expansion of both species quite so wildly.

Perfect balance in mutualisms seems like a demanding and unlikely solution to mutualism’sdestabilization influence. “They do find a special case where they can maintain a diverse stablecommunity that’s mutualistic. But it has very strict requirements on the nature of [the] interactions,”said Katharine Z. Coyte, a theoretical ecologist now at Boston Children’s Hospital. There may bemore plausible ways for real ecosystems to cope. In a 2015 paper in Science, Coyte and hercolleagues reported that intense competition among the bacteria in the microbiome may itself be astabilizing force, keeping in check any species that might otherwise overrun the system.

Nevertheless, Coyte doesn’t rule out the possibility of the balanced mutualisms that O’Dwyer andButler modeled. “It would be interesting to see if there are biological scenarios that are like this,”she said.

Indeed, O’Dwyer and his colleagues want to use real-life data to adjust their models. Snapshots ofthe species in the gut microbiome, taken from people’s fecal samples over months or years, could behelpful to look at, O’Dwyer said, along with detailed information about the microbes’ feedingchoices. This would help narrow down the parameters for which their model could realistically work.

Quanta Magazine

https://www.quantamagazine.org/how-nature-defies-math-in-keeping-ecosystems-stable-20180926/ September 26, 2018

Meanwhile, the task of modeling large microbial communities continues to draw many researchers’interest. What should biologists expect when they run experiments where many bacteria are livingtogether, competing and probably exchanging resources?

At present, there is not much of a null hypothesis, according to Allesina. In a recent paper in NatureEcology & Evolution, he and his collaborators asked what would happen if, for instance, they threw ahundred varied bacterial samples onto the lush, well-provisioned plane of a petri dish and watchedto see who survived. They found that when you model such a scenario, many species die off, buteventually a stable ecosystem does often arise, and it remains stable regardless of how the speciesare connected to each other.

He hopes that such theoretical work may eventually help advance work in the lab. “People havemade a lot of progress in genetics by studying model organisms,” he said. “It would be fun to havemodel ecosystems that we can repeat in the lab several times.” If researchers better understood howstandard communities of gut bacteria behaved in the dish, this might lead to more nuanced anduseful theory as well. Knowing that what’s seen in nature never arises under the simplest classicalforms of ecosystem modeling, researchers could ask, which of all these newer models comes closest?