Hon­ey­bees have been dying in record num­bers, threat­ening the con­tinued pro­duc­tion of nutri­tious foods such as apples, nuts, blue­ber­ries, broc­coli, and onions. Without bees to pol­li­nate these crops, the envi­ron­mental ecosystem—and our health—stands in the bal­ance. Have we reached the tip­ping point, where the plant-​​pollinator system is due to collapse?

There was no way to cal­cu­late that—until now.

Using sta­tis­tical physics, North­eastern net­work sci­en­tist Albert-​​László Barabási and his col­leagues Jianxi Gao and Baruch Barzel have devel­oped a tool to iden­tify that tip­ping point—for every­thing from eco­log­ical sys­tems such as bees and plants to tech­no­log­ical sys­tems such as power grids. It opens the door to plan­ning and imple­menting pre­ven­tive mea­sures before it’s too late, as well as preparing for recovery after a disaster.

The tool, described in a new paper pub­lished on Wednesday in the pres­ti­gious journal Nature, fills a long­standing gap in sci­en­tists’ under­standing of what deter­mines “resilience”—that is, a system’s ability to adjust to dis­tur­bances, both internal and external, in order to remain functional.

The failure of a system can lead to serious con­se­quences, whether to the envi­ron­ment, economy, human health, or tech­nology,” said Barabási, Robert Gray Dodge Pro­fessor of Net­work Sci­ence and Uni­ver­sity Dis­tin­guished Pro­fessor in the Depart­ment of Physics. “But there was no theory that con­sid­ered the com­plexity of the net­works under­lying those systems—that is, their many para­me­ters and com­po­nents. That made it very dif­fi­cult, if not impos­sible, to pre­dict the sys­tems’ resilience in the face of dis­tur­bances to those para­me­ters and components.”

Our tool, for the first time, enables those pre­dic­tions,” said Barabási, who is also a leader in Northeastern’s Net­work Sci­ence Institute.

Taking a system’s temperature

Barzel, a post­doc­toral fellow in Barabasi’s lab who col­lab­o­rated on the research and is now at Bar-​​Ilan Uni­ver­sity, draws an ele­gant analogy between the role of tem­per­a­ture in iden­ti­fying that tip­ping point in a pot of water and the single parameter—a tem­per­a­ture equiv­a­lent, as it were—that their tool can uncover to iden­tify the tip­ping point in any com­plex system.

July 12, 2013 - Baruch Barzel, a Postdoctoral Research Associate in the Barabasi Lab, created a new mathematical method for finding the links between protein interactions in cells.

Baruch Barzel col­lab­o­rated on the research as a post­doc­toral fellow in Barabási’s lab. Photo by Brooks Canaday/​Northeastern University

Con­sider: 100 degrees Cel­sius is the tip­ping point for water changing from liquid to vapor. Think of liquid as the desir­able state for the system and vapor as the unde­sir­able one, sig­ni­fying col­lapse. Mil­lions of para­me­ters and com­po­nents quan­tify what is going on within that pot of water, from the rela­tion­ship of the water mol­e­cules to one another to their speed and the chem­ical bonds linking their elements.

As the water heats up, those para­me­ters and com­po­nents con­tin­u­ally change. Mea­suring those mul­ti­tudi­nous changes over time—a micro­scopic approach to assessing the water’s state—would be impos­sible. How, then, are we to know when the water is reaching the threshold that divides the desir­able (liquid) state from the unde­sir­able (vapor) state?

Simple: Using a single parameter—temperature. As the water in the pot reaches, say, 99 degrees Cel­sius, alarms go off and we know to remove it from the heat.

Sta­tis­tical physics has found that you can crunch down all of these mil­lions of para­me­ters and com­po­nents into one number—the tem­per­a­ture,” said Barzel. “We take it for granted now, but that was a tremen­dous sci­en­tific achievement.”

The researchers’ tool sim­i­larly crunches down all the para­me­ters and com­po­nents of any com­plex system into a single cru­cial number. It enables us, essen­tially, to take the system’s “tem­per­a­ture” to deter­mine its health and respond accordingly.

02/09/16 - BOSTON, MA. - Jianxi Gao poses for a portrait in the Network Science Institute on Feb. 09, 2016. Photo by Adam Glanzman/Northeastern University

Jianxi Gao, who col­lab­o­rated on the research, is a post­doc­toral fellow in Barabási’s lab. Photo by Adam Glanzman/​Northeastern University

We col­lect all the data and map it to one number, a uni­versal resilience curve,” said Gao, a postdoc in Barabási’s lab. “That’s the only number we need in order to quan­tify whether the system is on the desir­able or unde­sir­able side of the threshold, or even approaching the danger zone.”

From theory to application

Of course, the inter­ac­tion between, say, bees and plants in an eco­log­ical system is not the same as the inter­ac­tion between water mol­e­cules in a pot, noted Barzel. “But the way of thought and the math­e­mat­ical tools that we use—statistical physics—are very similar.”

A big dif­fer­ence, how­ever, is that we know how to pre­vent the water system from col­lapsing: Turn off the heat before the tem­per­a­ture reaches 100 degrees Cel­sius. Indeed, the water system on its own pro­vides a vis­ible clue as it approaches the tip­ping point: bub­bles. You can’t say the same for the dying bees. The problem leads nat­u­rally to the researchers’ next steps: Using sta­tis­tical physics both to detect trouble in a system early on and to bring about its recovery if it has crossed the threshold.

Once you iden­tify the rel­e­vant para­meter that con­trols the system’s resilience, you can begin to tackle how to manip­u­late that resilience—how to enhance resilience or restore resilience,” said Gao. “These are not easy ques­tions, but our theory, by giving us a pic­ture of the entire system, paves the way to the answers.”