There's rarely time to write about every cool science-y story that comes our way. So this year, we're once again running a special Twelve Days of Christmas series of posts, highlighting one science story that fell through the cracks each day, from December 25 through January 5. Today: Azteca ant formations show evidence of Turing patterns.

Azteca ants build their nests in shade trees, and it's relatively common to find other nests in trees nearby. But these clusters of ant nests are often separated by large sections of shade trees where there are no nests at all. A December overview paper in BioScience by scientists at the University of Michigan argued that there is now substantial evidence that this unusual clustering is the result of self-organizing behavior of the ants—not external factors like temperature or moisture. In fact, the mechanism at work is strikingly similar to a process described by the late Alan Turing in a seminal 1952 paper.

Turing was attempting to understand how natural, nonrandom patterns emerge (like a zebra's stripes), and he focused on chemicals known as morphogens. He devised a mechanism involving the interaction between an activator chemical and an inhibitor chemical that diffuse throughout a system, much like gas atoms will do in an enclosed box. The BioScience paper draws an analogy to injecting a drop of black ink into a beaker of water. Normally this would stabilize a system: the water would gradually turn a uniform gray. But if the inhibitor diffuses at a faster rate than the activator, the process is destabilized. That mechanism will produce a so-called "Turing pattern:" spots, stripes, or, when applied to an ecological system, clusters of ant nests.

The authors of the BioScience paper write:

The basic idea is that the activating chemical starts the reaction at a specific point in the space but begins its diffusion away from that point immediately... The repressive chemical is eventually produced by the reaction and cancels the effect of the activator but, because it diffuses at a rate that is greater than that of the activating chemical, it eventually occupies a space where the activator had not yet arrived, therefore canceling the effect of the activator at that point.

So you get spots, like on a leopard, or stripes, like on a tiger.

Scientists have tried to apply this basic concept to many different kinds of systems. For instance, neurons in the brain could serve as activators and inhibitors, depending on whether they amplify or dampen the firing of other nearby neurons—possibly the reason why we see certain patterns when we hallucinate. There is evidence for Turing mechanisms at work in zebra-fish stripes, the spacing between hair follicles in mice, feather buds on a bird's skin, the ridges on a mouse's palate, as well as the digits on a mouse's paw. And certain species of Mediterranean ants will pile the dead bodies of ants into structures that seem to exhibit Turing patterns. The challenge is moving from Turing's admittedly simplified model to pinpointing the precise mechanisms serving in the activator and inhibitor roles.

"The same equations that Turing used for chemistry, we can use in ecology," said co-author John Vandermeer, an ecologist of the University of Michigan. "Those equations say you should get spots of predators and spots of prey in a system, and we've proven you do."

Basically, any two processes that act as activator and inhibitor will produce periodic patterns and can be modeled using Turing's diffusion function. For instance, Vandermeer has uncovered Turing-like features in how species are distributed in a given ecological system, including predator-prey models.

Vandermeer has been studying Azteca ants and the coffee farm ecology system in general for a good 20 years, and he noticed that ant nests tended to form patterns while working in the field. One of Vandermeer's graduate students had done a study on parasitic phorid flies and realized the tremendous impact the fly had on the ants' behavior.

"The predator was dispersed around by the wind, so it had a relatively rapid diffusion rate, compared to where the ant was," he told Ars. "Biologically, we had a clear reaction-diffusion system." In other words, they had the defining elements of a classic Turing mechanism.

Vandermeer and his colleagues mapped the distribution of shade trees with nests of Azteca ants on an organic coffee farm in Mexico—roughly 700 trees out of a total of between 7,000 and 11,000 trees overall. It's an intricate ecosystem. For instance, when phorid flies find a cluster of ant nests, they plant their eggs in the heads of ants. Those heads will fall off once the larvae are fully developed, releasing new flies to venture out and find more ant hosts to implant.

That relationship between predator and prey, the authors contend, is the driver behind the emergence of ant-nest clusters distributed in a Turing pattern. The ant nests serve as the activator in this system, increasing in size and number while forming spatial clusters. This kicks off a corresponding increase in the population of the flies, whose parasitic behavior acts as an inhibitor, decreasing the population of ants.

Complicating matters is that the ecosystem also includes a pest known as the green coffee scale and a predatory species of beetle (Azya orbigera) that eats the scale. The Azteca ants, in turn, are motivated to protect the scale insects from the beetles, since the former are a source of food for the ants. That combination ensures that the ecosystem maintains a delicate balance. If the scales are so well protected by the ants that their numbers become too large, for instance, a white halo fungal disease can break out, decimating the scale insect population to restore the balance.

"At a very local level, the predator and prey form an unstable relationship, whereas adding diffusion to the mix may result in stabilizing the system," the authors wrote.

There is also a disease called coffee rust, spread by spores on the wind. The same fungal disease that keeps scale insects under control can also target coffee rust. But sometimes a coffee-rust epidemic breaks out, such as the one that devastated crops in Guatemala, Honduras, and El Salvador in 2012. The likely cause: in the preceding years, according to Vandermeer, there was a gradual deforestation of the affected areas, converting much of the forest to pasture and upsetting the delicate balance of the ecosystem.

"It's a reasonable hypothesis to suggest that it was an indirect consequence of the gradual deforestation of the region leading to a critical transition, [such that] the disease suddenly turned into an epidemic," said Vandermeer.

Said co-author Ivette Perfecto, also with the University of Michigan:

This is an important finding because it shows how organisms in nature are embedded within a complex web of interactions and, therefore, the simplistic pest management approach of "One pest, one natural enemy" may not be the most appropriate one for pest management.' Rather, a complex systems approach that accounts for nonlinearities and networks of interactions is what is needed.

There is still plenty of skepticism among scientists about whether true Turing mechanisms are at work in natural systems. "Distinguishing between a Turing pattern and other methods of pattern formation is not all that easy in a large-scale system like this," Vandermeer admitted. "If you're dealing with slime molds in a laboratory, you have much more control over the system." Nonetheless, "My position is that Turing's insight was so foundational, that all the assumptions that go into his qualitative insight are there in nature. It just seems right."

DOI: BioScience, 2019. 10.1093/biosci/biz127 (About DOIs).