Meadows and vegetation in arid areas sometimes form bare patches, circular and regularly spaced, and are usually surrounded by a ring of more than normal growth. The patches are two to 15 metres across and the remarkable feature is that they distribute themselves in a pattern of hexagons.

They are best viewed from a distance and can be seen clearly in satellite images. The mechanism by which these patches form and why they distribute themselves in a pattern has been a subject of conjecture and somewhat inconclusive study.

Earlier this year, Corina E Tarnita, Juan A Bonachela, Efrat Sheffer, Jennifer A Guyton, Tyler C Coverdale, Ryan A Long and Robert M Pringle at Princeton, Idaho, Glasgow, Israel and Kenya, in a paper in the journal Nature, brought together the two principal but competing lines of thought on the subject. Another group comprising Daniel RuizReynés, Damià Gomila, Tomàs Sintes, Emilio Hernández-García, Núria Marbà and Carlos M Duarte, working in Spain and in Saudi Arabia, now propose, in the journal, Science Advances, a model to explain the same formations that have been found on the seabed.

A simplistic explanation of fairy circles, as these formations are called, is that grasses position themselves along the periphery of circular patches so that moisture can collect in the central portion, to the benefit of those that stand outside the circle.

What this explanation lacks, however, is the mechanism by which this prudent behaviour comes about. One theory is the action of termites and other insects that feed on the grass in the centre. The other theory is based on “scale dependent feedback”, and a tendency for plants to stick with close neighbours and move away from the distant ones.

Thus, plants on the periphery of any bare spot would benefit from the greater nutrition saved for them by the bare spot. If they were to move to colonise the bare spot, there would be negative consequences but widening, in the form of a circle, would lead to the greatest benefit of the plants in the periphery.

A proposed mechanism is that the patches start when some plants defeat others in the competition for scarce resources. The patches are then maintained, and grow, because any plant that moves into the circle needs to compete with the stronger plants in the periphery.

This is till the patch grows so large that the competitive advantage at the periphery is reduced and the patch gets invaded. And then there are mathematical models that describe how it is the distribution of different patches in hexagons that maximises the benefit for each of the patches.

This is based on the idea that patches are competitors and it is best for each patch to stay stable, equidistant from neighbours in the hexagon pattern. That a matrix made of hexagons allows many entities to be equidistant from neighbours is seen in many places in nature, one being the patterns that pigments make on animal coats.

Another ready example is the way the “base stations” of a cellular phone network are positioned, so that each one is insulated from all others by the six surrounding base stations. The other, competing model of fairy circles, which may be more empirical, is that the circles arise because of termites that feed on the plants inside the circle. While this explains how the circles arise, there are also instances of patterns that action of insects form over an area.

The paper in Nature cites the instance of social insects, which build nests like ant-hills. While the insects exploit the surrounding of the nest, reproductive individuals, like new queens or kings, move out to start other colonies. Colonies, however, cannot be close together, as there would be insufficient resources and conflict. A series of nests would hence, in time, tend to form a regular, hexagon-based pattern over a large area.

While these two ideas of how fairy circles come about have so far claimed that one or the other is correct, Corina E Tarnita and her group find that both theories are valid as well as necessary. While it is competing for resources that lead to the decline of plants within the circles, it is the termites that make sure the circles remain bare and able to concentrate moisture. The presence and the evolution of termites is clearly an adaptation to the adaptation of the grass varieties to shrinking water sources.

The research team then integrated the two models of how fairy circles arise and the interplay of both mechanisms has been found better able to explain the self-organisation of vegetation landscapes as well as make predictions about features that were not noticed before, the paper says.

As fairy circles have been observed only in semi-arid areas, it would come as a surprise that these formations have been found in grasslands that cover parts of the bottom of the sea! The group writing in the journal, Science Advances, studies the meadows of the seagrass, Posidonia Oceanica, an important part of the ecosystem in the Mediterranean Sea. These grasslands also show complex self-organisation patterns, which have not been noticed so far, the paper says.

The mechanism behind fairy circles under the sea is clearly different from that in semi-arid areas and the mechanism has only partly been understood, the paper says. Seagrass meadows are found along the shoreline of all continents except Antarctica and they provide valuable ecosystem services, the paper says. But they are also among the most threatened of ecosystems in the world. P Oceanica, the dominant seagrass of the Mediterranean, supports great biodiversity and is a major agent of C02 sequestration.

But human-caused factors are reducing P Oceanica by 6.9 per cent every year. And as it grows and spreads very slowly, the losses are essentially irreversible, the paper says. The group has developed a model to explain the emergence of the fairy circle seascape and the model shows that the patterns that are seen are the result of local imbalances of competing plant varieties.

The model can be extended to other seascape instances and can be used as an indicator of how close the seagrass meadow being observed is to extinction. This capacity of the model is an important tool to monitor environmental degradation and guide conservation measures, the paper says.

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