Math helps predict where trees cluster

Where trees cluster in the world’s savannas is not chiefly determined by environmental influences, but instead follows distinct patterns that can be mathematically described, according to a study appearing the week of May 13 in the journal Proceedings of the National Academy of Sciences.

“Concluding that some universal process governs spatial patterns in tree distributions may be premature,” said lead author Carla Staver, assistant professor of ecology and evolutionary biology. “However, we can say that although the tree clustering may look unpredictable locally, vegetation is instead strongly structured by regular statistical distributions.”

Scientists studying issues such as the global carbon cycle or biodiversity conservation want to understand why vegetation grows in some places and not others. The patterns of tree clusters dotting the savanna, which covers 40% of the global tropics and is rich in large mammal diversity, have been difficult to explain by environmental factors such as rainfall or soil type. Also, research has been hindered because investigations with limited localized data make it difficult to discover patterns in the distribution of tree clusters over wide areas.

Staver and colleagues used airplanes equipped with sophisticated remote sensing technology to examine tree clusters over an area the size of Israel within Kruger National Park in South Africa. At that scale, discernable patterns emerged.

“When you are looking at things from the ground, what you see is a messy jumble,” Staver said. “What we found was still a jumble, but it was a very structured jumble.”

The pattern of clusters they found at the larger scale can be explained neatly by an statistical phenomenon known as a power-law or scale-free distribution, which typically can only be applied with large datasets. The same type of distribution also describes a wide range of other phenomena, such as incomes, the sizes of cities, forest fires, and even earthquakes.

Staver and her colleagues plan to investigate whether the same sort of law may govern trees in other savannas.

“The possibility that all savannas follow the same mathematical rules is intriguing, but we need to look more broadly,” Staver said. “We might actually manage to predict where savannas might support vegetation or even discover more general ecological rules.”

Scientists from Arizona State University, Texas A & M University, Princeton University, and South African National Parks are co-authors of the study.

Primary funding for the study was provided by the Andrew W. Mellon Foundation and by the National Science Foundation.