Forests defy a mesmerizing law that is prevalent in nature

Fractals are self-repeating patterns found in nature. They are mesmerizing due to their infinite repetition, which runs infinitely deep. Objects like fern fronds and snowflakes have branching patterns that repeat in miniature, sometimes down to atomic and quantum matter.

However, a recent study found that forest canopies don’t replicate the fractal patterns of individual trees. Biologists Fabian Fischer and Tommaso Jucker from the University of Bristol wanted to test the idea that fractal patterns might explain how forest canopies are organized. They thought that if fractal patterns extended from the small branches and leaves of a single tree to entire forest canopies, it could help ecologists describe complex landscapes using simple mathematical language.

“Scientifically, this self-similarity has the attractive property that it allows you to describe an apparently complex object using some very simple rules and numbers,” explains Fischer.

Fischer and Tommaso proposed that if forest canopies were to behave like fractals, they could use this property to evaluate the complexity of forest ecosystems. This would allow them to compare structural differences between forests across the world.

The structural complexity of forest ecosystems is crucial to their ability to store carbon, cycle water and nutrients, and provide habitats for biodiversity. While there have been a few studies that pointed to evidence of fractal patterning in patchy or fire-affected forests, it remained unclear whether it was a genuine property of forested landscapes.

Recent analytical models have attempted to compute the structural complexity of forests to understand what conditions give rise to more complex ecosystems.

To investigate this, Fischer and Tommaso analyzed data from airborne laser surveys of nine different forest types in Australia, ranging from dry shrublands and tropical savannas to dense rainforests and towering mountain ash forests. The nine sites, each measuring 5 square kilometers, varied substantially in rainfall and structure.

The researchers built high-resolution models of the forest canopies from each laser scan to see how closely the sites followed fractal scaling. However, the analysis found that none of the nine canopy sections behaved like fractals beyond the crowns of individual trees.

Despite this, the traits of forests and how they deviated from fractal patterning exhibited some predictability. For example, taller and wetter forests showed a higher degree of self-similarity than shorter and drier ecosystems. These findings may still be useful for ecosystem comparisons.

“We found that forest canopies are not fractal, but they are very similar in how they deviate from fractality, irrespective of what ecosystem they are in,” says Fischer.

“It was surprising,” he added, “how similar all forest canopies were in the way they deviated from true fractals, and how deviations were linked to the size of the trees and how dry their environment was.”

The researchers plan to compare various forest ecosystems around the world and analyze multiple scans over time to understand how forest structure evolves. It is tempting to believe that we can understand the complexity of nature through a few mathematical equations. However, forests might be unpredictable ecosystems that do not follow mathematical principles, from their canopies to their cells. Nevertheless, this unpredictability of forests also adds to their beauty.

This news is a creative derivative product from articles published in famous peer-reviewed journals and Govt reports:

References:
1. AFischer, F. J., & Jucker, T. (2023). No evidence for fractal scaling in canopy surfaces across a diverse range of forest types. Journal of Ecology.
2. Arseniou, G., & MacFarlane, D. W. (2021). Fractal dimension of tree crowns explains species functional-trait responses to urban environments at different scales. Ecological Applications, 31(4), e02297.
3. Asner, G. P., Mascaro, J., Anderson, C., Knapp, D. E., Martin, R. E., Kennedy-Bowdoin, T., van Breugel, M., Davies, S., Hall, J. S., Muller-Landau, H. C., Potvin, C., Sousa, W., Wright, J., & Bermingham, E. (2013). High-fidelity national carbon mapping for resource management and REDD+. Carbon Balance and Management, 8(1), 7.
4. Atkins, J. W., Bohrer, G., Fahey, R. T., Hardiman, B. S., Morin, T. H., Stovall, A. E. L., Zimmerman, N., & Gough, C. M. (2018). Quantifying vegetation and canopy structural complexity from terrestrial LiDAR data using the forestr r package. Methods in Ecology and Evolution, 9(10), 2057–2066.
5. Atkins, J. W., Costanza, J., Dahlin, K. M., Dannenberg, M. P., Elmore, A. J., Fitzpatrick, M. C., Hakkenberg, C. R., Hardiman, B. S., Kamoske, A., LaRue, E. A., Silva, C. A., Stovall, A. E. L., & Tielens, E. K. (2023). Scale dependency of lidar-derived forest structural diversity. Methods in Ecology and Evolution, 14(2), 708–723.
6. Atkins, J. W., Walter, J. A., Stovall, A. E. L., Fahey, R. T., & Gough, C. M. (2022). Power law scaling relationships link canopy structural complexity and height across forest types. Functional Ecology, 36(3), 713–726.