New Mathematical Model for Forest Canopy Competition

Scientists have studied competitive growth among trees and their interaction within the forest canopy layer for years.

Determining which species of trees are overtopping and/or crowding out other species can give important clues regarding the health and diversity of a particular section of forest. Hoping to improve the canopy analysis, scientists at Brown University and the Carnegie Institution for Science created a mathematical model for the prediction of how trees will compete for space within the canopy layer of a forest. Their work was published in a recent online edition of Ecology Letters.

The lead author, James Kellner of Brown University, was inspired to create this model by some interesting work done in a forested area on the windward flank of Manua Kea, a dormant volcano on the big island of Hawaii. Kelllner was studying the growth of the forest using overhead LIDAR images, and noticed what appeared to be small areas of implausible growth changes, in the range of 10-15 meters in height difference, within a two-year time span. The data was indeed correct, but it didn't indicate a sudden change in height-it indicated horizontal growth. Taller trees were growing slightly to the side and either filling in a hole in the canopy or overtopping a nearby, shorter tree.

Kellner and his colleague from the Carnegie Institution, Gregory P. Asner, were able to construct a mathematical model to assess the probability that a height change is through normal tree growth, lateral growth of that tree, or an overtopping of that tree by a taller neighbor. They discovered that aside from relatively short trees (shorter than 11 meters), the overall tree height was a minor factor in whether or not it would be overtopped. What did matter the most was the proximity of any taller neighbors. In almost 4,000 cases of overtopping they noted, only two involved distances greater than 1.77 meters (a little under six feet)-not a very large distance at all relative to the heights of the trees involved.

In other words, taller trees can overtop their neighbors, but need to be reasonably close to do so. While that may seem obvious, the maximum distance for the Hawaiian forest may not be the same for other forests, since different species of trees have different lateral growth rates. Since the model uses the normal growth for the forest rate as a baseline to look for anomalies, this model can be applied to any variety of forest where the baseline growth rate is known.

What are the uses of such a model? Accurate measurement of forest growth and correct interpretation of the data could help scientists note when a particular species of tree is in jeopardy of being displaced, how well a particular species is filling in any holes in the canopy and of how much more carbon can be removed from the atmosphere due to the increased growth of the trees. This model should be a useful tool to provide more accurate results, and may find utility elsewhere in the plant world.