Model works out trees' maximum height

Researchers hope the model will help ecologists improve their understanding of forest ecosystems

Scientists have developed a mathematical model that predicts the maximum height trees can reach in particular environmental conditions.

They hope their model will help ecologists get a better understanding of the relationship between trees and the surrounding ecosystem.

The tool could also help policymakers calculate how climate shifts could affect timber yields, they added.

The findings have been published in the journal Plos One.

"The real goal of the model was to produce something that was based in fundamental mechanisms," explained co-author Chris Kempes, a PhD researcher from the Massachusetts Institute of Technology's (MIT) Department of Earth, Atmosphere and Planetary Sciences.

"This looks at the basic physics affecting a tree, such as internal fluid flow and the structure of the canopy," he told BBC News.

"We really wanted something that was based in those mechanisms but at the same time was, conceptually, relatively simple."

He said tree branches formed a fractal, which meant that if you effectively cut off a branch and then enlarged it, it looked like a whole tree.

"If you nail down that network structure correctly, then you can use it to predict how things change with size."

From this framework, the team then incorporated local meteorological data, such as rainfall and mean annual temperatures, to allow them to predict the maximum height of trees in the area.

When compared with official data collected by the US Forest Service, the team found that their predictions tied in closely with the actual measurements.

Interestingly, the model was based upon an "idealised" tree - one that was designed to represent all tree species, and was not adapted to reflect the type of tree being modelled.

"If we are making a prediction in the North-West, where there is a lot of rain and very tall trees, or if we are making a prediction in the South-West, we don't actually change the model in terms of species traits," Mr Kempes said.

"Our 'test tree' that we use to make these predictions remains the same across environments."

The team also used the model to look at what would happen to maximum tree heights if there was a change in the national mean annual temperature.

They found that a 2C (3.6F) increase resulted in the average maximum height of trees shrinking by 11%, while a 2C decrease in the nation's average temperature saw a 13% increase in the predicted maximum height of trees.

Mr Kempes observed that this sort of prediction could be useful for policymakers who wanted to know what sort of impact climatic shifts would have on the country's forests.

"[The model] might help inform any number of policies in terms of how much you could expect timber yields to change," he said.

He added that the model was likely to work in other regions of the world, not just in the US.

The team hope to develop the model in a way that will allow them to predict the potential height of particular tree species.

"If you take a really small juniper tree that lives in the desert and you put it in the North-West, it will grow to perhaps four times as tall, but it won't grow to be the height of a redwood.

"This is what all of ecology is interested in: how much of your existence is determined by the environment verses your genetics?"