Mathematics Of Decomposition And Carbon Dioxide
October 4, 2012

MIT Researchers Devise Mathematical Model To Track Leaf Decomposition

April Flowers for - Your Universe Online

The fall leaves look like confetti piling up in your back yard with brilliant reds, golds, and oranges. They can be thought of as natural stores of carbon, as well as a beautiful nuisance that you have to rake up each Autumn. Leaves soak up carbon dioxide from the atmosphere in the spring, converting the gas into organic carbon compounds. In the fall, the leaves fall from the trees and decompose in the soil as they are eaten by microbes. Decaying leaves release this carbon back into the atmosphere as carbon dioxide.

More than 90 percent of the yearly carbon dioxide released into the atmosphere and oceans can be accounted for by natural decay of organic materials. Understanding the rate at which leaves decay helps researchers predict the annual global flux of carbon dioxide and develop better models for climate change.

This isn't as straightforward as it seems. A single leaf may undergo different rates of decay based on a number of different elements: the local climate, soil, microbes and the composition of the leaf. With this many variables, differentiating the decay rates among various species, let along whole forests, is a task of monumental proportions.

A research team from MIT has analyzed data from a variety of forests and ecosystems across North America to discern general trends in decay rates among all leaves. To transform observations of decay into distribution routes, they devised a mathematical model. The shape of the resulting curve is independent of climate, location and leaf composition. However, the details of that shape — the range of rates that it spans, and the mean rate — vary with climatic conditions and plant composition. In general, the team found that the range of rates was determined by plant composition, and as temperatures increase, all plant matter decays more rapidly.

"There is a debate in the literature: If the climate warms, do all rates become faster by the same factor, or will some become much faster while some are not affected?" says Daniel Rothman, a co-founder of MIT's Lorenz Center, and professor of geophysics in the Department of Earth, Atmospheric and Planetary Sciences. "The conclusion is that all rates scale uniformly as the temperature increases."

An independent 10-year analysis of North American forest called the Long-term Intersite Decomposition Experiment Team (LIDET) provided the data for this study. Researchers collected leaf litter, including grass, roots, leaves and needles, from 27 locations throughout North and Central America. The sites range from the Alaskan tundra to the Panamanian rainforests.

LIDET scientists separated the litter into like types and then weighed it. They then identified litter composition and nutrient content. The samples were stored in porous bags and buried in each of the 27 geographic locations, each bag filled with a different litter type. The sample bags were dug up annually and reweighed. The data collected represented the mass of litter, of different composition, remaining over time in different environments.

Using the publicly available DATA, the MIT team accessed and analyzed each dataset; the litter originating at one location, subsequently divided and distributed at 27 different locations, and weighed over a 10 year period. This allowed the team to develop a mathematical model to convert the hundreds of mass measurements of each dataset into rates of decay. The scientists then plotted the converted decay rates on a graph, with surprising results. The distribution of decay rates for each dataset was roughly the same, forming a bell curve when plotted as a function of the order of magnitude of rates. This made a surprisingly tidy pattern, considering the complexity of parameters affecting the decay rate.

"Not only are there different environments like grasslands and tundra and rainforest, there are different environments at the microscale too," David Forney from the Department of Mechanical Engineering says. "Each plant is made up of different tissues “¦ and these all have different degradation pathways. So there's heterogeneity at many different scales “¦ and we're trying to figure out if there's some sort of commonality."

Forney and Rothman investigated parameters that affect leaf decay rates. While all of the datasets resembled a bell curve, there were slight variations between them. Some curves were flatter, while others had high peaks. Some curves shifted to the left of the graph, while still others shifted to the right. Trying to understand the variations, the team discovered the two parameters that most affected the details of a dataset's curve; climate and leaf composition.

Warmer climates tend to speed the decay of all plants and colder climates slow plant decay at a uniform rate. The implication, the researchers found, is that as temperatures increase, all plant matter, regardless of composition, will decay more quickly, with the same relative speedup in rate.

The study revealed that plant matter such as needles that contain more lignin, which is a sturdy building block, have a smaller range of decay rates than leafier plants with less lignan. The leafier plants also have more nutrients which attract microbes, further increasing their decay rate.

"This is an interesting ecological finding," Forney says. "Lignin tends to shield organic compounds, which may otherwise degrade at a faster rate."

The team might use the model in the future to predict the turnover rates of various ecosystems, which in turn may improve climate change models and help scientists understand the flux of carbon dioxide around the globe.

"It's a really messy problem," Rothman says. "It's as messy as the pile of leaves in your backyard. You would think that each pile of leaves is different, depending on which tree it's from, where the pile is in your backyard and what the climate is like. What we're showing is that there's a mathematical sense in which all of these piles of leaves behave in the same way."

The results of this study have been published in the Journal of the Royal Society Interface.