Deforestation and mathematics

Summary: Mathematicians study and model many aspects of deforestation.

Deforestation is the removal of forests by logging or burning. While some deforestation can occur accidentally as a result of wildfires, most is deliberate. Trees may be sold for lumber or charcoal, and land may be cleared for housing, farming, or pasturing livestock. Trees may also be removed for beneficial purposes, such as directing water flow or controlling future forest fires. Many people believe that deforestation is a significant factor in climate change and biodiversity loss, and research has shown that deforested regions are much more vulnerable to soil erosion and desertification.

While logging is linked to deforestation in the popular imagination, the United Nations Framework Convention on Climate Change actually found that in the early twenty-first century, logging actually accounted for less than 20% of deliberate deforestation. In contrast, commercial agriculture claimed about one-third of deforested lands and subsistence farming nearly one-half. This statistic indicates one reason why deforestation is increasing primarily in relatively poorer countries. However, within an industrialized country, like the United States, logging and clearing land for housing or other real estate development account for far more deforestation than subsistence farming, which few Americans have practiced since the dawn of the twentieth century. Mathematicians study and model many aspects of deforestation, including possible causes and the biological, geological, social, and economic effects; uses of deforested land; patterns of regrowth and biodiversity in areas where the forest has been allowed to return; and spatial mapping and visualizations of geographical regions before, during, and after deforestation. Data collection, statistical analyses, and spatial dependency analyses, as well as stochastic spatial modeling, linear programming, geometry, and digital image analysis, are all mathematical methods that have played a role in such analyses.

Environmental Effects

Deforestation is implicated in numerous environmental problems. The relationship between the forest and atmospheric carbon dioxide, for instance, is complicated. While they are alive and actively growing, trees remove carbon dioxide from the atmosphere, store it as carbon, and release oxygen back into the atmosphere through respiration. This process reduces the amount of greenhouse gases in the atmosphere, and this basic dichotomy—plants breathing in carbon dioxide and releasing oxygen, while humans and animals do the opposite—has long been taught to schoolchildren as the critically interdependent relationship between flora and fauna on Earth. In the early twenty-first century, the world’s forests store roughly three-quarters or greater of aboveground and soil carbon. When trees are cut down and burned, they release their stored carbon back into the atmosphere. When trees die and decay, they do the same, as fungi and bacteria break down the carbon products into carbon dioxide and methane. Their effect on the world’s oxygen supply is actually very minor—the amount of oxygen they release is not as significant as the amount of carbon dioxide involved in a tree’s lifespan.

But cutting trees down and turning them into long-lived products (using them to build houses, for instance) stores the carbon just as efficiently. For forests to continue to take carbon dioxide in from the atmosphere, the trees must be harvested regularly—with new trees planted—so that there are always actively growing trees. Left to their own devices, mature forests cycle through periods as carbon dioxide sources (when the carbon dioxide released by decaying or wildfire-burned trees exceeds that taken in by growing trees) and sinks (when the net carbon dioxide release is negative).

The greatest amount of carbon dioxide is taken in by deciduous trees when spring leaves are growing, which results in an observable dip in the Keeling Curve (a graph that tracks variation in the concentration of atmospheric carbon dioxide from 1958 onward). The dip is mirrored by a rise corresponding to the release of carbon dioxide back into the air every fall when these leaves fall and decay. The curve is named for Charles Keeling, a University of California, San Diego, oceanographer whose observations helped bring global attention to anthropogenic climate change. Measurements continue to be taken at Mauna Loa, in Hawaii, and those data have shown a roughly 20% to 25% increase in the amount of atmospheric carbon dioxide between 1958 and 2010. There have been no declining trends in that time, countering the pre-Keeley claim that an apparent rise in carbon dioxide atmospheric concentration was the result of random fluctuations. Periodic local decreases and increases of about 1% to 2% are associated with seasonal cycles.

Anti-Deforestation Efforts

Recent efforts to reduce greenhouse gas emissions, and international agreements binding countries to do so, have brought more focus to the task of accurately measuring those emissions. It came to light in 2010 that Australia’s efforts to reduce emissions in order to comply with the Kyoto Protocol goals were hampered by their inaccurate measurement of deforestation emissions. Since 1990, Australia has had the highest rate of deforestation in the developed world, and thus is the only developed country targeting deforestation emissions as its primary way of reducing overall emissions. But its inability to generate an accurate figure of what those emissions currently are, to establish a baseline, or reliably measure them in the future, has thrown a wrench in its efforts.

Data Collection and Mathematical Modeling

The highly complex nature of forest ecosystems and even individual trees makes it virtually impossible to collect complete data on the system dynamics of natural forests. As a result, investigations of long-term dynamics rely heavily on scientific inference. One way of making any estimate, heavily relied on when considering the environmental costs of possible actions, is through ecosystem modeling, which constructs mathematical representations of ecosystems. The entire ecosystem need not be represented (though this leaves open the possibility of unforeseen consequences in parts of the ecosystem not modeled). Typically, models are constructed to examine the inventory of a specific chemical in the environment, like carbon, nitrogen, phosphorous, or a toxin. The ecosystem is reduced to a set of state variables that describe the state of a dynamic system, like the population of a specific species or the concentration level of a particular substance.

Mathematical functions define the relationships between those variables, such as the relationship between new leaf growth and carbon dioxide intake. A usable model typically requires many variables and much fine-tuning to affirm that the relationships have been defined accurately, and, in some cases, a model may be constructed simply to test a hypothesis about those relationships, by comparing the behavior of the model ecosystem to the real one. For example, mathematician and ecologist Nandi Leslie developed mathematical models using techniques such as spatial statistics, mean field and pair approximation, and the theory of interacting particle systems to investigate questions about forest fragmentation and degradation, ecology and biodiversity in lands reclaimed by forests, and landscape-level impact of land-use activities in Bolivia and Brazil. Leslie is included on a Web site called Mathematicians of the African Diaspora and is the daughter of mathematician Joshua Leslie, who has published widely in the fields of algebraic and differential geometry. The applications of modeling in deforestation are as broad as the types of models. Some mathematicians have used calculus to measure tree density, including the number of trees per acre and the quantity of foliage. Logistic functions have been used to estimate insect density or infestations. Many linear and nonlinear modeling techniques, like regression analysis, are widely employed to help reveal and explain associations between multiple variables, such as social choices and government policies; economic measures; environmental measures; geographic features, like altitude and slope; and human constructions, like roads. These models are then frequently used to forecast important quantities of interest, like deforestation rates and the overall proportion of deforested land. However, inappropriate extrapolations and generalizations can lead people to make inaccurate predictions or conclusions. For example, extrapolations from exponential models tend to lead to overestimation of future values. This has an impact on contentious and world-reaching scientific debates, such as global warming.

Bibliography

Babin, Didier. Beyond Tropical Deforestation: From Tropical Deforestation to Forest Cover Dynamics and Forest Development. Paris: UNESCO, 2005.

Fowler, Andrew. Mathematical Models in the Applied Sciences. New York: Cambridge University Press, 1997.

Harte, John. Consider a Spherical Cow: A Course in Environmental Problem Solving. Sausalito, CA: University Science Books, 1988.

Shugart, Hurman. A Theory of Forest Dynamics: The Ecological Implications of Forest Succession Models. Caldwell, NJ: Blackburn Press, 2003.