Modeling the forest … and the trees

When building computer models of the ecosystems that cover the earth’s surface, it is tempting to incorporate sweeping generalizations in your calculations.

The difficulty, of course, is that there is no guarantee that nature generalizes in the same way. All the interactions of individual plants and animals have their own sets of causes and effects.

Accurately capturing the aggregate response of an ecosystem or an animal population that arises from all those causes and effects is critical if computer models are to be effective crystal balls for predicting how ecosystems respond to climate change, or how an animal population will respond to changes in its landscape. Paul Moorcroft, professor of organismic and evolutionary biology, is using tools borrowed from statistical physics to create models that will increase our ability to evaluate different courses of action in environmental management and global warming.

“He had this beautiful insight that we should look at a forest from the level of individual trees,” said Steven Wofsy, Abbott Lawrence Rotch Professor of Atmospheric and Environmental Science and collaborator with Moorcroft. “He could look at systems and take apart systems at a level nobody else could.”

Moorcroft borrowed concepts that physicists use in modeling fluids and gases, where the properties and behaviors of individual particles are used to predict the dynamics and flow patterns of the fluid or gas. His models treat the individual plants within an ecosystem as a physicist would “particles,” taking into account that those individuals respond to the environmental conditions they experience, interact and affect each other’s behavior, and govern the aggregate response of the system.

“The big question facing us is how are terrestrial ecosystems responding to climate change and how will these responses feed back onto climate,” Moorcroft said.

Because ecosystems are so large, the standard approach to designing ecosystem computer models has been to aggregate large tracts into a single generalization of their behavior. The scale of a grid cell in a climate computer model is 1 degree latitude by 1 degree longitude or larger, or more than 4,000 square miles.

“It has generally been assumed that the ecosystem within each grid cell will behave like a single giant plant. That’s problematic, because we know that ecosystems are much more complex and that the true ensemble of plants is likely to behave quite differently,” Moorcroft said.

The problem with this so-called “ecosystem as big leaf” modeling approach is, of course, that 4,000-plus square miles of forest doesn’t just hold one kind of plant. Rainforests in particular hold a dazzling array of tree and plant species, each of which will respond differently to changing conditions. Those differences are particularly important when a forest is stressed, Moorcroft said, because it can affect a tree’s ability to survive following the change in environmental conditions.

That could mean that, even if all individuals of a particular tree species do in fact die off from hotter days and lower rainfall, other species of tree are likely to survive, or even thrive. When building a computer model of how global warming might impact the Amazon forest basin, capturing this reality can mean the difference between predicting a changing but persisting forest and one that will die out entirely, to be replaced by grasslands.

“In real ecosystems, there are different types of plants in different places that behave differently. This heterogeneity can be important when an ecosystem is stressed in response to climate change,” Moorcroft said. “We have been able to show that capturing this heterogeneity leads to more accurate predictions of the ecosystem’s behavior.”

Moorcroft remembers always being interested in both biology and mathematics. As an undergraduate at Cambridge University, he studied natural sciences, especially ecology, and math. Moorcroft’s interest in predicting how the terrestrial biosphere will respond to climate change grew into his doctoral thesis research at Princeton on predicting how the spatial pattern of animals on landscapes is governed by the movements of individuals.

While he was at school in the 1990s, Moorcroft said there was a movement in ecology to understand how individual dynamics collectively determine the behavior of populations, communities, and ecosystems. Coupled with that was the emphasis at Princeton of employing mathematical models to address ecological questions.

Moorcroft joined field biologists collecting radio tracking data on coyotes in Yellowstone National Park in advance of the wolf reintroduction. He searched the literature to see how the populations had been analyzed in the past and was surprised to see that the work to date was merely descriptive. In response, he dove into an effort to use mathematical approaches similar to those used in physics to understand how the movement behavior and interactions of the coyotes resulted in their eventual distribution across the landscape.

In building his model, he started with a set of movement rules for an individual coyote. He then compared the spatial distribution of coyotes across the landscape that would result from those rules. The result was a model that was able to predict how the spatial pattern of the coyotes would change in the future.

“We showed that it was possible to translate hypotheses about the movement behavior of animals into a testable prediction,” Moorcroft said. “The movements of coyotes are influenced by the availability of food in different habitats, but they are also affected by avoidance responses that coyotes exhibit when they encounter individuals from different packs. We were able to use observational data to obtain quantitative estimates for these two different forms of movement behaviors, and once we had done so we were able to accurately predict how the spatial pattern of coyotes across the landscape would change in response to the loss of coyote packs.”

Moorcroft received his doctorate in ecology and evolutionary biology from Princeton in 1997 and worked as a postdoctoral fellow at the Princeton Environmental Institute until 2001.

It was during that time that Moorcroft began applying similar methods to plants, drawing up equations to explain how the properties and dynamics of individual plants give rise to an ecosystem’s dynamics.

“The mathematical approach for scaling from individual plants up to ecosystem dynamics is similar to scaling from individual movements up to the spatial distribution of animals on a landscape,” Moorcroft said.

Moorcroft came to Harvard in 2001 as an assistant professor. He was named an associate professor in 2005 and professor of organismic and evolutionary biology in 2007.

Today, Moorcroft runs a research group with four postdoctoral fellows, three graduate students, and a research assistant. All but one are working on predicting how ecosystems around the globe will be affected by climate change. Their studies span the world, encompassing tropical forests in the Amazon and Southeast Asia, temperate forests in the eastern United States, the boreal forests of Canada and Alaska, and the Greater Yellowstone ecosystem. The other researcher is working with the U.S. Fish and Wildlife Service to apply Moorcroft’s predictive models of animal movement to the conservation and management of animal populations.

“It’s a dynamical model, once you have it you can make predictions about how changes in habitat, management practices, and climate will affect populations,” Moorcroft said.

Using data collected by Wofsy at Harvard Forest, Moorcroft has been able to show that the ability to quantitatively link the ecosystem-level responses to the dynamics and properties of individual plants leads to improved regional scale predictions of ecosystem dynamics. They are now engaged in a similar exercise for the forests of the Amazon basin in order to better predict how climate variability and change are going to affect the Amazon forest and the exchanges of carbon, water, and energy between Amazonian ecosystems and the atmosphere.

“That’s what other people can’t do,” Wofsy said. “He can predict very difficult-to-predict systems.”