The Stochastic Forest

Modeling Black Rock Forest of the future

By Jeff Simms


Want to know the connection between the 3,914-acre Black Rock Forest and the study of probability? Better yet, want to know what Black Rock Forest could look like 200 to 300 years from now? Stay tuned, you may just get a preview as a research project at the Forest evolves.  

Pace University mathematics professor Meng Xu has begun analyzing nearly a century of data on the Forest as a means for modeling biomass, or the sum of all natural life in a given area, and projecting what it might look like many decades into the future — as climate change and other factors affect the Forest’s long-term health.

Xu, who became familiar with Black Rock Forest while completing his postdoctoral studies at Rockefeller University from 2011 to 2013, is analyzing three “demographic functions” found in current and historical Forest data: the mean growth rate for individual trees, the variance of the growth rate for those individuals, and the trees’ mortality rates. He is pursuing a grant proposal to explore those long-term dynamic statistics through a stochastic, or randomly determined, model, which he believes can help predict the unpredictable, so to speak, by projecting what the Forest’s composition could look like in the future.

While history isn’t likely to repeat itself exactly, it can provide valuable clues about how the forest has reacted to external changes over time. 

How many trees in the Forest, for example, are five centimeters in diameter, and what has their mortality rate been, presently and historically? “The key implication is to understand how the forest will change,” Xu says. 

His work continues a line of inquiry begun in Japan in the 1980s by forest ecologists who were attempting to understand individual size distribution of trees. Over time, they also asked questions like, Were there more large trees or small ones in a given region? The answers would help them evaluate how the total biomass of the forest was changing over time.

At the time, those scientists were limited to a few relatively simple mathematical functions to apply to their research. Today, Xu, whose specialties are applied statistics and ecological patterns, is able to use models that employ demographic functions — the trees’ growth and mortality rates — which are both more complex and more powerful, enabling more accurate predictions about forest composition and health.

Predicting “the distribution of biomass as it’s related to global warming will be the ultimate implication of this research,” Xu continues.

Climate change represents perhaps the greatest challenge the natural world has ever faced. But by by analyzing historical data — which has been recorded at the Forest since the 1930s — through the lens of probability, Xu and his colleagues hope to make educated predictions about wildlife habitat and overall ecosystem health.

As the planet continues to warm, those predictions could form a roadmap for the future, says Bill Schuster, the executive director of Black Rock Forest. 

“Humans now exert major influences on nature and life on Earth, and with that development has come significant potential for us to harm our own future and that of other organisms,” Schuster says. “For example, if science indicated that the Forest was on a trajectory in 200 years to have lost its productivity, its native species, and its ability to clean our air and water, that would be valuable information for helping us decide if and how to act to alter that trajectory. But only if we are aware of what the future likely holds can we design attempts to influence its course.”