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The Greener Side of Math: A Statistician in the Plant Science World

Andrew Fazekas
Canada
10 February 2006

Whereas many people marvel at the natural beauty of plants and trees, when Pierre Dutilleul (pictured left) looks, he sees the mathematics behind their elegant designs. Although trained as a statistician--he is one of only a handful of stats-trained professors in the world situated in a plant science department--Dutilleul has spent 2 decades branching out. “I am curious and have an open mind,” he says. “I like to think that I am building bridges between the worlds of mathematics and applied sciences.” After 2 decades of research, he continues to build bridges between two distinct approaches, the theoretical and the experimental.

Since joining the faculty of McGill University's Department of Plant Science in 1992, Dutilleul has teamed up with scores of applied researchers and graduate students, tackling diverse problems in the plant sciences, from agriculture to forest ecology. Because he is the department's resident statistician, his talents have remained in great demand by researchers looking to optimize experimental designs and spatio-temporal analyses. He has managed consistently to extract new information from data via powerful and efficient methods of estimating and testing.

Branching Out

Nowhere is the convergence of his mathematics and plant science works more evident than in the up-and-coming field of phytometrics. Best described as an offshoot of biometrics, the work involves collecting data on plant structures, such as root systems and branching patterns, and analyzing structural complexity statistically. Dutilleul and his McGill group have started by applying phytometrics to study the branching patterns in trees and assess the effects of architecture on the ability of a tree to capture light.

The CT scanner operator pre-screening the CT images that are being produced for the 'subject' on the couch in the CT scanner room.

Researchers have long known that there is a relationship between light interception and the amount of leaves. But Dutilleul and his group have found a way to add a measure of branching complexity into this relationship. He hopes his research can shed light on CO₂-recycling patterns in trees, and consequently, on climate change. “If we can understand better how trees with different structures intercept light in the process of photosynthesis, then we can try to grow trees of a given type or a given structure to do a better job in recycling CO₂,” he explains.

Using a recently acquired computed tomography (CT) scanner like those used in the medical field, the McGill team has been able to follow live cedar saplings through space and time as their canopies grow. The large data set resulting from CT scanning at a given time is run through software developed by one of Dutilleul’s graduate students, which applies fractal analysis to the branching pattern from a skeletonized, 3-dimensional model of the canopy. It's the first time a CT scanner has been used to study plant canopies like this. Sowing Seeds Dutilleul traces his roots in plant science to his doctoral studies in mathematics in Belgium at the Université Catholique de Louvain, which he started in 1985. Because his supervisor was in the Faculté des sciences agronomiques, he had many opportunities to apply his statistical skills to ongoing research projects within the university. “I was in touch with other students and researchers who were constantly asking me to consult on their projects in plant breeding and related topics," he says.

False-colored and skeletonized three-dimensional renderings of the complete canopy of a pyramidal cedar (Thuja occidentalis, Fastigiata)

By the time he finished his degree in 1990, he had published several papers in plant breeding and in agricultural economics and tree-ring series analysis in Africa. He had already decided that he did not want to be a theoretical mathematician; rather, he wanted to grow a career where he could develop and apply statistical models to applied sciences. He expanded his collaborations with chronobiologists, ecologists, and plant geneticists while doing a postdoc at Université de Montréal over the next 2 years.

Dutilleul and 'Thuja', the 'subject' to be CT scanned, as photographed from behind the CT scanner.

In 1992, he heard of the opening for an applied statistician position at McGill’s Department of Plant Science. The job description matched him perfectly. It was, he insists, pure coincidence; he was at the right place at the right time. The department was looking for a “true” statistician to teach undergraduate and graduate courses, but also someone who could combine teaching, consulting, and collaborative research. “They saw that, because of the real-world statistical applications that I had already done, I was probably open to working with researchers in agriculture, environment, and plant science,” he says. He wonders, though, if perhaps it was more than just coincidence; his name, he points out, is the French word for the Linden tree! Don Smith, Professor and Chair of the McGill Department of Plant Science, describes Dutilleul’s contributions as vitally important. “He’s been an asset to the department, and I think what he’s doing will in the long term be enormously beneficial to plant biology,” Smith says, while praising Dutilleul's patience, openness to new ideas, and special knack for making the right mathematical connection. “I think it has a lot to do with Pierre’s personality in that he is willing to venture out on a limb and has the drive to do it. He merges recent advances in statistics with new technologies and applies the result to plant science; having someone who brings these things together definitely creates unique opportunities.”

Shaking the Tree

Dutilleul believes his success has come in part from his desire to communicate with other scientists. Many times when people come to him with statistical questions, the answers that he gives set off a train of thought which leads to new ideas, just as with the tree branching study.

He follows his instincts and hunches when choosing projects and does try not to let life’s chance events dictate the path his career will follow, despite the serendipity that led to his current position. “In the last 15 years, I had some good intuition that I always made sure I would follow up on,” says Dutilleul. “It’s good to have long-term objectives and a clear vision; even if the idea seems crazy at first sight, don’t give up.”

Collaboration, says Dutilleul, is crucially important, and that requires good communication with a clear line of dialogue. “When people come to me with questions about statistical analysis of data, the first few minutes are spent on discussing the work they do in their field and what it means. Then I spend some time explaining what my work means.”

Since he was hired in 1992, Dutilleul has seen both his own attitude and the attitudes of others around his department evolve. Working on what he describes as “real-world” problems has given him a deeper understanding of applied sciences, while his colleagues have come to treat him as one of their own, and as someone who can help them improve their research and bring it to a new level. He sees it as an exercise in translation between two languages. “I translate their questions and problems that are in apparently unrelated situations, using words and statistical concepts that are more familiar to me, and then try to form links with previous problems I have solved in the past. Some may have seen me as a ‘number cruncher’ the first time I came onboard, but I think those people have rapidly changed their minds.”

Andrew Fazekas is a correspondent at Next Wave and may be reached at afazekas@aaas.org.

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