Biology's Coefficient

Joel Cohen uses the tools of mathematics to deconstruct questions of life.

By | December 1, 2013

Laboratory of Populations
Rockefeller University & Columbia University
New York, New York
In 1992, Joel Cohen received a phone call from a journalist at Discover magazine. The journalist asked Cohen, a professor of populations at Rockefeller University with doctorates in applied mathematics and public health, “How many people can the Earth hold?” Cohen replied honestly: “I said to him, ‘I don’t know. I’ll try to find out for you.’ I said to myself, ‘This is your business. You’re supposed to know! What’s the matter with you?’”  

Cohen spent the next six weeks reading studies that estimated Earth’s human carrying capacity based on a variety of data, from water and land use to food production to mineral availability to energy. “The more I dug, the more fascinated I became that everybody had an answer, but none of the answers agreed,” says Cohen. “They were all based on different assumptions. . . . The substance just was not there.”

Cohen became so irritated with the answers available that he spent the next four and a half years compiling more than 60 studies and developing mathematical models of the planet’s human carrying capacity. The book and Science paper he ultimately published on the topic concluded that Earth’s human carrying capacity is dynamic, uncertain, and shaped by the interactions of populations, economics, the environment, and cultures. The ecological notion of carrying capacity, while excellent for describing antelope populations on the plains, is not a useful tool for thinking about the challenges facing humans.

“Mathematical thought is the railroad over which we carry the freight of scientific discoveries. And I’ve wanted to help lay a few additional tracks.”

That study of Earth’s human population is only a drop in the bucket of the diverse, seemingly disparate, subjects that Cohen has addressed in his five-decade-long career. His studies of food webs, asbestos-related litigation, and infectious disease have resulted in more than 390 papers and 14 books, and all these pursuits are underwritten by Cohen’s passionate belief that mathematics contains the most powerful tools for considering the problems of life. “Mathematical thought is the railroad over which we carry the freight of scientific discoveries,” says Cohen. “And I’ve wanted to help lay a few additional tracks.”

Here Cohen illuminates how he chose some of those tracks, from a bathtub epiphany about a geometric probability model, to an illustration in a textbook that led him to redefine the study of food webs, to a just-for-the-fun-of-it map of human population by elevation that led to insights about a rare form of cancer.


Logarithmic worms. Cohen grew up in the small town of Battle Creek, Michigan, known best as the birthplace of Kellogg’s Corn Flakes. In junior high, “the teacher permitted me to sit in the back and teach myself mathematics one year ahead of my grade level,” recalls Cohen. The young student also excelled at piano, and while studying music composition at the University of Michigan, Cohen occasionally found himself waiting inside the University of Michigan library for his ride home. “Once, I was in the library, and on a table was a fat, bound volume of the Journal of General Physiology. It was open, so I just started reading it, and there was an article about some worms. If you shined light on them from the side, they would turn their head, and the amount of turning was proportional to the logarithm of the light intensity. I had just learned about logarithms, and I was astonished that the worm apparently knew about logarithms when it had just taken me a lot of trouble to understand them. That’s what gave me the idea that maybe mathematics has some key to understanding life processes.”

Rock and a hard place. Cohen enrolled as an undergraduate at Harvard in 1961. “When I arrived as a freshman, I went to the math department and said I’d like to major in mathematics and biology. They said, ‘I’m sorry, we don’t do that. We study mathematics. You should go to the biology department.’ So I went down the street to the biology department, and they said, ‘We can’t help you. We study biology.’ I looked at the criteria for both majors and picked the one requiring fewer courses, that left me the most room to take courses in the other subject. That turned out to be mathematics. Then, in my senior year, the university created a new undergraduate major called applied mathematics, and that was perfect for me.”

Thought bubble. For his undergraduate thesis, Cohen took on a unique project, one that wove together ideas from his ecology and economics classes. He adopted a mathematical model of ecological competition, previously used to measure the abundance of bird species competing for similar food, and used it to predict the size of industrial firms producing similar products, such as concrete or steel plate. “It was the same idea dressed up in a different context,” says Cohen. Shortly after graduating, while he was on a 14-month fellowship traveling the world, that thesis came back to haunt him. “I bought a pirated edition of a famous textbook of statistics by Kendall and Stuart, The Advanced Theory of Statistics, and I carried it around in my suitcase. I remember lying in the bathtub in Hong Kong, reading Kendall and Stuart, and I came across the same formula I had used in my undergraduate thesis for firm sizes, but derived in a completely different way. I almost jumped out of the bathtub. The realization that completely different mechanisms could lead to the identical mathematical formula was an education to me.”

Monkeying around. After a summer spent in East Africa studying baboon populations with Jeanne and Stuart Altmann, Cohen completed a PhD at Harvard in applied mathematics. His thesis project was a mathematical model describing the distribution of primate social groups. “I went into [my advisor] Fred Mosteller’s office with my results, and he said, ‘That’s lovely, but you haven’t collected your own data. You need to do that.’ I was upset because I thought I was finished—and it added a year and a half to my PhD—but in the end, I was enormously grateful to him for insisting.” To collect data on primate social groups, Cohen visited a local nursery school, where he sat in the corner recording the size and composition of toddler social groups every 10 seconds. “The kids came over and wanted to play with me, but I would just smile and not respond, so they left me alone. Well, except one little kid who kept yelling, ‘Teacher, there’s a man sitting in the corner!’”  

Making an impact. Cohen went on to earn a second doctorate at Harvard, this time in public health, inspired by his 14 months abroad after college. “I was not going through rich urban centers; I was out in the boondocks on these travels. It completely changed my image of the world. It is a gut-wrenching experience to see children go blind because of trachoma, an infectious disease. It is easily treatable, it’s just they don’t know anything about the treatment and they don’t have access to it. That convinced me that medical school, which I had thought of as a way to get biological training, was not going to fly. Instead, it convinced me that public health was a way to respond.” 


The value of variation. In 1975, at the age of 31, Cohen began research at Rockefeller University, where he has continued to develop mathematical models to understand populations. His work has spanned three primary biological areas: food webs, population dynamics, and infectious diseases. His fascination with food webs began at Harvard. “Ed [E. O.] Wilson assigned a textbook, Growth and Regulation of Animal Populations by L.B. Slobodkin, in his course on evolution. [The book] was new and hot at that time. And in it, there were pictures of food webs: there was a picture of one food web on one page; a picture of another food web on another. And that was it. It was like butterfly collecting before Darwin. There was absolutely no theory of their structure, no generalizations. It was just, ‘Aren’t these beautiful?’ Well, yes, they are beautiful, but come on! Where do they come from? How do they work? So I started looking around in the scientific literature for more examples.”

Tangled web. “I was burning to get more of these [food webs] and analyze them statistically. I collected a few, then a few more, and by the early 1970s I had a few dozen. It was about a 15-year project, with no publications for the first 14 years.” But eventually Cohen did publish the work, including two papers in 1977, one in Nature and one in PNAS, and a book in 1978. Across those works, Cohen developed probabilistic models of food web structure and introduced the concepts of community food webs, source food webs, and sink food webs. More recently, he and colleagues premiered a new food web graph that incorporates body-mass measurements and species abundance.

Unexpected applications. In 1974, Cohen spent a year at the University of Cambridge in the United Kingdom as a visiting scholar, doing an intense study of uncertainty in population projections. “If you look at birth and death rates, they are not constant—they fluctuate. But the models most people were using for population dynamics assumed constant birth and death rates. So I started to look around for mathematical models which would permit me to recognize and analyze the true variability.” In 1976 and 1977, Cohen published some of the first methods for assessing the uncertainty of population projections. Unexpectedly, the work attracted the attention of lawyers and federal judges who were trying to predict how many asbestos-related tort liability claims might arise, yet were unable to account for uncertainty in their bankruptcy models. Cohen worked as a legal consultant to banks in defining that uncertainty, then served as a neutral expert for a U.S. Federal Court for asbestos-related claims, eventually analyzing huge amounts of claims data and coauthoring a book on the topic in 2004. “Purely basic research . . . led to expertise in uncertainty in population projects, which led to a very practical application affecting the health and incomes of lots of people,” says Cohen. “That is a chain that you could not predict.”

Such great heights. Many of Cohen’s basic-research projects, in fact, have had unexpected practical applications. In 1995, researchers in California published the first digital map of the Earth’s population. “I asked a geophysicist, Chris Small, what we could do with this. He said he had a digital map of the Earth’s elevation, so just for the fun of it we put one map on top of the other map in a computer.” The result, the first distribution of human population by elevation, was published in 1998. “We did it because we could do it, out of curiosity. Then we started getting inquiries.” Procter & Gamble called for more details because the formulation of laundry soap depends on elevation. Intel called to learn more because cooling fans in computers depend upon the density of air. And a cancer epidemiologist from the University of Pittsburgh called to ask Cohen to perform a few calculations concerning what appeared to be an elevated risk of a rare form of head and neck cancer for people at high altitudes, work that was published in 2003. “These are not applications we could possibly have foreseen,” says Cohen. “But once we published the idea, other people jumped on it. Basic research has the most unexpected practical applications.”

Interrupting infection. Cohen also kept up his interest in public health. One major area of his infectious disease research has been the transmission cycle of Chagas disease, which is caused by a protozoan parasite, Trypanosoma cruzi, transmitted by bloodsucking “kissing bugs” in rural, tropical areas of the Americas. “The parasite infects dogs and cats, and to make it more complicated, chickens also provide blood meals to the insects, but aren’t vulnerable to infection. It’s a really hairy food web. People in arid regions in northwest Argentina, where the fieldwork I’m involved in goes on, like to keep dogs under their beds at night, which provides a source of infection to the bugs. We tried to model this whole system of populations in a simple way, and the bottom line was if you can get dogs out of the bedroom, you can reduce the risk of infection dramatically.” Following the conclusion of the study, published in Science in 2001, Cohen and his colleagues have begun to educate villagers about the risks of dogs in the bedroom.


And the award goes to . . . Over his career, Cohen has been awarded numerous accolades, including a MacArthur Fellowship. “I like all awards—they flatter my ego—but I don’t take them too seriously. I’ve been on selection committees enough to know there’s a very large random element, and there are many, many deserving people who don’t get awards. So I’m quite philosophical about whether these awards mean you’re a better person. I don’t think so. It’s no substitute for trying to do good science.”

Sense of humor. In 1992, Cohen and coauthor Betsy Devine published a book of science jokes called Absolute Zero Gravity: Science Jokes, Quotes, and Anecdotes. “I use jokes a lot in my lecturing. It’s a way to get people to pay attention and often to make a point. I recently gave a plenary lecture at the International Congress of Ecology to 2,000 people, and I was talking about Taylor’s Law, [a mathematical law in ecology] that I’m working on right now. I started to go into details, then I stopped and said, “No. Mathematics is like sex. It’s okay to talk about it, but you probably shouldn’t really do it in public.”

Future generations. “I wish more young people found science attractive. I think it’s important. When I was a kid, it was just post-Sputnik and there was money to do science. I think we should be investing more in long-term basic science education and research.” 

Greatest Hits

  • Was the first to investigate ensembles of food webs; introduced the concepts of community food webs as well as source and sink food webs.
  • Developed a framework for assessing the uncertainty of population projections and applied that framework to asbestos-related tort liability claims.
  • Showed that the concept of carrying capacity has limited utility when applied to human populations.
  • Developed a mathematical model of the risk of household transmission of Chagas disease to humans.

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