The editorial contained a disclosure that the group had received an "unrestricted education gift" from Coca-Cola.
In response to a request made under the state Freedom of Information Act, the University of South Carolina disclosed that Dr. Blair had received more than $3.5 million in funding from Coke for research projects since 2008.
The university also disclosed that Coca-Cola had provided significant funding to Dr. Hand, who left the University of South Carolina last year for West Virginia. The company gave him $806,500 for an "energy flux" study in 2011 and $507,000 last year to establish the Global Energy Balance Network.
It is unclear how much of the money, if any, ended up as personal income for the professors.
"As long as everybody is disclosing their potential conflicts and they're being managed appropriately, that's the best that you can do," Dr. Hand said. "It makes perfect sense that companies would want the best science that they can get."
The group's president, Dr. Hill, also has financial ties to Coca-Cola. The company last year gave an "unrestricted monetary gift" of $1 million to the University of Colorado Foundation. In response to a request made under the Colorado Open Records Act, the university said that Coca-Cola had provided the money "for the purposes of funding" the Global Energy Balance Network.
Dr. Hill said he had sought money from Coke to start the nonprofit because there was no funding available from his university. The group's website says it is also supported by a few universities and ShareWIK Media Group, a producer of videos about health. Dr. Hill said that he had also received a commitment of help from General Mills, as well as promises of support from other businesses, which had not formally confirmed their offers.
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He said he believed public health authorities could more easily change the way people eat by working with the food industry instead of against it.
On its website, the group recommends combining greater exercise and food intake because, Dr. Hill said, " 'Eat less' has never been a message that's been effective. The message should be 'Move more and eat smarter.' "
He emphasized that weight loss involved a combination of complex factors and that his group's goal was not to play down the role of diet or to portray obesity as solely a problem of inadequate exercise.
"If we are out there saying it's all about physical activity and it's not about food, then we deserve criticism," he said. "But I think we haven't done that."
But in news releases and on its website, the group has struck a different tone.
"The media tends to blame the obesity epidemic on our poor eating habits," one recent news release states. "But are those french fries really the culprit? Dr. Steve Blair explains that you shouldn't believe everything you see on TV."
In the news release, Dr. Blair suggests that sedentary behavior is a bigger factor.
Most public health experts say that energy balance is an important concept, because weight gain for most people is about calories in vs. calories out. But the experts say research makes it clear that one side of the equation has a far greater effect.
While people can lose weight in several ways, many studies suggest that those who keep it off for good consume fewer calories. Growing evidence also suggests that maintaining weight loss is easier when people limit their intake of high glycemic foods such as sugary drinks and other refined carbohydrates, which sharply raise blood sugar.
Physical activity is important and certainly helps, experts say. But studies show that exercise increases appetite, causing people to consume more calories. Exercise also expends far fewer calories than most people think. A 12-ounce can of Coca-Cola, for example, contains 140 calories and roughly 10 teaspoons of sugar. "It takes three miles of walking to offset that one can of Coke," Dr. Popkin said.
In one of the most rigorous studies of physical activity and weight loss, published in the journal Obesity, scientists recruited 200 overweight, sedentary adults and put them on an aggressive exercise program. To isolate the effects of exercise on their weight, the subjects were instructed not to make any changes in their diets.
Participants were monitored to ensure they exercised five to six hours a week, more than double the 2.5 weekly hours of exercise recommended in federal guidelines. After a year, the men had lost an average of just 3.5 pounds, the women 2.5. Almost everyone was still overweight or obese.
"Adding exercise to a diet program helps," said Dr. Anne McTiernan, the lead author of the study and a researcher at the Fred Hutchinson Cancer Center in Seattle. "But for weight loss, you're going to get much more impact with diet changes."
But much like the research on sugary drinks, studies of physical activity funded by the beverage industry tend to reach conclusions that differ from the findings of studies by independent scientists.
Last week, the Pennington Biomedical Research Center in Louisiana announced the findings of a large new study on exercise in children that determined that lack of physical activity "is the biggest predictor of childhood obesity around the world."
The news release contained a disclosure: "This research was funded by The Coca-Cola Company."
Kelly D. Brownell, dean of the Sanford School of Public Policy at Duke, said that as a business, Coke "focused on pushing a lot of calories in, but then their philanthropy is focused on the calories out part, the exercise."
In recent years, Coke has donated money to build fitness centers in more than 100 schools across the country. It sponsors a program called "Exercise is Medicine" to encourage doctors to prescribe physical activity to patients. And when Chicago's City Council proposed a soda tax in 2012 to help address the city's obesity problem, Coca-Cola donated $3 million to establish fitness programs in more than 60 of the city's community centers.
The initiative to tax soda ultimately failed.
"Reversing the obesity trend won't happen overnight," Coca-Cola said in an ad for its Chicago exercise initiative. "But for thousands of families in Chicago, it starts now, with the next push-up, a single situp or a jumping jack."