Stuart Bradford

The basic formula for gaining and losing weight is well known: a pound of fat equals 3,500 calories.

That simple equation has fueled the widely accepted notion that weight loss does not require daunting lifestyle changes but “small changes that add up,” as the first lady, Michelle Obama, put it last month in announcing a national plan to counter childhood obesity.

In this view, cutting out or burning just 100 extra calories a day — by replacing soda with water, say, or walking to school — can lead to significant weight loss over time: a pound every 35 days, or more than 10 pounds a year.

While it’s certainly a hopeful message, it’s also misleading. Numerous scientific studies show that small caloric changes have almost no long-term effect on weight. When we skip a cookie or exercise a little more, the body’s biological and behavioral adaptations kick in, significantly reducing the caloric benefits of our effort.

But can small changes in diet and exercise at least keep children from gaining weight? While some obesity experts think so, mathematical models suggest otherwise.

Saul Loeb/Agence France-Presse — Getty Images

As a recent commentary in The Journal of the American Medical Association noted, the “small changes” theory fails to take the body’s adaptive mechanisms into account. The rise in children’s obesity over the past few decades can’t be explained by an extra 100-calorie soda each day, or fewer physical education classes. Skipping a cookie or walking to school would barely make a dent in a calorie imbalance that goes “far beyond the ability of most individuals to address on a personal level,” the authors wrote — on the order of walking 5 to 10 miles a day for 10 years.

This doesn’t mean small improvements are futile — far from it. But people need to take a realistic view of what they can accomplish.

“As clinicians, we celebrate small changes because they often lead to big changes,” said Dr. David Ludwig, director of the Optimal Weight for Life program at Children’s Hospital Boston and a co-author of the JAMA commentary. “An obese adolescent who cuts back TV viewing from six to five hours each day may then go on to decrease viewing much more. However, it would be entirely unrealistic to think that these changes alone would produce substantial weight loss.”

Why wouldn’t they? The answer lies in biology. A person’s weight remains stable as long as the number of calories consumed doesn’t exceed the amount of calories the body spends, both on exercise and to maintain basic body functions. As the balance between calories going in and calories going out changes, we gain or lose weight.

But bodies don’t gain or lose weight indefinitely. Eventually, a cascade of biological changes kicks in to help the body maintain a new weight. As the JAMA article explains, a person who eats an extra cookie a day will gain some weight, but over time, an increasing proportion of the cookie’s calories also goes to taking care of the extra body weight. Eventually, the body adjusts and stops gaining weight, even if the person continues to eat the cookie.

Similar factors come into play when we skip the extra cookie. We may lose a little weight at first, but soon the body adjusts to the new weight and requires fewer calories.

Regrettably, however, the body is more resistant to weight loss than weight gain. Hormones and brain chemicals that regulate your unconscious drive to eat and how your body responds to exercise can make it even more difficult to lose the weight. You may skip the cookie but unknowingly compensate by eating a bagel later on or an extra serving of pasta at dinner.

“There is a much bigger picture than parsing out the cookie a day or the Coke a day,” said Dr. Jeffrey M. Friedman, head of Rockefeller University’s molecular genetics lab, which first identified leptin, a hormonal signal made by the body’s fat cells that regulates food intake and energy expenditure. “If you ask anyone on the street, ‘Why is someone obese?,’ they’ll say, ‘They eat too much.’ ”

“That is undoubtedly true,” he continued, “but the deeper question is why do they eat too much? It’s clear now that there are many important drivers to eat and that it is not purely a conscious or higher cognitive decision.”

This is not to say that the push for small daily changes in eating and exercise is misguided. James O. Hill, director of the Center for Human Nutrition at the University of Colorado Denver, says that while weight loss requires significant lifestyle changes, taking away extra calories through small steps can help slow and prevent weight gain.

In a study of 200 families, half were asked to replace 100 calories of sugar with a noncaloric sweetener and walk an extra 2,000 steps a day. The other families were asked to use pedometers to record their exercise but were not asked to make diet changes.

During the six-month study, both groups of children showed small but statistically significant drops in body mass index; the group that also cut 100 calories had more children who maintained or reduced body mass and fewer children who gained excess weight.

The study, published in 2007 in Pediatrics, didn’t look at long-term benefits. But Dr. Hill says it suggests that small changes can keep overweight kids from gaining even more excess weight.

“Once you’re trying for weight loss, you’re out of the small-change realm,” he said. “But the small-steps approach can stop weight gain.”

While small steps are unlikely to solve the nation’s obesity crisis, doctors say losing a little weight, eating more heart-healthy foods and increasing exercise can make a meaningful difference in overall health and risks for heart disease and diabetes.

“I’m not saying throw up your hands and forget about it,” Dr. Friedman said. “Instead of focusing on weight or appearance, focus on people’s health. There are things people can do to improve their health significantly that don’t require normalizing your weight.”

Dr. Ludwig still encourages individuals to make small changes, like watching less television or eating a few extra vegetables, because those shifts can be a prelude to even bigger lifestyle changes that may ultimately lead to weight loss. But he and others say that reversing obesity will require larger shifts — like regulating food advertising to children and eliminating government subsidies that make junk food cheap and profitable.

“We need to know what we’re up against in terms of the basic biological challenges, and then design a campaign that will truly address the problem in its full magnitude,” Dr. Ludwig said. “If we just expect that inner-city child to exercise self-control and walk a little bit more, then I think we’re in for a big disappointment.”