A hormone called leptin has been trumpeted as an appetite suppressor and a possible treatment for obesity. New research shows that “a clear connection also exists between fat, or energy storage, and the ability to reproduce,” says Corrine Welt, an assistant professor of medicine who works at Massachusetts General Hospital, a Harvard affiliate. The women whose fertility was boosted by leptin injections had stopped menstruating as a result of losing an abnormal amount of fat, mainly by overexercising. In their 20s and early 30s, they pared themselves down to carrying about 40 percent less fat than is average for women their age. Such loss of menses, or amenorrhea, is also associated with abnormal levels of thyroid hormones and a loss of bone mass, which can lead to brittle, easily fractured bones. The findings thus raise the possibilities of new treatments for exercise-induced bone loss and for eating disorders, as well as for certain cases of infertility.