Eating disorders like anorexia nervosa and bulimia nervosa are difficult psychiatric disorders. They are especially tragic because, while they may seem like just messed up eating, they are far, far more. Eating disorders have some of the highest rates of death of any psychiatric disease, as malnutrition puts the body at risk.
When we think of eating disorders, though, we tend to think of them from a cultural angle. It's because our culture is so obsessed with thin, no one can ever be thin enough, and so that must bring out eating disorders. It is true that a culture which glorifies skinny the way ours does tend to bring out more extreme dieting than one that does not. But it is also true that eating disorders are far more than the product of a culture which glorifies the size 0. Reports and descriptions of anorexia, for example, date all the way back to the Greeks, and famous case studies that fully described the disorder date from the 1860's. There is clearly a genetic component, anorexia in particular runs strongly in families. There is also a potential sex effect, eating disorders are far more common in women than in men.
Eating disorders are a combination disease, a combination of genetic risks and environmental triggers, including things like stress. Unfortunately, it's been difficult to identify specific genes that predispose people to eating disorders. Studying large populations of people with the disease and find some common genetic variants, for example, but for such a complex disorder that is not dependent on a single gene, many of those will also be present in healthy populations.
Another approach is instead to look at families which have a strong history of eating disorders, to see what common genes are passed down. While this has its own limitations (for example, you then have to look for the occurrence of those genes in the wider population, and being within a single family or two, there are bound to be environmental factors that aren't present elsewhere), it's a way to uncover genetic variants that my have previously gone undiscovered. And it means you might, as they did here, uncover two genes that, when screwed up in very precise ways, result in the same eating disorder.
Cui et al. "Eating disorder predisposition is associated with ESRRA and HDAC4 mutations" Journal of Clinical Investigation, 2013.