Can eating disorders cause small intestinal bacterial overgrowth (SIBO)?

Anorexia and bulimia have been associated with methane dominant SIBO.

People who have elevated levels of methanogens within their digestive tract have constipation more often than diarrhoea. 

If someone has not been eating appropriate levels of nutrients and calories, one of the theories is that the microbiome adapts by deliberately increasing these methanogens.

Methane producing organisms are not technically bacteria. They're older organisms than bacteria, and they extract more calories from our food. So they've also been associated with obesity.