Obesity is an important medical problem affecting humans and animals in the developed world, but the evolutionary origins of the behaviours that cause obesity are poorly understood. The potential role of occasional gluts of food in determining fat-storage strategies for avoiding mortality have been overlooked, even though animals experienced such conditions in the recent evolutionary past and may follow the same strategies in the modern environment. Humans, domestic, and captive animals in the developed world are exposed to a surplus of calorie-rich food, conditions characterised as 'constant-glut'. Here, we use a mathematical model to demonstrate that obesity-related mortality from poor health in a constant-glut environment should equal the average mortality rate in the 'pre-modern' environment when predation risk was more closely linked with foraging. It should therefore not be surprising that animals exposed to abundant food often over-eat to the point of ill-health. Our work suggests that individuals tend to defend a given excessive level of reserves because this level was adaptive when gluts were short-lived. The model predicts that mortality rate in constant-glut conditions can increase as the assumed health cost of being overweight decreases, meaning that any adaptation that reduced such health costs would have counter-intuitively led to an increase in mortality in the modern environment. Taken together, these results imply that efforts to reduce the incidence of obesity that are focussed on altering individual behaviour are likely to be ineffective because modern, constant-glut conditions trigger previously adaptive behavioural responses.