Beneficial (hormetic) effects of ionizing radiation have been largely ignored in developing radiobiological theory, chiefly because a suitable explanatory hypothesis is lacking. Examination of the relevant literature has revealed that food restriction effects in animals resemble those of low-level, low-LET, whole-body ionizing radiation exposure (without food restriction) in two major respects: increased longevity and change in the variance of longevity. These physiological changes can be interpreted as resulting from alteration of the "steady-state" flux of oxygen radicals which affect the endocrine balance. Oxy-radical-producing, low-level ionizing radiation exposure (whole body) is interpreted by the body as excess food intake, thus lowering the appetite and reducing caloric intake which, in turn, increases longevity. The greater variance in longevity accompanying increases in the median age at death with food restriction alters the ratio of long-lived to short-lived descendants and hastens the population's adaptation to semi-permanently diminished rates of food supply. Less variance and earlier mean ages at death result from an increased rate of food supply. Whole-body ionizing radiation exposure results in a mixed response, because it reduces caloric intake while signaling that an increase has occurred.