When heavier birds lose more mass during breeding: statistical artefact or biologically meaningful?

Several studies on mass loss during breeding in female birds have shown a significant correlation between initial body mass and subsequent loss of body mass. The significant positive regression coefficient of mass loss on initial mass was interpreted as evidence for a greater mass loss of initially heavier birds. However, the positive correlation between mass loss and initial mass arises automatically even when initial and final body masses are uncorrelated and has no necessary biological meaning. This is shown analytically here. In general, a spurious correlation arises when one variable (e.g. mass loss ) is part of another variable (e.g. initial mass ) and then regressed on it.