No evidence for squaring the survival curve: lifespan-extending treatments increase variation in age- at-death.

Geroscience has the goal of extending lifespan through geroprotective interventions. These interventions are typically imparted on groups of individuals, with their efficacy judged by increases in the average age-at-death. A more equitable outcome, which looks beyond the average, is to attain a long life for all individuals, such that the average age-at-death is high while variability (e.g. standard deviation in age-at-death) is low. This goal of increasing the mean while reducing variation is sometimes referred to as 'squaring the survival curve'. A recent meta-analysis of vertebrate data found that dietary restriction (DR) and the DR-mimetic, rapamycin, generally increase the average age-at-death, while metformin (also considered a DR-mimetic) is less effective. We have re-analysed this recently published data to study the effects of lifespan-extending treatments on variation in the age-at-death. On average, all three treatments increase the variance in the age-at-death, but not the coefficient of variation (i.e. standard deviation relative to the mean). This suggests that lifespan-extending treatments do not reduce variance and 'square the survival curve'. Rather, any gains in mean age-at-death are matched by corresponding increases in variation. Interestingly, this result is consistent with the treatments proportionally reducing both the age-dependent and age-independent parameters in a Gompertz model of mortality.