A survival curve looks like the profile of a crowd walking down a long corridor: at first everyone is together, then some fall behind, and finally only a handful remain. If the corridor ends in a steep cliff, the crowd falls almost simultaneously, which on a graph looks like a rectangle. If the exit is a gentle, long slope, people leave gradually and the curve stretches into a triangle. Biologists have long noticed that these profiles differ between animal populations, but what exactly makes them rectangular or triangular remained a mystery.
In a new study, researchers tracked 30 groups of tiny nematode worms, subjecting them to changed temperature, an added antibiotic, or different genetic lines. Every two or three days each worm was checked: does it move sinusoidally (like a wave), merely wiggle, or lie still, and does it approach the bacterial lawn it feeds on. This made it possible to split each individual's life into two stretches: the healthspan, when the worm crawls actively, and the period of frailty, when movement is impaired. It turned out that the shape of the survival curve depends directly on how these stretches are distributed among individuals.
The key finding concerns variability. When an intervention made the curve rectangular, the spread of lifespan, healthspan and frailty between individuals shrank. When it made the curve triangular, that spread grew. This resembles a well-known statistical effect: if a group is initially diverse, after a treatment it often contracts toward the mean, and if it is uniform, it does the opposite and spreads out. And indeed, in those control groups that later showed a rectangular shape, the initial spread was greater than in the groups with a triangular shape.
The practical takeaway: if we want to predict how a given intervention (a drug, a diet, a genetic modification) will change the survival curve, we need to look at the population's initial heterogeneity. Heterogeneous groups are more likely to respond with a rectangular shape, homogeneous ones with a triangular shape. For gerontology this means that average lifespan is no longer the only goal: it matters just as much how healthy and frail years are distributed among individuals. In human populations a shift from a rectangular shape to a triangular one is already under way, and understanding this mechanism will help design interventions that extend healthy life specifically, rather than merely postponing death.
The term "triangular survival curve" was introduced in this very paper. Previously people spoke only of the rectangular shape and of curve crossing, and the triangular shape was not singled out as a separate type.
Robert Heinlein's novel "Methuselah's Children" describes a society in which the long-lived accumulate frailty rather than preserve health. This work shows that such a thing is possible under a certain type of intervention, one that extends lifespan by stretching out the period of frailty among the long-lived.
Not published on arXiv. Here are its page, the PDF and the formalization: you can check it yourself, not only read our account.