A survival curve looks like the profile of a crowd walking down a corridor: at first everyone moves together, then some fall behind, and in the end only a handful are left. If the corridor ends in a sheer drop, the crowd goes over the edge almost all at once, 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. Scientists wanted to pin down exactly what makes a curve rectangular or triangular.
They took tiny nematode worms, split them into 30 groups kept under different conditions, and every two or three days checked how each worm moved. A worm was scored as healthy if it crawled in waves, and as frail if it barely stirred. It turned out that when an intervention (a change in temperature or genes, say) extends healthy life mainly in short-lived individuals, the curve turns rectangular. When health and frailty both stretch out in the long-lived, the curve turns triangular.
This insight helps predict how drugs or diets will affect aging. If a population is mixed, an intervention is more likely to make the curve rectangular, meaning it extends healthy life for many. If the population is uniform, the curve turns triangular, and then the long-lived are the main winners, though the spread grows wider. For people, that means it is not enough simply to raise average life expectancy; we also need to watch how healthy years are distributed across different people.
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.