October 14th, 2005
Aubrey de Grey On Gompertz Slopes
Something a little more mathematical and abstract today; via the Gerontology Research Group and transhumantech mailing lists, here are some interesting comments on the relevance to aging of the slope of the Gompertz curve:
In keeping with my prevailing status as angry young man of gerontology I think it is time I commented on the use of the Gompertz slope as a measure of the rate of aging. Let's be quite clear, this idea rests on a generalisation that is broadly true across natural species (ones that have not been manipulated by biotechnology to live longer) but that we have absolutely no reason to believe will be true for ones that have been thus manipulated, and in particular for humans that are receiving future medical care. This generalisation is that the mortality rate doubling time (which is just ln(2) over the Gompertz slope) is pretty accurately a constant multiple (across species) of the life expectancy -- around 1/10 of it. In other words, survival curves for different species are rather well superimposable just by altering the scale on the x-axis. (This is the same statement because the maximum slope of the survival curve is essentially a constant multiple of the Gompertz slope in populations exhibiting a negligible Makeham term, and we are generally considering such populations if we look at vertebrates in captivity with state-of-the-art husbandry, or at humans in the West.) It is therefore of very little scientific (let alone biomedical) value to say that when an intervention lowers the Gompertz intercept but not the slope that it has not slowed aging: one could just as well say that it has indeed slowed aging but has also lowered the variability of the rate of aging within the population. The example I used in my latest editorial in Rejuvenation Research is that if you take two populations with somewhat different Gompertz intercepts and identical Gompertz slopes, and you then compute the Gompertz parameters of the population made by combining these two populations into one, it will have a lower slope (a longer mortality rate doubling time) than the component ones do. If that doesn't make a mockery of using the slope as a measure of the rate of aging, I don't know what would.
You'll find a little more exposition on the use of Gompertz slopes in the middle of a recent post at Longevity First. As for most topics in gerontology, discussions on the validity of Gompetz slopes as a measure of aging have extended over many years. Here is the abstract for a paper from 2001, for example:
The Gompertz transform of the distribution function for the age at death expresses mortality in a form R = R_0e^[alpha] t where R_0 is the mortality at time zero and [alpha] is the rate of increase of mortality, frequently taken as the rate of ageing. The slope of the line [alpha] is frequently used as a measure of the rate of ageing. It is argued that it is incorrect to use [alpha] in this way. To support this contention, a paradox is produced whereby selection for longevity increases [alpha], which could lead to the absurd conclusion that selection for longevity increases the rate of ageing.