Changes in physiological parameters are interesting for comparative studies of aging but they are potentially expensive and difficult to study. One alternative is to employ demographic measurements of aging. Aging can also be defined as an age-related increase in vulnerability and decrease in viability (Comfort, 1964). One of the features of aging in species with gradual senescence, like most mammals, is an exponential increase in mortality after maturity. For example, in humans, our chance of dying roughly doubles every 8 years after about age 30. This is remarkably similar among different human populations, independently of average lifespan (Finch 1990). Therefore, one way to compare rates of aging across different species is to calculate the rate at which mortality increases with age, which gives a measure of senescence (Pletcher et al., 2000). As an example, Figure 2.1 shows the hazard function—which represents the probability of death—of chimpanzees according to age based on published mortality rates (Hill et al., 2001).

In chimpanzees, hazard rates begin to increase near the end of the second decade of life, while human hazard rates generally begin to climb at the end of the third decade of life. This time it takes for mortality rates to climb has also been suggested as a measure of aging (Finch, 1990),

Figure 2.1. Natural logarithm of chimpanzee mortality rates as a function of age. The straight black line represents the estimated adult mortality trajectory based on Gompertz parameters calculated using a weighted linear regression. The data comes from five field studies of chimpanzees (Hill et al., 2001) and was fitted using the T4253H smoothing algorithm from the SPSS package (SPSS Inc., Chicago, IL).

0 10 20 30

Age (years)

Figure 2.1. Natural logarithm of chimpanzee mortality rates as a function of age. The straight black line represents the estimated adult mortality trajectory based on Gompertz parameters calculated using a weighted linear regression. The data comes from five field studies of chimpanzees (Hill et al., 2001) and was fitted using the T4253H smoothing algorithm from the SPSS package (SPSS Inc., Chicago, IL).

and in this case suggests aging commences earlier ages in chimpanzees than in humans. To calculate the age-related increase in mortality, the Gompertz function is typically used. Although other functions have been proposed (Wilson, 1994), the Gompertz function is generally the most adequate for these calculations, particularly when using small populations as is common in studies of higher vertebrates. It is also the most widely used function, making it a good term for comparisons. The Gompertz equation is Rm = R0eat where Rm is the chance of dying at age t—i.e., the hazard rate—R0 is the nonexponential factor in mortality, and a is the exponential parameter. Based on the Gompertz equation it is possible to calculate the mortality rate doubling time (MRDT), which is an estimate of rate of aging given by MRDT = 0.693/a (Finch, 1990; Mueller et al., 1995).

Depending on the quantity and quality of the data, there are different ways of calculating the Gompertz parameters (Mueller et al., 1995), and a certain amount of subjectivity is unavoidable. In this case, and as previously described (de Magalhaes et al., 2005b), the weighted linear regression was obtained from the ln-transformed Gompertz equation: ln (Rm) = ln (R0) + at. The chimpanzee curve was estimated as: ln (Rm) = -4.56 + 0.0798t with r2 = 0.81. Hence, a = 0.0798 with 95% confidence intervals of 0.0627 and 0.0969. This means that the MRDT for chimpanzees is around 8-9 years, similar to that of humans.

The great advantage of the Gompertz function and estimating a and the MRDT is that it allows us to quantify the rate of aging. As shown above, however, MRDT estimates indicate chimpanzees and humans age at similar paces, which may not be true from a physiological level. Our results from rodents also suggest that MRDT is a good but not perfect estimate of rate of aging (de Magalhaes et al., 2005b). Therefore, even though the MRDT is a useful measurement of aging rates, it should be used in conjunction with physiological observations.

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