## Demographic Studies

In aging studies it is of course important to measure the rate of aging. However, the rate at which an individual ages is difficult to measure. There is no consensus on biomarkers of aging. Furthermore, if one were to follow the changes in a biomarker, the assay would need to be noninvasive to avoid biasing the measure, and certainly could not kill the organisms. In contrast, the measurement of the rate of aging in a population can be achieved easily by analyzing patterns of age-at-death. Age-at-death is an unambiguous and easily measurable end point. Age-specific mortality is a measure of the instantaneous hazard of death for an individual at a given age. It allows independent comparisons of vulnerability to death at different ages. The main drawback of such demographic studies is that they require very large population sizes, especially for estimates of age-specific mortality and maximum lifespan. Drosophila is ideally suited for demographic analyses because it is easier to culture and monitor large numbers of individuals than with other short-lived model organisms such as yeast (Saccharomyces cerevisiae) and nematode worms (Caenorhabditis elegans). One assumption of such demographic measures of aging is that physiological and functional declines correlate with increases in death rate, which might not be the case. Therefore, ideally studies should be supplemented with some physiological measures such as the number of eggs laid and locomotive function.

The mortality rate (mx) at age x can be expressed mathematically as

where P(x) is the probability of an individual alive at age x surviving to age x + 1 (Carey, 1993). The data are often gathered so as to fit explicit models in order to (a) reduce complexity and day-to-day variations of mortality data, and (b) allow parametric statistical tests. The most popular model is the Gompertz model:

where the constant a is the intrinsic baseline mortality rate and b is the rate at which mortality rates accelerate with age (Promislow and Haselkorn, 2002). The natural logarithm of the Gompertz equation gives a linear function:

which is analogous to a straight line with slope b and intercept a on the vertical axis. The slope b represents the rate of aging (Magwere et al., 2004; Mair et al., 2003). In the Gompertz model, the baseline mortality rate is not independent of aging rate. It should be noted that the Gompertz model assumes a constant, exponential increase in mortality rate throughout adulthood.

However, the early and very late mortality rates do not appear to fit the model completely: the increase in mortality rates slows down at the end of the lifespan.

Using this approach, experimental manipulations to extend lifespan can be classified into two types depending on the pattern of changes in mortality trajectory: treatments that change the slope (i.e., the rate of aging) and treatments that change the intercept (i.e., the underlying baseline mortality rate is changed) (Finch, 1990). A good illustration is a study by Mair et al. (2003) which performed a demographic analysis of effects of dietary restriction in flies (see ''Drosophila in aging studies'' Figure 22.1).

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