In 1966, William D. Hamilton published “The Moulding of Senescence by Natural Selection” in *Journal of Theoretical Biology.* At the time, the paper was hardly noticed. Forty years later, as of this writing, it is clear that this paper was another milestone in Hamilton's miraculous decade of the 1960s. His best-known articles from this period are his two 1964 articles on kin selection (Hamilton 1964a,b) and his 1967 article on evolutionary strategies of sex-ratio manipulation. In those three articles, he laid foundations for contemporary research in behavioral ecology and cognate fields, including research on inclusive fitness and frequency-dependent strategies. These three publications are among the most heavily cited in the evolutionary literature, broadly construed. Here we will argue that Hamilton's 1966 article is at least as important as those three articles.

Hamilton was an avid disciple of R.A. Fisher (see the marginalia of Hamilton's 1996 volume), whose 1930 book *The Genetical Theory of Natural Selection* contained elliptical remarks on the parallels between age-specific reproductive value and age-specific survival probabilities, particularly the parallel between the decline of reproductive value and the decline of age-specific survival probability with increasing age. Haldane (1941), Medawar (1946, 1952), and Williams (1957) took up the same theme, although, like Fisher, none supplied a useful formal analysis. It was Medawar, especially in his 1952 publication, who popularized the term “force of natural selection.” But there was no quantitatively explicit and cogent analysis of this evolutionary concept before Hamilton's 1966 analysis.

Like his other 1960s publications, Hamilton's 1966 analysis of the forces of natural selection contains obscure wording and inelegant mathematical notation. But he finally made the verbal hints and circumlocutions of his predecessors mathematically explicit. Hamilton's assumption, taken from Fisher, was that the Malthusian parameter defines Darwinian fitness. He derived the first partial derivative for the proportional effect on fitness of age-specific changes in survival probability. This effect is given by *s(x)/T*, where *T* is a measure of generation length and

where *r* is the Malthusian parameter, or the growth rate of the population, associated with the specified *l*(*y*) survivorship and *m*(*y*) fecundity functions. The dummy variable *y* is used to sum up the net expected reproduction over all ages after age *x*. Ultimately, the *s*(*x*) function represents the fitness impact of an individual's future reproduction. Note that, before the first age of reproduction, *s* is always equal to 1; once reproduction has ended, *s* is equal to zero; and during the reproductive period, *s*(*x*) progressively falls.

Like mortality, the age-specific force of natural selection acting on fecundity has a scaling function

An interesting difference between these scaling functions is that the force of natural selection acting on survival only decreases with age *after the onset of reproduction*, whereas the force of natural selection acting on fecundity can increase or decrease before the onset of reproduction (Charlesworth 1994). When plotted against age, these functions have the general form exemplified in Figure 1.

From these equations and some numerical calculations, Hamilton (1966) argued that Fisher's (1930) reproductive value is not a valid explanation of the existence of aging, if aging is defined as an endogenous decline in adult life-history characters, which seems to have been Hamilton's definition (see also Rose 1991). (Here we use the term “life history” to refer to the complete spectrum of age-specific survival probabilities and fecundities, whether these characters are components of fitness or not.) Thus, Hamilton gave examples of life histories that produce steadily increasing reproductive value, when Hamilton's *s(x)* function instead always declines. Hamilton's reasoning was that if we assume that falling age-specific survival probability is universal among adult somata, in the absence of exogenous mortality, his *s(x)* function provided a more plausible theoretical explanation for aging than Fisher's reproductive value.

More generally, Hamilton contended that his scaling functions would correctly predict the evolution of the rate of aging among populations that are subject to different demographic regimes. Hamilton used historical life tables from human American and Taiwanese populations to illustrate the impact of different demographic patterns on the evolution of aging. The Taiwanese life-table that he used exhibited higher rates of early reproduction and population growth compared with the American life-table, which Hamilton calculated would lead to a more rapid fall in his Forces of Natural Selection among the Taiwanese. However, he did not make this comparison to predict the future evolution of aging in these two human populations; the calculations were only illustrative.

Hamilton also discussed the population genetics of the evolution of aging, although his treatment was verbal and intuitive, without a mathematically explicit population genetic analysis.

Although there were few published signs that Hamilton's 1966 article was noticed in the remaining years of that decade, starting in 1970 research predicated on Hamilton's results began to spread. The first results were theoretical, primarily a series of articles by Brian Charlesworth and his colleagues (e.g., Charlesworth and Williamson 1975). Experimental publications based on Hamilton's Forces of Natural Selection also appeared, particularly research on *Drosophila melanogaster* (e.g., Rose and Charlesworth 1980).

In the remaining sections of this article, we take up the twists and turns by which Hamilton's 1966 findings have redefined evolutionary research on life history, including such topics as the evolution of aging and the possibility of a late life after the cessation of aging. We treat the radiating impact of Hamilton's paper on both evolutionary theory and evolutionary experimentation. We discuss quantitative theory first, then research on standing genetic variation, followed by experimental evolution. We include an historical perspective on the parallels between Hamilton's Forces of Natural Selection and Einstein's Theories of Relativity.