Medawar and Hamilton on the selective forces in the evolution of ageing

Abstract

Both Medawar and Hamilton contributed key ideas to the modern evolutionary theory of ageing. In particular, they both suggested that, in populations with overlapping generations, the force with which selection acts on traits declines with the age at which traits are expressed. This decline would eventually cause ageing to evolve. However, the biological literature diverges on the relationship between Medawar's analysis of the force of selection and Hamilton's. Some authors appear to believe that Hamilton perfected Medawar's insightful, yet ultimately erroneous analysis of this force, while others see Hamilton's analysis as a coherent development of, or the obvious complement to Medawar's. Here, the relationship between the two analyses is revisited. Two things are argued for. First, most of Medawar's alleged errors that Hamilton would had rectified seem not to be there. The origin of these perceived errors appears to be in a misinterpretation of Medawar's writings. Second, the mathematics of Medawar and that of Hamilton show a significant overlap. However, different meanings are attached to the same mathematical expression. Medawar put forth an expression for the selective force on age-specific fitness. Hamilton proposed a full spectrum of selective forces each operating on age-specific fitness components, i.e. mortality and fertility. One of Hamilton's expressions, possibly his most important, is of the same form as Medawar's expression. But Hamilton's selective forces on age-specific fitness components do not add up to yield Medawar's selective force on age-specific fitness. It is concluded that Hamilton's analysis should be considered neither as a correction to Medawar's analysis nor as its obvious complement.

Keywords: Age; Reproductive value; Senescence; Theory.

Fig. 1

Mortality and fertility in women, Italy 1954. Mortality data are from the Human Mortality Database (https://www.mortality.org/). Mortality at each age is here approximated by the central death rate. Fertility data are from the Human Fertility Database (https://www.humanfertility.org/). Both databases were accessed on the 19th Dec 2019

Fig. 2

The first four plots (reading row-wise from left to right) report Hamilton’s main forces of selection against age, see Sect. 2.3 and equations therein. The three subsequent plots report newborn survivorship l(a), stable age distribution c(a), and reproductive value v(a) against age with v(0) scaled so that $\int c(a)v(a)=1$. All quantities are computed on the same data as Fig. 1. Age (x-axis) is shown from birth up to just before menopause