The MRS in fitness is obtained by rearranging this expression to obtain

10 The MRS in fitness is obtained by rearranging this expression to obtain Ak(?) 4 where = eT r(ym®) + (1 —y)P@v)\ (6 (15) and y = a/(a + (2) measures the relative importance of marginal fertility. In what follows, I will take «@) = «@) so that the final term in 7 disappears. This restricts attention to the MRS at points along the 45° line in figure 1. In intergenerational transfers there is good reason for interest in these values. At stationary equilibrium, the consumption of an in- dividual at age x‘ must equal that of her daughter one generation hence. Thus, intergenrational investments are governed by the MRS in preferences along the 45° line, which must also equal the MRS in exchange and the marginal productivity of intergenerational investment.4 These quantities could all be predicted from the MRS in fitness along the 45° line. For transfers over shorter inter- vals, there is less reason for concern with the MRS along the 45° line. For these cases, the present approach will tell only part of the story. 3.1.1 The evolutionary discount function To facilitate presentation of numerical results, I define an evolutionary discount function X, which satisfies air MRS p = ede *(@w)dw (16) For example, when ) is a constant, future benefits are discounted exponentially at a constant rate. \ can accomodate nearly any form of discounting, and is closely related to the marginal rate of time preference (MRTP): the average value of \ over any age-interval predicts the MRTP over that interval [15, Eqn. 15]. I calculate from age-specific fertility and survival data using the methods described by Rogers [15]. 3.1.2 Demographic statistics Ideally, \ should be estimated using demographic statistics that reflect some sort of long-term average of human demographic history. This, of course, is impossible. I have instead relied on demographic statistics from modern “natural-fertility” populations, whose vital rates are thought to resemble those of pre-industrial populations.° It would be unwise, however, to take any single modern population as the examplar of our unknown ancestors. We do not know whether prehistoric human demography was more similar to that of 19th century Taiwan, or that of 19th century Utah, to name just two possibilities. Nonetheless, it seems likely that species-wide mean demographic 4See [13, p. 172] and [15, Footnote 12]. 5A natural-fertility population is one in which birth-control is either absent, or else is applied independently of the number of a woman’s existing children. In natural-fertility populations, women may use birth control to space births, but they do not use it to achieve a target family size [1]. HOUSE_OVERSIGHT_011164