Figure 1. Demographic changes in Finland from 1761-1980 in longevity, childhood mortality, and fertility. (A) Hazard functions for survival of women born in pre-industrial (dark grey), transitional (medium grey), and posttransition (light grey) periods. On the left side of the figure, it can be seen that early -life hazard of death became lower. At older ages, the hazards increased greatly in all time periods, but started rising earliest in the pre-industrial period and latest in the post-transitional period (see also Figure S1). (B) Cumulative hazard functions for survival of women in pre-industrial (dark grey), transitional (medium grey), and post-transition (light grey) periods. Risk of death accumulated fastest in the pre -industrial period we would expect that a woman living in this period would die earlier than in the other periods. (C) Decennial early childhood mortality rates.

Following the onset of the transition, mortality rates decline continuously to negligible levels by the later 20 th century. (D) Mean number of children by birthing cohort (95% confidence intervals shown with the shaded area). Over the pre-industrial period, family sizes were larger, with over 5 children on average. During the transition, average family sizes declined, and continued to do so to the end of the study period. Horizontal lines in Published online by Cambridge University Press each part of D are the mean and 95% confidence intervals of number of children per family across each period. Dashed lines in C and D demarcate the beginning and end of the transition (1871 -1910).

Declining Importance of Grandmothers for Grandchild Survival For the grandmother hypothesis, child mortality rates are one of the most important indicators of need. In the pre-industrial period, the child mortality rate was typically high, and in Finland 30.2% of the population died before the age of five during 1761-1870 (Figure 1C). Though there was considerable variation in mortality between birth cohorts, all had under-five mortality rates of over 20%. The mortality in the transitional period (1871-1910) was almost a third lower, at 19.3%, and there was a continuous decline in mortality rate with each passing decade. Post-transition (1911-1980), pre-five childhood mortality was at 6.6%, though again there was a continual decrease to the point that less than 1% of children died before the age of five in the 1960s and 1970s, and the majority of these deaths occurring in early infancy. Hence, the need for kin help to ensure child survival seemingly col-

The association between grandmother presence and the fitness outcomes of grandchild survival similarly changed over the transition (time period interaction: 2 2 = 9.69, p = 0.010; Figure 2A). Whilst survival outcomes for grandchildren were higher pre-industrially when their maternal grandmother was present ( = 0.514 0.209, p = 0.014), this association was no longer present in the transition period ( = 0.308 0.209, p = 0.141; but see supplementary information), and was absent again post-transition ( = -0.228 0.200, p = 0.254). The birth cohort interaction with maternal grandmother presence was significant (2 1 = 4.27, p = 0.041; see Methods for caveats), Figure 2B shows a trend of grandchild survival being higher with a maternal grandmother present (cf. dead) across the pre-industrial and early transitional cohorts, before converging by the turn of the 20th century, re-