Fig. 1

The different theories. Grey arrows denote parental help, purple arrows denote forward help from grandmothers to a grandchild, and finally, yellow arrows denote the backward transfer of resources from parents to grandparents. Upward blue and downward red arrows denote the positive and negative effects from the trade-offs, respectively. a Standard life-history model with no menopause, no forward help, and no backward help. b Grandmother (purple arrow from VI to I) and altriciality (grey arrow from VI to I) hypotheses. The menopause has evolved and there is no backward help from parents to grandmothers. c Mother and embodied capital hypotheses. The menopause has evolved and there is no backward help from parents to grandmothers. d Filial piety. The menopause has evolved, there is a synergistic division of labor with backward help from parents to grandmothers, and there are no trade-offs; e Fifth rule. The menopause has evolved, there is backward help from parents to grandmothers, and there is a three-way trade-off for the parents between survival, fecundity, and helping their grandmothers. f Fifth Rule. The menopause has evolved, there is backward help from parents to grandmothers, and there is a two-way trade-off for the parents between fecundity and helping their grandmothers