the optimal investment can nonetheless be achieved if the parents loan the child the incremental amount for education, in excess of the parental outright transfer. The child repays the parents later, in the form of old age support or perhaps assistance with the educational costs of younger siblings.
More generally, the parental investment t which maximizes the reproductive fitness of a given child is larger than the parental investment T which maximizes the reproductive fitness of the parent. In this circumstance, the reproductive fitness of both parent and child might be increased if the parent transferred outright the amount T to the child and then additionally "loaned" an amount of food or care to the child in excess of T, say L = T- t, with this amount L to be repaid by the child to the parent at a later life-cycle stage. The later repayment could take the form of assistance with a younger generation of the parent's children, as when adolescents help care for infants during a life-cycle stage in which they can generate a surplus to be transferred but are not yet capable of their own reproductive effort. Alternatively, the children could give food to their parent to replenish depleted reserves. Either way, parents could achieve more surviving offspring and greater reproductive fitness.
If a mutation should yield a gene that affected behavior so that children partially repaid parental investments in this way, the parents could then produce more surviving offspring by investing more in each or by having a greater number. Thus this gene would raise the reproductive fitness of those who had it, because it would be transmitted to their own children, who would behave similarly toward them. Furthermore, a gene for reneging would convey lower reproductive fitness in this example, because it also would be transmitted to offspring, and reproductive fitness would return to the original baseline level, which is by hypothesis lower than that with the repayment gene.
In this way, evolution could lead to life-cycle patterns of intergenerational transfers in which some parental investment in children is subsequently "repaid" by the child at a later life-cycle stage—that is, patterns in which transfers in both directions occur between parents and children, at different ages.
This theory has somewhat different implications than the inclusive fitness theory, according to which animals act to increase the reproductive fitness of those who share their genes. The repayment theory could explain such behavior independent of shared genes—for example, the behavior might be predicted to be as strong in relation to half siblings as to full siblings (if the exchange occurs with only one of the parents, rather than with both). At the same time, under the repayment theory and in contrast to the inclusive fitness theory, one would not expect any helpful behavior toward more distant relatives with whom a parent is not shared.
Austad (in this volume) discusses the transfer of assets from parents to their children. This transfer of a stock is usefully distinguished from transfer flows,