There is no quantity-quality trade-off


Jason Collins


February 4, 2013

Following his disappearance from Psychology Today, Satoshi Kanazawa has reappeared in big think (with not all happy with this move [Update: he’s now gone again, along with the post]). In a recent post, Kanazawa asks an interesting question - Why do people with many siblings have many children? Kanazawa writes:

Studies show that fertility is substantially heritable; genes partly influence how many children one has. Children of parents who have many children also have many children; children of parents who have few children also have few children. As a result, there is a strong positive correlation between the number of siblings one has (which equals the number of children that one’s parents had minus one) and the number of children one has.

… [T]he positive correlation between the number of siblings and the number of children makes no evolutionary sense. Evolutionary theory actually predicts a negative correlation. …

This is because people with many siblings have the option of investing in their younger siblings and increasing their reproductive success by doing so. Humans are just as genetically related to their full siblings as they are to their own biological children; both share half their genes. … So investing in and “raising” younger siblings is just as good genetically and evolutionarily as investing in and raising one’s own genetic children.

A second reason for expecting a negative correlation is that the parents face a quality-quantity trade-off. As a parent increases the number of their children, they have fewer resources to invest in each child. If that harms their children’s reproductive success, this will reduce the number of children in the following generation.

I would argue that the answer to this puzzle (as Kanazawa terms it) lies in what happened after the demographic transition - that is, when fertility rates declined with industrialisation. Before the transition, fertility was generally not heritable and any correlation in family size between generations was due to environmental factors and chance. But after the transition, heritability increased. This suggests that different people responded to the transition in different ways.

One of those differences is how they respond to the quantity-quality trade-off in the new, plentiful environment that accompanies industrialisation. Human history is one of Malthusian conditions, where available resources constrain the population. In that environment, any additional children will affect the resources available for the other children.

In the modern environment, there is essentially no such constraint. Increased quantity does not harm quality in a way that reduces the quantity of children in the next generation. Adoption studies generally show a low cost to more children, and those small costs are to income or education, not reproductive success. As a result, the optimal strategy in the modern environment is to have as many children as you can. If you have a genetic predisposition to do that (or even a culturally transmitted predisposition), your children are likely to too, leading to the positive correlation that Kanazawa observes.

This argument also applies to Kanazawa’s argument that we should expect a negative correlation through care for siblings. In the modern environment, that care for siblings does not assist the sibling in having more children. They are not resource constrained. The optimal strategy is for each sibling to have as many children as they can. Those that follow this strategy have more children in successive generations with little cost to quality.

This argument relates to my latest working paper. With the heritability of fertility increasing after the demographic transition, “high-fertility genotypes” can be expected to increase in number. One day a cost for those excessive children may emerge as the population starts to hit Malthusian constraints, but until then, fertility is not constrained by resources and the evolutionary dynamics point to fertility going up.