In a paper published today deCODE scientists establish a substantial and consistent positive correlation between the kinship of couples and the number of children and grandchildren they have. The study, which analyzes more than 200 years of deCODE’s comprehensive genalogical data on the population of Iceland, shows that couples related at the level of third cousins have the greatest number of offspring.It is of course clear why close relatives (closer than 3rd cousins) should have fewer children: this is due to the well known phenomenon of inbreeding depression. However, why should fertility increase up to a certain degree of kinship (~3rd cousins) and decrease after that?
One explanation is that there is some biological factor which decreases fitness as genetic dissimilarity increases. Perhaps more distantly related genomes don't "mesh" that well.
I suggest that the phenomenon could be partially explained by the fact that as kinship decreases, the age distribution of potential marriage partners becomes more varied.
A man's age difference from his sister is constrained by the fact that one's mother has a limited reproductive age range. In other words, one's sister is usually a few years older or younger than oneself, and rarely much older or younger.
But, if we look at first or second cousins, this difference increases. Your uncle or aunt is younger or older than your parents, and correspondingly their children can be more different than you in age.
As kinship decreases, your n-degree cousins become less constrained to be close to you in age. They could be much much older (if they are descended from short branches of one's family tree), or much much younger (if they are descended from long ones).
Of course, men usually marry women who are not that different from them in age (see data for Norway). But, the opportunity to marry someone much younger (or much older) than oneself is greater as kinship decreases.
It would be interesting to see data on average age differences correlated with degree of kinship in Iceland. If it turns out that, say, third-cousin marriage partners are less different in age than fourth-cousin partners, then an alternative explanation may be behind the observed fertility curve: age difference among spouses is negatively correlated with fertility.