In the MIDUS study (Midlife Development in the United States) scores for the Big Five supertraits were calculated for respondents (there is no description of the scales). Most of the sample is between the ages of 40 and 60, and I limited the analysis to whites. Here are the mean number of offspring for low and high groups:
People high in extraversion and agreeableness and those low in neuroticism (negative emotionality) have significantly more children than their counterparts.
The finding that agreeable people have more offspring is consistent with GSS data which indicate that agreeable women have larger families.