The optimal number of offspring per gamete donor

Our aim was to create a mathematical basis to calculate the risks for unintended matings of consanguineous half-siblings from a donor in a society with approximately 10 million inhabitants. The Curie-Cohen model for calculation of the risk for consanguineous mating was used. When the number of offspring per donor is limited to 10, then the model gives a yearly risk for consanguineous matings below 1%. Thus 10 offspring gives a risk for consanguineous matings of 0.9% per year, or approximately once in every 100 years. The risk increases exponentially: with 15 offspring it exceeds 2% and with 25 it reaches up above 5%.