Background: The maximal number of live births (k) per donor was usually determined by cultural and social perspective. It was rarely decided on the basis of scientific evidence or discussed from mathematical or probabilistic viewpoint. Methods and Results: To recommend a value for k, we propose three criteria to evaluate its impact on consanguinity and disease incidence due to artificial insemination by donor (AID). The first approach considers the optimization of k under the criterion of fixed tolerable number of consanguineous mating due to AID. The second approach optimizes k under fixed allowable average coefficient of inbreeding. This approach is particularly helpful when assessing the impact on the public, is of interest. The third criterion considers specific inheritance diseases. This approach is useful when evaluating the individual's risk of genetic diseases. When different diseases are considered, this criterion can be easily adopted. All these derivations are based on the assumption of shortage of gamete donors due to great demand and insufficient supply. Conclusion: Our results indicate that strong degree of assortative mating, small population size and insufficient supply in gamete donors will lead to greater risk of consanguinity. Recommendations under other settings are also tabulated for reference. A web site for calculating the limit for live births per donor is available.
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