Maximum avoidance of inbreeding in haplodiploid populations

Maximum avoidance of inbreeding (MAI) is a mating system, in which mates are as distantly related as possible. Although theoretical aspects and applications of MAI in diploid populations have been studied by many researchers, extension of MAI to haplodiploid populations is an unresolved problem. In this paper, this problem is addressed, and the following conclusions are derived. For a haplodiploid population with a Fibonacci number of females, a set of mating systems (one cycle MAI-hd) to avoid inbreeding to the maximum after one cycle practice of the set can be defined. But unlike MAI in diploid populations, repetition of one cycle MAI-hd cannot be MAI in the global range of generations. Numerical comparison with random mating and circular half-sib mating shows that as in diploid populations, repetition of one cycle MAI-hd in haplodiploid populations attains a lower inbreeding coefficient in early generations at the expense of a higher asymptotic rate of inbreeding.