A New Mathematical Model for Inbreeding Depression in Large Populations

It has been widely recognized that inbreeding mating results in increased homozygosity which generally leads to a decreased fitness of population. This conclusion was supported by a large number of experimental observations in natural populations. However, a theoretical analysis of this phenomenon is still lacking. Here we present a theoretic proof showing that for most natural populations, inbreeding mating does reduce the mean fitness of populations. It also suggests that inbreeding depression depends on not only the mating system but also the structure of population. As a consequence, we conclude that, for a natural inbreeding population without any inbreeding depression, most genotypes should be additive or co-dominant. This result gives an explanation to the question why hermaphroditism populations do not show severe inbreeding depression. Another major result of this research is that, for a large inbreeding population with directional relative genotype fitnesses, the mean fitness increases monotonically for any value of inbreeding coefficient. This result may provide a reason to explain the frequent occurrence of self-fertilization populations. We also characterize pseudo-overdominance for single locus, which suggests that there are many pseudo-overdominance populations among the class of over-dominance populations.