### Description:

Effective population size is defined as the number of breeding individual in an idealized population that would show the same amount of dispersion of allele frequencies under random genetic drift or the same amount of inbreeding as the population under consideration. Effective population size depends on the census size of the population and the mating system. In autotetraploid population, effective population size also depends on the probability of double reduction, i.e., a meiotic event when two sister chromatids end in the same gamete. In this research, we will study the effect of the probability of double reduction on the effective size of autotetraploid population reproduced by partial selfing. The formula for the effective population size was derived by equating the variance of the change in gene frequency in idealized population and its value in the autotetraploid population with arbitrary rate of partial selfing and double reduction. The resulted formula, and numerical study based on the formula, indicated that the effective size decreases by the increase of probability of double reduction and the rate of selfing. When there is complete selfing, however, the effective size is not affected by the probability of double reduction.