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In aquaculture, sterile triploids are commonly used for production as sterility gives them potential gains in growth, yields, and quality. However, they cannot be reproduced, and DNA parentage assignment to their diploid or tetraploid parents is required to estimate breeding values for triploid phenotypes. No publicly available software has the ability to assign triploids to their parents. Here, we updated the R package APIS to support triploids induced from diploid parents. First, we created new exclusion and likelihood tables that account for the double allelic contribution of the dam and the recombination that can occur during female meiosis. As the effective recombination rate of each marker with the centromere is usually unknown, we set it at 0.5 and found that this value maximizes the assignment rate even for markers with high or low recombination rates. The number of markers needed for a high true assignment rate did not strongly depend on the proportion of missing parental genotypes. The assignment power was however affected by the quality of the markers (minor allele frequency, call rate). Altogether, 96–192 SNPs were required to have a high parentage assignment rate in a real rainbow trout dataset of 1,232 triploid progenies from 288 parents. The likelihood approach was more efficient than exclusion when the power of the marker set was limiting. When more markers were used, exclusion was more advantageous, with sensitivity reaching unity, very low false discovery rate (<0.01), and excellent specificity (0.96–0.99). Thus, APIS provides an efficient solution to assign triploids to their diploid parents. [ABSTRACT FROM AUTHOR]