Probability of paternity exclusion and the number of loci needed to determine the fathers in a troop of macaques

We calculated the probability of paternity exclusion (P) in 6 troops of rhesus and Japanese macaques housed in open enclosures and 68 wild troops of Japanese, crab-eating, and toque macaques using 33 genetic loci which encoded the blood protein variations detected by electrophoretic techniques. In the open enclosures, especially of rhesus troops, we obtained a fairly high probability of paternity exclusion and succeeded in determining the fathers of offspring. However, we found significant differences between the observed and calculated probabilities in most of the troops. These differences were ascribed to a situation whereby the Hardy-Weinberg equilibrium had not been attained in the troops and/or the numbers of variable loci were too small. In the wild troops of Japanese, crab-eating, and toque macaques, the means ofP were 0.2274 (0.0192–0.5017), 0.4635 (0.1676–0.7151), and 0.7382 (0.6266–0.7954), respectively. We also estimated the number of loci needed to determine the fathers of offspring with a probability of 0.8 assuming that ten males were present in the troop. The estimated number was about 13.5 times, 5 times and 1.8 times the number of loci examined on average in the troops of Japanese, crab-eating and toque macaques, respectively. This means that determination of most of the fathers of offspring in wild troops of these macaques, even of toque macaques which have a rather high probability of paternity exclusion, is difficult so long as we employ only electrophoretic techniques.