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Since carriers of the acheiropodia gene cannot be distinguished from noncarriers, parents and normal sibs of affected individuals have been used to estimate the fitness of heterozygotes. No significant difference in biologic fitness (viability and fertility) between normal sibs and the general population could be detected. A comparison between acheiropods and their normal sibs showed the following: (1) a nonsignificant difference in stillbirth rate; (2) a higher mortality rate of acheiropods in the first 5 years of life; (3) a relative viability not larger than .7; (4) a relative fertility no greater than .14, due to "cosmetic effects"; and (5) a fitness of .10 or lower. The total number of acheiropodia genes in Brazil has been calculated as 25,000 in the 1970s. The data are compatible with an extremely low mutation rate and a very stable locus. It is suggested that all Brazilian acheiropods can be traced to a single mutation. A conservative estimate of the number of acheiropods to appear in the future in Brazil is 14,000 with an extinction time of no less than 2,300 generations or almost 70,000 years. A variety of other parameters have been calculated.

Formulae for the arrival probability and first arrival time for a single mutant gene to reach a certain number have been obtained by using a continuous branching process. If the mean of the progeny number of heterozygotes is less than one the arrival probability increases with increasing variance of the progeny distribution whereas if the mean is greater than one the contrary is true. Since most human populations are growing at fairly high rates, the result indicates that the probability for a single mutation to grow to a large number is quite high. Numerical computations show that the mean first arrival time decreases with increasing variance of the progeny distribution of the mutant carriers. The results have been applied to investigate the case of the acheiropodia gene in Brazil. The hypothesis that all acheiropodia genes in Brazil were derived from a single mutation seems to be tenable.