The distribution of allele frequencies has beena major focus in population genetics. Classical approaches usingstochastic arguments depend highly on the choice of mutationmodel. Unfortunately, it is hard to justify which mutation modelis suitable for a particular sample. We propose two methods toestimate allele frequencies, especially for rare alleles, withoutassuming a mutation model. The first method achieves its goalthrough two steps. First it estimates the number of alleles in apopulation using a sample coverage method and then models rankedfrequencies for these alleles using the stretchedexponential/Weibull distribution. Simulation studies have shownthat both steps are robust to different mutation models. Thesecond method uses Bayesian approach to estimate both the numberof alleles and their frequencies simultaneously by assuming anon-informative prior distribution. The Bayesian approach is alsorobust to mutation models. Questions concerning the probability offinding a new allele, and the possible highest (or lowest)probability for a new-found allele can be answered by bothmethods. The advantages of our approaches include robustness tomutation model and ability to be easily extended to genotypic,haploid and protein structure data.
