Schematic figure.

<p>(A) We observe a population with different haplotypes. From the population we extract two measures—the haplotype frequency distribution (B) and the number of unique haplotypes as a function of the sample size (C). We assume that the frequency distribution (B) is a scale free distribution with upper and lower cutoff values <i>X</i>_min≤<i>x</i>≤<i>X</i>_max. For the sake of simplicity, we assume a zero probability to observe haplotypes with frequencies beyond these values. We provide an initial guess for the lower cutoff to be limited by the total population size, and the upper cutoff, we limit by an upper estimate from the total population size (Eq B6). We use an initial guess of <i>X</i>_min at its boundary, the Clauset estimate for the slope, and the observed highest frequency <i>X</i> 0 _max. We then fit the observed unique haplotype curve (C) with an analytical formula for the expected shape (D) with a cost function of </p><p></p><p></p><p></p><p></p><p><mo>∑</mo></p><p>R'</p><p></p><p></p><p></p><p></p><p><mo>(</mo></p><p><mi>log</mi><mo stretchy="false">(</mo>U(R')-log(observed (R')</p><mo>)</mo><p></p><p></p><mn>2</mn><p></p><p></p><p></p><mo>*</mo><mi>log</mi><mo stretchy="false">(</mo>observed (R'))<p></p><p></p><p></p> for different values of sample sizes R'. Finally, we extract the optimal parameters (E) and produce an estimate of the number of unique haplotypes for any population size N, where N is the target population size.<p>