The efficiency of PCR amplification is either specified by an universal success rate , or, by a normal distribution  parameterized to capture GC preferential biases (default mean_GC=0.5 and SD_GC=0.1). Given p, the number of copies produced from a certain fragment is determined by random sampling under the cumulative binomial:

\[P_S(N)= \sum_{0}^{\lceil \frac{N}{2} \rceil}P_{S-1}(N-k) {N-k \choose k}  p^k (1-p)^{n-2k} \]

with S denoting the PCR cycle and N the number of molecules. As default, we assume 15 PCR cycles (S=15), and sample randomly the number of duplicates yielded by PCR amplification under the corresponding probability distribution P₁₅(N) for all possible values of N=[1;2¹⁵]. The recursion terminates by

\[ 
\begin{array}{l}
P_0=0 \\

P_1=\left\{ \begin{array}{rl}
1 &\mbox{ if $N=1$} \\
0 &\mbox{ otherwise}
       \end{array} \right.
\end{array}

\]