Computerintensive Methoden - Coalescent Theory - Chapter 1 - Task 2

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Using the table of random numbers given, generate a standard coalescent tree starting with 4 individuals.

Kochrezept

  1. Coalscent times t_k \sim\mathrm{Exp} \left( \frac{k (k-1)}{2} \right)\, bzw.  U \sim \mathrm{Unif}(0,1) \Rightarrow t_k = \frac{-\ln(U/100)}{\lambda}\,
  2. Wähle Allel durch U aus (also einfach in k Teile teilen)
  3. Baum durch Werte aus 1. und 2. zeichnen

Solution

The times between coalescent event is T_k \sim\mathrm{Exp} \left( \frac{k (k-1)}{2} \right)\,

Starting from uniform distributed random numbers U between 0 and 99, we get realisations t_k = \frac{-\ln(U/100)}{\lambda}\, with \lambda = \frac{k (k-1)}{2} \,

Choosing the position


\begin{array}{lrcl}
1 \ldots &  & U & < 25 \\
2 \ldots & 25 \le & U & < 50 \\
3 \ldots & 50 \le & U & < 75 \\
4 \ldots & 75 \le & U &  \\
\end{array}
\,