Computerintensive Methoden - Coalescent Theory - Chapter 1 - Task 2

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

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