#
Errata page for

*Gene Genealogies, Variation and Evolution*

A Primer in Coalescent Theory

by Jotun Hein, Mikkel H. Schierup, and Carsten Wiuf

ISBN 0-19-852996-1

## Page 30

### Equation 1.40

The \((1 - 1/(2 N))\) term should be omitted

### Equation 1.41

The \(\approx\) should be replaced with \(=\).

## Page 153

### Equation 5.20

The third sigma should be \[
\sum_{j=2}^i
\]

### Equation 5.21

The equation should be \[
E(R_n^3) \approx \left( \log(n) - 1.56 \right) \rho
\]

# Proof for Corrections

## Page 30

### Equation 1.40

From Professor Carsten Wiuf:

In the two sex model, one forms pairs of males and females, so going backwards, two genes come from the female population with probability \(1/4\) and the male with probability \(1/4\). If from female population, the two genes have probability \(1/(2N_f)\) for common ancestor and similar when males. So this yields

\[
\frac{1}{4} \left( \frac{1}{2N_f} + \frac{1}{2N_m} \right) = \frac{1}{8} \frac{N}{N_f N_m}
\]

## Page 153

### Equation 5.21

From A Simulation Study of the Reliability of Recombination Detection Methods: \[
\frac{ E(R_n^3) }{\rho} = \sum_{i=1}^{n-1} \frac{1}{i} - C(n)
\] and \[
C(n) \approx 2.14
\]

From the well known Euler-Mascheroni constant \(\gamma\): \[
\sum_{i=1}^n \frac{1}{i} \approx \log(n) + \gamma \approx \log(n) + 0.577
\]

Thus \[
E(R_n^3) \approx \left( \log(n) + 0.577 - 2.14 \right) \rho
\]