# Errata page forGene 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 $E(R_n^3) \approx \left( \log(n) + 0.577 - 2.14 \right) \rho$