Chapter 25.4, Problem 40AQP

a.

Summary Introduction

To determine:

The evolutionary forces that affect the $Adh$ alleles in these populations.

Explanation of Solution

The alcohol presence increases the rate of mutation from $Ad{h}^S$ to $Ad{h}^F$ allele. The frequency of $Ad{h}^F$ allele is increasing by founder effect. In addition, the frequency of $Ad{h}^S$ allele has been decreased by bottleneck effect. Directional selection is occurring in favor of the $Ad{h}^F$ allele and against the $Ad{h}^S$ allele.

b.

Summary Introduction

To determine:

The fitness for the three genotypes using relative viabilities and the expected frequency of $Ad{h}^F$ in next generation in ethanol experiment based on these fitness values.

Explanation of Solution

The genotypes and their relative viability are as follow:

Genotype	Relative viability
$Ad{h}^F/Ad{h}^F$	$0.932$
$Ad{h}^F/Ad{h}^S$	$1.288$
$Ad{h}^S/Ad{h}^S$	$0.596$

The initial frequency $(p)$ is $f(Ad{h}^F)$ and is equal to $0.5$.

The $Ad{h}^S$ allele’s frequency ($(q)$) is $f(Ad{h}^S)$.

The sum of $p$ and $q$ is $1$. Therefore, the value of $q$ is as follows:

Fitness ($W$) for a given genotype is estimated as follows:

$W=\left(\frac{\text{Average number of offspring produced}\text{of}\text{that}\text{genotype }}{\text{Average number of offspring produced}\text{of}\text{that}\text{genotype}\text{that}\text{is}\text{most}\text{enriched}\text{with}\text{alcohol}}\right)$

$\begin{array}{c}{W}_{FF}=\frac{0.932}{1.288}\\ =0.724\end{array}$

$\begin{array}{c}{W}_{FF}=\frac{1.288}{1.288}\\ =1.0\end{array}$

$\begin{array}{c}{W}_{FF}=\frac{0.596}{1.288}\\ =0.463\end{array}$

The relative fitness of genotype $FF$ is $0.724$.

The relative fitness of genotype $FS$ is $1.0$.

The relative fitness of genotype $SS$ is $0.463$.

The mean fitness is calculated as follows:

$\overline{w}=p^2{W}_{SS}+2pq{W}_{Ss}+q^2{W}_{ss}$

$\begin{array}{c}\overline{w}={(}^{0.5}(0.724)+2(0.5)(0.5)(1)+{(}^{0.5}(0.463)\\ =(0.25)(0.724)+2(0.25)+(0.25)(0.463)\\ =0.181+0.5+0.116\\ =0.797\end{array}$

The genotypic frequency for next generation will be:

$\begin{array}{c}f(FF)=\frac{p^2{W}_{FF}}{\overline{w}}\\ =\frac{{(0.5)}^2(0.724)}{0.797}\\ =\frac{(0.25)(0.724)}{0.797}\\ =\frac{0.181}{0.797}\\ =0.227\end{array}$

$\begin{array}{c}f(FS)=\frac{2pq{W}_{FS}}{\overline{w}}\\ =\frac{2(0.5)(0.5)(1)}{0.797}\\ =\frac{2(0.25)}{0.797}\\ =\frac{0.5}{0.797}\\ =0.627\end{array}$

$\begin{array}{c}f(SS)=\frac{q^2{W}_{SS}}{\overline{w}}\\ =\frac{{(0.5)}^2(0.463)}{0.797}\\ =\frac{(0.25)(0.463)}{0.797}\\ =\frac{0.116}{0.797}\\ =0.145\end{array}$

The probable frequency of $FF$ after a generation is as follows:

$\begin{array}{c}p=f(FF)+\frac{f(FS)}{2}\\ =0.227+\frac{0.627}{2}\\ =0.227+0.3135\\ =0.54\end{array}$

Conclusion

The directional selection is increasing the occurrence of favor of the $Ad{h}^F$ allele and against the $Ad{h}^S$ allele. The frequency of $FF$ after a generation is $0.54$.