Problem ER3

The common eider (Somateria mollissima, Fig. 1) is a large sea-duck that is distributed over the northern coasts of Europe, North America and eastern Siberia. Here below we report the genetic data (Milne and Robertson, 1965) of a small Scottish population; they pertain to two alleles (F and S) at an egg-white protein locus.

Genotypes	FF	FS	SS	total
Numbers	37	24	6	67

**Figure 1:** A pair of common eiders.
$\includegraphics[width=0.4\linewidth]{EiderDuck.eps}$

calculate the frequencies of genes F and S and the genotypic frequency H of heterozygotes;
calculate the theoretical frequency $H_{EQ}$ of heterozygotes that would establish if the population were actually at Hardy-Weinberg equilibrium; verify that $H_{EQ} >$ H;
assume that the smaller frequency of heterozygotes is due to a bottleneck: at the very beginning the duck population was large, thus the heterozygote frequency was $H_{EQ}$ ; then the population has been drastically reduced so that the effective population size was 30 ducks for a certain time T, during which genetic drift has been operating; calculate the time T (years, because reproduction occurs once a year) that is necessary for letting heterozygosity go down to H.