Population Genetics Problem #1

Microsatellite loci are widely used in population genetics for analysis of population structure, for inferring parentage, and estimating relationships. They have two features that make them very attractive for such purposes: (1) They have a high rate of mutation, leading to a large amount of variability within populations. (2) They are co-dominant, meaning that alleles contributed by both parents can be seen in their offspring - or so we usually assume.

It turns out that microsatellite loci often have ``null'' alleles, i.e., alleles that fail to amplify in a PCR reaction. If you're not aware that these alleles are present, then you may mistakenly think an individual is homozygous for a particular allele, when she's actually heterozygous for that allele and a null allele. de Sousa et al. [1] investigated this problem in Norway spruce, Picea abies. The following table shows a portion of the data they collected in their analysis. Using these data, answer the following questions:

Maternal Genotype	Seed genotype
$A_0A_{123}$	$A_0A_0$	$A_0A_x$	$A_{0}A_{123}$	$A_{123}A_x$	$A_{123}A_{123}$
	1	10	0	10	3
$A_{113}A_{119}$	$A_{113}A_{113}$	$A_{113}A_y$	$A_{119}A_y$	$A_{113}A_{119}$	$A_{119}A_{119}$
	1	12	10	0	0

1. Does meiosis appear to be fair in both mothers?¹

2. Given that $A_0$ is a null allele, what are the estimated frequencies of $A_0$, $A_{113}$, $A_{119}$, $A_{123}$, and all alleles other than these four in pollen that fertilized the ovules on these trees? You can group all of the other alleles together into a single ``pseudoallele'' and call it $A_u$.²

   The allele denoted as $A_x$ for the first mother refers to all alleles other than $A_0$ or $A_{123}$, including $A_{113}$ and $A_{119}$. The allele denoted as $A_y$ for the second mother refers to all alleles other than $A_0$, $A_{113}$ or $A_{119}$, including $A_{123}$.

3. Bonus question: What frequency of homozygotes would you expect given these estimates of allele frequencies? Now suppose that you didn't know there was a null allele and that you calculated allele frequencies from these data.³ What frequency of homozygotes would you expect?