Introduction

Mendel's rules describe how genetic transmission happens between parents and offspring. Consider a monohybrid cross:

$A_1A_2$ $\times$ $A_1A_2$
	$\downarrow$
$\frac{1}{4}A_1A_1$	$\frac{1}{2}A_1A_2$	$\frac{1}{4}A_2A_2$

Population genetics describes how genetic transmission happens between a population of parents and a population of offspring. Consider the following data from the Est-3 locus of Zoarces viviparus:¹

	Genotype of offspring
Maternal genotype	$A_1A_1$	$A_1A_2$	$A_2A_2$
$A_1A_1$	305	516
$A_1A_2$	459	1360	877
$A_2A_2$		877	1541

This table describes, empirically, the relationship between the genotypes of mothers and the genotypes of their offspring. We can also make some inferences about the genotypes of the fathers in this population, even though we didn't see them.

1. 305 out of 821 male gametes that fertilized eggs from $A_1A_1$ mothers carried the $A_1$ allele (37%).

2. 877 out of 2418 male gametes that fertilized eggs from $A_2A_2$ mothers carried the $A_1$ allele (36%).

Question

How many of the 2,696 male gametes that fertilized eggs from $A_1A_2$ mothers carried the $A_1$ allele?

Recall

We don't know the paternal genotypes or we wouldn't be asking this question.

• There is no way to tell which of the 1360 $A_1A_2$ offspring received $A_1$ from their mother and which from their father.

• Regardless of what the genotype of the father is, half of the offspring of a heterozygous mother will be heterozygous.²

• Heterozygous offspring of heterozygous mothers contain no information about the frequency of $A_1$ among fathers, so we don't bother to include them in our calculations.

Rephrase

How many of the 1336 homozygous progeny of heterozygous mothers received an $A_1$ allele from their father?

Answer

459 out of 1336 (34%)

New question

How many of the offspring where the paternal contribution can be identified received an $A_1$ allele from their father?

Answer

(305 + 459 + 877) out of (305 + 459 + 877 + 516 + 877 + 1541) or 1641 out of 4575 (36%)