Question

A recessive allele in mice results in abnormally long necks and sometimes death during embryogenesis. Crosses were made between pure breeding normal mice and pure-breeding long neck mic. All of the F1 mice had normal necks. Following an F1 x F1 cross, the F2 data below was observed for all mice born alive.

1044 Mice with normal necks

123 mice with long necks

How many total mice were expected in the progeny?

The answer is 348, how do we get this answer ?

Answer 1

The first cross was between pure breeding normal mice and pure breeding Long Neck Mice. Since the strains are pure breeding, it means both strains are Homozygous at the locus determining Neck length.

Let's take the Normal allele to be L and the long neck allele to be l.

So,

Cross 1
Normal mice x Long neck mice
LL x ll

The F1 progeny of this cross has the genotype Ll.

When F1 is selfed, the following Punnet Square depicts the proportion of progeny

		Parent 1 Gametes
		L	l
Parent 2 Gametes	L	LL	Ll
	l	Ll	ll

Based on the Punnet square we can summarise that 1/4th of the progeny has the genotype LL, 1/2 of the progeny has the genotype Ll and 1/4th of the progeny has the genotype ll.

Now, progeny with the genotype LL and Ll have a normal neck length since they have the Normal (L) allele.

Progeny with the genotype ll have a long neck.

So the phenotypic ratios are Normal Neck : Long Neck :: 3 : 1

That is, the F2 progeny would ideally have three times as many mice with Normal neck length as mice with long necks.

So,

Expected Number of progeny with long neck = (Number of progeny with Normal Neck)/3 = 1044/3 = 348