Question

In the cross between a female A/a;B/b;c/c;D/d;e/e and male A/a;b/b;C/c;D/d;e/e, (Assume independent assortment of all genes and complete dominance.)What proportion of the progeny will be phenotypically identical to

(1) the female parent?
(2) the male parent,
(3) either parent and
(4) neither parent?What proportion of the progeny will be genotypically identical to
(1) the female parent?
(2) the male parent,
(3) either parent, and
(4) neither parent?

Answer 1

The expected proportion of dominant phenotype offspring from a tetrahybrid cross in all loci (A-D) is 81/256. To be phenotypically identical to either parent, offspring must have the dominant phenotype, regardless of homozygosity or heterozygosity. The genotypic likeness to a parent is difficult to calculate without a Punnett square, especially in tetrahybrid crosses.

Step-by-step explanation:

To answer the question regarding the inheritance patterns from a cross between a female A/a;B/b;c/c;D/d;e/e and a male A/a;b/b;C/c;D/d;e/e, we must consider each gene locus independently due to the assumption of complete dominance and independent assortment.

Phenotypic Proportions

For phenotypic proportions, we are interested in the offspring that exhibit the dominant phenotype for each of the four loci. Using the sum rule and product rule, the probability for each dominant allele being present (either homozygous dominant or heterozygous) is 3/4. So, the expected proportion of offspring with the dominant phenotype at all four loci (A-D) is 81/256 (3/4 x 3/4 x 3/4 x 3/4).

Genotypic Proportions

The genotypic ratio for a cross of Aa x Aa individuals is 1:2:1, which results in a phenotypic ratio of 3:1 for the dominant trait. This calculation can be applied to each locus separately. To be phenotypically identical to either parent, they must express the dominant trait regardless of whether they are homozygous or heterozygous for it.

• Phenotypically identical to the female parent: The proportion is 81/256 (dominant phenotype at all loci).
• Phenotypically identical to the male parent: The proportion is also 81/256 since the dominant phenotype is the same for both parents.
• Phenotypically identical to either parent: Since both options above are the same, the proportion remains 81/256.
• Phenotypically identical to neither parent: This case is not possible since all dominant phenotypes will match the parents.

Answer 2

Phenotypically identical

(1) the female parent: 9/64

(2) the male parent: 9/64

(3) either parent: 9/32

(4) neither parent: 23/32

Genotypically identical

(1) the female parent: 1/16

(2) the male parent: 1/16

(3) either parent: 1/8

(4) neither parent: 7/8

Step-by-step explanation:

To find out the answers, we will have to find out probability of each gene separately:

female male

A/a;B/b;c/c;D/d;e/e A/a;b/b;C/c;D/d;e/e

If we will look at only A gene combinations in both the parents the results will be as under:

Parentals : A/a x A/a

The 4 gametes in the progeny will be as under :

AA = 1/4

Aa = 1/4 Combined probability of Aa = 1/4+ 1/4 = 1/2

Aa = 1/4

aa = 1/4

If we will look at only B gene combinations in both the parents the results will be as under:

Parentals : B/b x b/b

The 4 gametes in the progeny will be as under :

Bb = 1/4 Combined probability of Bb = 1/4+ 1/4 = 1/2

Bb = 1/4

bb = 1/4 Combined probability of bb = 1/4+ 1/4 = 1/2

bb = 1/4

If we will look at only C gene combinations in both the parents the results will be as under:

Parentals : c/c x C/c

The 4 gametes in the progeny will be as under :

Cc = 1/4 Combined probability of Cc = 1/4+ 1/4 = 1/2

Cc = 1/4

cc = 1/4 Combined probability of cc = 1/4+ 1/4 = 1/2

cc = 1/4

If we will look at only D gene combinations in both the parents the results will be as under:

Parentals : D/d x D/d

The 4 gametes in the progeny will be as under :

DD = 1/4

Dd = 1/4 Combined probability of Dd = 1/4+ 1/4 = 1/2

Dd = 1/4

dd = 1/4

If we will look at only E gene combinations in both the parents the results will be as under:

Parentals : e/e x e/e

The 4 gametes in the progeny will be as under :

ee = 1/4

ee = 1/4 Combined probability of ee = 1/4+ 1/4 + 1/4 +1/4 = 1

ee = 1/4

ee = 1/4

It is given that genotype of first parent is A/a;B/b;c/c;D/d;e/e or AaBbccDdee .

Also, it is pertinent to mention here that AA and Aa genotype will produce same kind of phenotype. In the progeny, we can calculate the probability of AA & Aa will be 1/4 + 1/2 = 3/4

Similarly with respect to gene B, BB and Bb will produce same kind of phenotype but BB genotype will not get produced so we will only find out probability of Bb alone which is 1/2

Similarly the allelic combinations of gene C which will be similar to first parent will be 1/2

The combinations of gene D which will be similar to first parent will be a combination of DD & Dd which is 1/4 + 1/2 = 3/4

For gene e the combinations which will produce same phenotype as of first parent will be 1 because all the combinations are ee.

CALCULATIONS FOR PROGENY WHICH ARE SIMILAR TO PARENTS PHENOTYPICALLY.

(1) So, the combined probability of resemblance of phenotype of progeny with first parent which is female = 3/4 x 1/2 x 1/2 x 3/4 x 1 = 9/64.

(2) The genotype of male parent is A/a;b/b;C/c;D/d;e/e or AabbCcDdee.

So, in a similar way we can find out the combined probability of resemblance of phenotype of progeny with second parent = 3/4 x 1/2 x 1/2 x 3/4 x 1 = 9/64

(3) The progeny which are similar to either parent will be 9/64 + 9/64 = 18/64 = 9/32.

(4) The progeny which will have phenotype which does not match any parent will be 1 - 9/32 = 32 - 9 /32 = 23/32.

CALCULATIONS FOR PROGENY WHICH ARE SIMILAR TO PARENTS GENOTYPICALLY.

When we will look for progeny which are genotypically similar to parents, we will look for allelic combinations which are exactly similar to parents. While finding genotypes, homozygous dominant and heterozygous will not be same. For example, AA and Aa will not produce same genotype.

(1) The probability of progeny which will be genotypically identical to female parent (AaBbccDdee) is 1/2 x 1/2 x 1/2 x 1/2 x 1 = 1/16.

(2) The probability of progeny which will be genotypically identical to male parent (AabbCcDdee) is 1/2 x 1/2 x 1/2 x 1/2 x 1 = 1/16.

(3) The progeny which will be genotypically similar to either parent will have probability = 1/16 + 1/16 = 1/8

(4) The progeny which will have genotype which does not match any parent will be = 1 - 1/8 = 7/8