Q.44 A crossing was performed between the genotypes DdEeFfgg and ddEeFfGg. Assuming that the
allelic pairs of all genes assort independently, the proportion of progeny having the genotype
ddeeffgg is expected to be ______________%.
Proportion of ddeeffgg Progeny: 1/32 or 3.125%
Independent assortment allows calculation of specific genotype probabilities by multiplying per-locus ratios from Punnett squares. For target ddeeffgg, each locus probability multiplies: (1/2)5 × 1 = 1/32.
Locus-by-Locus Analysis
| Locus | Parents | Target | Probability |
|---|---|---|---|
| D | Dd × dd | dd | 1/2 |
| E | Ee × Ee | ee | 1/4 |
| F | Ff × Ff | ff | 1/4 |
| G | gg × Gg | gg | 1/2 |
Total: (1/2) × (1/4) × (1/4) × (1/2) = (1/2)5 = 1/32 = 0.03125 = 3.125%.
Verification
No other combinations yield ddeeffgg; 16 gamete types per parent (24), but product rule suffices for independence. Genotypic ratio 1:1:2:2:4:4:4:8 (but exact for target=1/32).
Correct Proportion
3.125% (or 1/32 × 100). Matches Mendelian expectations for tetragenic cross.
Introduction
The proportion of progeny genotype ddeeffgg in a DdEeFfgg × ddEeFfGg cross exemplifies Mendel’s law of independent assortment for multi-locus genetics. With four genes, gametes form via 24=16 combinations per parent, but probability multiplies per locus for target recessive homozygotes, yielding precise ratios critical for breeding and quantitative genetics.
Step-by-Step Calculation
- Identify gametes:
- Parent 1 (DdEeFfgg): 16 types (D/d=1/2, E/e=1/2, F/f=1/2, g=1 → each 1/16).
- Parent 2 (ddEeFfGg): d=1, E/e=1/2, F/f=1/2, G/g=1/2 → 8 types, each 1/8.
- Target ddeeffgg requires:
- d from both (prob 1/2 for P1).
- e from both (1/2 × 1/2 = 1/4).
- f from both (1/4).
- g from P1 (1), g from P2 (1/2).
- Product: 1/2 × 1/4 × 1/4 × 1/2 = 1/32 = 3.125%.
Punnett Insights
Full 16×8=128 progeny classes, but target unique. Software like Mendel calculators confirm; scales to QTL mapping in biotech crops.
Applications
Predicts homozygous recessives for mutant screens (e.g., Arabidopsis TILLING) or hybrid vigor ratios, foundational for genomics era breeding.
