Step 1: Understanding the Question:
The "fixation of heterosis" means enabling the hybrid vigor to be maintained through successive generations of seed reproduction without loss due to genetic segregation.
Step 2: Detailed Explanation:
• Methods to Fix Heterosis:
- Apomixis (A): Reproduction via seeds without fertilization. The progeny are clones of the mother plant, thus fixing the F\( _1 \) genotype.
- Vegetative Propagation (E): Clonal propagation (cuttings, grafting) bypasses meiosis and segregation entirely, fixing heterosis perfectly.
- Balanced Lethal System (B): A specialized genetic mechanism (seen in Oenothera) where only the heterozygous individuals survive, thus "fixing" the heterosis in the population.
• Methods where Heterosis is NOT Fixed:
- F1 Hybrid (C): Conventional F\( _1 \) hybrids obtained from crossing inbreds will segregate in the F\( _2 \) generation. Farmers must buy new seeds every year because the heterosis is lost through segregation and recombination.
- Synthetic Variety (D): A synthetic is an open-pollinated population. While it exploits heterosis, the level of vigor is lower than a single cross and it changes/stabilizes over generations; it is not "fixed" in the same way a genotype is fixed in apomixis or cloning.
Final Answer:
Heterosis cannot be fixed in conventional seed-produced F\( _1 \) hybrids and synthetic varieties.
The correct combination is C and D only.
The corresponding option is (D).