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Q5:
Define and design a test-cross.

Solution :

Definition of Test Cross

A test cross is a specialized genetic cross used to determine the zygosity (genotype) of an organism displaying a dominant phenotype. In this procedure, an individual of unknown genotype (exhibiting the dominant trait, denoted as $A\_$) is crossed with a homozygous recessive individual (denoted as $aa$). By analyzing the phenotypic ratio of the offspring, the unknown genotype can be definitively identified [Per Mendel’s Law of Segregation].

Theoretical Foundation

  • Unknown Parent: Either homozygous dominant ($AA$) or heterozygous ($Aa$).
  • Tester Parent: Always homozygous recessive ($aa$), which produces only recessive gametes ($a$).
  • Diagnostic Logic: If the unknown is $AA$, 100% of offspring will show the dominant phenotype ($Aa$). If the unknown is $Aa$, the offspring will exhibit a 1:1 phenotypic ratio of dominant ($Aa$) to recessive ($aa$).

Visual Representation of the Test Cross

Case 1: Unknown is AA P: AA x aa Gametes: (A) (A) x (a) (a) F1: All Aa (Dominant Phenotype) Case 2: Unknown is Aa P: Aa x aa Gametes: (A)(a) x (a) F1: 50% Aa (Dom), 50% aa (Rec)

Analytical Tabulation of Genotypic Outcomes

Unknown Genotype Cross Offspring Genotypes Phenotypic Ratio
Homozygous ($AA$) $AA \times aa$ $100\% \ Aa$ All Dominant
Heterozygous ($Aa$) $Aa \times aa$ $50\% \ Aa, 50\% \ aa$ $1 \ Dominant : 1 \ Recessive$

Conclusion and Application

The test cross acts as a diagnostic tool in classical genetics. If the unknown dominant individual produces even one recessive offspring in a test cross, the unknown parent must be heterozygous ($Aa$). Conversely, if only dominant offspring are observed across a statistically significant sample size, the unknown parent is likely homozygous dominant ($AA$). [By the Principle of Dominance and Segregation].

Final Solution: A test cross is a cross between an individual of unknown genotype and a homozygous recessive individual. It yields a 1:1 phenotypic ratio if the unknown is heterozygous, and a 100% dominant phenotypic result if the unknown is homozygous dominant.


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