In tomato plants (*Solanum lycopersicum*), red fruit color (R) is dominant over yellow fru… — JAMB UTME

In tomato plants (*Solanum lycopersicum*), red fruit color ( $R$ ) is dominant over yellow fruit color ( $r$ ), and tall stem height ( $T$ ) is dominant over dwarf stem height ( $t$ ). A geneticist crosses two heterozygous tall, red-fruited tomato plants ( $RrTt \times RrTt$ ). If this dihybrid cross yields a total of $1,600$ offspring in the $F_2$ generation, how many plants are expected to exhibit both yellow fruit and dwarf stems?

Answer: 100 plants

Answer

The expected number of offspring with yellow fruit and dwarf stems is 100 plants.

In a dihybrid cross of two heterozygous individuals (

RrTt \times RrTt

), allele pairs segregate independently. The probability of obtaining recessive yellow fruit (

rr

) is

\frac{1}{4}

, and the probability of obtaining recessive dwarf stem (

tt

) is

\frac{1}{4}

. By the product rule of probability, the combined probability of both recessive traits (

rrtt

) occurring simultaneously is

\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}

. Multiplying this fraction by the total offspring count (

1,600

) gives

100

plants.

Step-by-Step Solution

Determine the genotype of the specified phenotype

Yellow fruit and dwarf stem phenotype corresponds to the double recessive genotype

rrtt

Yellow (

r

) and dwarf (

t

) are both recessive alleles, requiring homozygous recessive conditions at both loci.

Determine the phenotypic ratio for a dihybrid cross of two heterozygotes (

RrTt \times RrTt

)

The expected

F_2

phenotypic ratio according to Mendel's Law of Independent Assortment is

9:3:3:1

The double recessive phenotype (

rrtt

) makes up

\frac{1}{16}

of the total offspring.

Calculate the expected count in a population of 1,600 offspring

1,600 \times \frac{1}{16} = 100

plants.

Multiplying the total offspring count by the probability of the double recessive phenotype yields the expected number of individuals.

Key Concept

Mendel's Law of Independent Assortment and F2 Dihybrid Phenotypic Ratios

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