Assume that the length of wheat leaves is controlled by three loci, each with two alleles: L and l, W and w, H and h. Determine the differences in leaf length between two homozygous strains of wheat. Assume each allele contributes equally to the length of the plant leaves. One homozygous strain, ll ww hh, has leaves that are 100 mm in length, and the other strain, LL WW HH, has 220 mm leaves. The two homozygous strains are crossed, and the resulting F1 are selfed to produce F2 progeny.

Quantitative heritability refers to the expression of a trait that depends on the contribution of each of the alleles involved in the interaction. More than two genes interact to express a phenotype. 1) 140 mm / 2) 0.2344

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Quantitative heritability is the transmission of a phenotypic trait in which expression depends on the additive effect of a series of genes.

The interaction of more than one gene determines the expression of the trait. And these genes can also have more than two alleles.

The action of many genes and alleles can cause many different combinations that are the reason for genotypic graduation.

Quantitative traits can be measured, such as longitude, weight, eggs laid per female, among others.

These characters do not group individuals by any precise and clear categories. Instead, they group individuals in many different categories that depend on how the genes were intercrossed and distributed during meiosis.

The result depends on the magnitude in which each allele contributes to the final phenotype and genotype. When they interact, they create a gradation in phenotypes, according to the level of contribution.

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In the exposed example, we know that

→ three diallelic genes control the length of wheat leaves L/l, W/w, H/h.

→ each allele contributes equally to the length of the plant leaves

ll ww hh → leaves of 100 mm in length
LL WW HH → leaves of 220 mm in length

Knowing that each allele contributes equally to the length, we can assume there are 7 possible phenotypes

LLWWHH ⇒ 220 mm

LlWWHH, LLWwHH, LLWWHh

LlWwHH, LlWWHh, LLWwHh, llWWHH, LLwwHH, LLWWhh

LlWwHh

llWwHh, LlwwHh, LlWwhh, llwwHH, llWWhh, LLwwhh

llwwHh, llWwhh, Llwwhh

llwwhh ⇒ 100 mm

The differences in leaf length between the two h0m0zyg0us strains of wheat is 220 - 100 mm = 120 mm

We know that

The minimal length of leaves is 100 mm and correspond to the h0m0zyg0us recessive genotype, llwwhh.

Each dominant allele contributes equally to the leaves legth.

The difference between the minimal length and the maximum one is 120 mm.

There are six dominant alleles.

The contribution of each dominant allele is

120mm / 6 alleles = 20 mm/allele.

Gentoype Dominant Length Phenotype

alleles contibution

llwwhh 0 0 100 mm

llwwHh, llWwhh, Llwwhh 1 20 mm 120mm

llWwHh, LlwwHh, LlWwhh,

llwwHH, llWWhh, LLwwhh 2 40 mm 140 mm

LlWwHh, LLWwhh, LLwwHh,

llWWHh, llWwHH, LlWWhh 3 60 mm 160 mm

LlwwHH

LlWwHH, LlWWHh, LLWwHh,

llWWHH, LLwwHH, LLWWhh 4 80 mm 180 mm

LlWWHH, LLWwHH, LLWWHh 5 100 mm 200 mm

LLWWHH 6 120 mm 220 mm

Now, let us analyze the crosses.

1st cross:

Parentals) LL WW HH x ll ww hh

F1) Ll Ww Hh

2nd cross: F1 selfed-cross

Parentals) Ll Ww Hh x Ll Ww Hh

F2) Genotypes

1/64 LLWWHH
2/64 LLWWHh
1/64 LLWWhh
2/64 LLWwHH
4/64 LLWwHh
2/64 LLWwhh
1/64 LLwwHH
2/64 LLwwHh
1/64 LLwwhh
2/64 LlWWHH
4/64 LlWWHh
2/64 LlWWhh
4/64 LlWwHH
8/64 LlWwHh
4/64 LlWwhh
2/64 LlwwHH
4/64 LlwwHh
2/64 Llwwhh
1/64 llWWHH
2/64 llWWHh
1/64 llWWhh
2/64 llWwHH
4/64 llWwHh
2/64 llWwhh
1/64 llwwHH
2/64 llwwHh
1/64 llwwhh

Phenotypes

1/64 ⇒ 220mm

6/64 ⇒ 200 mm

15/64 ⇒ 180 mm

20/64 ⇒ 160 mm

15/64 ⇒ 140 mm

6/64 ⇒ 120 mm

1/64 ⇒ 10 mm

Leaves of the llwwHH genotype plant will be 140 mm
The proportion of the F2 progeny with the same phenotype as the llwwHH genotype will be 15/64 = 0.2344

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