13. Two varieties of maize averaging 48 and 72 inches in height, respectively, are crossed, The F1 progeny is quite uniform averaging 60 inches in height. Of the 500 F₂ plants, the shortest 2 are 48 inches and the tallest 2 are 72 inches. What is the probable number of polygenes involved in this trait?
(1) Four.          (2) Eight
(3) Sixteen.      (4) Thirty two

Explanation and Calculation of Polygenes Controlling Maize Height

Polygenic inheritance involves multiple genes (polygenes) contributing additively to a quantitative trait such as plant height. In this case, the two parental varieties of maize have average heights of 48 inches and 72 inches. The F1 generation shows an intermediate height of 60 inches, which indicates additive gene action.

Given Data

• Short parent (P1): 48 inches
• Tall parent (P2): 72 inches
• F1 hybrid: 60 inches

Formula Used

Substituting the given values:

The value 1 suggests one gene pair would explain the difference if each gene contributed equally. However, considering the F2 distribution extremes (48 and 72 inches), further analysis using the formula for phenotypic classes clarifies the actual number of gene pairs involved.

Using F2 Phenotypic Classes

The number of phenotypic classes in F2 can be represented as:

By observing the number of distinct height classes between the F2 extremes, the most probable number of polygenes is determined to be 4 pairs (8 polygenes total). The tallest and shortest individuals correspond to homozygous dominant and homozygous recessive combinations for all polygenes, respectively.

Option Analysis

• (1) Four gene pairs (8 polygenes): Matches the expected calculation and observed F2 range.
• (2) Eight pairs (16 polygenes): Implies an unusually high number of genes for the given range.
• (3) Sixteen pairs (32 polygenes): Unlikely, as the data show a narrow phenotypic range.
• (4) Thirty-two pairs (64 polygenes): Excessive; beyond the realistic scope of polygenic control.

Detailed Explanation

In maize, height is determined by multiple genes that contribute additively, resulting in intermediate F1 plant height. The range in F2 plants reflects the segregation of these polygenes. By analyzing the height extremes and averages, we determine the number of polygenes (gene pairs) controlling the trait. The problem shows two parent varieties with differing heights, a uniform F1 height, and F2 extremes matching the parents, suggesting four gene pairs (or eight polygenes) control this trait. This is consistent with the genetic principle that F2 phenotypic classes equal $2n+1$, where $n$ is the number of gene pairs.

This approach aids plant geneticists and breeders in estimating gene action contributing to quantitative traits like height.

This explanation and article outline address the given question in detail with clear reasoning and SEO-optimized structure for educational use. The most accurate polygenes estimate for the trait is 8 polygenes (4 pairs) based on the data provided.