Chapter 19, Problem 28P

Suppose the mature height of a plant is a multifactorial trait under the control of five independently assorting genes, designated A, B, C, D, and E, and five environmental factors. There are two alleles of each gene ( ${\text{A}}_{\text{1}}$, ${\text{A}}_2$, etc.). Each allele with a subscript $\text{1}$ (i.e., ${\text{A}}_{\text{1}}$, etc.) contributes $\text{5}$ cm to potential plant height, and each allele with a $\text{2}$ subscript (i.e., ${\text{A}}_2$, etc.) contributes $\text{10}$ cm to potential plant height. In other words, a genotype containing only $\text{1}$ alleles ${\text{(A}}_{\text{1}}{\text{A}}_{\text{1}}{\text{B}}_{\text{1}}{\text{B}}_{\text{1}}{\text{C}}_{\text{1}}{\text{C}}_{\text{1}}{\text{D}}_{\text{1}}{\text{D}}_{\text{1}}{\text{E}}_{\text{1}}{\text{E}}_{\text{1}}\text{)}$ would have a potential height of $\left[\left(\text{10}\right)\left(\text{5}\right)\right]\text{ = 50}$ cm, and a genotype with only $\text{2}$ alleles ${\text{(A}}_2{\text{A}}_2{\text{B}}_2{\text{B}}_2{\text{C}}_2{\text{C}}_2{\text{D}}_2{\text{D}}_2{\text{E}}_2{\text{E}}_2\text{)}$ would have a potential height of $\text{[(10)(10)] = 100 cm}$.

The five environmental factors are ( $\text{1}$) amount of water, ( $\text{2}$) amount of sunlight, ( $\text{3}$) soil drainage, ( $\text{4}$) nutrient content of soil, and ( $\text{5}$) temperature. Each environmental factor can vary from optimal to poor. If all factors are optimal, assume that full potential height is attained. However, if one or more of the environmental factors is less than optimal, then height is reduced. The state of each environmental factor has an effect on growth. In this exercise, we’ll assume that the growth is affected according to the following scale:

Thus, for example, if one environmental factor is optimal, two are good, one is fair, and one is marginal, the loss of potential height is $\left(\text{0 + 4 + 4 + 8 + 12}\right)\text{ = 28}$ cm. If the loss of height potential is greater than the height potential of the plant, the plant does not survive.

a. Calculate the potential height, based on inherited alleles, and the attained height, based on growth in the environmental circumstances given, for the three plants (a, b, and c) in the accompanying table.

b. How many $\text{1}$ and $\text{2}$ alleles must be present to give a height potential of $\text{80}$ cm?

c. List two genotypes that have a height potential of $\text{80}$ cm.

d. If two plants that each have a height potential of $\text{75}$ cm are crossed, what proportion of the progeny will have a height potential of $\text{80}$ cm? (Hint: See Figure $\text{19}\text{.3}$ e for assistance making this determination.)