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The mean and variance of plant height of two highly inbred strains \(\left(P_{1} \text { and } P_{2}\right)\) and their progeny \(\left(F_{1} \text { and } F_{2}\right)\) are shown here. $$\begin{array}{ccc}\text { Strain } & \text { Mean (cm) } & \text { Variance } \\\\\mathrm{P}_{1} & 34.2 & 4.2 \\\\\mathrm{P}_{2} & 55.3 & 3.8 \\\\\mathrm{F}_{1} & 44.2 & 5.6 \\\\\mathrm{F}_{2} & 46.3 & 10.3\end{array}$$ Calculate the broad-sense heritability \(\left(H^{2}\right)\) of plant height in this species.

Short Answer

Expert verified
Answer: The broad-sense heritability (H^2) of plant height in this species is approximately 0.365 or 36.5%.

Step by step solution

01

Calculate the Average Environmental Variance

The environmental variance (\(V_E\)) can be calculated as the mean of the variances of the two inbred parent strains (\(P_1\) and \(P_2\)): $$V_{E}=\frac{4.2+3.8}{2}=4.0$$
02

Calculate the Phenotypic Variance

We will use the formula to calculate the phenotypic variance (\(V_P\)) as the difference between the variance of the \(F_2\) progeny and the environmental variance (\(V_E\)): $$V_{P}=V_{F_2}-V_{E}=10.3-4.0=6.3$$
03

Calculate the Genetic Variance

Now, to calculate the genetic variance (\(V_G\)), we use the following formula: $$V_{G}=V_{P}-V_{E}=6.3-4.0=2.3$$
04

Calculate the Broad-sense Heritability

Finally, to calculate the broad-sense heritability \((H^2)\), we divide the genetic variance (\(V_G\)) by the phenotypic variance (\(V_P\)): $$H^{2}=\frac{V_{G}}{V_{P}}=\frac{2.3}{6.3}\approx0.365$$ Thus, the broad-sense heritability \(H^2\) of plant height in this species is approximately 0.365 or 36.5%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Genetic Variance
Genetic variance refers to the diversity of genetic traits within a population. It is a crucial component because it determines how much of the variation in a trait, like plant height, is due to genetic differences among individuals. In this exercise, genetic variance was calculated as 2.3.
This was determined by subtracting the environmental variance from the phenotypic variance. Genetic variance is symbolized as \( V_G \), and it is key to understanding how a trait is inherited.
Genetic variance is influenced by several factors:
  • Mutations, which introduce new genetic information.

  • Gene flow, which involves genes moving between populations.

  • Genetic drift, where chance events cause random changes in gene frequencies.
Understanding genetic variance helps breeders and scientists predict how traits will be passed on to future generations.
Phenotypic Variance
Phenotypic variance represents the overall variation in a trait that can be observed in a population. For this plant height example, phenotypic variance \( V_P \) was calculated by considering variances from the offspring \( F_2 \) and the environment \( V_E \). It was found to be 6.3.
Phenotypic variance includes both genetic variance and environmental variance, showing how traits may present differently even within a similar gene pool. It is derived from the formula:
- \( V_P = V_F - V_E \)
Here is why phenotypic variance matters:
  • It shows the total variation in a trait in the population.

  • It allows scientists to distinguish which part of the variation is due to genetics versus the environment.

  • It is important for predicting breeding outcomes, especially in plants and animals.
By understanding phenotypic variance, we gain insights into the total observable differences in traits within a given context.
Environmental Variance
Environmental variance, denoted by \( V_E \), is the portion of phenotypic variance that arises from differences in environment rather than genetics. In this exercise, the environmental variance was averaged from two inbred parent strains and found to be 4.0.
Environmental variance is critical because even genetically identical plants can exhibit differences in height based on their surroundings. Changes in nutrition, light, water, and other environmental conditions contribute to this variance.
Here are some aspects that affect environmental variance:
  • The influence of climate and weather conditions on growth patterns.

  • Nutritional variations in soil quality or water availability.

  • Human interventions like fertilization or pruning.
Understanding environmental variance helps differentiate inherited traits from those influenced by external factors, thus providing a clearer picture of trait development.

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Most popular questions from this chapter

If one is attempting to determine the influence of genes or the environment on phenotypic variation, inbred strains with individuals of a relatively homogeneous or constant genetic background are often used. Variation observed between different inbred strains reared in a constant or homogeneous environment would likely be caused by genetic factors. What would be the source of variation observed among members of the same inbred strain reared under varying environmental conditions?

A dark-red strain and a white strain of wheat are crossed and produce an intermediate, medium-red \(\mathrm{F}_{1}\). When the \(\mathrm{F}_{1}\) plants are interbred, an \(\mathrm{F}_{2}\) generation is produced in a ratio of 1 darkred: 4 medium-dark-red: 6 medium-red: 4 light-red: 1 white. Further crosses reveal that the dark-red and white \(\mathrm{F}_{2}\) plants are true breeding. (a) Based on the ratios in the \(\mathrm{F}_{2}\) population, how many genes are involved in the production of color? (b) How many additive alleles are needed to produce each possible phenotype? (c) Assign symbols to these alleles and list possible genotypes that give rise to the medium-red and light-red phenotypes. (d) Predict the outcome of the \(F_{1}\) and \(F_{2}\) generations in a cross between a true-breeding medium-red plant and a white plant.

Height in humans depends on the additive action of genes. Assume that this trait is controlled by the four loci \(\mathrm{R}, \mathrm{S}, \mathrm{T}\) and \(\mathrm{U}\) and that environmental effects are negligible. Instead of additive versus nonadditive alleles, assume that additive and partially additive alleles exist. Additive alleles contribute two units, and partially additive alleles contribute one unit to height. (a) Can two individuals of moderate height produce offspring that are much taller or shorter than either parent? If so, how? (b) If an individual with the minimum height specified by these genes marries an individual of intermediate or moderate height, will any of their children be taller than the tall parent? Why or why not?

A 3 -inch plant was crossed with a 15 -inch plant, and all \(\mathrm{F}_{1}\) plants were 9 inches. The \(F_{2}\) plants exhibited a "normal distribution," with heights of \(3,4,5,6,7,8,9,10,11,12,13,14,\) and 15 inches. (a) What ratio will constitute the "normal distribution" in the \(\mathrm{F}_{2}\) ? (b) What will be the outcome if the \(\mathrm{F}_{1}\) plants are testcrossed with plants that are homozygous for all nonadditive alleles?

The following variances were calculated for two traits in a herd of hogs. $$\begin{array}{lccc}\text { Trait } & V_{P} & V_{C} & V_{A} \\\\\text { Back fat } & 30.6 & 12.2 & 8.44 \\\\\text { Body length } & 52.4 & 26.4 & 11.70\end{array}$$ (a) Calculate broad-sense \(\left(H^{2}\right)\) and narrow-sense \(\left(h^{2}\right)\) herita bilities for each trait in this herd. (b) Which of the two traits will respond best to selection by a breeder? Why?

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