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Chapter 24: Problem 32

A graduate student is studying a population of bluebonnets along a roadside. The plants in this population are genetically variable. She counts the seeds produced by 100 plants and measures the mean and variance of seed number. The variance is \(20 .\) Selecting one plant, the student takes cuttings from it and cultivates them in the greenhouse, eventually producing many genetically identical clones of the same plant. She then transplants these clones into the roadside population, allows them to grow for 1 year, and then counts the number of seeds produced by each of the cloned plants. The student finds that the variance in seed number among these cloned plants is \(5 .\) From the phenotypic variance of the gen etically variable and genetically identical plants, she calculates the broad-sense heritability. a. What is the broad- sense heritability of seed number for the roadside population of bluebonnets? b. What might cause this estimate of heritability to be inaccurate?

Short Answer

Expert verified
a. The broad-sense heritability is 0.75. b. Inaccuracies might stem from environmental variance or the assumption of similar environments for clones and original plants.

Step by step solution

01

Understand Phenotypic Variance

Phenotypic variance (\(V_P\)) is the total variance observed in a trait within a population, which includes genetic variance (\(V_G\)) and environmental variance (\(V_E\)). The formula is \(V_P = V_G + V_E\).
02

Identify Given Values

We are given two types of variance: the variance among genetically variable plants, \(V_P = 20\), and the variance among genetically identical clones, \(V_E = 5\). Since these clones are genetically identical, \(V_G = 0\), so \(V_E = \) total variance observed among clones.
03

Calculate Genetic Variance

Since we have \(V_P\) from the genetically variable population and \(V_E\) from the clones, calculate the genetic variance (\(V_G\)) using \(V_G = V_P - V_E\). Substitute the known values: \(V_G = 20 - 5 = 15.\)
04

Calculate Broad-Sense Heritability

Broad-sense heritability (\(H^2\)) is calculated using the formula \(H^2 = \frac{V_G}{V_P}\). Substitute \(V_G = 15\) and \(V_P = 20\): \(H^2 = \frac{15}{20} = 0.75.\)
05

Discuss Possible Inaccuracies

Heritability estimates can be inaccurate due to various factors such as genotype-environment interactions, environmental heterogeneity, or measurement errors. In this study, the assumption that the roadside and greenhouse environments are similar may affect the estimate.

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Key Concepts

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

Phenotypic Variance
Phenotypic variance, denoted as \(V_P\), represents the total variability in a particular trait within a population. This includes all factors contributing to differences in the trait among individuals, such as genetics and environment. Think of phenotypic variance as a broad umbrella that covers all variations, visual and measurable, within a population.

The phenotypic variance formula is straightforward:
  • \(V_P = V_G + V_E\)
where \(V_G\) is genetic variance and \(V_E\) is environmental variance.

In simpler terms, \(V_P\) combines the effects of both genetic differences among organisms and different environmental influences they experience. In the bluebonnet study, the phenotypic variance of seeds produced by the genetically diverse population is 20. This value sets the stage to understand how much of the trait variability is due to genetic versus environmental factors.
Genetic Variance
Genetic variance, symbolized as \(V_G\), refers to the portion of the phenotypic variance attributed specifically to genetic differences. It answers the question: how much of the observed diversity in a trait is due to genetic makeup?

In the exercise involving bluebonnets, calculating genetic variance is crucial. When the variance among genetically identical clones was observed to be 5, we inferred that environmental factors contributed this amount to the phenotypic variance. Since these clones share identical genetics, any variation in their traits is purely due to environmental variance.

We use the equation:
  • \(V_G = V_P - V_E\)
This calculation helped us find that genetic variance among the diverse population is 15 (i.e., 20 - 5 = 15). This means that most of the diversity in seed numbers is due to genetic factors. Understanding \(V_G\) is vital in studies aiming to improve or understand how traits are passed on through generations.
Environmental Variance
Environmental variance, denoted as \(V_E\), is the part of phenotypic variance caused by environmental factors. It's the difference in trait expression due to variations in living conditions like temperature, nutrition, and other non-genetic factors.

For the bluebonnets, \(V_E\) was derived from the variance in seed numbers among genetically identical clones. Given that these clones were genetically the same, any differences in their seed production were purely environmental. Thus, \(V_E\) was determined to be 5.

Environmental variance helps us understand how external factors can influence traits independently of genetic factors. This insight is crucial for determining how much of a trait's expression is due to nurture rather than nature.

In scientific studies, accurately accounting for environmental variance is essential for understanding true genetic influences and for devising strategies to enhance desirable traits.

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Most popular questions from this chapter

Mr. Jones is a pig farmer. For many years, he has fed his pigs the food left over from the local university cafeteria, which is known to be low in protein, deficient in vitamins, and downright untasty. However, the food is free, and his pigs don't complain. One day a salesman from a feed company visits Mr. Jones. The salesman claims that his company sells a new, high-protein, vitamin-enriched feed that enhances weight gain in pigs. Although the food is expensive, the salesman claims that the increased weight gain of the pigs will more than pay for the cost of the feed, increasing Mr. Jones's profit. Mr. Jones responds that he took a genetics class at university and that he has conducted some genetic experiments on his pigs; specifically, he has calculated the narrow-sense heritability of weight gain for his pigs and found it to be 0.98. Mr. Jones says that this heritability value indicates that \(98 \%\) of the variance in weight gain among his pigs is determined by genetic differences, and therefore the new pig feed can have little effect on the growth of his pigs. He concludes that the feed would be a waste of his money. The salesman doesn't dispute \(\mathrm{Mr}\). Jones' heritability estimate, but he still claims that the new feed can significantly increase weight gain in Mr. Jones' pigs. Who is correct and why?

Briefly describe common misunderstandings or misapplications of the concept of heritability.

How do broad-sense and narrow-sense heritabilities differ?

Assume that three loci, each with two alleles \((A \text { and } a, B\) and \(b, C \text { and } c),\) determine the differences in height between two homozygous strains of a plant. These genes are additive and equal in their effects on plant height. One strain (aa bb \(\alpha\) ) is \(10 \mathrm{cm}\) in height. The other strain \((A A B B C C)\) is \(22 \mathrm{cm}\) in height. The two strains are crossed, and the resulting \(\mathrm{F}_{1}\) are interbred to produce \(\mathrm{F}_{2}\) progeny. Give the phenotypes and the expected proportions of the \(\mathrm{F}_{2}\) progeny.

A genetics researcher determines that the broad-sense heritability of height among Southwestern University undergraduate students is 0.90. Which of the following conclusions would be reasonable? Explain your answer. a. Since Sally is a Southwestern University undergraduate student, \(10 \%\) of her height is determined by nongenetic factors. b. Ninety percent of variation in height among all undergraduate students in the United States is due to genetic differences. c. Ninety percent of the height of Southwestern University undergraduate students is determined by genes. d. Ten percent of the variation in height among Southwestern University undergraduate students is determined by variation in nongenetic factors. e. Because the heritability of height among Southwestern University students is so high, any change in the students' environment will have minimal effect on their height.
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