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Chapter 23: Problem 13

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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Most popular questions from this chapter

Type A1B brachydactyly (short middle phalanges) is a genetically determined trait that maps to the short arm of chromosome 5 in humans. If you classify individuals as either having or not having brachydactyly, the trait appears to follow a single-locus, incompletely dominant pattern of inheritance. However, if one examines the fingers and toes of affected individuals, one sees a range of expression from extremely short to only slightly short. What might cause such variation in the expression of brachydactyly?

Describe the value of using twins in the study of questions relating to the relative impact of heredity versus environment.

Erma and Harvey were a compatible barnyard pair, but a curious sight. Harvey's tail was only \(6 \mathrm{cm}\) long, while Erma's was \(30 \mathrm{cm} .\) Their \(\mathrm{F}_{1}\) piglet offspring all grew tails that were \(18 \mathrm{cm}\) When inbred, an \(\mathrm{F}_{2}\) generation resulted in many piglets (Erma and Harvey's grandpigs), whose tails ranged in \(4-\mathrm{cm}\) intervals from 6 to \(30 \mathrm{cm}(6,10,14,18,22,26, \text { and } 30) .\) Most had \(18-\mathrm{cm}\) tails, while \(1 / 64\) had \(6-\mathrm{cm}\) tails and \(1 / 64\) had \(30-\mathrm{cm}\) tails. (a) Explain how these tail lengths were inherited by describing the mode of inheritance, indicating how many gene pairs were at work, and designating the genotypes of Harvey, Erma, and their 18 -cm-tail offspring. (b) If one of the \(18-\mathrm{cm} \mathrm{F}_{1}\) pigs is mated with one of the \(6-\mathrm{cm}\) \(\mathrm{F}_{2}\) pigs, what phenotypic ratio will be predicted if many offspring resulted? Diagram the cross.

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?

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?
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