Genetics: A Conceptual Approach 6E w/ SaplingPlus (Six-Month Access)
Genetics: A Conceptual Approach 6E w/ SaplingPlus (Six-Month Access)
6th Edition
ISBN: 9781319125929
Author: Benjamin A. Pierce
Publisher: W. H. Freeman
Question
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Chapter 24.3, Problem 35AQP
Summary Introduction

To calculate:

The regression coefficient of mean offspring length against mean parental length and also to estimate the narrow-sense heritability for the trait.

Introduction:

The regression line is mathematically expressed as follows:

y=a+bx

Here, y is the mean offspring length of the middle joint of right index finger.

x  is the mean parental length of the middle joint of the right index finger.

b  is the slope of the regression line (regression coefficient).

a  is the intercept of the line.

Expert Solution & Answer
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Explanation of Solution

Regression coefficient (b) can be calculated as follows:

b=covxysx2

Here, covxy is the covariance of the x and y.

sx2 is the variance of x.

xiyi(xix¯)(yiy¯)(xix¯)2(yiy¯)2(xix¯)×(yiy¯)
3031-1.7-1.42.891.962.38
35363.33.610.8912.9611.88
2831-3.7-1.413.691.965.18
33351.32.61.696.763.38
2627-5.7-5.432.4929.1630.78
32300.3-2.40.095.76-0.72
3134-0.71.60.492.56-1.12
2928-2.7-4.47.2919.3611.88
40388.35.668.8931.3646.48
33341.31.61.692.562.08
Total =317324  (xix¯)2=140.1(yiy¯)2= 114.4(xix¯)(yiy¯)= 112.2

Mean of xi and yi are as follows:

Mean (x¯)=xinMean(x¯)=31710Mean(x¯)=31.7Mean (y¯)=yinMean(y¯)=32410Mean(y¯)=32.4

Covariance is calculated as follows:

covxy=(xix¯)(yiy¯)n1covxy=112.2101covxy=112.29covxy=12.47

Now, the variance of x can be calculated as follows:

sx2=(xix¯)2n1sx2=140.1101sx2=140.19sx2=15.57

Now, putting the values of variance and covariance in the formula of the regression coefficient as follows:

b=covxysx2b=12.4715.57b=0.80

The value of the regression coefficient is 0.80 and the narrow-sense heritability is equal to the regression coefficient. So, narrow-sense heritability is also 0.80.

Conclusion

The value of the regression coefficient and narrow-sense heritability is 0.80.

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