Caballero QG Chp. 1, Problem set Q2 (R)

Chapter 1: Continuous variation

Problem 2

The following table shows the number of sternopleural bristles in 50 individuals of Drosophila melanogaster.

Knowing that the genetic variance of the trait is V_G = 4, deduce the value of the environmental variance (V_E) and the phenotypic (CV_P) and genotypic (CV_G) coefficients of variation. A good place to start here is creating an array of the phenotypes for bristle number:

b <- c(24,24,21,21,21,20,19,19,18,24,23,25,22,24,22,22,18,20,22,28,23,27,23,20,23,21,26,27,27,28,26,26,24,26,27,26,20,22,21,18,18,21,17,21,18,20,23,22,34,22)
str(b)
num [1:50] 24 24 21 21 21 20 19 19 18 24 ...

The solution to this problem requires solving for a few variables from equation (1.2), V_P = V_G + V_E. Let’s start by getting the mean of the bristle phenotype:

mb <- mean(b)
print(mb)
[1] 22.68

We also need to estimate the phenotypic variance:

vb <- var(b)
print(vb)
[1] 11.3649

Great! Now we can easily get our V_E value since it’s just the result of subtracting V_G from V_P, or:

ve <- vb - 4
print(ve)
[1] 7.364898

Getting (CV_P) is similarly easy since we now have V_P and the mean phenotypic value. Specifically, we see in the text on page 12 that CV²_P = $(\frac{V_P}{\bar{P}^2})$. Solving for CV_P we have:

cvp <- (sqrt(vb))/mb
print(cvp)
[1] 0.1486414

Finally, and similar to CV_P, we can estimate CV_G as:

cvg <- (sqrt(4))/mb
print(cvg)
[1] 0.08818342

All done with chapter 1!