Caballero QG Chp. 2, Problem set Q1 (R)

Chapter 2: Forces of change in allele frequencies

In a population of gazelles, 200 individuals were analyzed for the $\alpha$ - amylase gene, finding three allelic variants (A$_1$,A$_2$,A$_3$) and the observed genotype frequencies indicated in the following table.

(a) What is the value of the expected heterozygosity in the population?

Here we can write out the expected heterozygosity, H, as:

H = 1 - $\sum_{i=1}^{n} p^2_i$,

So, let’s get the frequency for each of these alleles by defining population size and also a variable for each genotype:

N <- 200;
a <- 23;
b <- 61;
c <- 28;
d <- 39;
e <- 49;
f <- 8;
# Now, let's get the frequencies of each allele
p1 <- (23+(61/2)+(28/2))/200
print(p1)
p2 <- ((61/2)+39+(41/2))/200
print(p2)
p3 <- ((28/2)+(41/2)+8)/200
print(p3)
[1] 0.3375
[1] 0.45
[1] 0.2125

Now we just need subtract the squares from 1

H <- 1 - (p1)^2 - (p2)^2 - (p3)^2
print(H)
[1] 0.6384375