Question

(4) Professor Snape is attempting to raise his own population of bloody-nosed beetles (Timarcha tenebricosa) because of their many uses in potions. Unfortunately, the batch of 100 beetles he bought in Diagon Alley seem a bit on the small side – their average length was just 13 mm. He chose the 20 largest beetles and moved them into their own enclosure, hoping their offspring would be a bit larger. The average length of the offspring of the larger beetles was 15.5 mm. According to the shop where Snape bought his beetles, heritability (ha) of length in the shop's colony of bloody-nosed beetles is 0.7. Using this information and the breeder's equation, calculate the average size of the beetles that Snape isolated for breeding.

Answer 1

We have from the Breeder's Equation;

h² = R/S

Where h² is the Narrow sense Heritability, R is the Response to Selection (Difference between Progeny population and original population) and S is the Selection Differential (Difference between Breeding individuals and original population)

h² = 0.7
R = Average Progeny size - Average size of original population = 15.5 cm - 13 cm = 2.5 cm
S = Average Size of Breeding Individuals - Average size of original population = x - 13 cm

From the Breeder's equation:

0.7 = 2.5/(x - 13)
=> x - 13 = 2.5/0.7
=> x - 13 = 3.57
=> x = 3.57 + 13 = 16.57 cm

The Average sie of beetles that Snape isolated for breeding is 16.57 cm.