Question

An entomologist is trying to increase body hairs in Drosophila. Her original population has a mean of 7.5 hairs, and she selects flies with a mean of 10 hairs to inter-mate and produce his next generation. The mean number of hairs in the resulting population was 9. Could you show me the process on how to do this I just want to double check my work.

1.What is the narrow sense heritability (h2) for number of body hairs in this Drosophila population (show your work)?

2. What would have been the mean number of body hairs in the next population if she had selected individuals with a mean of 8.5 hairs?

3. If she wanted a mean of 10 hairs in the progeny, what should have been the mean number of hairs in the individuals selected as parents?

Answer 1

1)

Narrow Sense Heritability = h2 = Response to Selection (R)/Selection Differential (S)

Here;

Response to Selection (R)
= Mean No. of Body Hairs in Progeny Population - Mean No. of Body Hairs in Original Population
= 9 - 7.5 = 1.5

Selection Differential (S)
= Mean No. of Body Hairs in Breeding Individuals - Mean No. of Body Hairs in Original Population
= 10 - 7.5 = 2.5

So, h2 = R/S = 1.5/2.5 = 0.6

2)

Had Breeding individuals been selected such that the mean number of body hair were 8.5;

Selection Differential (S) = 8.5 - 7.5 = 1

Since h2 = R/S,
=> R = h2 * S = 0.6 * 1 = 0.6
=> R = 0.6

So,

Mean No. of Body Hairs in Progeny Population - Mean No. of Body Hairs in Original Population = 0.6
=> Mean No. of Body Hairs in Progeny Population - 7.5 = 0.6
=> Mean No. of Body Hairs in Progeny Population = 7.5 + 0.6 = 8.1

If Breeding individuals with mean number of body hair = 8.5 were selected, the Progeny population would have a mean hair number of 8.1

3)

If the mean number of hair in the progeny were 10;

R = Mean No. of Body Hairs in Progeny Population - Mean No. of Body Hairs in Original Population
=> R = 10 - 7.5 = 2.5

Now,

h2 = R/S
=> 0.6 = 2.5/S
=> S = 2.5/0.6 = 4.167

So,

S = Mean No. of Body Hairs in Breeding Individuals - Mean No. of Body Hairs in Original Pop. = 4.167
=> Mean No. of Body Hairs in Breeding Individuals - 7.5 = 4.167
=> Mean No. of Body Hairs in Breeding Individuals = 4.167 + 7.5 = 11.667

Thus, in order to get a progeny population with mean number of body hair = 10; the Mean No. of Body hair in the Breeding individuals must be 11.667