A Saruman a minion of Sauron wishes to conguer Middle Earth

A. Saruman, a minion of Sauron, wishes to conguer Middle Earth. To accomplish this, he wants the orcs under his command to be stronger. The mean strength (measured by the amount of weight they can bench press) in Saruman\'s current population oforcs is 300 pounds. selects 20 of the strongest Orcs for breeding stock (see info on original population above). Ores have a mean strength of 400 pounds. The next oros of the next (from these 20 havea mean strength of340 pounds. Use this information to calculate your estimate of narrow sense heritability. B. You decide that Orcs are much too nasty to study and switch to an investigation of behavioral traits in hobbits. You want to see what proportion of the variation in foot size and foot hairiness is genetic. Calculate an estimate of heritability of these traits from the following data. Use the twin method for the twin data and calculate the average heritability using the relationship method on all the data. Type of Relationship Correlation coefficient Correlation coefficient Foot size Foot hairiness Parent-child 0.115 0.420 Sibling-sibling 0.110 0.411 DZ twins (fraternal 0.113 0.415 MZ twins (identica 0.230 0.837

Solution

A. We know that, h²=R/S.

We can see from the given information that response to selection (R) = 340-300 = 40, and selection differential (S) = 400-300 = 100.

Therefore, h² = 0.4

B. H² = 2(r_mz-r_dz)

Thus, heritability of foot size = 2(0.230-0.113) = 0.234.

Similarly, heritability of foot hairiness = 2(0.837-0.415) = 0.844.

Average heritability = (sum of coefficients of correlation)/(sum of coefficients of relationship)

We know that coefficients of relationship for parent-child, sib-sib, and dz twin are 0.5 each, and that for mz twin is 1.0.

Thus, average heritability of foot size = (0.115+0.110+0.113+0.230)/(0.5+0.5+0.5+1.0) = 0.2272.

Similarly, average heritability of foot hairiness = (0.420+0.411+0.415+0.837)/(0.5+0.5+0.5+1.0) = 0.8332.