Saruman a minion of Sauron wishes to conquer Middle Earth To

Saruman, a minion of Sauron, wishes to conquer Middle Earth. To accomplish this, be wants the Ores under this command to be stronger. The mean strength (measured by the amount of weight they can bench press) in Saruman\'s current population of Ores is 300 pound. Saruman selects 20 of the strongest Ores for breeding stock (see info on original population above). These Ores have a mean strength of 400 pounds. The next Ores of the next generation (from these 20 selected Ores) have a mean strength of 340 pounds. Use this information to calculate your own estimate of narrow sense heritability. You decide that Ores 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.

Solution

A. Response to selection = heritability×selection differential

Given that, mean of initial population = 300 lbs, mean of selected individuals = 400 lbs, and mean of offspring = 340 lbs.

Therefore, (340-300) = h²×(400-300), or h² = 40/100 = 0.4

Hence, heritability (narrow sense) = 0.4

B. Broad-sense heritability (H²) = 2(r_mz-r_dz)

Therefore, 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 between parent-child, sibling-sibling, dz twins, and mz twins are 0.5, 0.5, 0.5, and 1.0 respectively.

Therefore, 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.