Chpt. 18 homework 2. The mean (or average) is calculated by dividing the sum of all measurements by the total number of measurements, or in this case, the total number of bristles divided by the number of individuals. = 564/120 = 4.7 average number of bristle/individual The variance is useful for studying the distribution of measurements around the mean and is defined in this example as variance = s2 = average of the (actual bristle count – mean)2 = 1/120∑[(1 – 4.7)2 + (2 – 4.7)2 + (3 – 4.7)2 + (4 – 4.7)2 + (5 – 4.7)2 + (6 – 4.7)2 + (7 – 4.7)2] = 0.26 The standard deviation, another measurement of the distribution, is simply calculated as the square root of the variance. 3. a. H2 has meaning only with respect to the population that was studied in the environment in which it was studied. Even if a trait shows high heritability, it does not imply the trait is unaffected by its environment. The only acceptable analysis is to study directly the norms of reaction of the various genotypes in the population over the range of projected environments. Because it is so difficult to fully replicate a human genotype so that it might be tested in different environments, there is no known norm of reaction for any human quantitative trait. b. Neither H2 nor h2 is a reliable measure that can be used to generalize from a particular sample to a “universe” of the human population. They certainly should not be used in social decision making (as implied by the terms eugenics and dysgenics). c. Again, H2 and h2 are not reliable measures, and they should not be used in any decision making with regard to social policies. 5. a. Broad heritability measures that portion of the total variance that is due to genetic variance. The equation to use is H2 = the genetic variance/phenotypic variance where genetic variance = phenotypic variance – environmental variance Narrow heritability measures that portion of the total variance that is due to the additive genetic variation. The equation to use is h2 = additive genetic variance additive genetic variance + dominance variance + environmental variance Shank length: H2 = (310.2 – 248.1)/(310.2) = 0.200 h2 = 46.5/(46.5 + 15.6 + 248.1) = 0.150 Neck length: H2= (730.4 – 292.2/(730.4) = 0.600 h2= 73.0/(73.0 + 365.2 + 292.2) = 0.010 Fat content: H2 = (106.0 – 53.0)/(106.0) = 0.500 h2 = 42.4/(42.4 + 10.6 + 53.0) = 0.400 b. The larger the value of h2,the greater the difference between selected parents and the population as a whole, and the more that characteristic will respond to selection. Therefore, fat content would respond best to selection. c. The formula needed is selection response = h2 selection differential Therefore, selection response = (0.400)(10.5% – 6.5%) = 1.6% decrease in fat content, or 8.9% fat content.