NOTE 14B: This standard calculation gives the broad-sense heritability. Note that it applies only to this backcross population: The heritability in the F2, for example, would be higher and would include dominance components (because three genotypes would be present at each gene, not two as in a backcross). The assumption that the environmental variance in the F1 is the same as that in the backcross is dubious because the genotypes are different and, in particular, because the trait mean in the F1 is lower than in the backcross (2.25 g vs. 5.30 g). We would expect the variance to be higher if the mean is higher.
NOTE 14C: Finding the consequences of assortative mating is quite complex; see Bulmer (1985).
NOTE 14D: Even with assortment, it remains true that provided variation is additive, the covariance between full siblings is the same as that between parent and offspring.
NOTE 14E: A subtle issue has been ignored in iii): The genotypic values are the average of the trait expressed by each genotype. On a log scale, the genotypic values are not exactly equal to the logarithms of the values on the original scale because the average over environmental variance will be weighted differently. The error will tend to be small if the environmental variance, Ve, is small.
NOTE 14F: There are some subtle issues concerned with multiple testing here. There is an approximately 12% chance that an association with 1 of the 12 markers will be significant at the 1% level, even if there is no real association. Conversely, there may be real associations that miss the 1% threshold.
NOTE 14G: The expectation that directional selection fixes QTL with effects in the same direction is the basis for a simple statistical test for selection devised by Orr (1998).
NOTE 14H: This is a method for mapping QTLs for any trait that affects the growth of Plasmodium in mice. In this example, a single gene for drug resistance was found; however, the method can detect multiple QTLs.