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Measurement of Heritability
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Three general methods are used to estimate heritability. First, as discussed earlier, we can measure heritability by the response of a population to selection. Second, we can directly estimate the components of variance by minimizing one component; the remaining variance can then be attributed to other causes. For example, by minimizing environmental causes of variance, we can estimate the genetic component directly. Or, by eliminating the genetic causes of variance, we can estimate the environmental component directly. Third, we can measure the similarity between relatives. We look now at the latter two methods. Variance components can be minimized in several different ways. If we use genetically identical organisms, then the additive, dominance, and epistatic variances are zero, and all that is left is the environmental variance. For example, F. Robertson determined the variance components for the length of the thorax in Drosophila. The total variance (VPh) in a genetically heterogeneous population was 0.366 (measured directly from the distribution of the trait, as in tables 18.2 and 18.3). He then looked at the variance in ies that were genetically homogeneous. These were from isolated lines inbred in the laboratory over many generations to become virtually homozygous. Robertson studied the F1 in several different matings of inbred lines and found the variance in thorax length to be 0.186 (VE). By subtraction (0.366 0.186), we know that the total genetic variance (VG) was 0.180. From this, we can calculate heritability in the broad sense as HB VG/VPh 0.180/0.366 0.49
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Genetic variance can be measured directly by minimizing the in uence of the environment. This is most easily done with plants grown in a greenhouse. Under that circumstance, environmental variables, such as soil quality, water, and sunlight, can be controlled to a very high degree. Hence, the variance among individuals grown under these circumstances is almost all genetic variance. The total phenotypic variance can be obtained from the plants grown under natural circumstances. This allows us to calculate heritability in the broad sense. Several methods exist to sort out the additive from the dominant and epistatic portions of the genetic variance. The methods rely mostly on correlations between relatives. That is, the expected amount of genetic similarity between certain relatives can be compared with the actual similarity. The expected amount of genetic similarity is the proportion of genes shared; this is a known quantity for any form of relatedness. For example, parents and offspring have half their genes in common. The relation of observed and expected correlations between relatives is a direct measure of heritability in the narrow sense. We can thus de ne HN robs rexp
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(18.13)
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To calculate a heritability in the narrow sense, it is necessary to extract the components of the genetic variance, VG.
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in which robs is the observed correlation between the relatives, and rexp is the expected correlation. The expected correlation is simply the proportion of the genes in common. We must point out that the observed correlation between relatives can be arti cially in ated if the environments are not random. Since we know that relatives frequently share similar (or correlated) environments, they may show a phenotypic similarity irrespective of genetic causes. It is important to keep that in mind, especially when we analyze human traits, where it may be almost impossible to rule out or quantify environmental similarity. Hence, robs may be in ated, which will in ate HN. In human beings, nger-ridge counts ( ngerprints, g. 18.15) have a very high heritability; there seems to be very little environmental interference in the embryonic development of the ridges (table 18.6). Monozygotic twins are from the same egg, which divides into two embryos at a very early stage. They have identical genotypes. Dizygotic twins result from the simultaneous fertilization of two eggs. They have the same genetic relationship as siblings. (However, environmental in uences may be different; they may be treated differently by relatives and friends.) The data therefore suggest that human nger ridges are almost completely controlled by additive genes with a negligible input from environmental and dominance variation. Few human traits are controlled this simply (table 18.7). This brief discussion should make it clear that the components of the total variance can be estimated. For a given quantitative trait, the total variance can be mea-
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