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19. Population Genetics: The Hardy Weinberg Equilibrium and Mating Systems
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The McGraw Hill Companies, 2001
Nineteen
Population Genetics: The Hardy-Weinberg Equilibrium and Mating Systems
BOX 19.1
he average person carries about four lethal-equivalent alleles that are hidden because they are recessive. Four lethal equivalents means four alleles that are lethal when homozygous, or eight alleles conferring a 50% chance of mortality when homozygous, or any similar combination of lethal and semilethal alleles. The exact arrangement cannot be determined with current analytical methods. We arrive at the estimate of hidden defective and lethal alleles by using inbreeding data. J. Crow and M. Kimura, in 1970, analyzed data showing that in Swedish families in which marriages occurred between rst cousins, between 16 and 28% of the offspring had genetic diseases. For unrelated parents, the comparable gure is between 4 and 6%. Therefore, it is estimated that the offspring of rst cousins have an added risk of 12 to 22% of having a genetic defect. The children of first cousins have an inbreeding coefficient of one-
Experimental Methods
The Determination of Lethal Equivalents
sixteenth. Hence, a theoretical individual who is completely inbred has the risk of genetic defect increased sixteenfold over an individual whose parents are rst cousins. If 100% risk is considered 1 lethal equivalent, then a completely inbred individual would carry 2 to 3.5 lethal equivalents (16 12% 16 22%). However, a completely inbred individual is, in essence, a doubled gamete. Since our interest is in the number of deleterious alleles a normal person carries, it is necessary to further multiply the risk by a factor of two to determine the number of lethalequivalent alleles carried by a normal individual. The conclusion is that the average person carries the equivalent
of four to seven alleles that would, in the homozygous state, cause a genetic defect. A similar calculation can be made using viability data rather than genetic defects to determine the occurrence of lethal equivalents. A study from rural France, also analyzed by Crow and Kimura, showed that the mortality rate of offspring of first cousins was 25%, whereas the analogous figure for the offspring of unrelated parents was about 12%, an increased risk of 13% for the offspring of cousins. Multiplying this risk gure of 0.13 by 32 (16 2) presents a figure of four lethal equivalents per average person in the population. In 1971, L. Cavalli-Sforza and W. Bodmer, using data primarily from Japanese populations, reported an estimate of about two lethal equivalents per average person. Despite some interpopulation differences in these estimates, they are about the same order of magnitude two to seven lethal equivalents per person.
Thus, inbreeding does not change allelic frequencies. We can also see intuitively that inbreeding affects zygotic combinations (genotypes), but not allelic frequencies: Although inbreeding may determine the genotypes of offspring, inbreeding does not change the numbers of each allele that an individual transmits into the next generation. In summary, inbreeding causes an increase in homozygosity, affects all loci in a population equally, and, in itself, has no effect on allelic frequencies, although it can expose deleterious alleles to selection. The results of inbreeding are evident in the appearance of recessive traits that are often deleterious. Inbreeding increases the rate of fetal deaths and congenital malformations in human beings and in other species that normally outbreed. In outbred agricultural crops and farm animals, decreases in size, fertility, vigor, and yield often result from inbreeding. Once deleterious traits appear due to inbreeding, natural selection can cause their removal from the population. However, in species adapted to inbreeding, including many crop plants and farm animals,
inbreeding does not expose deleterious alleles because those alleles have generally been eliminated already.
Pedigree Analysis
Path Diagram Construction
The inbreeding coef cient, F, of an individual (the probability of autozygosity) can be determined by pedigree analysis. This is done by converting a pedigree to a path diagram by eliminating all extraneous individuals, those who cannot contribute to the inbreeding coef cient of the individual in question. A path diagram shows the direct line of descent from common ancestors. An example of the conversion of a pedigree to a path diagram is shown in gure 19.3, in which individuals C and F are omitted from the path of descent because they are not related to anyone on the other side of the family tree and, therefore, do not contribute to the common ancestry of individual I. The pedigree in gure 19.3 shows an offspring who is the daughter of rst cousins. Since rst
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