Читать книгу Principles of Plant Genetics and Breeding - George Acquaah - Страница 130

The point has already been made that the methods used by plant breeders depend on the natural means of reproduction of the species. This is because each method of reproduction has certain genetic consequences. In Figure 3.3a, there is no inbreeding because there is no common ancestral pathway to the individual, A (i.e. all parents are different). However, in Figure 3.3b inbreeding exists because B and C have common parents (D and E), that is, they are full sibs. To calculate the amount of inbreeding, the standard pedigree is converted to an arrow diagram (Figure 3.3c). Each individual contributes ½ of its genotype to its offspring. The coefficient of relationship (R) is calculated by summing up all the pathways between two individuals through a common ancestor as: R_BC = Σ(½)^s, where s is the number of steps (arrows) from B to the common ancestor and back to C. For example, B and C probably inherited (½)(½) = ¼ of their genes in common through ancestor D. Similarly, B and C probably inherited ¼ of their genes in common through ancestor E. The coefficient of relationship between B and C, as a result of common ancestry, is hence R_BC = ¼ + ¼ = ½ = 50%. Other more complex pedigrees are shown in Figure 3.4.

Figure 3.3 Pedigree diagrams can be drawn in the standard form (a or b) or converted to into an arrow diagram (c).

Figure 3.4 The inbreeding coefficient may be calculated by counting the number of arrows which connect the individual through one parent back to the common ancestor and back again to the other parent and applying the formula in the figure.

As previously indicated, prolonged selfing is the most extreme form of inbreeding. With each selfing, the percent heterozygosity decreases by 50%, whereas the percent homozygosity increases by 50% from the previous generation. The approach to homozygosity depends on the intensity of inbreeding as illustrated in Figure 3.5. The more distant the relationship between parents, the slower is the approach to homozygosity. The coefficient of inbreeding (F), previously discussed, measures the probability of identity of alleles by descent. This can be measured at both the individual level as well as the population level. At the individual level, F measures the probability that any two alleles at any locus are identical by descent (i.e. they are both products of a gene present in a common ancestor) At the population level, F measures the percentage of all loci which were heterozygous in the base population but have now probably become homozygous due to the effects of inbreeding. There are several methods used for calculating F. The coefficient of inbreeding (Fx) of an individual may be obtained by counting the number of arrows (n) that connect the individual through one parent back to the common ancestor and back again to the other parent, and using the mathematical expression:

Figure 3.5 Increase in percentage of homozygosity under various systems of inbreeding. (a) Selfing reduces heterozygosity by 50% of what existed at the previous generation. (b) The approach to homozygosity is most rapid under self‐fertilization.