If F = 0, then the equation reduces to the familiar p ² + 2pq + q ² . However, if F = 1, it becomes p : 0 : q. The results show that any inbreeding leads to homozygosis (all or nearly all loci homozygous), with extreme inbreeding leading to a complete absence of heterozygosis (all or nearly all loci heterozygous).

      Differential fitness is a factor that mitigates against the realization of the Hardy‐Weinberg equilibrium. According to Darwin, the more progeny left, on average, by a genotype in relation to the progeny left by other genotypes, the fitter it is. It can be shown that the persistence of alleles in the population depends on whether they are dominant, intermediate, or recessive in gene action. An unfit (deleterious) recessive allele is fairly quickly reduced in frequency but declines slowly thereafter. On the other hand, an unfit dominant allele is rapidly eliminated from the population, while an intermediate allele is reduced more rapidly than a recessive allele because the former is open to selection in the heterozygote. The consequence of these outcomes is that unfit dominant or intermediate alleles are rare in cross‐breeding populations, while unfit recessive alleles persist because they are protected by their recessiveness. The point that will be made later but is worth noting here is that inbreeding exposes unfit recessive alleles (they become homozygous and are expressed) to selection and potential elimination from the population. It follows that inbreeding will expose any unfit allele, dominant or recessive. Consequently, species that are inbreeding would have opportunity to purge out unfit alleles and hence carry less genetic unfitness load (i.e. have more allele fitness) than outcrossing species. Furthermore, inbreeders (self‐pollinated species) are more tolerant of inbreeding whereas outcrossing species are intolerant of inbreeding.

      Whereas outcrossing species have more heterozygous loci and carry more unfitness load, there are cases in which the heterozygote is fitter than either homozygote. Called overdominance, this phenomenon is exploited in hybrid breeding (see Chapter 18).

3.9 Inbreeding and its implications in plant breeding

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.

      3.9.1 Consequences

The genetic consequences of inbreeding were alluded to in Section 3.8. The tendency toward homozygosity with inbreeding provides an opportunity for recessive alleles to be homozygous and hence expressed. Whereas inbreeding generally has little or no adverse effect in inbred species, crossbred species suffer adverse consequences when the recessive alleles are less favorable than the dominant alleles. Called inbreeding depression, it is manifested as a reduction in performance, because

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