where F is inbreeding coefficient or the measurement used for the probability that two genes (on the same locus) in a zygote are identical. It is clear, therefore, that if a recessive disease with genotype 'aa' occurs with frequency q2 in a random outbred population, its frequency will be increased by pqF in an inbred population. The ratio of frequencies of recessive homozygotes in inbred and outbred population's will, therefore, be :
It is evident from the above ratio, that if q is large (p will be small) and F is small, the inbreeding increment pF will be relatively small and the increase in frequency of recessive homozygotes will hardly be noticeable. However, if q is very small and p is large, pF provides a notable increase in recessives even when F is fairly small. Since different inbred families, will often produce homozygotes for different genes, paradoxically, one of the consequences of inbreeding is increase in variability between inbred families. The increase in homozygosity under inbreeding is accompanied by a change in the means of quantitative traits towards that of the homozygous recessive. It can be shown that if dominance is incomplete, the change will be somewhat diminished but nevertheless in the same direction. However, if dominance is completely absent, quantitative value of heterozygote is exactly midway between both homozygotes. In other words, the change in this value of heterozygote will be zero and the average" quantitative change or inbreeding effect reduces to zero. It appears, therefore, that there are four primary features of inbreeding. These are: (i) increase in frequency of homozygotes, (ii) increase in variability between different inbred families, (iii) reduction in value of quantitative character in the direction of recessive values, and (iv) the dependence of this reduction in value upon dominance. If this inbreeding effect is multiplied for many genes at many loci, there may be a large reduction in value for many traits, including those that affect fitness and survival. In corn, for example, E.M. East (1908) and G.H. Shull (1909) studied the effects of inbreeding for 30 generations of inbreeding and found independently, that the yielding ability in these lines finally reduced to about one third of the open pbllinate'd variety from which these samples were derived. In general, these authors reported the following important effects of inbreeding, (i) A number of lethal and sub-vital types appear in early generations of selfing. (ii) The material rapidly separates into distinct lines, which become increasingly uniform for differences in various morphological and functional characteristics, (iii) Many of the lines decrease in vigour and fecundity until they can not be maintained even under the most favourable cultural conditions, (iv) The lines that survive show a general decline in size and vigour.
The decline in size and vigour due to inbreeding is illustrated in Figure 47.1, where the plant height and grain yield of three lines are shown for 30 generations of inbreeding. It can be noticed that fixation for plant height occurred after five generations of inbreeding. However, yield continued to decline for at least 20 generations until it reached one-third that of open-pollinated variety from which they were derived.
Among the cross pollinated species, fairly tolerant to inbreeding, are also sunflowers, rye, timothy, smooth broomgrass and orchardgrass. The number of recessive abnormals appearing on inbreeding seems to be less in these species than in maize. There are also species in which inbreeding can be continued indefinitely with seeming impunity. The self-pollinating species are the best example of this category but some of the normally cross fertilizing species of plants, like cucurbits, also fall in this category.
In animals, however, the results are not marked. In a study on rats, it was found that by continuous brother-sister mating for 25 generations, the progenies compared favorably with cross-bred stock as controls. In Drosophila inbreeding usually results in a rapid loss of vigour, but some strains compare favourably with outbred populations after long continued inbreeding.
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