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  Section: Genetics » Quantitative Inheritance
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Quantitative Inheritance

Quantitative Inheritance
Multiple factors
Binomial distribution
Effect of degree of dominance, number of genes and environment
Quantifying variability 
Variance and standard deviation
Partitioning of phenotypic variance
Heritability in broad sense and narrow sense

In Mendel's Laws of Inheritance and Lethality and Interaction of Genes, cases have been discussed where invariably the heterozygous condition of a gene had the same phenotypic effect as the homozygous dominant had. However in Mendel's Laws of Inheritance, while discussing the deviations from Mendel's findings, a reference was made to cases where the F1individual which is heterozygous would show intermediate character with respect to the two parents. These cases.earlier referred to as cases of blending inheritance are now explained on the basis of incomplete dominance.

Mendel, however, believed in alternate characters or sharp categories. For instance, if tall and dwarf plants were crossed, in F1 only tall plants and in F2, only tall and dwarf plant were obtained. No plants of intermediate type were ever obtained. It is believed that, if ever intermediate types were obtained with respect to any character by Mendel or by some other workers, they perhaps discarded these results, since these results could not be easily explained. However, Mendel was also able to observe small differences among plants belonging to one class.

For example his short or dwarf pea plants as well as tall plants differed among themselves within a small range which was not striking. It was quite natural to attribute these small differences to environmental effects among individuals, which were genetically similar. This led to development of a concept that continuous variation is not inherited and that only discontinuous variation is inherited and controlled by genes. Such a hypothesis was supported by early geneticists like Bateson and de Vries. On the other hand, during later half of 19th century, Galton, an English geneticist and statistician formed a group, who devoted themselves to the study of continuous variation and sought an explanation for its origin. Galton found that although many of these traits involved differences, which were not perceptible, but these characters which were called metrical characters, were found to be inherited. To study these metrical traits and their inheritance, new biometrical techniques were used and in human beings it was shown that relatives of a family resembled with respect to numerous continuously distributed quantitative traits.

As a result of above controversy, soon after rediscovery of Mendel's experiments, two main groups of geneticists emerged : (i) mendelians, who believed that all evolutionary important heritable differences are qualitative and discontinuous, and (ii) biometricians, who proposed that heritable variation is basically quantitative and continuous and that genes did not exist as separate units. Since views of these two groups were contradictory, it was difficult to reconcile these views. However, it will be seen that both these views were only partly correct. To prove that both mendelians and biometricians were only partly correct, Johannsen (1903) used the character of seed weight in beans and analysed its breeding behaviour. In a commercial seed lot of a variety, seed weight ranged from 1 cg (cg = centigram) to 90 cg. In the progeny of seed of every weight group, great variation was observed, and by successive self pollinations for several generations, it was possible to isolate 19 pure lines. Each pure line had a distinct average seed weight, which was maintained in the progeny although variation did exist in each pure line and was attributed to environmental effect. Thus by Johannsen's experiment, it could be shown that continuous variation can be heritable, a belief opposed by mendelians. However since differences between 19 different pure lines isolated by Johannsen (1903) could not be ascribed to specific genes, genetic basis of quantitative traits still remained disputed and it could not be proved that like qualitative traits, quantitative traits exhibiting continuous variation are also controlled by individual genes comparable to Mendelian factors.

Subsequently, it was Yule (1906), who suggested that quantitative variation may be controlled by large number of individual genes, each having a small effect. Soon after Yule's proposal, H. Nilsson-Ehle (1908) and East (1910), demonstrated segregation and assortment of genes controlling quantitative traits, kernel colour in wheat and corolla length in tobacco. Such genes were later called polygenic systems and inheritance due to such a system was explained in the form of multiple factor hypothesis.


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