Gregor Mendel could find the basic theories of genetics because he worked with discrete traits. Different alleles of the same gene gave rise to different phenotypes which were countable in the progeny. This helped to formulate the law of independent assortment and law of segregation.

However, researchers faced problems with multiple genes controlling the same phenotype. The quantitative traits such as height for instance are the result of multiple genes along with the influence of environment. Quantitative genetics deals with such quantitative traits. Examples include height, weight, athletic ability, kernel color, yield per acre and risk of diseases such as cancer, diabetes etc.

Theory of quantitative genetics is also based on the Mendelian principles. The genotypes follow the strict Mendelian ratio whereas the phenotypes do not adhere to the ratio and express in a varied way depending on the environment, effect of other genes etc.
The traits can be either continuous taking any value (e.g.: height), meristic which can take integer values only (e.g.: number of seeds in a pod) and threshold traits which express only on reaching a threshold value (e.g.: sex ratio, wing dimorphism).

The phenotype is the result of genotype plus environmental factors. There are three major questions posed by researchers about the basis of quantitative genetic transfer, how to identify the environmental influence and how to predict or control the outcome. The genes follow the simple Mendelian pattern of inheritance. Inbreeding is used to separate the effect of environment on the inheritance pattern and artificial selection methods have been devised to control the outcome and get the desired progeny. The method has been used by farmers to increase the yield and is a great tool in agricultural field.

The phenomenon was first observed in an experiment conducted by Johannsen to find the relation between seed weight of parental and filial generations. He coined the words 'genotype' and 'phenotype' to distinguish the effects. There was a distinct correlation between the two and he found out that the significant variation among the filial generation was due to environmental factors. The polygenic nature of such traits was confirmed by the experiments on wheat kernel color by Herman Nilsson in 1909.

By subsequent experiments it was confirmed that extreme parents gave rise to offspring having trait averages more than the parent generation. The phenomenon of 'regression to mean' proved that offspring of extreme parents benefit from suitable environmental conditions which can't be inherited. Repeated inbreeding among the filial generation gave rise to little or no variation among the progeny thus eliminating the environmental influence. The process cannot be applied to already inbred population since the variation will be limited.

The reduction of genetic variation can lead to a condition called 'inbreeding depression' in which the species encounters a population bottle neck. This is marked by reduced fitness of the individuals in the population and thus increasing the risk of extinction. 'Heterosis' or outbreeding experiments are used to enhance the fitness and thereby this has a notable value in conservation approaches.

Mathematical basis of quantitative genetics

Any distribution is distinguished by two statistical parameters mean and variance. The quantitative traits can be better expressed through the variance.
VT = VG + VE
Where VT = total variance, VG - variance due to genetics, and VE = variance due to environmental (non-inherited) causes.
The equation often has another covariance term which describes the combined effect of genetics and environmental variance.
This equation is often written with an additional covariance term: the degree to which genetic and environmental variance depend on each other.

Total variance is equal to phenotypic variance VP
Genetic variance or VG is further inclusive of the additive and dominance variance.
Hence VG = VA +VD

VA is the effect due to additive effect of alleles and /or genes whereas VD is due to dominance of alleles or genes.
Thus the total or phenotypic variance becomes VP = VA +VD+ VE

The proportion of variation of a trait due to genetics out of the total variance is termed as heritability. It is expressed as broad sense heritability
H = VG / VT
Since the variations are not often countable to accurate value, breeders have identified the narrow sense heritability as an alternate for measuring the efficacy of natural and artificial selection methods. This is represented by h2 where

h = VA / VT
It can also be calculated as
h = (next generation mean - original mean) / (parent mean - original mean)
Original mean represents the mean value of the trait in reference to the population and parent mean is the mean of the selected parents.

Realized or narrow sense heritability is often used in selection of parents and prediction of progenies in breeding and forms the basis of breeder's equation.

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