Quantitative Genetics

Several studies have been carried out particularly on polygenic traits that have different alternate forms for example, white flower color vs. purple flower color. However many traits are more multifaceted than this and can take on any number of incessant values. For instance in humans there are not just two groups of people i.e. tall vs. short- but a full range of possible heights. To add on, many traits are not controlled by a single pair of gene but by numerous genes that interact with each other and also with the environment.

The study done on traits controlled by multiple genes and also by the environment is referred to as quantitative genetics.  This is regarded as one of the complex area of genetics but a little understanding of quantitative genetics is necessary for evolution since evolution usually acts on complex traits which are influenced both by genetics and by the surroundings/environment.

Polygenic and appearance of blending inheritance.

One of the main challenges in genetics during the early years of the 20th century concerned the following question: If Mendel’s thoughts were right then how can one clarify the inheritance of quantitative traits? Statistical research reveals that for quantitative traits the offspring of a cross breed tend to be intermediate in looks between the two parents.

For example if one parent is short and the other tall, the offspring tends to be intermediate in height.  This means, the offspring in a cross tend to be a mixture of both parents. This presents a challenge for evolution, since for evolution to occur by natural selection needs the presence of genetically based disparity in the value of a quantitative trait.

However if an offspring lean towards the average value of the trait for the two parents then, the required variation for evolution to occur would be lost. The inheritance of quantitative traits is characteristically viewed in terms of what is referred to as polygenic inheritance.

The Assumptions of the Polygenic Model:

This polygenic model makes the following six simplifying assumptions: Every contributing gene has relatively equal and small effects, the effects of every allele are additive, there are no dominance; instead the genes at every locus behave as if they pursue an incomplete dominance, there is no interaction or epistasis among the different loci that contribute to the value of the trait, there is no connection involved and, the value of the trait relies only on genetics & environmental influences can be overlooked .

Example of Polygenic inheritance:

The core color in wheat is decided by two pairs of gene, known as polygenes which produce a variety of colors ranging from white to dark red depending on the mixtures of alleles. Dark red plants are known as homozygous AABB and white plants are referred to as homozygous aabb.  If these homozygotes are mixed/ crossed the F1 offspring are all dual heterozygotes AaBb.  Therefore crossing individuals with the phenotype extremely yields an offspring that is a ‘mixture’ of the two parents. This demonstrates a significant point that many times when one has two parents who vary in phenotype for some traits, then there will be a likelihood of the offspring to be an intermediate to the parents in phenotype. This occurrence is sometimes called regression to the mean.

The following punnett Square will illustrate what happens if 2 double heterozygotes are crossed: Take note that there are five phenotypic classes which corresponds to the number of upper case alleles 0 through to 4 that can be there in the offspring. Also note that even if both parents are intermediate, there will be no blending in the offspring such that one will see that 1/16 of the offspring will be dark red and 1/16 will be white. This replica suggests that when intermediate individuals mate, they produce an offspring that can be greater than either parent. Even if the polygenic replica makes several simplified assumptions it does seem to be a good estimate to the blending inheritance of a big number of quantitative traits.

A more complex example and a detailed mathematical study is shown below:

The height of a tobacco plant is controlled not by a single pair of genes but by a chain of genes at multiple loci that have a small additive effect on the phenotype of the plant. Take for example three loci, each having two alleles i.e. (A, a B, b C, c). Assume in pure-breeding, short plants are all aabbcc and that tall plants are all AABCC, circumstance whereby the height of the plant is determined depends entirely by the number of high case alleles regardless of  which locus the allele is at. Consequently a plant with the genotype AaBbcc is of the similar height as a plant with genotype AabbCc. There are seven probable classes of plant heights but depends with the number of upper case alleles (0, 1, 2,3,4,5 or 6).

If one conceders a pure breeding between a short plant aabbcc which is crossed with a pure breeding AABBCC plant then the F1’s which are as a result of this cross are obviously the triple heterozygote:

AaBbCc

It should be noted that these plants will be intermediate in height between the two parents. However what happens when these intermediate individuals are mate/breed? So as to examine this, assume that the gene pairs are not linked, this will allow us to use independent variety to predict the product. The anticipated fraction of offspring in each height class is specified by the following idiom based on the binomial theorem:

N/ (M (N-M)

Whereby N is the figure/ number of alleles in total (6) while M is the number/ figure of upper case alleles in a given class. One way to understand this formula is as the number of methods of choosing a particular plant can have M upper case alleles out of N. At times we say N chooses M for this. N for our illustration is 6. This means that when M is zero there is just one way to get the number of upper case alleles. But if M = 1 there are 6! / (1! (5!) ) = 6 ways to do this.

Consider M = 3. Then we have 6! / (3! 3!) = 6x5x4/3x2x1 = 120/6 = 20.

Note: every gene has a little additive effect; the resulting allocation of phenotype classes closely resembles the Normal Distribution. Other complex replicas in quantitative genetics suppose that the phenotype effects are from both environmental factors and genetics, perhaps intermingle in complex ways. These types of models are known as multifactorial models.