I hope I don't get fired. I went ahead and cut and pasted the page for you to read the info:
Gregor Mendel studied mainly traits that have distinct alternate forms for instance, purple flower color vs white flower color. But many traits are more complex than this and basically can take on any number of continuous values. For example in humans there is not just two classes of people - short vs tall- but a whole range of possible heights. In addition many traits are not controlled by a single gene pair but by many genes interacting with each other and also with the environment.. The study of traits controlled by many genes and also by the environment is called quantitative genetics. This a complex area of genetics but some understanding of quantitative genetics is useful for evolution because evolution often acts on complex traits influenced both by genetics and by the environment.
Polygenic inheritance.
Previous Page, Next Page, Top of Page
One of the major problems in genetics during the early part of the 20th century involved the following question. If Mendel's ideas were correct then how can one explain the inheritance of quantitative traits? Statistical research suggested that for quantitative traits the offspring of a cross tended to be intermediate in appearence between the two parents. For instance if one parent is tall and the other short, the offspring tend to be intermediate in height. In other words, the offspring in a cross tend to be a blend of both parents. This presents a problem for evolution, since for evolution to happen by natural selection requires the presence of genetically based variation in the value of a quantitative traits. Yet if offspring tend toward the mean value of the trait for the two parents then, the necessary variation for evolution to happen would be lost. The inheritance of quanitative traits is typically viewed in terms of what is called polygenic inheritance.
Assumptions of the Polygenic Model:
Previous Page, Next Page, Top of Page
This model makes the following 6 simplifying assumptions:
Each contributing gene has small and relatively equal effects.
The effects of each allele are additive.
The is no dominance, instead the genes at each locus behave as if they follow incomplete dominance.
There is no epistasis or interaction among the different loci contributing to the value of the trait
There is no linkage involved.
The value of the trait depends solely on genetics; environmental influences can be ignored .
Example I Polygenic inheritance of color in wheat.
Previous Page, Next Page, Top of Page
Kernal color in wheat is determined by two gene pairs, so called polygenes that produce a range of colors from white to dark red depending on the combinations of alleles. Dark red plants are homozygous AABB and white plants are homozygous aabb. When these homozygotes are crossed the F1 offspring are all double heterozygotes AaBb. Thus crossing individuals with the phenotype extremes yield offspring that are a 'blend' of the two parents.
This illustrates an important point that many times when you have two parents who differ in phenotype for some characteristic, there is a tendency for the offspring to be intermediate to the parents in phenotype. This phenomenon is sometimes called regression to the mean.
But what happens when the two double heterozygotes are crossed? The results are shown in the following Punnett Square
Notice that there are 5 phenotypic classes corresponding to the number of upper case alleles 0 through 4 that can be present in the offspring. Observe too that even though both parents are intermediate, there is not blending in the offfspring in that one does see that 1/16th of the offspring are dark red and 1/16 are white. This model suggests that intermediate individauls when they mate produce offspring that can be more extreme than either parent. Even though the polygenic model makes a number of simplyfying assumptions it does seem to be a good approximation to the inheritance of a large number of quantitative traits.
A more complex example and detailed mathematical analysis is presented next.
AB
Ab
aB
ab
AB
AABB
AABb
AaBB
AaBb
Ab
AABb
AAbb
AaBb
Aabb
aB
AaBB
AaBb
aaBB
aaBb
ab
AaBb
Aabb
aaBb
aabb
Example II Polygenic inheritance of plant height in tobacco: Analysis using the binomial theorem.
Previous Page, Next Page,Top of Page
Plant height in tobacco is controlled not by a single pair of genes but by a series of genes at multiple loci that each has a small additive affect on the phenotype of the plant. Assume three loci, each of which has two alleles. (A,a B,b C,c). Imagine pure-breeding short plants are all aabbcc and tall plants are all AABCC and a situation where the height of the plant is determined entirely by the number of upper case alleles regardless of which locus the allele is at. Thus a plant with the genotype AaBbcc is the same height as a plant with genotype AabbCc. In contrast to the claim of your text the upper case alleles are not dominant but behave as incomplete dominant alleles.
There are 7 possible classes of plant heights depending on the number of upper case alleles.
0,1,2,3,4,5 or 6.
Consider a pure breeding short plant aabbcc crossed with a pure breeding AABBCC plant. The F1's resulting from this cross are clearly the triple heterozygote:
AaBbCc
Notice that these plants are going to be intermediate in height between the two parents.
But what happens when these intermediate individuals are bred with each other? To analyze this, assume that the gene pairs are unlinked. This allows us to use independent assortment to predict the results. The expected fraction of offspring in each height class is given by the following expression based on the binomial theorem:
where N is the number of alleles in total(6) and M is the number of upper case alleles in a particular class. One way to interpret this formula is as the number of ways of choosing an individual plant can have M upper case alleles out of N. Sometimes we say N choose M for this.
N for our example is 6. Thus when M is zero there is only one way to get no upper case alleles. But when M is 1 there are 6!/(1!(5!) ) = 6 ways to do this.
Consider when M = 3. Then we have 6! / (3! 3!) = 6*5*4/3*2*1 = 120/6 = 20. All the possible classes out of 64 are shown in the graph here.
Notice that the frequency distribution of phenotypes in the F2 generation looks a little like the bell shaped curve familiar to students of statistics as the 'Normal Distribution'. Indeeed for large numbers of genes invovled in a quantitative trait where each gene has a small additive effect the resulting distribution of phenotype classes very closely resembles the Normal Distribution.
More complex models in quantitative genetics assume that the phenotype results from both environmental factors and genetics, perhaps interacting in complex ways. These sorts of models are called multifactorial models.
VBS Home page,VBS Course Navigator, Evolution, Quantitative Genetics, Previous Page, Next Page
Previous Page, Next Page, Top of Page
pgd 10/14/02
-----
Jeremy Pierce
Shade Tree Exotics
shade-tree-exotics@att.net
-med.jpg)
