Mendelian Genetics: Principle of Independent Assortment

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Principle of Independent Assortment. The principle of independent assortment says that when gametes are formed in diploid organisms, the segregation of each gene pair does not affect the segregation of other gene pairs as long as the gene pairs are on separate chromosomes. For example suppose an organism has the following genotype: AaBb. Aa represents a gene pair and Bb represents the other gene pair. By the principle of segregation half the gametes have the 'A' allele and the other half have the a 'a' allele. But half the gametes also have the 'B' allele and half the gametes have the 'b' allele.

What Gregor Mendel realized was that for both gene pairs the fraction of gametes getting alleles A and B or in other words having genotype 'AB' (one gene from each gene pair) is 1/2 * 1/2 = 1/4. In other words the gene pairs are behaving independently from one another. So our parent with genotype AaBb produces the following gametes and in the following proportions:

Gamete genotype Expected proportion
AB 1/4
Ab 1/4
AB 1/4
AB 1/4

This works because when the gene pairs are on separate chromosomes, that is unlinked then we can use the multiplication rule for independent probabilities to figure out the expected proportion of gametes. In other words the proportion of gametes produced by the AaBb individual which have the genotype 'AB' is

The proportion of gametes with the 'A' allele times the proportion of gametes with the 'B' allele, or 1/2 * 1/2 = 1/4.

Suppose we have the following cross: AaBb x AaBb. What would be the expected genotypes of the offspring? The quickest way to answer this is to set up a Punnett Square putting the gametes from one parent along the top and the gametes from the other parent along the side like so:

  AB AB AB AB
AB AABB AABb AaBB AaBb
AB AABb AAbb AaBb Aabb
AB AaBB AaBb aaBB aaBb
AB AaBb Aabb aaBb aabb

 

I will leave it to you to figure out the expected number of each genotype by counting!

Tips: When writing genotypes remember these rules for clarity:

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Dihybrid Cross

Mendel did not know about Punnett Squares and as far as we know did not understand the connection between genes and chromosomes and could only analyze heredity in terms of what phenotypes resulted from his crosses. When he analyzed genes for single traits he typically used a monohybrid cross.

When looking at two traits together he used basically the same procedure except that he started out with parents that were true breeding for alternate forms of two traits. One trait might be flower color, the other trait might be plant height.

For example he might have a parent pea plant that was true breeding for purple flower, tall plant and cross that with a plant which was pure breeding for white flower and short plant.

What Mendel did was make a prediction as to what phenotypes the F2's would have and in what proportion if the principle of independent assortment was correct for the traits he studied.

Mendel made a bold leap. He reasoned that if the principle of independent assortment were correct then he could assume that the genotype and phenotype ratios for the F2's could be obtained by assuming that the dihybrid cross can be treated as two independent monohybrid crosses. He reasoned that since he knew the expected phenotypic rations for the monohybrid crosses, that he could combine the ratios for the monohybrid crosses using the rule of multiplication for independent probabilities. The reasoning is shown first in terms of a tree or branch diagram and then as a modified Punnett Square in terms of phenotypes for the F2's.

 

 

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Tree or Branch representation of the dihybrid F2 generation

 

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Modified Punnett square representation for the dihybrid F2 generation

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Tip: Using the rule of multiplication. The rule of multiplication for independent events provides a good way to compute the expected proportions of a certain phenotype in the F2's without doing Punnett squares or branching diagrams. For example for the dihybrid cross the proportion of offspring which are purple and tall in the F2 generation is simply (The proportion of offspring which are purple) x (The proportion of offspring which are tall) = 3/4 * 3/4 = 9/16.

If you do more complicated crosses, say trihybrid crosses or a cross involving any number of traits then Punett Squares or branch diagrams become too complex. But do make sure you completely understand the dihybrid cross in terms of Punnett squares or branch diagrams first for the dihybrid cross.

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