Mendelian Principles -  Independent Assortment

Mendel looked at crosses involving pea plants that differed  in two characters.  From his initial experiments, he had already demonstrated that each trait showed segregation. 

Pod color Green > Yellow [ A > a ]

Pod Form         Inflated > Constricted [ B > b ]

P₁                    Inflated green x Constricted Yellow

F₁                    All inflated green

F₂                    Inflated Green             9

                        Inflated yellow3

                        Constricted Green       3

                        Constricted yellow     1

Ways of calculating F₂ results

Punnett Square

                        AB                  Ab              aB              ab

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            AB      AABB            AABb        AaBB         AaBb

            Ab       AABb             AAbb         AaBb         Aabb

            aB       AaBB              AaBb         aaBB          aaBb

            ab        AaBb              Aabb          aaBb           aabb

Count up appropriate genotypes to get the appropriate phenotypes.

A_B_ = 1 AABB: 2 AABb: 4 AaBb: 2 AaBB = 9

A_bb   = 1 AAbb: 2 Aabb                                            = 3

aaB_ = 1 aaBB: 2 aaBb                                                 = 3

aabb = 1 aabb                                                                = 1

A second way is to use segregation at each locus

Segregation at A locus: 3 green to 1 yellow

Segregation at B locus: 3 inflated to 1 constricted

Multiple the binomial together 

[3(green): 1(yellow)] x [ 3(inflated): 1 (constr)]

9(infl, green): 3(infl, yel.): 3(const., green): 1(const, yel).

Independent assortment:

It says that every trait is inherited independently of the others and it thus covers the case that new combinations of genes can arise, which were not existing before. We know today that this principle is just valid in the case of genes that are not coupled, i.e. that are not located at the same chromosome.

Alleles at one locus loci segregate into gametes independently of alleles at other loci. Such gametes are formed in equal frequencies: Subsequent fertilization is at random.

Example:

            1 locus Aa = 2 gametes a & A with freq. of 1/2

            2 loci AaBb = 4 gametes AB, Ab, aB, & ab with freq. of 1/4

            3 loci AaBbCc = 8 gametes ABC, ABc, AbC, Abc, aBC, aBc, abC, & abc each with freq. 1/8

The expected distributions are combinatorial series for each character. That is for two characters A and B the disftibution of genotypes would be (A + 2Aa+ a) (B + 2Bb + b)

Note: Mendel also developed trihybrid crosses.

Test Cross - 2 loci

A_B_ might be one of four genotypes with following results

                                    Phenotypes

                        AB      Ab       aB       ab                    Genotype

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AABBx aabb 1                                                          AABB

AaBB x aabb  1                      1                                  AaBB

AABb x aabb 1          1                                              AABb

AaBb  x aabb 1          1          1          1                      AaBb