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Punnett Squares
Punnett Squares

• A Punnett square is a grid that enables
  one to predict the outcome of simple
  genetic crosses
• Proposed by the English geneticist,
  Reginald Punnett
Plant genes can have dominant and recessive alleles

Example:
              The dominant allele
      R         R produces …



                                    … a red flower

              r
                        The recessive
                     allele r produces …




                                         … a white flower
A genetic cross in plants: Rr x Rr

There is only one way to make a homozygous plant with
two dominant genes…

 R                R                     RR



… and only one way to make a homozygous plant with
two recessive genes

  r                r                     rr
In the genetic cross Rr x Rr there are two ways of
 making a heterozygous plant…

      R                     r                 Rr


OR
     r                  R                    Rr



… so, heterozygous offspring are twice as likely as either
homozygous dominant or homozygous recessive offspring
We can show the likeliness or probability of different
genotypes in different ways:


1. As a percentage - Probability of RR is… 25%
                     Probability of Rr is… 50%
                     Probability of rr is… 25%


2. As a fraction -   Probability of RR is…   ¼
                     Probability of Rr is…   ½
                     Probability of rr is…   ¼

3. As a ratio -      RR : Rr : rr = 1 : 2 : 1
There are three ways to make a plant with red flowers…

… one produces a homozygous plant…
R           R                RR



 … and two produce heterozygous plants…
 R           r                Rr



 r           R                Rr
…but, there is only one way to produce a plant with white
                        flowers…

r           r              rr



So, in the genetic cross, Rr x Rr…

                    …red flowers are three
                    times more likely than
                    white flowers!!!
We can show the likeliness or probability of different
phenotypes in different ways:


1. As a percentage - Probability of red is…     75%
                     Probability of white is… 25%



2. As a fraction -   Probability of red is…     ¾
                     Probability of white is…   ¼


3. As a ratio -      red : white =   3:1
The Punnett Square
We can use the Punnett Square to work out the probability of
 the different genotypes and phenotypes in a genetic cross
  Step 1: Write down the genotypes of the parents.


                  x                    = Rr x Rr

  Step 2: Write down the genotypes of the gametes that
  each parent produces.
 pollen                      Egg
                             cells


                      = R+r                      = R+r
Step 3: Draw your Punnett Square             Egg cells

Step 4: Write the genotype                   R        r
of the different gametes
into your Punnett Square
                                       R     RR R r




                              Pollen
Step 5: Write in the
different ways in which the            r     rR       rr
gametes can be combined…

…this shows you the
possible genotypes of the
                                       Genotypes of
offspring                              offspring
Probability of Genotypes
                                               Egg cells
There are four possible ways to
combine egg cells and pollen                    R      r
Count up how many times
each genotype appears in                 R     RR R r




                                Pollen
the Punnet Square – this
gives you its probability:               r     rR      rr

 Probability of RR is…   ¼       = 25 %
 Probability of Rr is…
                         2
                         4   = ½ = 50 %      The ratio of
 Probability of rr is…   ¼       = 25 %      RR : Rr : rr is…
                                                 1:2:1
Probability of Phenotypes
                                                Egg cells
Look at the genotypes of the
offspring in your Punett Square…                 R         r
…decide which phenotype
each one should produce.                  R     RR R r




                                 Pollen
Count up how many times
each phenotype appears in                 r     rR     rr
the Punnet Square – this
gives you its probability:

Probability of red is…     ¾   = 75 %         The ratio of
                                              red : white is…
Probability of white is…   ¼   = 25 %                3:1
Mendel’s Experiments

• Mendel also performed dihybrid crosses
  – Crossing individual plants that differ in two
    traits
• For example
  – Trait 1 = Seed texture (round vs. wrinkled)
  – Trait 2 = Seed color (yellow vs. green)
• There are two possible patterns of
  inheritance for these traits
Figure 2.7
Figure 2.8
DATA FROM ONE OF MENDEL’S DIHYBRID CROSSES


P Cross        F1           F2 generation
               generation
Round,         All round,   315 round, yellow
Yellow seeds   yellow       seeds
X wrinkled,                 101 wrinkled, yellow
green seeds                 seeds
                            108 round, green seeds
                             32 green, wrinkled
                            seeds
Interpreting the Data

• The F2 generation contains seeds with
  novel combinations not found in the
  parentals
  – Round and Green
  – Wrinkled and Yellow
• These are nonparentals
• Occurrence contradicts the linkage
  model
• Independent assortment is also revealed by a
  dihybrid test-cross
   – TtYy X ttyy




• Thus, if the genes assort independently, the
  expected phenotypic ratio among the offspring
  is 1:1:1:1
Dihybrid
Punnett
Square
Forked-line Method (fork
                 diagram)
    • Calculate predicted ratios of offspring
      by multiplying probabilities of
      independent events
P    yellow, round x green, wrinkled
Fork Diagram for Trihybrid
          Cross

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Punnett squares

  • 2. Punnett Squares • A Punnett square is a grid that enables one to predict the outcome of simple genetic crosses • Proposed by the English geneticist, Reginald Punnett
  • 3. Plant genes can have dominant and recessive alleles Example: The dominant allele R R produces … … a red flower r The recessive allele r produces … … a white flower
  • 4. A genetic cross in plants: Rr x Rr There is only one way to make a homozygous plant with two dominant genes… R R RR … and only one way to make a homozygous plant with two recessive genes r r rr
  • 5. In the genetic cross Rr x Rr there are two ways of making a heterozygous plant… R r Rr OR r R Rr … so, heterozygous offspring are twice as likely as either homozygous dominant or homozygous recessive offspring
  • 6. We can show the likeliness or probability of different genotypes in different ways: 1. As a percentage - Probability of RR is… 25% Probability of Rr is… 50% Probability of rr is… 25% 2. As a fraction - Probability of RR is… ¼ Probability of Rr is… ½ Probability of rr is… ¼ 3. As a ratio - RR : Rr : rr = 1 : 2 : 1
  • 7. There are three ways to make a plant with red flowers… … one produces a homozygous plant… R R RR … and two produce heterozygous plants… R r Rr r R Rr
  • 8. …but, there is only one way to produce a plant with white flowers… r r rr So, in the genetic cross, Rr x Rr… …red flowers are three times more likely than white flowers!!!
  • 9. We can show the likeliness or probability of different phenotypes in different ways: 1. As a percentage - Probability of red is… 75% Probability of white is… 25% 2. As a fraction - Probability of red is… ¾ Probability of white is… ¼ 3. As a ratio - red : white = 3:1
  • 10. The Punnett Square We can use the Punnett Square to work out the probability of the different genotypes and phenotypes in a genetic cross Step 1: Write down the genotypes of the parents. x = Rr x Rr Step 2: Write down the genotypes of the gametes that each parent produces. pollen Egg cells = R+r = R+r
  • 11. Step 3: Draw your Punnett Square Egg cells Step 4: Write the genotype R r of the different gametes into your Punnett Square R RR R r Pollen Step 5: Write in the different ways in which the r rR rr gametes can be combined… …this shows you the possible genotypes of the Genotypes of offspring offspring
  • 12. Probability of Genotypes Egg cells There are four possible ways to combine egg cells and pollen R r Count up how many times each genotype appears in R RR R r Pollen the Punnet Square – this gives you its probability: r rR rr Probability of RR is… ¼ = 25 % Probability of Rr is… 2 4 = ½ = 50 % The ratio of Probability of rr is… ¼ = 25 % RR : Rr : rr is… 1:2:1
  • 13. Probability of Phenotypes Egg cells Look at the genotypes of the offspring in your Punett Square… R r …decide which phenotype each one should produce. R RR R r Pollen Count up how many times each phenotype appears in r rR rr the Punnet Square – this gives you its probability: Probability of red is… ¾ = 75 % The ratio of red : white is… Probability of white is… ¼ = 25 % 3:1
  • 14. Mendel’s Experiments • Mendel also performed dihybrid crosses – Crossing individual plants that differ in two traits • For example – Trait 1 = Seed texture (round vs. wrinkled) – Trait 2 = Seed color (yellow vs. green) • There are two possible patterns of inheritance for these traits
  • 17. DATA FROM ONE OF MENDEL’S DIHYBRID CROSSES P Cross F1 F2 generation generation Round, All round, 315 round, yellow Yellow seeds yellow seeds X wrinkled, 101 wrinkled, yellow green seeds seeds 108 round, green seeds 32 green, wrinkled seeds
  • 18. Interpreting the Data • The F2 generation contains seeds with novel combinations not found in the parentals – Round and Green – Wrinkled and Yellow • These are nonparentals • Occurrence contradicts the linkage model
  • 19. • Independent assortment is also revealed by a dihybrid test-cross – TtYy X ttyy • Thus, if the genes assort independently, the expected phenotypic ratio among the offspring is 1:1:1:1
  • 21. Forked-line Method (fork diagram) • Calculate predicted ratios of offspring by multiplying probabilities of independent events P yellow, round x green, wrinkled
  • 22. Fork Diagram for Trihybrid Cross

Editor's Notes

  1. Figure: 03-06 Caption: Computation of the combined probabilities of each F 2 phenotype for two independently inherited characters. The probability of each plant being yellow or green is independent of the probability of it being round or wrinkled.
  2. Figure: 03-09 Caption: Generation of the F 2 trihybrid phenotypic ratio using the forked-line method.