A true breeding plant with red flowers and pointy leaves is crossed to a true breeding plant with white flowers and round leaves.  The F2 progeny are

 

451      pink      heart-shaped

221      pink      round

215      white    heart-shaped

205      red                   heart-shaped

198      pink      pointy

113      white    round

111      red                   pointy

105      white    pointy

98              red             round

 

1. Figure out the plausible mendelian segregation for this cross—justify this using mendelian concepts

 

2. Test to see what happens

 

 

 

 

Solution

 

 

If we have a two loci, two alleles trait we have nine possible genotypes.  If each possible genotype has a phenotype then we have nine phenotypes.  Since we see nine phenotypes we hypothesize that this is the case. 

 

So we hypothesize two loci, two alleles each with both loci co-dominant. In this case the segregation is

1:2:1:2:4:2:1:2:1

 

(1:2:1  times 1:2:1)

 

 

reorganizing the phenotypes and assigning hypothesized genotypes

 

 

 

111      red                   pointy                                       AABB

198      pink      pointy                                       AaBB

105      white    pointy                                       aaBB

205      red                   heart-shaped                AABb

451      pink      heart-shaped                AaBb

215      white    heart-shaped                aaBb

98              red             round                                       AAbb

221      pink      round                                       Aabb

113      white    round                                       aabb

 

 

 

 

observed

expected

0-e

(0-e)^2

(0-e)^2/e

 

111

107

3.7

13.598

0.12671

 

198

215

-17

276.39

1.28778

 

105

107

-2

5.3477

0.04983

 

205

215

-10

92.641

0.43164

 

451

429

22

473.06

1.10207

 

215

215

0.4

0.1406

0.00066

 

98

107

-9

86.723

0.80813

 

221

215

6.4

40.641

0.18936

 

113

107

5.7

32.348

0.30143

total

1717

 

 

 

 

 

 

 

 

X2

4.29761

 

 

 

 

 

 

 

 

 

 

p-value

0.8291

 

 

Fail to reject and I conclude:  There is not enough evidence to conclude that the ratio is different from

 

1:2:1:2:4:2:1:2:1

 

Let’s do another

 

 

A true breeding plant with red flowers and pointy leaves is crossed to a true breeding plant with white flowers and round leaves.  The F2 progeny are

 

316      red                   pointy

98              red             round                                      

221      pink      round                                      

649      pink      pointy                          

320      white    pointy

113      white    round  

 

 

1.  Propose a plausible mendelian segregation

 

2.  Test it

 

Solution

 

If we have a two loci two alleles trait we have nine possible genotypes.  If one locus is co-dominant and one locus is dominant then we have six phenotypes.  Since we see six phenotypes we hypothesize that this is the case.   So we propose two loci,  two alleles,  one locus has a dominant allele,  the other locus has co-dominant alleles. In this case the segregation is

3:6:3:1:2:1

 

(3:1 times 1:2:1)

 

Reordering the phenotypes

 

316      red                   pointy                           AABB /AABb

649      pink      pointy                           AaBB/ AaBb

320      white    pointy                           aaBB /aaBb

98              red             round                                       AAbb

221      pink      round                                       Aabb

113      white    round                                       aabb

 

 

o

e

0-e

(0-e)^2

(0-e)^2/e

316

322

-6

35

0.11

649

644

5.1

26

0.041

320

322

-2

4

0.012

98

107

-9

87

0.808

221

215

6.4

41

0.189

113

107

5.7

32

0.301

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

X2

 

1.461

 

 

 

 

 

 

 

pvalue

0.92

 

Fail to reject and I conclude:  There is not enough evidence to conclude that the ratio is different from 3:6:3:1:2:1.

 

 

 

 

Example

 

A wild legume with white flowers and long pods is crossed to one with purple flowers and short pods.  The F1 flowers are allowed to self fertilize and the F2 generation has 301 long purple, 99 short purple, 612 long pink, 195 short pink, 295 long white, 98 short white

 

What is the mendelian segregation and test to see whether this follows.

 

Building the hypothesis:

 

PPll x ppLL                  p1xp2

 

    PpLl                                       F1

 

 

F2 genotypes

 

   PPLL            2 PpLL            ppLL
2 PPLl       4 PpLl           2 ppLl

   PPll        2 Ppll               ppLL

 

I have nine genotypic categories but now 6 phenotypic categories so I need to figure out what the mapping is between the genotype and the phenotype…

 

Long seems dominant to short.  White and Purple appear to be co-dominant with pink as the heterozygote.

 

I hypothesize this is the relationship between genotype and phenotype

 

Genotype                     Phenotype                    Exp

PPLL+2PPLl    purple long                   3/16

PPll                         purple short                       1/16

2PpLL+4PpLl  pink long                                  6/16

2Ppll                            pink short                    2/16

ppLL+2ppLl    white long                    3/16

ppll                               white short                   1/16

 

Can also get the ratio by multiplying

1:2:1 by 3:1!

 

The null hypothesis is : 3:1:6:2:3:1

o

e

o-e

(o-e)2

(o-e)2/e

301

300

1

1

0.003333

99

100

-1

1

0.01

612

600

12

144

0.24

195

200

-5

25

0.125

295

300

-5

25

0.083333

98

100

-2

4

0.04

 

 

 

 

 

1600

 

 

X2

0.501667

 

 

 

 

 

 

 

 

 

 

 

 

 

p

0.992062

 

Fail to reject the null

 

There is not enough evidence to conclude that the ratio is different from 3:1:6:2:3:1.