Brief Summary of Mendelian Inheritance

Segregation, independent assortment, and linkage: examples from the OWB

  1. Monohybrid Model(Segregation)
  2. Dihybrid Model


1.Monohybrid Model (Segregation)

Example: Number of kernel rows (Vrs1/vrs1) in barley (Hordeum vulgare)

Generation:             Parent 1        X       Parent 2 
Genotype:               Vrs1Vrs1                vrs1vrs1
Phenotype:              Two-row                 Six-row

Generation:                             F1 
Genotype:                               Vrs1vrs1
Phenotype:                              Two-row

If the F1 is selfed to give an F2 generation,  the  genotypic ratio  will be    
1Vrs1Vrs1; 2Vrs1vrs1; 1vrs1vrs1
and the phenotypic  ratio will be 
3 two-row: 1 six-row

Since the OWB is a doubled haploid population there are no heterozygotes.
Thus, the expected phenotypic and the genotypic ratios are the same 
1 Vrs1Vrs1: 1 vrs1vrs1
1 two-row: 1 six-row

The actual numbers in the OWB are 40 Vrs1Vrs1 and 54 vrs1vrs1.

A chi-square test can be used to test the goodness of fit of the expected and observed 
ratios.

Phenotype       #Observed       #Expected       O - E           (O - E)2/E
Vrs1Vrs1        40              47             -7               1.04
vrs1vrs1        54              47              7               1.04
Totals          94              94              0               2.08 (chi square; X2)
at 1 df  0.10<(chi-square greater than or equal to 2.08)<0.25

This chi-square is well within the realm of acceptance, so we conclude that there is indeed a 1:1 
ratio of Vrs1Vrs1:vrs1vrs1 genotypes in the OWB.

2. Dihybrid Model

a. Segregation and independent assortment

Example: Number of kernel rows (Vrs1/vrs1) and seedling white stripe (Wst/wst) in barley

Generation:             Parent 1        X       Parent 2 
Genotype:               Vrs1Vrs1/WstWst         vrs1vrs1/wstwst
Phenotype:              Two-row                 Six-row


                       Normal seedling White stripe seedling

Generation:                             F1 
Genotype:                        Vrs1vrs1/Wstwst
Phenotype:                      Two-row; Normal seedling

In the OWB DH population, the expected frequencies of  female gametes used to produce 
haploid plants are:     
  0.25 Vrs1/Wst     0.25 Vrs1/wst             0.25 vrs1/Wst             0.25 vrs1/wst

After chromosome doubling, this would give the genotypic ratio: 
1 Vrs1Vrs1/WstWst; 1 Vrs1Vrs1/wstwst; 1 vrs1vrs1/WstWst; 1 vrs1vrs1/wstwst
and the phenotypic ratio: 
1 two-row/normal:1 two-row/white stripe: 1 six-row/normal: 1 six-row/white stripe.

Data from the OWB can be used to test the goodness of fit to a two-locus model with 
independent assortment: 

Phenotype       #Observed       #Expected       O - E           (O - E)2/E
WstWst/Vrs1Vrs1  24             23.5            0.5             0.011
WstWst/vrs1vrs1  24             23.5            0.5             0.011
wstwst/Vrs1Vrs1  16             23.5           -7.5             2.394
wstwst/vrs1vrs1  30             23.5            6.5             1.837
Totals           94             94              0               4.253 (chi square; X2)

at 3 df  0.10<(chi-square greater than or equal to 4.253)<0.25

Accept hypothesis.  

These two loci show independent assortment. Alleles segregate independently; members 
of different allelic pairs assort independently into gametes. Independent assortment 
applies to allelic pairs on different chromosomes, or to pairs sufficiently distant on the 
same chromosome.  Based on previous reports (Shin et al. 1990) we know that these loci 
are both on chromosome 2.  However, they are sufficiently far apart that they show 
independent assortment.

b. Segregation and linkage:

Example: Short awn (Lks2/lks2) and naked kernel (Nud/nud) are
two easily scored phenotypes in the OWB. 
When we test for independent assortment (1:1:1:1), however,  we find a very poor fit. 

 Lks2Lks2/NudNud  Lks2Lks2/nudnud  lks2lks2/NudNud  lks2lks2/nudnud
O     42              12              5              35
E     23.5            23.5            23.5           23.5

Overall chi square for a 1:1:1:1 ratio is 40.38 (3 df).  This is not a good fit.



We then compute separate chi squares for each of the two traits to determine if there is 
aberrant segregation:

        Lks2Lks2               lks2lks2               Total
O       42 + 12 = 54           5 + 35 = 40                94
E          47                      47                     94

Chi square (1 df) = 2.09. Reasonable fit.


 Likewise:       NudNud                 nudnud               Total
O    42 + 5 = 47            12 + 35 = 47             94 
E       47                        47                 94

Chi square (1 df) = 0. Excellent fit.



Alleles at each of the two loci are showing  expected segregation, but there is not 
independent assortment.  This indicates that lks2 and nud may be linked.  That is, they are 
located on the same chromosome and sufficiently close together that independent 
assortment does not occur. 

The next step is to calculate a chi square for linkage:

If parental combinations are Lks2/Nud and  lks2/nud, each of the four classes of progeny 
can be classified as parental if Lks2/Nud or lks2/nud;  or recombinant if Lks2/nud or 
lks2/Nud.  With independent assortment,  the frequency of recombinant types = frequency 
if parental types. 


       (Parental phenotypes)                       (Recombinant phenotypes)
      Lks2Lks2/NudNud + lks2lks2/nudnud            Lks2Lks2/nudnud + lks2lks2/NudNud
O               77                                              17
E               47                                              47

Chi square (1 df) = 38.30. Reject null hypothesis that frequency of parental = frequency of 
recombinant.  With confidence conclude there is linkage.

If loci are linked, they are located on the same chromosome and they are close enough 
that crossovers do not occur often enough  to give independent assortment.  In the above 
example, 17 out of 94 progeny represent recombinant types. The recombination 
frequency between Lks2 and nud is 18%. 

We can use this recombination value to make a map: 


lks2            18               nud

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This was the first step in building the OWB linkage map!

Building a linkage map with multiple loci is not something you do by hand! Linkage map construction is facilitated by mapping software. In our lab we have experience with MAPMAKER and G-Mendel, and can offer assistance with these packages.

Shin, J.S., S. Chao, L. Corpuz, and T. Blake. 1990. A partial map of the barley genome incorporating restriction fragment length polymophism, polymerase chain reaction, isozyme, and morphological marker loci. Genome. 33:803-810.