Answer:
height -------- color --------- mood
(13.2cM) (14.5cM)
C=0.421
I = 0.579
Explanation:
We have the number of descendants of each phenotype product of the tri-hybrid cross.
Phenotype Number
- pink, tall, happy 580
- blue, dwarf, gloomy 601
- pink, tall, gloomy 113
- blue, dwarf, happy 107
- blue, tall, happy 8
- pink, dwarf, gloomy 6
- blue, tall, gloomy 98
- pink, dwarf, happy 101
Total number of individuals = 1614 = N
Knowing that the genes are linked, we can calculate genetic distances between them. First, we need to know their order in the chromosome, and to do so, we need to compare the phenotypes of the parental with the ones of the double recombinants. We can recognize the parental in the descendants because their phenotypes are the most frequent, while the double recombinants are the less frequent. So:
Parental)
- Pink, tall, happy 580 individuals
- Blue, dwarf, gloomy 601 individuals
Simple recombinant)
- Pink Tall Gloomy 113 individuals
- Blue, Dwarf, Happy 107 individuals
- Blue Tall Gloomy 98 individuals
- Pink Dwarf Happy 101 individuals
Double Recombinant)
- Blue Tall Happy 8 individuals
- Pink Dwarf Gloomy 6 individuals
Comparing them we realize that parental and double recombinant individuals differ in the position of the gene codifying for <u>color</u><u>.</u> They only change in the position of Blue and Pink. This suggests that the position of the color gene is in the middle of the other two genes, height and mood, because in a double recombinant only the central gene changes position in the chromatid.
So, the alphabetic order of the genes is:
---- height ---- color ----- mood ----
Now we will call Region I to the area between Height and Color, and Region II to the area between Color and Mood.
Once established the order of the genes we can calculate distances between them, and we will do it from the central gene to the genes on each side. First We will calculate the recombination frequencies, and we will do it by region. We will call P1 to the recombination frequency between Height and color genes, and P2 to the recombination frequency between color and mood.
P1 = (R + DR) / N
P2 = (R + DR)/ N
Where: R is the number of recombinants in each region (the ones that have an intermediate phenotypic frequency), DR is the number of double recombinants in each region, and N is the total number of individuals. So:
Region I
Tall------ Pink--------happy (Parental) 580 individuals
Dwarf ---Pink------- Happy (Simple Recombinant) 101 individuals
Dwarf--- Pink-------Gloomy (Double Recombinant) 6 individuals
Dwarf----Blue-------Gloomy (Parental) 601 individuals
Tall ------Blue------- Gloomy (Simple Recombinant) 98 individuals
Tall ----- Blue------- Happy (Double Recombinant) 8 individuals
Region II
Tall------ Pink--------happy (Parental) 580 individuals
Tall-------Pink------- Gloomy (Simple Recombinant) 113 individuals
Dwarf----Pink------- Gloomy (Double Recombinant) 6 individuals
Dwarf----Blue-------Gloomy (Parental) 601 individuals
Dwarf ----Blue-------Happy (Simple Recombinant) 107 individuals
Tall ----- Blue------- Happy (Double Recombinant) 8 individuals
In each region, the highlighted traits are the ones that suffered recombination.
- P1 = (R + DR) / N
P1 = (101+6+98+8)/1614
P1 = 213/1614
P1 = 0.132
- P2= = (R + DR) / N
P2 = (113+6+107+8)/1614
P1 = 234/1614
P1 = 0.145
Now, to calculate the recombination frequency between the two extreme genes, height and mood, we can just perform addition or a sum:
- P1 + P2= Pt
0.132 + 0.145 = Pt
0.277=Pt
The genetic distance will result from multiplying that frequency by 100 and expressing it in map units (MU). One centiMorgan (cM) equals one map unit (MU).
The map unit is the distance between the pair of genes for which every 100 meiotic products, one results in a recombinant product.
Now we must multiply each recombination frequency by 100 to get the genetic distance in map units:
GD1= P1 x 100 = 0.132 x 100 = 13.2 MU = 13.2 cM
GD2= P2 x 100 = 0.145 x 100 = 14.5 MU = 14.5 cM
GD3=Pt x 100 = 0.277 x 100 = 27.7 MU = 27.7 cM
To calculate the coefficient of coincidence, CC, we must use the next formula:
CC= observed double recombinant frequency/expected double recombinant frequency
Note:
-observed double recombinant frequency=total number of observed double recombinant individuals/total number of individuals
-expected double recombinant frequency: recombination frequency in region I x recombination frequency in region II.
- CC= ((6 + 8)/1614)/0.132x0.145
CC=0.008/0.019
CC=0.421
The coefficient of interference, I, is complementary with CC.
I = 1 - CC
I = 1 - 0.421
I = 0.579