1. I. Allelic, Genic, and Environmental Interactions
II. Sex Determination and Sex Linkage
III. Linkage
- Overview:
‘Linkage’ is a pattern of correlated inheritance between traits governed by genes on the same chromosome. Because the genes are part of the same physical entity, they are inherited together rather than independently.
INDEPENDENT ASSORTMENT (IA)
LINKED A a AB ab B b ab A AB A a a B b B b

2. III. Linkage
- Overview:
‘Linkage’ is a pattern of correlated inheritance between traits governed by genes on the same chromosome. Because the genes are part of the same physical entity, they are inherited together rather than independently. Only ‘crossing-over’ can cause them to be inherited in new combinations.
Cross-over products

3. III. Linkage
A. ‘Complete’ Linkage
- if genes are immediate neighbors, they are almost never separated by crossing over and are ‘always’ inherited together. The pattern mimics that of a single gene.
AABB
aabb AB ab X ab AB

4. III. Linkage
A. ‘Complete’ Linkage
- if genes are immediate neighbors, they are almost never separated by crossing over and are ‘always’ inherited together. The pattern mimics that of a single gene.
AABB
aabb AB ab X ab AB
Gametes AB ab ab
Double Heterozygote in F1; no difference in phenotypic ratios compared to IA F1 AB

5. III. Linkage
A. ‘Complete’ Linkage
- if genes are immediate neighbors, they are almost never separated by crossing over and are ‘always’ inherited together. The pattern mimics that of a single gene. ab ab
1:1 ratio A:a
1:1 ratio B:b
1:1 ratio AB:ab
Test cross X AB ab ab
Phenotype
Gametes AB
AaBb
AB – 50%
aabb
Ab – 50% ab Ab
Aabb Ab
If it was I.A., also: aB
aaBb aB

6. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage

7. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
- Crossing over in a region is rare

8. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
- Crossing over in a region is rare
- Crossing over events increase as the distance between genes increases A B C a b c
LESS LIKELY IN HERE
MORE LIKELY IN HERE

9. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
- Crossing over in a region is rare
- Crossing over events increase as the distance between genes increases
- So, the frequency of crossing over (‘CO’) gametes can be used as an index of distance between genes! (Thus, genes can be ‘mapped’ through crosses…) A B C a b c
FEWER ‘CO’ GAMETES:
Ab, aB
MORE ‘CO’ GAMETES:
bC, Bc

10. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
- Crossing over in a region is rare
- Crossing over events increase as the distance between genes increases
- So, the frequency of crossing over (‘CO’) gametes can be used as an index of distance between genes! (Thus, genes can be ‘mapped’ through crosses…)
- How can we measure the frequency of recombinant (‘cross-over’) gametes? Is there a type of cross where we can ‘see’ the frequency of different types of gametes produced by the heterozygote as they are expressed as the phenotypes of the offspring?

11. TEST CROSS !!!
III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage B a b b a b A a

12. TEST CROSS !!!
III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
- So, since crossing-over is rare (in a particular region), most of the time it WON’T occur and the homologous chromosomes will be passed to gametes with these genes in their original combination…these gametes are the ‘parental types’ and they should be the most common types of gametes produced. B a b b a b A a a b A B

13. TEST CROSS !!!
III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
- Sometimes, crossing over WILL occur between these loci – creating new combinations of genes…
This produces the ‘recombinant types’ B a b b a b A a a b A B a B A b

14. TEST CROSS !!!
III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
As the other parent only contributed recessive alleles (whether crossing over occurs or not)… B a b b a b A a b a a b A B a B A b

15. B. ‘Incomplete’ Linkage
TEST CROSS !!!
III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
As the other parent only contributed recessive alleles (whether crossing over occurs or not)…
SO: the phenotype of the offspring is determined by the gamete received from the heterozygote… B a b b a b A a
gamete
genotype
phenotype ab
aabb
AaBb AB
aaBb aB
Aabb Ab a b A B a B A b

16. B. ‘Incomplete’ Linkage B a b
TEST CROSS !!!
III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage B a b b a b A a
ALTERNATIVES
‘IA’ LINKAGE
gamete
genotype
phenotype ab
aabb
AaBb AB
aaBb aB
Aabb Ab a b
LOTS of PARENTALS A B
FREQUENCIES EQUAL TO PRODUCT OF INDEPENDENT PROBABILITIES a B
FEWER CO’S A b

17. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Example:
How do we discriminate between these two alternatives?
Conduct a Chi-Square Test of Independence
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37

18. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Example:
How do we discriminate between these two alternatives?
Conduct a Chi-Square Test of Independence
- Compare the observed results with what you would expect if the genes assorted independently
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37

19. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Example:
How do we discriminate between these two alternatives?
Conduct a Chi-Square Test of Independence
- Compare the observed results with what you would expect if the genes assorted independently
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37
The frequency of ‘AB’ should = f(A) x f(B) x N = 55/100 x 51/100 x 100 = 28

20. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Example:
How do we discriminate between these two alternatives?
Conduct a Chi-Square Test of Independence
- Compare the observed results with what you would expect if the genes assorted independently
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37
The frequency of ‘AB’ should = f(A) x f(B) x N = 55/100 x 51/100 x 100 = 28
The frequency of ‘Ab’ should = f(A) x f(B) x N = 55/100 x 49/100 x 100 = 27
The frequency of ‘aB’ should = f(a) x f(B) x N = 45/100 x 51/100 x 100 = 23
The frequency of ‘ab’ should = f(a) x f(b) x N = 45/100 x 49/100 x 100 = 22

21. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Example:
How do we discriminate between these two alternatives?
Conduct a Chi-Square Test of Independence
This is fairly easy to do by creating a contingency table:
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 B b
Row Total A 43 12 a 8 37
Col. Total

22. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Example:
How do we discriminate between these two alternatives?
Conduct a Chi-Square Test of Independence
This is fairly easy to do by creating a contingency table:
Add across and down…
This gives the totals for each trait independently.
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 B b
Row Total A 43 12 55 a 8 37 45
Col. Total 51 49
100

23. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Example:
How do we discriminate between these two alternatives?
Conduct a Chi-Square Test of Independence
This is fairly easy to do by creating a contingency table:
Then, to calculate an expected value based on independent assortment (for ‘AB’, for example), you multiple ‘Row Total’ x ‘Column Total’ and divide by ‘Grand Total’.
55 x 51 / 100 = 28
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 B
Exp. b
Row Total A 43 28 12 55 a 8 37 45
Col. Total 51 49
100

24. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Example:
Repeat to calculate the other expected values… (This is just an easy way to set it up and do the calculations, but you should appreciate it is the same as the product rule:
F(A) x f(B) x N
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 B
Exp. b
Row Total A 43 28 12 27 55 a 8 23 37 22 45
Col. Total 51 49
100
55 X x = 55x51

25. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Compare our observed results with what we would expect if the genes assort independently.
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 B
Exp. b
Row Total A 43 28 12 27 55 a 8 23 37 22 45
Col. Total 51 49
100

26. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Compare our observed results with what we would expect if the genes assort independently.
. If our results are close to the expectations, then they support the hypothesis of independence.
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 B
Exp. b
Row Total A 43 28 12 27 55 a 8 23 37 22 45
Col. Total 51 49
100

27. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Compare our observed results with what we would expect if the genes assort independently.
. If our results are close to the expectations, then they support the hypothesis of independence. If they are far apart from the expected results, then they refute that hypothesis and support the alternative: linkage.
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 B
Exp. b
Row Total A 43 28 12 27 55 a 8 23 37 22 45
Col. Total 51 49
100

28. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Typically, we reject the hypothesis of independent assortment (and accept the hypothesis of linkage) if our observed results are so different from expectations that independently assorting genes would only produce results as unusual as ours less than 5% of the time…
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 B
Exp. b
Row Total A 43 28 12 27 55 a 8 23 37 22 45
Col. Total 51 49
100

29. B
Exp. b
Row Total A 43 28 12 27 55 a 8 23 37 22 45
Col. Total 51 49
100
III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
We determine this probability with a Chi-Square Test of Independence.
Phenotype
Obs
Exp
(o-e)
(o-e)2/e AB 43 28 15
8.04 Ab 12 27
-15
8.33 aB 8 23
9.78 ab 37 22
10.23
X2 =
36.38

30. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Our X2 = 36.38
First, we determine the ‘degrees of freedom’ = (r-1)(c-1) = 1 B b
Row Total A 43 12 55 a 8 37 45
Col. Total 51 49
100

31. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Our X2 = 36.38
First, we determine the ‘degrees of freedom’ = (r-1)(c-1) = 1
Now, we read across the first row in the table, corresponding to df = 1.
The column headings are the probability that a number in that column (diff. between observed and expected) would occur by chance.
In our case, it is the probability that our hypothesis of independent assortment (expected values are based on that hypothesis) is true. (and the diff is just due to chance).

32. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Our X2 = 36.38
Note that larger values have a lower probability of occurring by chance…
This should make sense, and the value increases as the difference between observed and expected values increases.

33. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Our X2 = 36.38
So, for instance, a value of 2.71 will occur by chance 10% of the time.

34. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Our X2 = 36.38
So, for instance, a value of 2.71 will occur by chance 10% of the time.
But a value of 6.63 will only occur 1% of the time... (if the hypothesis is true and this deviation between observed and expected values is only due to chance).

35. B. ‘Incomplete’ Linkage Our X2 = 36.38
III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Our X2 = 36.38
So, for instance, a value of 2.71 will occur by chance 10% of the time.
For us, we are interested in the 5% level. The table value is 3.84.
Our calculated value is much greater than this; so the chance that independently assorting genes would yield our results is WAY LESS THAN 5%. Our results are REALLY UNUSUAL for independently assorting genes.
36.38

36. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Our X2 = 36.38
Our results are REALLY UNUSUAL for independently assorting genes.
So, either our results are wrong, or the hypothesis of independent assortment is wrong. If you did a good experiment, then you should have confidence in your results; reject the hypothesis of IA and conclude the alternative – the genes are LINKED.

37. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
Our X2 = 36.38
Our results are REALLY UNUSUAL for independently assorting genes.
So, either our results are wrong, or the hypothesis of independent assortment is wrong. If you did a good experiment, then you should have confidence in your results; reject the hypothesis of IA and conclude the alternative – the genes are LINKED.
Of course, there is still that 5% probability that chance is responsible for the deviation you observed, and your conclusion is WRONG.

38. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
OK… so we conclude the genes are linked… NOW WHAT?
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37

39. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
OK… so we conclude the genes are linked… NOW WHAT?
We map the genes using the knowledge that crossing-over is rare, and the frequency of crossing-over correlates with the distance between genes.
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37

40. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
OK… so we conclude the genes are linked… NOW WHAT?
1. Crossing-over is rare; so the RARE COMBINATIONS must be the products of Crossing-Over. The OTHERS, the MOST COMMON products, represent the PARENTAL TYPES.
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37

41. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
OK… so we conclude the genes are linked… NOW WHAT?
Crossing-over is rare; so the RARE COMBINATIONS must be the products of Crossing-Over. The OTHERS, the MOST COMMON products, represent the PARENTAL TYPES.
This tells us the original arrangement of alleles in the heterozygous parent:
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 A B a b

42. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
OK… so we conclude the genes are linked… NOW WHAT?
Crossing-over is rare; so the RARE COMBINATIONS must be the products of Crossing-Over. The OTHERS, the MOST COMMON products, represent the PARENTAL TYPES.
This tells us the original arrangement of alleles in the heterozygous parent:
Segregation without crossing over produces lots of AB and ab gametes.
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 A B a b

43. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
OK… so we conclude the genes are linked… NOW WHAT?
Crossing-over is rare; so the RARE COMBINATIONS must be the products of Crossing-Over. The OTHERS, the MOST COMMON products, represent the PARENTAL TYPES.
2. The frequency of crossing-over is used as an index of the distance between genes:
The other progeny are the products of crossing over, and they occurred 20 times in 100 progeny, for a frequency of Multiply that by 100 to free the decimal, and this becomes 20 map units (CentiMorgans).
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 A B a b
20 map units

44. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
So, we used the chi-square test to determine whether genes are on the chromosome. Then, we mapped the distance between genes on the chromosome; all by looking at the frequency of phenotypes in the offspring of a test cross.
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 A B a b
20 map units

45. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
So, we used the chi-square test to determine whether genes are on the chromosome. Then, we mapped the distance between genes on the chromosome; all by looking at the frequency of phenotypes in the offspring of a test cross.
LIMITATION:
Genes that are 50 map units apart (or more) will recombine 50% of the time…. Producing parentals and recombinants in equal frequency… just like independent assortment predicts!!!
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 A B a b
20 map units

46. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
So, we used the chi-square test to determine whether genes are on the chromosome. Then, we mapped the distance between genes on the chromosome; all by looking at the frequency of phenotypes in the offspring of a test cross.
LIMITATION:
Genes that are 50 map units apart (or more) will recombine 50% of the time…. Producing parentals and recombinants in equal frequency… just like independent assortment predicts!!!
So, genes that are > 50 mu apart assort independently (even though they are on the same chromosome).
AaBb x aabb
Offspring
Number AB 43 Ab 12 aB 8 ab 37 A B a b
20 map units

47. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
C. Three-point Mapping
Suppose you conduct two-point mapping and find:
A - C are 23 centiMorgans apart
C – B are 10 centiMorgans apart: A C B OR A B C

48. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
C. Three-point Mapping
Three Point Test Cross
AaBbCc x aabbcc
Phenotypic Ratio:
ABC = 25
ABc = 3
Abc = 42
AbC = 85
aBC = 79
aBc = 39
abc = 27
abC = 5

49. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
C. Three-point Mapping
- combine complementary sets
Three Point Test Cross
AaBbCc x aabbcc
Phenotypic Ratio:
ABC = 25
ABc = 3
Abc = 42
AbC = 85
aBC = 79
aBc = 39
abc = 27
abC = 5
ABC = 25
abc = 27 52
ABc = 3
abC = 5
= 8
Abc = 42
aBC = 39 81
AbC = 85
aBc = 79
164

50. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
C. Three-point Mapping
- combine complementary sets
Three Point Test Cross
AaBbCc x aabbcc
Phenotypic Ratio:
ABC = 25
ABc = 3
Abc = 42
AbC = 85
aBC = 79
aBc = 39
abc = 27
abC = 5
ABC = 25
abc = 27 52
ABc = 3
abC = 5
= 8
Abc = 42
aBC = 39 81
AbC = 85
aBc = 79
164
MOST ABUNDANT ARE PARENTAL TYPES

51. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
C. Three-point Mapping
- combine complementary sets
Three Point Test Cross
AaBbCc x aabbcc
Phenotypic Ratio:
ABC = 25
ABc = 3
Abc = 42
AbC = 85
aBC = 79
aBc = 39
abc = 27
abC = 5
ABC = 25
abc = 27 52
ABc = 3
abC = 5
= 8
LEAST ABUNDANT ARE “DOUBLE CROSSOVERS” D E F
Abc = 42
aBC = 39 81
AbC = 85
aBc = 79
164 d e f
MOST ABUNDANT ARE PARENTAL TYPES
DCO’s = very rare, and gene in middle switches chromosomes

52. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
C. Three-point Mapping
- combine complementary sets
Three Point Test Cross
AaBbCc x aabbcc
Compare Parentals and DCO’s to determine which gene is in the middle…
Parentals: AbC aBc
DCO’s: abC ABc
B and C alleles stay together; A switches and so is in middle. REMAKE YOUR DRAWING TO DEPICT ALLELES AND ORDER:
ABC = 25
abc = 27 52
ABc = 3
abC = 5
= 8
LEAST ABUNDANT ARE “DOUBLE CROSSOVERS” b A C
Abc = 42
aBC = 39 81
AbC = 85
aBc = 79
164 B a c
MOST ABUNDANT ARE PARENTAL TYPES

53. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
C. Three-point Mapping
- combine complementary sets
Three Point Test Cross
AaBbCc x aabbcc
So, a “single cross-over” (SCO) between the B and A locus will produce the gametes/phenotypes:
BAC and bac – find their frequency:
52… plus add DCO’s (8) = 60/305
= x 100 = 19.7 cM
ABC = 25
abc = 27 52
ABc = 3
abC = 5
= 8
LEAST ABUNDANT ARE “DOUBLE CROSSOVERS” b A C
Abc = 42
aBC = 39 81
AbC = 85
aBc = 79
164 B a c
MOST ABUNDANT ARE PARENTAL TYPES
19.7 cM

54. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
C. Three-point Mapping
- combine complementary sets
Three Point Test Cross
AaBbCc x aabbcc
ABC = 25
abc = 27 52
= 89/306 = x 100 = 29.2
ABc = 3
abC = 5
= 8
LEAST ABUNDANT ARE “DOUBLE CROSSOVERS” b A C
Abc = 42
aBC = 39 81
AbC = 85
aBc = 79
164 B a c
MOST ABUNDANT ARE PARENTAL TYPES
19.7 cM
29.2 cM

55. III. Linkage
A. ‘Complete’ Linkage
B. ‘Incomplete’ Linkage
C. Three-point Mapping
- combine complementary sets
Three Point Test Cross
AaBbCc x aabbcc
“Coefficient of Coincidence” – are SCO’s occurring independently? If so, then DCO’s = product of SCO’s
(0.197) x (0.292) x 305 = 17
We only observed 8.
C.O.C. = obs/exp = 8/17 = 0.47
Interference = 1 – c.o.c. = 0.53
ABC = 25
abc = 27 52
ABc = 3
abC = 5
= 8
LEAST ABUNDANT ARE “DOUBLE CROSSOVERS” b A C
Abc = 42
aBC = 39 81
AbC = 85
aBc = 79
164 B a c
MOST ABUNDANT ARE PARENTAL TYPES
19.7 cM
29.2 cM