PROBLEM SET
Chapter 6 -- Linkage and Mapping in Eukaryotes

P. 134, #1. A homozygous groucho fly (gro, bristles clumped above the eyes) is crossed with a homozygous rough fly (ro, eye abnormality). The F1 females are testcrossed, with the following offspring produced:
     groucho        518
     rough          471
     groucho, rough   6
     wildtype         5
                -------
                  1,000
a) What is the linkage arrangement of these loci?

To determine the linkage arrangement of these two loci we need to calculate the map distance between them. The two classes in highest frequency are the non-recombinant classes and the two classes in lowest frequency are the recombinant classes. Thus groucho, rough and wildtype are recombinants. To calculate the map distance, we divide the total number of recombinants by the total number of flies and then multiply by 100.
                      11
   map distance =   ------ x 100 = 1.1 m.u. or 1.1 cM
                     1000
b) What offspring would result if the F1 dihybrids were crossed among themselves instead of being testcrossed?
This is a little complicated because we need to set-up a Punnett square but the four gametic genotypes will not have the same probability of occurrence of 0.25 each, as would expect if we had independent assortment. The first thing then is to estimate the probability of occurrence for each gametic genotype. To do this we must remember that a map distance of 1.1 m.u. means that a recombinant gamete will occur with a probability of 0.011. Thus the two recombinant gametes (gro,ro and +,+) will occur with a combined frequency of 0.011, which when divided evenly between them means that the frequency of occurrence for gro,ro is 0.0055 and that the frequency for +,+ is also 0.0055. The combined frequency of occurrence for the non-recombinant gametes (gro,+ and +,ro) is 0.989 (1 - 0.011), which when evenly divided between them means that the frequency of occurrence for gro,+ is 0.4945 and that the frequency of occurrence for +,ro is 0.4945. The other thing to remember is that in fruit flies, males do not crossover, thus one of the dihybrids (the male) will not produce any recombinant gametes, and our Punnett square is reduced to a Punnett rectangle.

By summing the frequency of occurrence for each cell in the Punnett Square, we can determine the expected frequency for each phenotype in the F2.
groucho 
    gro gro, + +   0.24755
    gro gro, ro +  0.00275
          ------------------
   total             0.2500

rough
    + +, ro ro     0.24755
    + gro, ro ro   0.00275
        --------------------
      total           0.2500

wildtype
    gro +, ro +    0.24725
    gro +, ro +    0.24725
    gro +, + +     0.00275
    + +, ro +      0.00275
        --------------------
      total           0.5000
Based upon the expected frequency of occurrence of the flies and assuming 1000 offspring, we would expect to see in the offspring of a dihybrid cross
wildtype 500
rough 250
groucho 250

P. 134, #2. A female fruit fly with abnormal eyes (abe) of a brown color (bis, bistre) is crossed with a wildtype male. Her sons have abnormal, brown eyes; her daughters are of the wildtype. When these flies F1 are crossed among themselves, the following offspring are produced:
                     sons    daughters
   abnormal, brown    219      197
   abnormal            43       45
   brown               37       35
   wildtype           201      223
What is the linkage arrangement of these loci?

In this case the two loci are on the X-chromosome. We know this because we see a difference in the expression of the traits between the sexes in the F1 generation. However, this does not affect the working of the problem because the ratio of males to females for each phenotypic class is approximately 1:1. We can simply pool the sexes for each phenotype. Thus
     abnormal brown  416
     abnormal         88
     brown            72
     wildtype        424
That two classes in highest frequency are the non-recombinants and the two classes in lowest frequency are the recombinants. To calculate the map distance between the two loci, we use the formula above such that
                  160
map distance =  ------ x 100 = 16 cM
                 1000
P. 134, #3. In Drosophila, the loci inflated (if, small, inflated wings) and warty (wa, abnormal eyes) are about 10 map units apart on the X chromosome. Construct a data set that would allow you to determine this linkage arrangement. What differences would be involved if the loci were located on an autosome.
To construct the data set, we need to setup the crosses and then calculate the expected occurrence of each phenotype in the F2 generation. We will cross an inflated, warty female with a wildtype male. This will produce in the F1 a heterozygous wildtype female and a hemizygous inflated, warty male. These two individual will then be mated to produce the F2 generation. As the male is hemizygous for recessive traits, this is essentially a testcross as the gamete from the F1 female will determine the phenotype of the F2 offspring. Also, there will be no difference in the frequency of expression of the traits between males and females in the F2 generation. For a map distance of 10, in the F2 generation 10% of the offspring must be recombinants. Thus from 1000 offspring, we expect 100 to be either inflated or warty as these are the recombinant conditions given that the P generation was either inflated and warty or wildtype. Of the 100 recombinant offspring, we will evenly divide them among inflated (50) and warty (50). The nonrecombinant offspring will be divided evenly among warty and inflated (450) and wildtype (450). As these traits are X-linked, we could also evenly divide each of the phenotypic classes evenly between males and females. This would give us a data set that is shown below.
                      sons    daughters   total
inflated, warty        225      225        450
inflated                25       25         50
warty                   25       25         50
wildtype               225      225        450
If these traits were on an autosome, the difference would be that to get the F2 generation, the female would have to be backcrossed to a male that was homozygous inflated and warty and could not be crossed to her brother in the F1 generation. In the F2 generation, the data set would look like that shown under the total column above.

P. 134, #4. A geneticist crossed female fruit flies that were heterozygous at three electrophoretic loci, each with fast and slow alleles, with males homozygous for the slow alleles. The three loci were got-1 (glutamate oxaloacetate transaminase-1) amy (alpha-amylase), and sdh (succinate dehydrogenase). The first 1,000 offspring isolated had the following genotypes:
  class 1) got-s got-s,amy-s amy-s,sdh-s sdh-s     441
  class 2) got-f got-s,amy-f amy-s,shd-f sdh-s     421
  class 3) got-f got-s,amy-s amy-s,sdh-s sdh-s      11
  class 4) got-s got-s,amy-f amy-s,sdh-f sdh-s      14
  class 5) got-f got-s,amy-f amy-s,sdh-s sdh-s      58
  class 6) got-s got-s,amy-s amy-s,sdh-f sdh-s      53
  class 7) got-f got-s,amy-s amy-s,sdh-f sdh-s       1
  class 8) got-s got-s,amy-f amy-s,sdh-s sdh-s       1
What are the linkage arrangements of these loci, including map units? If the three loci are linked, what is the coefficient of coincidence?

In this case only two classes are in highest frequency, which indicates that all three loci are linked. The next step is to determine the gene order. To do this we must compare the parental classes (highest frequency) to the double crossover classes (lowest frequency). As the male parent is homozygous for the slow alleles, we can easily determine the gamete donated to the offspring by the heterozygous female.
For the parental classes these are:
    got-s,amy-s,sdh-s    and    got-f,amy-f,sdh-f
For the double crossover classes these are:
    got-f,amy-s,sdh-f    and    got-s,amy-f,sdh-s
A comparison of the gametes from the parental classes with the double crossover classes shows that the locus amy is in the middle.
The next step is to calculate the map distance among the loci. To do this we need a table as given below
            number of recombinants between
       got-amy       amy-sdh         got-sdh
      ---------------------------------------
          11            58             11
          14            53             14
           1             1             58
           1             1             53
     ----------------------------------------
 totals   27           113            136
To calculate the distance between each locus, we use the same formula as before: the number of recombinants between the loci divided by the total number of flies and then times 100.
                       27
distance (got-amy) = ------ x 100 = 2.7 m.u.
                      1000
                       113
distance (amy-sdh) = ------ x 100 = 11.3 m.u.
                      1000
distance (got-sdh) = 2.7 + 11.3 = 14.0
To calculate the coefficient of coincidence we need to calculate the expected number of crossovers and then divide the number into the observed number of double crossovers. The expected frequency of double crossovers is given by multiplying the probability of a crossover between got-amy (0.027) by the probability of a crossover between amy-sdh (0.113). Thus the probability of a double crossover is 0.027 x 0.113 = 0.0031. Then multiplying this number by the total number of offspring (0.0031 x 1000) = 3.1, which is the expected number of offspring. The coefficient of coincidence is given by dividing the observed number of double crossovers by the expected number of double crossover (2/3.1) = 0.65.

P. 134, #5. The following three recessive markers are known in lab mice: h, hotfoot; o, obese; and wa, waved. A trihybrid of unknown origin is testcrossed, producing the following offspring:
hotfoot, obese, waved      357
hotfoot, obese              74
waved                       66
obese                       79
wildtype                   343
hotfoot, waved              61
obese, waved                11
hotfoot                      9
a) If the genes are linked, determine the relative order and the map distance between them.
b) What was the cis-trans allele arrangement in the trihybrid parent?
c) Is there any crossover interference? If yes, how much?

In this case only two classes are in highest frequency, which indicates that all three loci are linked. The next step is to determine the gene order. To do this we must compare the parental classes (highest frequency) to the double crossover classes (lowest frequency). As one parent is homozygous for the recessive alleles, we can easily determine the gamete donated to the offspring by the trihybrid parent.
For the parental classes these are:
    h o wa     and    h+ o+ wa+
For the double crossover classes these are:
    h+ o wa    and    h o+ wa+
A comparison of the gametes from the parental classes with the double crossover classes shows that the locus hotfoot (h) is in the middle. In addition, an examination of the nonrecombinant gametes shows that all widltype alleles are on the same chromosome in the trihybrid and all the recessive alleles are on the other chromosome. This is a cis arrangement of the alleles in the trihybrid.
The next step is to calculate the map distance among the loci. To do this we need a table as given below
            number of recombinants between
      obese-hotfoot    hotfoot-waved      obese-waved
      -----------------------------------------------
          79               74             79
          61               66             61
          11               11             74
           9                9             66
     -----------------------------------------------
 totals  160             160            160
To calculate the distance between each locus, we use the same formula as before: the number of recombinants between the loci divided by the total number of flies and then times 100.
                             160
distance (obese-hotfoot) = ------ x 100 = 16.0 m.u.
                            1000
                             160
distance (hotfoot-waved) = ------ x 100 = 16.0 m.u.
                            1000
distance (obese-waved) = 16.0 + 16.0 = 32.0
To calculate the coefficient of coincidence we need to calculate the expected number of crossovers and then divide the number into the observed number of double crossovers. The expected frequency of double crossovers is given by multiplying the probability of a crossover between obese and hotfoot (0.160) by the probability of a crossover between hotfoot and waved (0.160). Thus the probability of a double crossover is 0.160 x 0.160 = 0.0256. Then multiplying this number by the total number of offspring (0.0256 x 1000) = 25.6, which is the expected number of offspring. The coefficient of coincidence is given by dividing the observed number of double crossovers by the expected number of double crossover (20/25.6) = 0.78. The percent of interference is given by (1 - cc) x 100. percent interference = (1 - 0.78) x 100 = 22%.

P. 136, #23. In people, the ABO system (A, B, O alleles) is linked to the aldolase-B locus (al,al+ alleles), a gene that functions in the liver. Deficiency, which is recessive, results in fructose intolerance. A man with blood type AB had a fructose intolerant, type B father and a normal type AB mother. He and a woman with blood type O and fructose intolerance had ten children, of which five were type A and normal, three were fructose intolerant and type B, and two were type A and intolerant to fructose. Draw a pedigree of this family and determine the map distance involved. (Calculate a lod score to determine the most likely recombination frequency between the loci.
The first step is to create the pedigree for this cross and label the chromosomes with as much inofrmation as is possible. The man with type AB blood had a father who was homozygous for fructose intolerance, thus the B allele that the man has must have come from his father and is linked to a fructose intolerant allele. His mother had AB blood and was fructose tolerant and thus must have at least one fructose tolerant allele al+. In this case the A allele from the mother is linked to an al+ allele on the same chromosome. This makes the man with AB blood heterozygous for both loci. He marries a woman who had type O blood and is fructore intolerant, thus she is homozygous recessive at both loci. The cross (heterozygous dominant x homozygous recessive) is a testcross.

Of the ten children 5 inherit the chromsome with the A allele without any recombination and 3 inherit the chromosome with the B allele without any recombination. Two of the children inherited recombinant chromoses. To calculate the map distance between the two loci we use the formula below such that
                 # recombinants
map distance =  ---------------- x 100 
                     total #
                  2
map distance =  ---- x 100 = 20 cM
                 10
To calculate the lod score we must first calculate two probabilities. One is the probability of these offspring given a map distance of 20 cM and then the probability of these offspring given independant assortment. To determine the probability of these offspring given 20 cM distance between the loci we must first calculate the probability of any given child. Given a map distance of 20 cM, then 80% of the children will be nonrecombinants and 20% will be recombinats. Thus the probability of a type A and normal (nonrecombinant) is 0.40, and the probability of a type B and fructose intolerant (nonrecombinant) is 0.40, and the probability of a type A and fructose intolerant (recombinant) is 0.10. To get the probability of this family we then multiply the probabilities on each birth together.
prob(given 20 cM distance) = 0.40^5 * 0.40^3 * 0.10^2 = 0.0000065536

To get the probability of this family given independant assortment, we assign the probabiliy of any given phenotype the value of 0.25. Given a dihybrid testcross, each phenotype is equally likely. To get the probability of this family we then multiply the probabilities on each birth together.
prob(given independant assortment) = 0.25^10 = 0.0000009536743164062

To calculate the lod score we then take the logarithm of the ratio of these two probabilities.
lod = log ((prob given 20 cM distance)/prob given independant assortment))
           0.00000655360
lod = log  ------------- = log 6.872 = 0.83
           0.00000095368
Any lod score greater than zero indicates linkage, but it is considered strong evidence for linkage when the lod score is greater than 3.

P. 136, #24. In the mouse, the autosomal alleles Trembling and Rex (short hair) are dominant to normal and long hair, respectively. Heterozygous Trembling, Rex females were crossed to normal, long-haired males and yielded the following offspring:
     Trembling, Rex            42
     Trembling, long-haired   105
     normal, Rex              109
     normal, long-haired       44
a) Are the two genes linked? How do you know?

The cross is a dihybrid female testcrossed to a homozygous recessive male. If the two loci were not linked, then they would assort independently and you would see the four phenotypes in the offspring in a ratio of 1:1:1:1. In this case, two classes are in much higher frequency than the other two classes. This could be tested with a chi-square, which would reject the null hypothesis of independent assortment. Thus, we can see that the two loci do not assort independently and we must conclude that they are linked.
b) In the heterozygous females, were Trembling and Rex in cis or trans position? Explain.
The two classes in highest frequency represent the parental or nonrecombinant classes. This means that the parents of the dihybrid female were Trembling, long-haired and normal, Rex. The chromosomes of these parents would be homozygous for these traits.
      Trembling, long-haired               normal, Rex
          Tr       +                         +      R
         ------------          x            ----------
         ------------                       ----------
          Tr       +                         +      R
The F1 dihybrid female (Trembling, Rex) would have received one of each chromosome from her parents, one chromosome from Trembling, long-haired and 1 from normal, Rex. Thus her chromosomes look like this
                Tr          +
               ---------------
               ---------------
                +           R
In this case, Trembling is on one chromosome and Rex is on the homologue. As they are on opposite chromosomes, they are in the trans position.
c) Calculate the percent recombination between the two genes.
We know that Trembling, long-haired and normal, Rex are the parentals thus, Trembling, Rex and normal, long-haired must be recombinants. To calculate the map distance, we use the formula
                number of recombinants
map distance = --------------------------- x 100
                total number individuals

                  86
map distance =  ----- x 100  =  28.7 m.u.
                 300
P. 136, #25. In corn, a trihybrid Tunicate (T), Glossy (G), Liguled (L) plant was crossed with a nontunicate, nonglossy, liguleless one and produced the following offspring.
    Tunicate, liguleless, Glossy          58
    Tunicate, liguleless, nonglossy       15
    Tunicate, Liguled, Glossy             55
    Tunicate, Liguled, nonglossy          13
    nontunicate, Liguled, Glossy          16
    nontunicate, Liguled, nonglossy       53
    nontunicate, liguleless, Glossy       14
    nontunicate, liguleless, nonglossy    59
a. Determine which genes are linked.
In this case, an examination of the numbers of each phenotype shows that four classes are in essentially equal frequency. This indicates that not all of the loci are linked. The problem now becomes one of identifying which loci are linked. The next step is to look at the phenotypic ratios taking the data two loci at a time. The first pair will be the tunicate and ligule loci.
Ignore the phenotype at the glossy locus.
     Tunicate, liguless     58 + 15 = 73
     Tunicate, Liguled      55 + 13 = 68
     nontunicate, liguless  14 + 59 = 73
     nontunicate, Liguled   16 + 53 = 69
These four phenotypes are in about equal frequency, which indicates independent assortment between the tunicate and liguled loci, and thus these two loci are not linked.
The second pair will be the tunicate and glossy loci. Ignore the phenotype at the liguled locus.
     Tunicate, Glossy         58 + 55 = 113
     Tunicate, nonglossy      15 + 13 =  28
     nontunicate, Glossy      16 + 14 =  30
     nontunicate, nonglossy   53 + 59 = 112
These four phenotypes are not in equal frequency, in fact two classes are at much higher frequency (these are nonrecombinants) and two classes are at much lower frequency (these are recombinants). Thus, these data indicate that these two loci are linked. As we know that the liguled locus is not linked to the tunicate locus and that the tunicate locus is linked to the glossy locus, then we can assume that the liguled locus is not linked to the glossy locus. We could show this by the above method, if necessary.
b. Determine the genotypes of the heterozygote; be sure to indicate which alleles are on which chromosome.
At the tunicate, glossy loci, the nonrecombinants were tunicate, glossy and nontunicate, nonglossy (see table above). This indicates that the chromosomes in the heterozygote had the following arrangement.
     T         G                L
 ----------------           ----------
 ----------------           ----------
     t         g                l
The T and G alleles are cis on the same chromosome, however, the liguled locus is on a separate chromosome.
c. Calculate the map distance between the linked genes.
     Tunicate, Glossy         58 + 55 = 113
     Tunicate, nonglossy      15 + 13 =  28
     nontunicate, Glossy      16 + 14 =  30
     nontunicate, nonglossy   53 + 59 = 112
From this table, the number of recombinants is 58 and the total numbers of individuals is 283.
                     58
   map distance =  ----- x 100  =  20.5 m.u.
                    283

P. 136, #26. In Drosophila, kidney bean eye (k), cardinal eye (cd), and ebony body (e) are three recessive alleles. If homozygous kidney, cardinal females are crossed to homozygous ebony males, the F1 offspring are all wildtype. If heterozygous F1 females are mated with kidney, cardinal, ebony males, the following two thousand progeny appear:
     880 kidney, cardinal
     887 ebony
      64 kidney, ebony
      67 cardinal
      49 kidney
      46 ebony, cardinal
       3 kidney, ebony, cardinal
       4 wildtype
a. Determine the chromosomal composition of the F1 females.
From the flies in the P generation ("kidney, cardinal" and "ebony"), we know that in the F1 one chromosome will carry the alleles k,cd,+ while the other chromosome will carry the alleles +,+,e.
b. Derive a map of the three genes.
In this case only two classes are in highest frequency, which indicates that all three loci are linked. That next step is to determine the gene order. To do this we must compare the parental classes (highest frequency) to the double crossover classes (lowest frequency).
For the parental classes these are:
    kidney, cardinal           and    ebony
For the double crossover classes these are:
    kidney, ebony, cardinal    and    wildtype
A comparison of the phenotypes from the parental classes(for example, "kidney, cardinal") with the double crossover classes (for example "kidney, ebony, cardinal") shows that the locus ebony is in the middle, because it is the one locus that does not match.
The next step is to calculate the map distance among the loci. To do this we need a table as given below
            number of recombinants between
     kidney-ebony     ebony-cardinal      kidney-cardinal
    -----------------------------------------------------
          64                49                   49
          67                46                   46
           3                 3                   64
           4                 4                   67
   ------------------------------------------------------
 totals  138               102                  136
To calculate the distance between each locus, we use the same formula as before: the number of recombinants between the loci divided by the total number of flies and then times 100.
                            138
distance (kidney-ebony) = ------ x 100 = 6.9 m.u.
                           2000
                              102
distance (ebony-cardinal) = ------ x 100 = 5.1 m.u.
                             2000
distance (kidney-cardinal) = 6.9 + 5.1 = 12.0
The map is this.
       k            e            cd
    ---+------------+------------+-------
          6.9 m.u.      5.1 m.u.


P. 137, #30. Hemophilia and color blindness are X-linked recessive traits. A normal woman whose mother was color-blind and whose father was a hemophiliac mates with a normal man whose father was color-blind. They have the following children:
4 normal duaghters
1 normal son
2 color-blind sons
2 hemophiliac sons
1 color-blind, hemophiliac son
Estimate the distance between the two genes.


P. 137, #31. The results of an anlysis of five human-mouse hybrids for five enzymes are given in the following table along with the human chromosomal content of each clone (+ = enzyme of chromosome present; - = absence). Dedue which chromosome carries which gene.
       see your book for the large table (Table 1)


Table 2.                              Clone
                             ---------------------
      human enzyme           A    B    C    D    E
   -------------------------------------------------
   gluthathione reductase    +    +    -    -    -
   malate dehydrogenase      -    +    -    -    -
   adenosine deaminase       -    +    -    +    +
   galactokinase             -    +    +    -    -
   hexosaminidase            +    -    -    +    -
   -------------------------------------------------
The problem is to determine which clones have which enzymes. For example, gluthathione reductase is present in clones A and B, but absent from clones C, D, and E. The next step is to determine from Table 1 which chromosome or chromosomes are in clones A and B and also absent from clones C, D, and E. An examination of Table 1 shows that only chromosome 8 is present in clones A and B while being absent from clones C, D, and E. Thus gluthatione reductase is on chromosome 8.
For malate dehydrogenase we need to determine which chromosome is present in clone B and absent from clones A, C, D and E. The only chromosome that fits this criterion (present in B and absent from all others) is chromosome 2. Thus malate dehydrogenase is on chromosome 2.
By the same reasoning as outlined above; adenosine deaminase is on chromosome 20, galactokinase is on chromosome 17, and hexosaminidase is on chromosome 5.

P. 138, #32. You have selected three mouse-human hybrid clones and analyzed them for the presence of human chromosomes. You then analyze each clone for the presence or absence of particular human enzymes (+ = presence of human chromosome or enzyme activity). Based on the following results, indicate the probable chromosomal location for each enzyme.
Table 1.              Human Chromosomes
             -------------------------------
Clone        3    7    9   11   15   18   20
---------------------------------------------
  X          -    +    -   +    +    -    +
  Y          +    +    -   +    -    +    -
  Z          -    +    +   -    -    +    +
---------------------------------------------


Table 2.             Enzyme
             --------------------
Clone        A    B    C   D    E
----------------------------------
  X          +    +    -   -    +
  Y          +    -    +   +    +
  Z          -    -    +   -    +
----------------------------------
Enzyme A is on chromosome 11. We know this because enzyme A is found in clones X and Y but not in clone Z (Table 2). An examination of Table 1 reveals that chromosome 11 is the only chromosome in clones X and Y but not in clone Z. As the presence and absence of enzyme A matches that of chromosome 11, we conclude that enzyme A in on chromsomes 11.
Enzyme B is on chromosome 15
Enzyme C is on chromosome 18
Enzyme D is on chromosome 3
Enzyme E is on chromosome 7


Last updated on 22 August 1996.
Provide comments to Dwight Moore at mooredwi@esumail.emporia.edu.
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