Download Example 2 – Human Skin colour

Dihybrid Crosses, Recombinants, Gene Linkage and Chi-squared Test
(p. 158 – 160)
Mendel also investigated the simultaneous inheritance of two pairs of contrasting
characters, using the same garden pea plants. He referred to this as a dihybrid cross.
To test the theory, Mendel crossed pure breeding plants from round seeds with yellow
cotyledons (seed leaves) with pure breeding plants from wrinkled seeds with green
cotyledons. All of the F1 generation were round, yellow peas. When the F1 generation
was allowed to cross, Mendel found that there was a ratio of 9 yellow round peas, 3 green
round peas, 3 yellow wrinkled peas and 1 green wrinkled pea. The result from the
monohybrid crosses was still valid. Yellow is dominant to green, and round / smooth is
dominant to wrinkled.
Mendel’s Dihybrid Cross Example
Further Test Crosses – Drosophilia melanogaster (Fruit Fly)
Mendel died in 1884, in relative obscurity in the scientific community. Many did not
know of his work or thought he did not understand his results. When his papers were
rediscovered in 1900, Mendel’s results came to be confirmed and then extended by many
others.
One was by Thomas Morgan in 1908. He used the Drosophilia as an organism to test
Mendelian Genetics. For his work, he was awarded the Nobel Prize in 1933.
Morgan showed:
 Mendel’s factors are linear sequences of genes on chromosomes (what is now
known as the Chromosomal Theory of Inheritance)
 discovered sex chromosome and sex linkage
 demonstrated crossing over, and the exchange of alleles between chromosomes,
resulting from chiasmata formed during meiosis
Why was the fruit fly chosen? It is quite common around rotting vegetable material and
the female lays hundreds of eggs, which produce hundreds of offspring. The time from
hatching to adult takes about 10 days. They can be anaesthetized, and sorted. They have
four pairs of chromosomes. The characteristics, or phenotypes, are controlled by genes
not on the sex chromosomes. Therefore, the characteristics are controlled by the
autosomes, and are not sex-linked.
Morgan’s Test Cross
If a wild type fly is crossed with a mutant type, what will the offspring be. The wild type
has a white body and normal wings. These are dominant traits. The mutant has a red
body and vestigal wings (short). What will the F2 generation be? (The genes in both
cases are not linked)
Recombinants
Recombination is the re-assortment of genes or characters into different combinations
from those of the parents.
When cross over occurs (previous notes), we see that the genes on some of the
chromosomes are kept the same, while others change. Recombination can be applied to
non-linked genes but is often restricted to linked genes, which we will talk about later.
We can identify the recombinants in the above two examples. What are the parental
combinations and what are the recombinants?
Examples
1.
Two tomato plants were crossed. Tall plants (T) are dominant to short plants (t)
and round tomatoes (R) are dominant to oblong fruit (r). If one parent with the
genotype TTRr, is crossed with a parent homozygous recessive for both traits,
what will the F1 generation phenotypes and genotypes be?
2.
If the genotypes for the tomatoes above were TtRr, Ttrr, ttRr and ttrr, which two
pairs would a plant breeder select in order to obtain a phenotype ratio of 1:1:1:1?
3.
Frumpy plants have small flowers with green petals, which are dominant traits.
Large white flowers are recessive, and the genes are not linked. A plant with
small green flowers was crossed with one with large white flowers and the
offspring had either small green flowers or large green flowers. Determine the
genotypes of the parents. If the large green flowers were allowed to selfpollinate, determine the genotypes and phenotypes of the offspring.
Autosomal Gene Linkage
Autosomes are chromosomes, which are not sex chromosomes. They are the other 22
pairs, for example, in humans.
Sex chromosomes are those chromosomes, which help in determining the sex of an
individual (XX or XY).
In our studies, we have studied that genes independently assort. In other words, they are
located on different chromosomes, and have no effect on each other.
In reality, we only have 22 autosomes or homologous pairs, along with the sex
chromosomes. There are many more genes (about 60,000!) in our genetic make-up. This
means that some must be located on the same chromosome.
When cross over occurs in Prophase I, the alleles are exchanged, between non-sister
chromatids of a homologous pair. But since some genes are on the same chromosome,
when cross over occurs, the genes go together. This is called a linkage group.
Linkage group – a group of genes whose loci are on the same chromosome.
The Reason
Linked genes were discovered in 1906, by R. C. Punnett and W. Bateson. (the square
guy!) When Mendel’s work was rediscovered, geneticists looked at Mendel’s ratios.
Some worked out to the characteristic 9:3:3:1 ratio for the F2 generation. In some cases,
using plants, the ratio for the F2 generation was 7:1:1:7! What happened?
Let’s go over an example.
In sweet peas, purple flowered plants are dominant to red, and long pollen plants are
dominant to round pollen. When a homozygous purple and homozygous long plant is
crossed with a red and round pollen plant, the resulting F1 phenotype is all purple and
long, as you would expect.
What would be the expected ratio for the F2 generation, if two of the previous plants are
mated?
The results were:
7 purple long: 1 purple round: 1 red long: 7 red round
This seemed to mean that more PL and pl gametes were produced than the Pl and pL
gametes. What is the explanation?
If no cross over occurs, the phenotypes will have the parental characteristics and few
recombinants.
Example
In fruit flies (Drosophila) body colour and wing length are linked. A tan body (b+) is
dominant to a black body (b) and long wings (w+) are dominant to short wings. Cross a
homozygous tan, homozygous long winged fly with a mutant black and short wing fly.
What would be the F1 and F2 generations in terms of genotypes and phenotypes?
1.
The snowy gull has white feathers and a yellow beak, but some birds have black
feathers and an orange beak. Black and orange are recessive and the genes are
linked. A pure breeding bird with white feathers and a yellow beak was mated
with one with black feathers and orange beak. The offspring had white feathers
and yellow beak. Two of these were mated and 75% of the offspring had the
dominant phenotypes and the rest had the recessive. Explain.
2.
Transparent wings and clubbed antennae are autosomely lined dominant alleles
in the fairy fly. Grey wings and smooth antennae are the characteristics for
being homozygous recessive for both alleles. A fly with grey wings and smooth
antennae was mated with an unknown fly and all of the offspring had transparent
wings and clubbed antennae. These offspring were all mated to flies, with the
recessive traits and the total offspring were:
i.
ii.
iii.
iv.
227 transparent wings, clubbed antennae
10 transparent wings and smooth antennae
9 grey wings, smooth antennae
231 grey wings, clubbed antennae
Determine the genotypes of all the flies.
Chromosome Mapping Using Linkage (p. 174)
Remember that crossing over is a random occurrence, and can happen at any point along
the chromosome. It does follow that the further apart genes are, the more often they will
cross over, as there are more potential sites for the cross to occur.
When we speak of mapping the chromosomes, we are not dealing in the actual number of
crossover events, but percentages of recombination – this will tell us the order of genes
on the chromosome and their relative distances.
For example, in the pea plant example using purple and long linked genes, 2 out of the 16
showed crossing over – you would then find this percentage (12.5%) – and this is the
distance (12.5 units) between the two linked genes.
Now suppose we found another gene on this chromosome that crosses over with the long
gene 5% of the time – how can we determine the order of the genes?
The only way to know which is the correct map would be to analyze cross data between
purple and gene A. If the distance is shown to be 7.5, then the order would be purple, A,
and long. If the distance is shown to be 17.5, the order is purple, long, and A.
An example of this:
In Drosophila, a gene influencing eye colour has wild type (dominant) and purple
(recessive) alleles. Linked to this gene is another that determines wing length, with long
being dominant to short. Suppose a homozygous dominant female is crossed with a
purple eyed, short winged male. Two of the F1 are crossed and the offspring have the
following characteristics:
252 wild eyes and wild wings (long)
276 purple eyes, short wings
42 wild eyes, short wings
30 purple eyes, long wings
What is the distance between the two genes?
Problem
1. In fruit flies, the allele for grey colour is dominant over black and straight wings are
dominant over curly wings.
A heterozygous grey, straight winged fly was crossed with a black, curly winged fly. The
offspring were as follows:
43 grey, straight
12 grey, curly
39 black, curly
10 black, straight
a.
b.
c.
d.
If these genes are not linked, which phenotypes would you expect for the F1?
Give the expected numbers of the phenotypes.
Based on these results, would you expect the genes to be linked?
Can you find the map distance between the genes?
2. In rabbits, having coloured fur is dominant over producing no pigment (albino). Grey
fur is dominant over black. A homozygous completely recessive albino rabbit is mated
with a homozygous grey rabbit. The F1 are allowed to interbreed. The genes are not
linked.
a.
b.
c.
d.
e.
What are the genotypes and phenotypes of the F1?
Predict the genotypes for the F2?
What are the expected ratios?
Predict the phenotypes of the F2?
What are the expected ratios?
The Chi-squared Test
When you do a cross, generally you need a large amount of real life data to ensure that
your results are significant. You would then compare the ratio with the expected ratio.
The chi-squared test is used to analyze the data produced from a mono or dihybrid cross,
and determine if your results were simply by chance, or if the results are significant.
The formula is as follows:
A probability of less than 5% is considered to be significantly different than the expected
value, and therefore the original hypothesis or expectations need to be re-examined. To
put it another way, the greater the value of the chi-squared above the critical value, the
greater the difference between the observed and expected values.
Once we calculate the chi-square, we have to look at our degrees of freedom.
Degrees of freedom are the number of observations minus the minimum number required
to uniquely define the figure. In other words, if we are looking at two classes of a
phenotype, we calculate the degrees of freedom by:
n - 1
where n is the number of classes. For example, if you are looking at red eyes vs. white
eyes, the degree of freedom would be 1, as 2-1=1 or n-1.
For every degree of freedom, there is a critical value. Since in Biology, the probability is
5% or 0.05, we look at the probability (chi-square) vs. the degrees of freedom for 5%.
See handout.
Basically, if your value is smaller than the critical value for 5%, the result is by chance
and your original assumption (hypothesis) is correct. If the value is larger, there is a less
than 5% probability that the results are due to chance, so your original assumption may
be flawed.
Confused? Let’s do an example.
Ex. In a hypothetical cross, we expect the phenotypic ratio to be 1:1. The actual results
were 45:55, instead of 50:50. Is this deviation due to chance or is it significant?
Example 2
In a genetics experiment, tall pea plants were crossed with short pea plants. The resulting
F1 was self-fertilized and F2 consisted of 787 tall plants and 277 short plants. Does this
result confirm Mendel’s explanation?
Polygenetic Inheritance (p. 168 – 170)
In the previous section, we saw that the height of a pea plant was determined by one gene
with two alleles. This clear-cut difference is an example of discontinuous variation.
This means there is no intermediate form and no overlap between the two phenotypes.
Actually, very few characteristics of organisms are controlled by a single gene. Most
characteristics are controlled by a number of genes. Groups of genes which together
determine a characteristic are called polygenes.
Polygenetic inheritance is the inheritance of phenotypes that are determined by the
collective effect of several genes.
Genes that make up a polygene are often (but not necessarily always) located on different
chromosomes. Any one of these genes has a very small or insignificant effect on the
phenotype. The combined effect of all the genes on the polygene is to produce infinite
variety among the offspring.
Many features are controlled by polygenes. Here are some examples.
Example 1 – Shape of the comb in Poultry
Different shape of comb exist:
Looking at the above, some generalizations can be made. The trait is controlled by a pair
of genes that assort independently. If the genotype is P_rr, a pea comb is present. If the
genotype is P_R_, a walnut comb is present. If the genotype is ppR_, a rose comb is
present. If the genotype is pprr, a single comb is present.
What are the dominant alleles?
Cross a homozygous pea-combed chicken with a homozygous rose-combed chicken.
What is the F1 and F2, if the F1 was allowed to mate?
Example 2 – Human Skin colour
The colour of the human skin is due to the amount of the pigment called melanin that is
produced in the skin. Melanin synthesis is genetically controlled. It seems that three or
four or more separately inherited genes control melanin production. The outcome is an
almost continuous distribution of skin colour from very pale (no alleles coding for
melanin production) to very dark brown (all alleles coding for melanin production).
The example below is for only two independent genes, but dark is dominant to white in
all cases.
Some questions to really exercise your mind.
1.
If A, B, C are the alleles for dark skin, and a, b, c, represent the alleles for light
skin, what would the possible combinations be for two individuals mating who
are heterozygous for all the alleles?
2.
Seed colour in wheat is controlled by around 6 genes. Below are the
combinations in the genotypes and the phenotypes.
If two plants which produce mid pink seeds are crossed, what are the ratios of the
genotypes and phenotypes for the seed colours?
Extension 1 - Eye Colour
The exact color of the human eye is determined by the amount of a single pigment called
melanin. When a lot of melanin is present, the eye will appear brown or even black.
When little melanin is present, the iris appears blue.
Intermediate amounts of melanin produces gray, green, hazel or varying shades of brown.
Eye color genes, through the enzymes they produce, direct the amount and placement of
melanin in the iris. In general Caucasian babies are born with blue eyes because at the
time of birth they haven't begun to produce melanin in their irises.
At one time scientists thought that a single gene pair, in a dominant/recessive inheritance
pattern, controlled human eye color. At the present, three gene pairs controlling human
eye color are known. Two of the gene pairs occur on chromosome pair 15 and one
occurs on chromosome pair 19. The bey 2 gene, on chromosome 15, has a brown and a
blue allele. A second gene, located on chromosome 19 (the gey gene) has a blue and a
green allele. A third gene, bey 1, located on chromosome 15, is a central brown eye color
gene
Geneticists have designed a model using the bey 2 and gey gene pairs that explains the
inheritance of blue, green and brown eyes. In this model the bey 2 gene has a brown and
a blue allele. The brown allele is always dominant over the blue allele so even if a person
is heterozygous (one brown and one blue allele) for the bey 2 gene on chromosome 15
the brown allele will be expressed.
The gey gene also has two alleles, one green and one blue. The green allele is dominant
to the blue allele on either chromosome but is recessive to the brown allele on
chromosome 15.
This means that there is a dominance order among the two gene pairs. If a person has a
brown allele on chromosome 15 and all other alleles are blue or green the person will
have brown eyes.
If there is a green allele on chromosome 19 and the rest of the alleles are blue, eye color
will be green.
Blue eyes will occur only if all four alleles are for blue eyes.
This model cannot account for gray, hazel or multiple shades of brown, blue, green and
gray eyes, or how eye colour changes over time.
Try to chart this, using a modified Punnett Square.
Extension 2 – Other forms of Gene Interaction
Polygenetic inheritance adds to the range of phenotypes that may exist. But there are
other mechanisms by which genetic variety is controlled.
Cases where characteristics are controlled by two or more genes, one or more of which
masks or modifies the expression of other genes include:



Plumage pigmentation in birds
Agoutie coat colour in some mice
Shell banding in the snail Cepaea nemoralis
There are some examples below.
Other examples are controlled by factors in the environment. A tall plant may appear to
be dwarf if it has consistently been deprived of essential nutrients.
Genetics Problems
1.
List the possible gametes that would result from the segregation of the following
parental genotypes.
a. RR
b. Mm
c. AABB
d. DdSs
e. gGHhRr
2.
In a species of plants, flowers appearing at the end of the stem are dominant to
flowers appearing in the middle of the stem. Predict the phenotype for this F2
generation, for a cross involving a homozygous dominant plant with recessive
plant.
3.
In garden peas, red flowers dominate white flowers and green pod colour is
dominant to yellow pod colour.
a. Cross two heterozygous red flowered plants with green pods
b. Cross a heterozygous red flowered plant with green pods with a plant that
is completely recessive for all the traits.
c. Cross two plants that are recessive for both traits.
4.
In snapdragons, tallness (T) is dominant to dwarfness (t), while red flower (Cr)
and white flower (Cw) show incomplete dominance. A dwarf red snapdragon is
crossed with a plant homozygous for tallness and white flowers. Give the
genotypes and phenotypes of the expected F1. If the F1 flowers were crossed,
what would be the expected F2 genotypes and phenotypes.
5.
A dominant allele, A causes yellow colour in rats. The dominant allele of
another independent gene, R, produces black coat colour. When two dominants
occur together (A_R_), they interact to produce grey. Rats of the genotype (aarr)
are cream coloured. If a grey male and a yellow female, when mated, produce
offspring in the following approximate ratio, 3/8 yellow, 3/8 grey, 1/8 cream and
1/8 black, what are the genotypes of the two parents?
6.
What are the genotypes of a yellow male rat and a black female that, when
mated, produce 46 grey and 54 yellow offspring? Does a chi-square test bear
you out?