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Wize University Biology Textbook > Mendelian Genetics

Forked-Line and Probability Methods

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Forked Line Method

  • Used for dihybrid crosses or more (i.e. more than 2 alleles involved).
  • Easier than using a Punnett square for crosses that involve many alleles.
  • Diagram approach: at each level is one type of allele, multiply the levels to get the probability for the offsprings phenotypes.


Consider the following example of a trihybrid cross:

You cross two pea plants that are heterozygous for three traits: Aa color, Bb shape, Cc height where yellow, round and tall are dominant.


How this forked line diagram was made:

  1. Start off with the probability ratio for color where you if cross two heterozygous yellow peas (Aa x Aa), you get a 3:1 yellow to green pea ratio.
  2. Next level you put the ratio for shape but this time you divided the two color groups.
  3. Next level you divide each individual shape group into the heights.
  4. Note: because you are looking at crossing two heterozygous genotypes, the ratio is always 3:1 dominant to recessive. You can verify this with a simple Punnett square
  5. Multiply the levels leading down to the combination of traits (e.g. a yellow, round, tall = 3 x 3 x 3 = 27).
  6. The number of offsprings makes up the phenotypic ratio (27:9:9:9:3:3:3:1).
  7. You can also determine the probability of that phenotype by taking the number of offsprings and dividing by the total (eg. 27/64 = 42%.


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Probability Method

The Forked line method, although easier than Punnett squares, can't give you a genotype ratio.
  • To get the genotype probability/ratio, we must use the probability method.
  • To get the probability of different genotypes, we multiply the probabilities of the different genotypes (i.e. homozygous dominant, recessive, or heterozygous).


Consider the following example of a trihybrid:

You cross two pea plants that are heterozygous for three traits: Aa color, Bb shape, Cc height where yellow, round and tall are dominant.

Probability of getting all heterozygous AaBbCc?
  1. Consider the probability of Aa from an Aa x Aa cross is 1/2, Same for Bb and Cc
  2. Multiply all the probabilities (for Aa x Bb x Cc): 1/2 x 1/2 x 1/2 = 1/8

Try: Probability of getting AabbCC?

1/2 (Aa) x 1/4 (bb) x 1/4 (CC) = 1/32

Practice: Forked Line Method

What is the probability (%) of getting a small, pop-eyed, yellow goldfish when you cross a large, pop-eyed, orange (AaBbCc) goldfish with a small, normal eyed, yellow (aabbcc) goldfish?

A,a is for body size
B,b for eye shape
C,c for color

Practice: Probability Method

Calculate the probability (%) of producing AABbCcdd from the following cross:

AaBBccDd x AabbCcDd
Extra Practice
In a flowering plant species, gene A produces a pigment, resulting in red petals.
Mutation a causes the loss of pigment (white petals).
A second gene, S, represses the inhibitor of cytochrome P450, an enzyme that is responsible for the production of red pigment.
In cows, body color is controlled by two independently assorting loci, A and B.
When cows have at least one dominant allele at either loci (e.g. AaBb), they are agouti.
At the A locus, aa cows fail to deposit pigment and appear albino.
We are investigating the colour genes in a certain species of mice that generally have two colours (black and white). If you were to know that two genes (A and B) are responsible for those colours and that A only produces the black colour in the absence of B...
What is the proportion of black in the F2 given than P0 cross was AABB * aabb?
In the table below, six mutant types of Drosophila flies are showed.
How many complementation groups are there?
Which mutations belong to which group?
Mendel's Dihybrid Cross (Practice Questions)
To test whether the alleles for grape shape and colour sort dependently or independently, one homozygous dominant plant (RRGG = round & green) and one homozygous recessive plant (rrgg) = wrinkled & red) are tested using a Mendelian Dihybrid cross. The resulting F2 generation supports the hypothesis of independent assortment. What is the approximate likelihood of finding a wrinkled plant in the F2 generation?
Mendel's Dihybrid Cross (Practice Questions)
To test whether the alleles for grape shape and colour sort dependently or independently, one homozygous dominant plant (RRGG = round & green) and one homozygous recessive plant (rrgg) = wrinkled & red) are tested using a Mendelian Dihybrid cross. The resulting F2 generation supports the hypothesis of independent assortment. What is the approximate likelihood of finding a wrinkled plant in the F2 generation?
Mendel's Dihybrid Cross (Practice Questions)
To test whether the alleles for apple size and colour sort dependently or independently, one homozygous dominant plant (BBRR = big & red) and one homozygous recessive plant (bbrr = small & green) are tested using a Mendelian Dihybrid cross. The resulting F2 generation supports the hypothesis of dependent assortment. Which of the following is correct regarding the F2 generation?
If you cross two true-breeding lines of pigs, one is homozygous dominant; one is
homozygous recessive, what will be the phenotype of the progeny?
If you cross two true-breeding lines of pigs, one is homozygous dominant; one is
homozygous recessive, what will be the phenotype of the progeny?
The W allele in a flowering species gives rise to white plants and is dominant over the w
allele that gives rise to pink flowers. The T allele in this species gives rise to tall plants
while the t allele gives rise to short plants. What are the proportions of phenotypes
Inheritance of traits practice problem 3
In cats, big ears are dominant over short ears, and the gene is autosomal. Another gene controls eye colour, and is X-linked. "E" gives brown eyes, "e" gives blue eyes, and Ee gives green eyes.
Brown eyed male with the homozygous genotype for big ears is mated with a female with short ears and green eyes. What kittens could be produced?
Note: X-linked traits are on the X chromosome. Females have two X chromosomes while males have one X chromosome and one Y chromosome.
Inheritance of traits practice problem 2
A true breeding hamster with long fur and brown patches was crossed with a true breeding hamster with short fur and no patches. The F1 all had long fur and no patches. The F1 were crossed with hamsters with short fur and brown patches.
The pair produced 10 baby hamsters. What percentage do you expect to be:
Inheritance of traits practice problem 1
Consider a cross between two true-breeding zebrafish strains. The female parent has stripes (dominant) and a short tail fin and the male is spotted with a long tail (dominant) fin. All F1 progeny are striped with long tail fins.
Use S and s to represent the body patterning alleles and T and t to represent the tail fin alleles.
Punnett square
There are individuals who consult you since you are a geneticist. Both parents have brown eyes (B) but tell they each had a parent with blue eyes.
What percent chance is there that their kids are blue eyed?
[only enter the number not the % sign]
Punnett square
There are individuals who consult you since you are a geneticist. Both parents have brown eyes (B) but tell they each had a parent with blue eyes.
What percent chance is there that their kids are heterozygous for the brown eyed trait?
[only enter the number not the % sign]
Punnett square
There are two parents, one with brown eyes (B) and one with blue eyes (b).
They have 4 children together, two of which have blue eyes. What must the genotype for the brown eyed parent be?
Punnett square
There are individuals who consult you since you are a geneticist. Both parents have brown eyes (B) but tell they each had a parent with blue eyes.
What percent chance is there that there kids are blue eyed?
[only enter the number not the % sign]
If both parents have brown eyes (B) and they each had a parent with blue eyes (b), what percent chance is there that their kids are homozygous for the brown eyed trait?
[only enter the number not the % sign]
Punnett square
There are individuals who consult you since you are a geneticist. Both parents have brown eyes (B) but tell they each had a parent with blue eyes.
What percent chance is there that there kids are heterozygous for the brown eyed trait?
[only enter the number not the % sign]
Blue eyes = bb
Brown eyes = Bb or BB
Is it possible for two blue eyes parents to have a brown eyes son?
Assume the following monohybrid crosses where for a particular gene, A represents the dominant allele and a, the recessive allele which show complete dominance.
Two strains of zebra are crossed, one with the AaBbCc genotype and one with the aabbcc genotype. The A gene codes for stripe colour (A is blue and a is pink), the B gene codes for height (B is tall and b is short) and the C gene codes for ear shape (C is pointy and c is not pointy).
a) What is the probability that the pair will produce offspring with blue stripes, not pointy ears, and is tall).
b) What is the probability that the pair will produce offspring that shows all three dominant phenotypes?
A fly which has the genotype AaBb is cross with a fly that is homozygous recessive. The following offspring are obtained:
AaBb: 953 aabb: 910 Aabb: 200 aaBb: 192 a) Are these genes linked?
b) What is the recombination frequency? (one decimal place)
Assume the following dihybrid crosses where for a particular gene, A represents the dominant allele and a, the recessive allele, and for another trait, B represents the dominant allele and b, the recessive allele. Genes show complete dominance.
Inheritance of traits practice problem 3
In cats, big ears are dominant over short ears, and the gene is autosomal. Another gene controls eye colour, and is X-linked. "E" gives brown eyes, "e" gives blue eyes, and Ee gives green eyes.
Brown eyed male with the homozygous genotype for big ears is mated with a female with short ears and green eyes. What kittens could be produced?
Note: X-linked traits are on the X chromosome. Females have two X chromosomes while males have one X chromosome and one Y chromosome.
Inheritance of traits practice problem 2
A true breeding hamster with long fur and brown patches was crossed with a true breeding hamster with short fur and no patches. The F1 all had long fur and no patches. The F1 were crossed with hamsters with short fur and brown patches.
The pair produced 10 baby hamsters. What percentage do you expect to be:
Inheritance of traits practice problem 1
Consider a cross between two true-breeding zebrafish strains. The female parent has stripes (dominant) and a short tail fin and the male is spotted with a long tail (dominant) fin. All F1 progeny are striped with long tail fins.
Use S and s to represent the body patterning alleles and T and t to represent the tail fin alleles.
Practice: Multi-loci Crosses
A beetle species has the following genetic relationships:
Wing length - long (L) is sex-linked dominant to short (l) on the D chromosome
Wing colour - Blue (B) is co-dominant with black and makes purple wings (P) which are dominant to white (b)
Hufflelumps are small creatures that have three distinct nose shapes: square, triangular, and circular. In trying to determine the dominant and recessive phenotypes, you carry out the following crosses and count the offspring. Define the parental genotypes using "N" and "n" to denote nose shape. (*Hint: there may not be complete dominance)
Assume the following monohybrid crosses where for a particular gene, A represents the dominant allele and a, the recessive allele which show complete dominance.
Assume the following dihybrid crosses where for a particular gene, A represents the dominant allele and a, the recessive allele, and for another trait, B represents the dominant allele and b, the recessive allele. Genes show complete dominance.
Punnett square
There are two parents, one with brown eyes (B) and one with blue eyes (bb).
They have 4 children together, two of which have blue eyes. What must the genotype for the brown eyed parent be?
Senario:
A population of wild turkey has variation in a gene that affects yolk development.
When in the homozygous state, the recessive allele y causes yolk sac development to fail, this is lethal. The alternative wild type allele, Y, shows complete dominance.
Inheritance of traits
In cats, big ears are dominant over short ears, and the gene is autosomal. Another gene controls eye colour, and is X-linked. "E" gives brown eyes, "e" gives blue eyes, and Ee gives green eyes.
Brown eyed male with the homozygous genotype for big ears is mated with a female with short ears and green eyes. What kittens could be produced?
Note: X-linked traits are on the X chromosome. Females have two X chromosomes while males have one X chromosome and one Y chromosome.
A recessive mutant allele, purple, causes the skin of homozygotes to be purple instead of green. What would be the expected distribution of offspring from a cross of a purple male with a green female (whose father was purple)?
Humans have 46 chromosomes where the OCA2 gene encoding eye colour is located on
chromosome 15. If we assume only 3 eye colours exist in the human population blue (b),
brown (B) and green (G), where green is recessive to brown but dominant to blue.
A hermaphroditic flower plant has a heterozygous genotype at two independently assorted loci. If this plant were to self-fertilize, what proportion of the zygotes would be the same genotype as their parent?
There are 2 genes in an alien species that have an epistatic interaction (meaning, one
gene affects the expression of the other). Recessive alleles at the “bald” gene (bb)
inhibit the expression of different alien antennae lengths (AL for long, AS for short and
Imagine a population of sloths in which lazy “hanging” behaviour is controlled by the H locus. HH and Hh individuals are extra lazy and will hang on the same trees all day, whereas hh individuals will occasionally move from one branch to another. You get to take a trip to a sloth sanctuary and after watching 500 sloths you count 355 HH, 100 Hh,
and 45 hh individuals. What is the frequency of the h allele for this population?
You are studying a particular population of aliens and you determine that locus F
determines how friendly the aliens are. FF and Ff individuals are friendly and ff
individuals are hostile. You find that friendly individuals can produce 40 offspring, and
A recessive mutant allele, purple, causes the skin of homozygotes to be purple instead of green. What would be the expected distribution of offspring from a cross of a purple male with a green female (whose father was purple)?
Humans have 46 chromosomes where the OCA2 gene encoding eye colour is located on
chromosome 15. If we assume only 3 eye colours exist in the human population blue (b),
brown (B) and green (G), where green is recessive to brown but dominant to blue. What
Imagine a population of sloths in which lazy “hanging” behaviour is controlled by the H locus. HH and Hh individuals are extra lazy and will hang on the same trees all day, whereas hh individuals will occasionally move from one branch to another. You get to take a trip to a sloth sanctuary and after watching 500 sloths you count 250 HH, 100 Hh, and 150 hh individuals. What is the frequency of the h allele for this population?
Imagine that you are an alien scientist who has been asked to figure out why some aliens that have landed on Earth look the way they do. You an alien child that has green skin with scales, and you follow it until it grows up and mates with a similar alien with green skin and scales (assume the same genotype). After mating the parents give rise to many alien eggs which hatch into aliens with the following phenotypes:
21 green with scales, 7 blue with scales, 6 green without scales, and 2 blue without scales.
What can you conclude about the genetics surrounding alien skin appearance?
Imagine a set of genes that code for climbing speed of a sloth where there are slow, medium and fast climbers. The slow gene (S) and the fat (F) genes are the two loci that control climbing speed. If you produce a dihybrid cross of sloths from these two genes you get 9 slow, 3 medium and 4 fast.
What genotype would produce a sloth that climbs at medium speed?
You have identified 4 loci in the genome of a species of bird:
The B locus corresponds to wing colour where the colour black is dominant to brown.
The C locus corresponds to the number of feathers on the wings where lots of feathers is dominant to few feathers. But birds that are homozygous recessive at the B locus will always have few feathers.
You have identified 4 loci in the genome of a species of bird:
The B locus corresponds to wing colour where the colour black is dominant to brown.
The C locus corresponds to the number of feathers on the wings where lots of feathers is dominant to few feathers. But birds that are homozygous recessive at the B locus will always have few feathers.
You have identified 4 loci in the genome of a species of bird:
The B locus corresponds to wing colour where the colour black is dominant to brown.
The C locus corresponds to the number of feathers on the wings where lots of feathers is dominant to few feathers. But birds that are homozygous recessive at the B locus will always have few feathers.
If you cross two true-breeding lines of pigs, one is homozygous dominant; one is homozygous recessive, what will be the phenotype of the progeny?
Practice: Dihybrid Crosses
The sea slug has a pigmentation pathway where Gene B encodes an enzyme that creates blue pigment from a green substrate and Gene C encodes an enzyme that degrades all pigment cells causing slugs to be colourless. Homozygous recessive animals at either locus result in enzymes that are non-functional. If you were to mate two slugs, one with a blue pigment (Bbcc) and one that is colourless (BBCc) what would be the phenotypes of their offspring?
Practice: Epistasis
There are 2 genes in an alien species that have an epistatic interaction (meaning, one gene affects the expression of the other). Recessive alleles at the “bald” gene (bb) inhibit the expression of different alien antennae lengths (AL for long, AS for short and AN for no antennae where AL>AS>AN). Individuals who are homozygous recessive for the bald gene will show the AN phenotype regardless of their other antennae alleles. Individuals with at least one normal bald gene (B) express their antennae as expected from their genotype. If two parents are heterozygous for long antennae (ALAS) and heterozygous for the bald allele (Bb) mate, what is the probability that they have a child with no antennae?
To study inheritance, how was the F1 generation made during Mendel's monohybrid cross?
In the P generation of a dihybrid cross, what are the genotypes of the organisms being crossed?
What does the F1 generation consist of in successful monohybrid cross?
A Mendelian Dihybrid cross results in a phenotypic ratio of 9:3:3:1 in the F2 generation. What does this confirm?
In a successful Mendelian Monohybrid cross, what are the genotypes of the F1 and F2 generations?
Mendel's Dihybrid Cross (Practice Questions)
Mendel's Dihyrbid Cross Questions (Multiple Choice)
1. To test whether the alleles for apple size and colour sort dependently or independently, one homozygous dominant plant (BBRR = big & red) and one homozygous recessive plant (bbrr = small & green) are tested using a Mendelian Dihybrid cross. The resulting F2 generation supports the hypothesis of dependent assortment. Which of the following is correct regarding the F2 generation?
A - 75% of organisms have a small & green phenotype
You are examining a family in which both parents are known to be carriers for sickle cell anemia, which is a rare autosomal recessive disease with 2% of the population carrying the mutant allele. Their first child was born with the disease, and the parents have come to you to assess whether the new fetus is also diseased, is a carrier, or is homozygous normal. DNA samples from each family member and the fetus are tested by PCR and gel electrophoresis. The following results are obtained:
What is the probability that the child who will develop from this fetus will exhibit the disease?
When this child grows up and mates, what is the probability that any one of her children will be afflicted with the disease?
We are investigating the colour genes in a certain species of mice that generally have two colours (black and white). If you were to know that two genes (A and B) are responsible for those oculars and that A only produces the black colour in the absence of B. What is the proportion of black in the F2 given than P0 cross was AABB * aabb?
a) 1/2
b) 9/16
In the table below, six mutant types of drosophila flies are showed.
How many complementation groups are there?
Which mutations belong to which group?
Suppose that we are investigating five different traits in a type of tropical plants and we have two different species with identical genotypes: FfBbNnQqPp. If we test cross those two species of plants what is the probability of getting an offspring with all recessive traits?
How can we use reciprocal crosses to determine sex linkage using the following example:
In Drosophila, the gene for eye colour is found on the X-chromosome where having red eyes is dominant to having white eyes. What proportion of offspring will be
white eyed in the following crosses?
If you cross two true-breeding lines of pigs, one is homozygous dominant; one is
homozygous recessive, what will be the phenotype of the progeny?
The W allele in a flowering species gives rise to white plants and is dominant over the w
allele that gives rise to pink flowers. The T allele in this species gives rise to tall plants
while the t allele gives rise to short plants. What are the proportions of phenotypes
You cross two heterozygotes with the genotype AaRr, what is the proportion of
offspring that will have an AArr genotype?
Write the answer in the form of a fraction. For example if your answer is 3/4 enter the answer like that.
Practice: Genetic Inheritance 2
A team of scientists are looking into 5 different genes (A, B, C, D, E) responsible for 5 different traits in a rare species of wild rabbits. In case they cross a rabbit that is heterozygous for all 5 genes with another rabbit that has an identical genotype, what is the probability of having an offspring with the following genotype: AABbCCddEe
Practice: Genetic Inheritance 1
A true-breeding zebrafish with black stripes and a long tail fin was crossed with a true-breeding zebrafish with black spots and a short tail fin. The F1 all had black stripes and a long tail fin. The F1 were crossed with black spots and short tail fin.
The pair produced 1000 baby zebrafish. What are the possible phenotypes and how many babies with black spots and tall tail fin do you expect to see out of the 1000?
Use S and s to represent the body patterning alleles and T and t to represent the tail fin allele.
Genetic Inheritance: Cystic fibrosis
Cystic fibrosis is a recessive trait in humans. The gene that causes this disease is not located on the sex chromosomes. In a cross between a father who has cystic fibrosis and a mother who is heterozygous for the gene, what is the probability that their first three children will have the abnormal phenotype?