High School
SAT
ACT
University
MCAT
LSAT
DAT
Wize University Biology Textbook > Mendelian Genetics

History of Genetics and Laws of Probability

Meiosis IIPrevious Section
Genotype and PhenotypeNext Section
Popular Courses
Find My Course
0:00 / 0:00

History of Mendelian Genetics

  • Gregor Mendel (1822-1884) was a pioneer in the study of genetics.
  • Laws of inheritance derived by hybridization experiments using garden peas.
  • Hybridization is the interbreeding between two different varieties of an organism.
  • Mendel followed a small number of easily recognizable traits.



  • Mendel's strains were true breeding, meaning that the offspring's physical appearance is identical to that of the previous generation. Example: Plants with yellow seeds only produce plants with yellow seeds, plants with purple flowers only produce plants with purple flowers, etc.

PAGE BREAK

Mendel's Objective

His approach was to cross true-breeding strains and cross their progeny to identify any statistical patterns in the frequency of the seven traits. Mendel's approaches differed from other scientist in three important ways:
  1. The use of true breeding strains rather than complicated and poorly characterized ones.
  2. A test cross occurs when you breed an organism with one that is homozygous recessive.
  3. Focusing on just one or a few traits at a time.
  4. The counting of progeny and looking for statistical patterns.
  • P1 Generation: refers to the parental generation.
  • F1 Generation: refers to the first offspring generation.


0:00 / 0:00

Basics of Probability for Genetics

Genetics can involve calculating a lot of probabilities. Following are a couple of rules that might help you along the way.

The Product Rule

For interdependent events X and Y, the probability P of them both occurring (X and Y) is the product of the two individual probabilities (PX x PY).

Example: What is the probability that you will get two heads consecutively when flipping a coin?

The probability of getting heads for a regular coin is 1/2 (equal to the probability of getting tails).

Two get two heads in a row, you need the first head (PH,1st = 1/2) and also another head (PH,2nd = 1/2).
Therefore: [ PH,1st x PH,2nd ] = [ 1/2 x 1/2 ] = 1/4


The Sum Rule

For mutually exclusive events X and Y, the probability P that at least one occurs (X or Y) is the sum of the two probabilities (PX + PY) that each individual event will occur.

Example: You're flipping two different coins (coin 1 and coin 2). What is the probability that you will get heads in one coin and tail in the other?

This can be achieved in two ways: coin 1 is heads and coin 2 is tails OR coin 1 is tails, and coin 2 is heads. These two events are mutually exclusive. So:

Probability heads coin 1 = PH1 = 1/2
Probability tails coin 2 = PT2 = 1/2
Similarly for the opposite scenario.

Therefore: [ PH1 x PT2 ] + [ PH2 x PT1 ] = [ 1/2 x 1/2 ] + [ 1/2 x 1/2 ] = 1/2

0:00 / 0:00

Product Rule in Genetics


In a cross between two flowers of the same genotype AaBb, where gene A encodes for one characteristic and gene B for another. Capital letter (A or B) represents the dominant allele, such that AA or Aa will produce the same effect. Calculate the probability of having aabb offspring. (Note: the probability of getting aa is 1/4 and the probability of getting bb is also 1/4).

If you know about Punnett square already you should be able to calculate that Aa x Aa = 1 AA, 2 Aa and 1 aa, so overall aa = 1/4 of the possibilities. This is the exact same for the B gene.

Therefore, in order to get both: Paa x Pbb = 1/4 x 1/4 = 1/16
0:00 / 0:00

Example: Sum Rule in Genetics

Both parents have a "Bb" genotype. What is the probability of the offspring having the dominant phenotype?

Offspring showing the dominant phenotype could be BB OR Bb, so we need to use the sum rule. What are the possible ways we could get offspring with the dominant phenotype?

1. Mother contributes B allele and father contributes b allele (offspring are Bb), OR
2. Mother contributes b allele and father contributes B allele (offspring are bB), OR
3. Both mother and father contribute B allele (offspring are BB).

These three events are mutually exclusive, because only one fertilization even can occur at a time. The probability of each of the above events is 1/4 (we can determine this using the product rule). To determine the probability of the offspring with the dominant phenotype, we add the three individual probabilities together:

(1/4) + (1/4) + (1/4) = 3/4

Practice: Probability in Genetics

Both parents have the genotype Bb. What is the probability of offspring showing the recessive phenotype?
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?
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
A young couple has undergone a successful in vitro fertilization procedure. The father has cystic fibrosis and the mother has a sister with cystic fibrosis. Both of these affected individuals have ~F508 mutations. Before making the decision to conceive, the couple underwent extensive genetic counseling regarding the potential risks of having a child with cystic fibrosis. However, the mother refused prenatal screening for CF as it would not affect the decision to raise their child. The family pedigree is diagrammed below with the unborn child
marked by the red arrow.
What is the chance that this child will have cystic fibrosis?
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?
In order for a recessive trait to be expressed you would need ____ allele(s) to be recessive.
Assume the following monohybrid crosses where for a particular gene, A represents the dominant allele and a, the recessive allele which show complete dominance.
What are Gregor Mendel’s two laws of inheritance?
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.
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.
A trait that is an evolutionary innovation is called
derived
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.
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?
Which of the following is not part of Mendel’s model?
To study inheritance, how was the F1 generation made during Mendel's monohybrid cross?
If Mendelian genetics apply and independent assortment is true, what is the probability of a genetically and phenotypically recessive organism in the F2 generation of a dihybrid cross?
Which of the following is not part of Mendel’s Model?
If the F2 generation of a dihybrid cross displaying independent assortment consists of 16 organisms, how many organisms display the dominant phenotype for both characters being considered?
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
Mendel's Monohybrid Cross (Practice Questions)
Mendel's Monohybrid Cross Questions (Multiple Choice)
1. The sole gene determining size of the dill plant is controlled by one gene represented by the alleles D (large) and d (small), with the D (large) allele being dominant. If Mendelian Genetics apply, how many plants in the F2 generation will be homozygous after a monohybrid cross?
A - 0
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
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?
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
A young couple has undergone a successful in vitro fertilization procedure. The father has cystic fibrosis and the mother has a sister with cystic fibrosis. Both of these affected individuals have ~F508 mutations. Before making the decision to conceive, the couple underwent extensive genetic counseling regarding the potential risks of having a child with cystic fibrosis. However, the mother refused prenatal screening for CF as it would not affect the decision to raise their child. The family pedigree is diagrammed below with the unborn child
marked by the red arrow.
What is the chance that this child will have cystic fibrosis?
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?