Mendel was an Austrian monk who taught natural science and worked on plant breeding experiments.

He developed a basic understanding of genetics and inheritance.

It took him 2 years to select the pea plant as his subject.

He collected data for 10 years.

His sample sizes were large; he tabulated results from 28,000 pea plants.

He replicated his experiments.

He analyzed his data with statistics (probability theory).

Characteristics of Garden Peas:

Peas are easy to grow, and take little space. 

They are inexpensive.

They have a short generation time compared to large animals so that a large number of offspring can be obtained in a short amount of time.

They have some distinct characteristics that are easy to recognize.  These characteristics can be used when trying to determine patterns of inheritance.

They are easily self-fertilized or cross fertilized.

smooth or wrinkled seeds

yellow or green seeds

red or white flowers

inflated or constricted pods

green or yellow pods

axial or terminal flowers

tall or dwarf plants

Mendel used pure-breeding individuals in the first (P₁) generation.

P₁    yellow X green

                  ¯

F₁        all yellow

                  ¯

F₂    3/4 yellow, 1/4 green

Conclusions from Mendel's Crosses

The F₁ generation showed only one character that was present in the P₁. The other character reappeared in the F₂ (25%).

The sex of the parent did not matter.

The traits did not blend.

Mendel concluded that the F₁ plants must contain 2 discrete factors, one for each character.  The character that was seen in the F₁ is called dominant.   The character not seen in the F₁ is called recessive.

The characteristics studied by Mendel were due to single genes. On the pair of chromosomes diagrammed below, the letter "A" represents a gene for yellow seeds. The letter "a" on the homologous chromosome represents a gene for green seeds. By convention, upper case letters are used to represent dominant genes and lower case letters are used for recessive genes.

Because individuals are diploid, two letters can be used to represent the genetic makeup of an individual. In the case of seed color, the following three gene combinations are possible: AA, Aa, and aa.

Heterozygote (also called hybrid) refers to an individual that has two different forms of the gene. Example: Aa 

Homozygote refers to an individual that has two identical genes. Example: AA or aa

A hybrid is a heterozygote. Example: Aa

The three diagrams below show metaphase I, anaphase I and telophase I in an "Aa" individual.

As can be seen in the diagrams, an "Aa" individual can produce gametes that have "A" and gametes that have "a".

	Metaphase 1
	Anaphase 1
	Telophase 1

Principle of Segregation

Mendel’s principle of segregation states that paired factors (genes) separate during gamete formation (meiosis). Because the pair of genes (Aa, AA, or aa) separate, one daughter cell will contain one gene and the other will contain the other gene. (See diagram above.)

Gametes

Because pairs of chromosomes separate during meiosis I, gametes are haploid, that is, they carry only one copy of each chromosome. An Aa individual therefore produces two kinds of gametes: A and a.

Below: An "AA" individual produces all "A" gametes. Similarly, an "aa" individual produces all "a" gametes.

Individual (genotype)	Type of gametes produced
AA	all gametes will contain an "A"
Aa	1/2 will contain "A" and 1/2 will contain "a"
aa	all "a" gametes

Suppose that an "Aa" individual is crossed with another "Aa" individual. One will produce "A" eggs and "a" eggs. The other will produce "A" sperm and "a" sperm. What are all of the possible combinations of eggs and sperm? A Punnett square can be used to show all of these combinations.

The Punnett square in the diagram below is used to show between two Aa individuals.

The square below is used for this cross: AA X Aa.

One half of the offspring produced by this cross will be AA, the other half will be Aa.

The cross can also be written as shown below because the AA parent can produce only one kind of gamete (all A).

A Closer look at Mendel’s Crosses (One Gene Locus)

Y = yellow y = green

P₁    YY X yy

            ¯

F₁       Yy

 

       Yy   X   Yy            ¬ A cross between two individuals that are heterozygous for a trait is called a monohybrid cross.

F₂  The above cross is illustrated below.

The genetic makeup of P₁ plants was different from that of F₁ because the P₁ plants were true breeding and the F₁ plants were not. The genetic makeup of an individual is referred to as its genotype. Because the plants are diploid, two letters can be used to write the genotype. In this case, the genotype of the P₁ plants was YY; the genotype of the F₁ plants was Yy.

The characteristics of an individual are its  phenotpye. This word refers to what the individual looks like so ddjectives are used to write the phenotype. For example, "yellow" or "tall" are phenotypes. The yellow P₁ plants looked like the F₁; they had the same phenotype but different genotypes.

An individual with a recessive phenotype has two recessive genes. A dominant phenotype results from either one or two dominant genes. In the cross above, YY or Yy are yellow; yy is green. The phenotype ratio in the F2 is 3 yellow:1 green. The genotype ratio is 1YY:2Yy:1yy.

Genotype	Phenotype
AA or Aa	Yellow
aa	Green

P₁    SS X ss

           ¯

F₁       Ss

       Ss X Ss

F₂ genotype ratio = 1:2:1 (1SS : 2Ss : 1ss)

phenotype ratio = 3:1 (3Smooth : 1 wrinkled)

F = full f = constricted

P₁    FF X ff

            ¯

F₁       Ff

       Ff X Ff

F₂ genotype ratio = 1:2:1 (1FF : 2Ff : 1ff)

phenotype ratio = 3:1 (3full: 1 constricted)

An allele is a gene that has more than one form. Each of the forms is referred to as an allele. For example, the gene for red flowers and the gene for white flowers are two different alleles.

A locus (plural: loci) is the location of a gene on a chromosome. The gene for red flowers and the gene for white flowers are two different alleles at the same locus.  A single chromosome can have a gene for white flowers or a gene for red flowers but not both.

There are two loci illustrated below, one is for flower color and the other is for stem length. Flower color has five alleles and stem length has two.

Let " A" represent the allele for yellow seeds and " a" represent the allele for green seeds. For each cross below, give the genotype of the gametes and the expected genotypes and phenotypes in the offspring.

Cross	Gametes 1st parent	Gametes 2nd parent	Genotypes	Phenotypes
AA X AA
AA X Aa
AA X aa
Aa X Aa
Aa X aa
aa X aa

Click here to view the answers.

Application

Sickle-cell anemia is an abnormality of hemoglobin, the molecule that carries oxygen in our blood. Red blood cells of affected individuals often become distorted in shape, they then may break down or clog blood vessels causing pain, poor circulation, jaundice, anemia, internal hemorrhaging, low resistance, and damage to internal organs.

This condition is caused by a recessive gene.

A = normal hemoglobin

a = sickle-cell hemoglobin

AA = normal

Aa = normal (called sickle-cell trait)

aa = sickle-cell anemia

A man with sickle-cell trait marries a normal woman. What is the probability that their children will have sickle-cell trait?

If both parents have sickle-cell trait, what percentage of their children will:

have a normal phenotype?

have sickle-cell trait?

have sickle-cell anemia?

let A = red

a = white

Is a red flower AA or Aa?

Solution: cross it with aa

P₁    A? X aa

The A? individual can produce these kinds of gametes: "A" and "?"

gametes: A, ? and a

F₁    Aa and ?a

If the ?a individual is red, then ? = A. If it is white, then ? = a.

The population model described above predicts that gene frequencies will not change from one generation to the next even if there are more recessive alleles.

There is sometimes a misconception among students beginning to study genetics that dominant traits are more common than recessive traits. Sometimes this is true, sometimes it is not. For some traits, the dominant is more common; for other traits, the recessive is more common. For example, blood type O is recessive and is the most common type of blood. Huntington's disease (a disease of the nervous system) is caused by a dominant gene and the normal gene is recessive. Fortunately, most people are recessive; the dominant is uncommon.

The misconception comes from the observation that in a cross of Aa X Aa, 3/4 of the offspring will show the dominant characteristic. However, the 3:1 ratio comes only if the parents are both Aa. If there are many recessive genes in a population, then most matings are likely to be aa X aa and most offspring will be aa. 

In nature, natural selection may favor one- either the dominant or the recessive- and that one will become more common over time. Other forces such as genetic drift may also cause one or the other allele to become more common. In the absence of forces that change gene frequencies, there is no reason to expect dominant genes to be more common. 

Probability

The probability of two or more independent events occurring is equal to the product of their probabilities.

Example: What is the probability of tossing a coin two times and getting a heads both times? 

Solution: The probability of getting a heads on one coin is 1/2. The probability of getting a heads on the second coin does not depend on the outcome of the first coin, so the multiplicative rule is used. The probability of getting a heads on two coins is 1/2 X 1/2 = 1/4.

The probability of two or more mutually exclusive events occurring is equal to the sum of their probabilities.

What is the probability that a student will get an “A” or a “B” in a class if students generally earn the following grades:

A = 10% (or 0.10)

B = 35% (or 0.35)

C = 45%

D = 10%

Solution: In this example, the two outcomes (getting an "A" or getting a "B") are mutually exclusive because you can only get one or the other. The additive rule is used to determine the overall probability of getting an "A" or a "B". 10% + 35% = 45% (or 0.10 + 0.35 = 0.45).

Genes that are on different chromosomes assort independently. The following are four different metaphase I allignment patterns that are possible for a hypothetical species with a diploid chromosome number of 6.

The alignment pattern shown in the diagram below will produce Sy and sY gametes.

The alignment pattern shown in this diagram will produce SY and sy gametes.

Both of the patterns illustrated above are possible because S and Y are located on different chromosomes.

Possible Gametes for Several Different Genotypes

The table below shows the kinds of gametes that can be produced by several different kinds of genotypes. Each gene locus (A and B) is on a different chromosome.

Individual	Gametes
AABB	AB
AABb	AB, Ab
AaBB	AB, aB
AaBb	AB, Ab, aB, ab
Aabb	Ab, ab
AAbb	Ab
aaBB	aB
aaBb	aB, ab
aabb	ab

Genotypes and Phenotypes

let A = red, a = white

let B = smooth, b = wrinkled

The table below shows possible genotypes and phenotypes.

Genotype	Phenotype
AABB	red, smooth
AABb	red, smooth
AaBB	red, smooth
AaBb	red, smooth
Aabb	red, wrinkled
AAbb	red, wrinkled
aaBB	white, smooth
aaBb	white, smooth
aabb	white, wrinkled

Linkage

In peas, the locus for seed texture (smooth or wrinkled) and seed color (yellow or green) are on two different chromosomes so they assort independently.

Suppose that they are on the same chromosome as indicated in the diagram below. Independent assortment will not occur because the "S" gene is on the same chromosome as the "y" gene. Similarly, the "s" gene is on the same chromosome as the "Y" gene. Unless crossing-over occurs, "S" will always be found with a "y" and "s" will be found if there is a "Y".

Mendel studied seven different characteristics in peas. Each of these characteristics are on different chromosomes, so they assort independently.

Let S = smooth, s = wrinkled

Let Y = yellow, y = green

 

P₁ SMOOTH, YELLOW X wrinkled, green

genotypes: SSYY ssyy

gametes: SY sy

                    ¯

F₁ SMOOTH, YELLOW X SMOOTH YELLOW

genotypes: SsYy  X  SsYy  ¬ A cross between two individuals that are heterozygous for two gene loci is called a dihybrid cross.

gametes: SY, Sy, sY, sy

          ¯

F₂

Mendel's Results

SMOOTH, YELLOW	315
SMOOTH, green	108
wrinkled, YELLOW	101
wrinkled, green	32
	556

TRAIT 1, TRAIT 2 X trait 1, trait 2         (upper case traits are dominant)

9 - TRAIT 1 and TRAIT 2 expressed (A-B-)

3 - TRAIT 1 expressed (A-bb)

3 - TRAIT 2 expressed (aaB-)

1 - No dominant traits expressed (all aabb)

Remember that each of the individual traits in the dihybrid cross above behaves as a monohybrid cross, that is, they will produce a 3:1 phenotype ratio in the offspring.

SMOOTH X wrinkled

Refer to the F₂ data for the SMOOTH, YELLOW X wrinkled, green cross above.

The number of smooth offspring was 315 + 108 = 423.

The number of wrinkled was 101 + 32 = 133.

The ratio of smooth to wrinkled is therefore 423:133 or approximately 3:1.

YELLOW X green

yellow = 315 + 101 = 416

green = 108 + 32 = 140

ratio = 416:140 or approximately 3:1

9:3:3:1 can be obtained in a dihybrid cross by first calculating probabilities for two monohybrid crosses and then combining their probabilities.

probability of round = 3/4

probability of wrinkled = 1/4

probability of yellow = 3/4

probability of green = 1/4

 

probability of round and yellow = 3/4 X 3/4 = 9/16

probability of round and green = 3/4 X 1/4 = 3/16

probability of wrinkled and yellow = 1/4 X 3/4 = 3/16

probability of wrinkled and green = 1/4 X 1/4 = 1/16

Other Crosses

The following steps can be used to determine the expected number of offspring from any cross.

1. Determine the kinds of gametes that can be produced by each parent.

2. Determine all of the possible combinations of gametes that can be produced. A Punnett square may be useful for this. 

If you use a Punnett square, the gametes of one parent are written across the top and the gametes of the other parent written on one side. The number of cells in the square is therefore equal to the number of gametes that one parent can produce multiplied by the number of gametes that the other parent can produce.

Example: 

Let T = tall, t = short

      F = inflated, f = constricted

List the phenotypes produced by the following cross:

TtFf    X    ttFf

Step 1: List the kind of gametes produced by each parent.

TtFf can produced TF, Tf, tF and tf.

ttFf can produce tF and tf.

Step 2: Construct a Punnett square.

The Punnett square above shows that eight different genotypes are produced. The phenotype for each is listed in the table below.

Genotype	Phenotype
tTFF, tTFf, tTfF	tall, inflated
tTff	tall constricted
ttFF, ttFf, ttfF	short inflated
ttff	short, constricted

Y = yellow            R = red

y = green             r = white

What is the genotype of a plant with yellow seeds and red flowers?

In the cross below, the symbols "-" and "?" represent unknown alleles.  "-" is either "Y" or "y".  "?" is either "R" or "r".

The genotype of a plant with yellow seeds and red flowers is "Y-R?".

Cross it with yyrr to find out the "-" and "?" alleles.

Y-R? X yyrr

gametes: YR, Y?, -R, -? (parent 1) and yr (parent 2)

If the unknown alleles (- and ?) are recessive, the phenotype ratio will be 1:1:1:1.

Incomplete (Partial) Dominance

In the cases that are discussed above, blending does not occur. Flowers are either red or white but are never pink. Seeds are either yellow or green but not yellowish-green. In these cases, if a dominant gene is present, it is expressed. Some genes, however are neither dominant nor recessive and when mixed, blending occurs. 

Example: Snapdragons
A = Red flowers        A' = white flowers

A heterozygote (AA') is pink.

Up to this point, we have discussed two possible alleles for any gene locus.  For example, at the flower color locus, there is either the red or the white allele (A or a).  With human blood types, there are three alleles: A, B, or O.  This is referred to as multiple alleles.

I is dominant to i.

There are two forms of I: I^A and I^B but only one form of i.

6 possible genotypes, 4 phenotypes:

I^AI^A and I^Ai = blood type A

I^BI^B and I^Bi = blood type B

I^AI^B = blood type AB

i i = blood type O

People with blood type A have a specific kind of carbohydrate chain on the surface of their red blood cell. The carbohydrate chain is attached to a membrane protein or lipid. Blood type B cells have have a different carbohydrate chain. Type AB cells have both A and B chains. I^A and I^B are codominant because both phenotypes are expressed; there is no blending

Codominance is different than Incomplete dominance (blending).

Genes that affect more than one trait are called pleiotropic.

For example, people with Marfan syndrome may be tall, thin, have long legs, arms and fingers, and may be nearsighted.  Their connective tissue is defective. If unrepaired, the connective tissue surrounding the aorta will eventually rupture and kill the person.  All of these characteristics are due to a single gene.

Alleles at one locus prevent the expression of alleles at another locus. This interaction is referred to as epistasis.

Example: Flower color in peas

                    enzyme 1                        enzyme 2

                    AA or Aa                         BB or Bb

compound A ¾ ¾ ¾ ® compound B ¾ ¾ ¾ ® red pigment

An individual with AA or Aa genotypes will have red flowers. AA or Aa individuals could have white flowers if the individual also has a "bb" genotype (example: AAbb). In this case, the locus for enzyme 2 prevents the expresson of the locus for enzyme 1.

sometimes an allele is expressed differently if it is inherited from the mother than if it is inherited from the father.

Example: Huntington's disease is expressed earlier if inherited from the father.

The symptoms of Huntington's disease are caused by a slow deterioration of brain cells that begins at middle age. It is characterized by involuntary jerking movements of the body including facial muscles and slurred speech. Later, there is difficulty swallowing, loss of balance, mood swings, impaired reasoning, and memory loss. The person eventually dies, usually to pneumonia or heart failure.

A polygenic trait is due to more than one gene locus. It involves active and inactive alleles.

Active alleles function additively.

Height (tallness) in humans is polygenic but the mechanism of gene function or the number of genes involved is unknown.

Suppose that there are 3 loci with 2 alleles per locus (A, a, B, b, C, c).

Assume that:

Each active allele (upper case letters: A, B, or C) adds 3 inches of height.

The effect of each active allele is equal, A = B = C.

Males (aabbcc) are 5' tall.

Females (aabbcc) are 4'7".

Genotype	Males	Females
aabbcc	5'0"	4'7"
Aabbcc (or aaBbcc etc.)	5'3"	4'10"
AaBbcc etc.	5'6"	5'1"
AaBbCc etc.	5'9"	5'4"
AaBbCC etc.	6'0"	5'7"
AaBBCC etc.	6'3"	5'10"
AABBCC	6'6"	6'1"

The following is a cross between two people of intermediate height.

AaBbCc X AaBbCc

If there is independent assortment, the following gametes will be produced in equal numbers:

ABC, ABc, AbC, aBC, abC, aBc, Abc, abc

Punnett square analysis:

The Punnett square above can be summarized as follows:

Genotype	Males	Females	Frequency
AABBCC	6'6"	6'1"	1/64
AaBBCC etc.	6'3"	5'10"	6/64
AaBbCC etc.	6'0"	5'7"	15/64
AaBbCc etc.	5'9"	5'4"	20/64
AaBbcc etc.	5'6"	5'1"	15/64
Aabbcc etc.	5'3"	4'10"	6/64
aabbcc	5'0"	4'7"	1/64

The frequency column in the table above can be plotted to produce the graph below.

Variability results in a bell-shaped curve (see the diagram above).

Traits with many loci produce many categories. In the example above, 3 loci produced 7 possible heights because a person could have anywhere from 0 to 6 active alleles. If a trait were determined by 4 loci (AABBCCDD for example) there would be 9 possible categories because a person could have anywhere from 0 to 8 active alleles.

Variability in polygenic traits can result from genetics and also from the environment. A measure of the relative contribution of genetics is called heritability.

A trait with a high heritability is determined mostly by genes. A trait with a low heritability is determined mostly by the environment.

For example, skin pigmentation (darkness) is determined by 2 or 3 pairs of alleles, but exposure to sunlight (UV radiation) also causes the skin to darken due to the deposition of protective pigments.

stature

performance on IQ tests

skin color

neural tube defects (spina bifida, anencephaly)

cleft lip/palate