EVOLUTION:Molecular Genetics

Biology 11 Enriched

Mendelian GeneticsTuesday, December 4th,2 012

Introduction

Human have observed changes in population for many centuries. Humans have domesticated animals and

plants and have artificially selected for various traits in our livestock and crops.

Character – an observable physical feature

Trait – a particular form of a character

Introduction

In the 19th Century, 2 theories on how traits are passed on from one generation to the next:1. THEORY OF BLENDING

INHERITANCE2. THEORY OF PARTICULATE

INHERITANCE

19th Century theories on inheritance

BLENDING INHERITANCE That “hereditary

determinants” (genes) were found in gametes

Physical traits from both parents are blended and the offspring will exhibit an intermediate trait between the two.

PARTICULATE INHERITANCE That both

hereditary determinants remain in fertilized zygote.

Both parental traits will be exhibited in the offspring.

Gregor Mendel

He studied biology, physics, and mathematics  

Developed the fundamental laws of heredity Took some ideas from blended

model and particulate model

Mendel chose garden peas (Pisum sativum) as his subjects as they are easily grown and their pollination is easily controlled. He controlled pollination by

manually moving pollen between plants 

Funfact: Mendel originally wanted to breed mice, but wasn't allowed to because it was considered scandalous

Gregor Mendel

Pea flowers have both male and female sex organs so Mendel was able to developed “true-breeding” plants by self-pollination.

Mendel examined varieties of peas for inheritable characters and traits for his study. (stem length, pod shape, seed shape, seed color, etc.) 

Gregor Mendel

In 1865, Mendel published his findings in a paper called Experiments on Plant Hybridization, which was mostly ignored at the time due to a number of reasons. First, Mendel was not well known in

scientific community. Second, his theory ran against the popular

model of blended inheritance.

Mendel’s Three Laws of Inheritance

Mendel’s Three Laws1. Law of Dominance2. Law of Segregation3. Law of Independent

Assortment

Monohybrid Cross

A monohybrid cross involves one (mono) character and different (hybrid) traits.

Mendel crossed a parental generation with 2 different traits of the same character (in this example, flower color) The F1 seeds were all purple The white flower trait failed to

appear at all. There was also no “blending” of

colors

Monohybrid Cross

Mendel then took purple flowers from the F1 generation and allowed them to self-fertilize.

The flowers in the F2 generation showed a 3:1 ratio of purple:white flowers

Monohybrid Cross

The purple trait completely masks the white trait when true-breeding plants are crossed the purple flower trait

is called dominant the white flower trait is

called recessive. The Law of Dominance

Monohybrid Cross

When Mendel repeated the procedure but for other characters and traits, he would observe a F1 generation with only 1 trait and the 3:1 ratio in the F2 generation.

Mendel’s Conclusion / Law of Segregation

The Law of Segregation Mendel concluded that each gamete

must hold 1 copy of a gene and the zygote will hold 2 copies (1 from each parent) Character = genes traits = alleles of the gene.

But why that 3:1 ratio?

Why 3:1 Ratio?

An organism has 2 alleles of a gene (1 from each parent). If both alleles are the same

homozygous If alleles are different heterozygous

Let’s assign the each allele a letter/symbol.P = purple p = white

Why 3:1 Ratio?

BY CONVENTION:

The dominant trait is given a capital letter, the lowercase of that same letter is the recessive trait.  DO NOT MIX LETTERS.  Pick one and stick to it.

Also, some letters are better than others.  Capital S looks a lot like a lowercase (s).  Pick a different letter...

Okay                                     Better (use H for hair)

Short  hair  = SS                                 HHShort hair = Ss                                  HhLong hair = ss hh 

Why 3:1 Ratio?

Both parents are homozygous.

Generation

ParentalGenotype PP x ppPhenotype

Purple x white

Why 3:1 Ratio?

We can use a Punnett Square to show us the allele combinations

Genotype

Male gametes

P P

Female

gametes

p Pp Pp

p Pp Pp

All offspring in the F1 generation are heterozygous dominant

Why 3:1 Ratio?

In his experiment, he then crossed the F1 generation to produce F2 generation

Genotype

Male gametes

P p

Female

gametes

P PP Pp

p Pp pp

3 out of 4 are purple• 1 is

homozygous• 2 are

heterozygous

1 out 4 is white• Homozygous

recessive

Why 3:1 Ratio?

Practice picking letters.... the following traits are found in the common Shirtus canadianus.1. Polka dots are dominant to stripes.

2. Long sleeves are dominant to short sleeves.

3. Collared shirts are recessive.

4. Buttons are dominant over snaps.

5. Pockets are recessive.   

Practice with Punnett Squares

1. A  round seeded plant (RR) is crossed with a wrinkle seeded plant (rr).  What are the phenotypes of the offspring?

2. Two heterozygous purple flowered pea plants are crossed.  What are the phenotypes of their offspring and in what proportion?

3. A plant with green seeds (yy) is crossed with a heterozygous plant.  What percentage of their offspring have yellow seeds?

In dragons...wings are a dominant trait, but some dragons are born wingless.

1. What are the chances that two heterozygous dragons have a whelp that is wingless?

2. If a wingless dragon is crossed with one that is heterozygous, how many of its offspring will also be wingless?

What is a Test cross?

Help, help!  I don't know what my genotype is!!

Am I Dd or DD?

I can help you!  Let's have offspring!

D = wingedd = wingless

What is a Test Cross?

Because we know wingless dragons are homozygous recessive, we can breed wingless dragons with a winged dragon. By looking at the ratios, we can tell if the winged

dragon is homozygous or heterozygous

• If female dragon is PP then 100% heterozygous winged dragons

Genotype

Male gametes

p p

Female gametes

P Pp Pp

P Pp Pp

What is a Test Cross?

If female dragon is Pp then a 1:1 ratio is observed.

Genotype

Male gametes

p p

Female gametes

P Pp Pp

p pp pp

Dihybrid Cross

Mendel's Law of Independent Assortment is illustrated by the dihybrid cross The second law describes the outcome of dihybrid

(two character) crosses, or hybrid crosses involving additional characters.▪ A dihybrid is an individual that is a double

heterozygote (e.g., with the genotype RrYy - round seed, yellow seed).R = round/r = bumpy, Y = yellow/y = green

▪ What are the gametes that can be produced by an individual that is RrYy?

▪RY, Ry, rY, ry

Dihybrid Cross (RrYy x RrYy)

RY Ry rY ry

RYRRYY

round, yellow

RRYyround, yellow

RrYYround, yellow

RyYyround, yellow

RyRRYy

round, yellow

RRyyround, green

RrYyround, yellow

Rryyround, green

rYRrYY

round, yellow

RrYyround, yellow

rrYYbumpy, yellow

rrYybumpy, yellow

ryRrYy

round, yellow

Rryyround, green

rrYybumpy, yellow

rryybumpy, green

Dihybrid Cross

The ratio that is seen is a 9:3:3:1 ratio a total of 4 phenotypes are

observed:▪ 9 round, yellow▪ 3 round, green▪ 3 bumpy, yellow▪ 1 bumpy, green (double recessive)

Dihybrid Cross – Practice

You have 30 minutes to complete as much of this package as you can.

At 2:20, we are moving to notes.

Probability and Inheritance

A Punnet Square for a dihybrid cross is pretty epic! a Punnett Square is helpful for 1 or 2

genes but a little troublesome for more characters▪ A trihybrid cross needs 64 boxes▪ A tetrahybrid cross needs 256 boxes▪ TOO MUCH EPIC!

Probability and Inheritance

Mendel’s laws of segregation and independent assortment reflect the rules of probability

Probability and Inheritance

Remember that the alleles of different (and unlinked) traits ending up in a gamete is independent of the chances of other alleles.

To find the probability of an series of INDEPENDENT events happening together, the individual probabilities of the events are multiplied together:

P(A and B) = P(A) x P(B)

Probability and Inheritance

If an event is absolutely certain to happen, its probability is 1.

If it cannot possibly happen, its probability is 0.

All other events have a probability between 0 and 1.

Probability and Inheritance

An example of independent events is the flipping of a coin.

Each flip of a coin is independent from the previous or next flips. They don’t influence each other.

Probability and Inheritance

P(A and B) = P(A) x P(B)

What is the probability of getting 5 “tails” in a row?

If P(tails) = 0.5 (or ½)

P(5 tails) = ½ x ½ x ½ x ½ x ½ = 1/32 or 0.03125 (never use

%)

Rr RrSegregation of

alleles into eggs

Sperm

Segregation ofalleles into sperm

Eggs

R

R

R RR

R rrr

r

r

r1/2

1/2

1/2

1/2

1/41/4

1/41/4

Heads ¼ + ¼ + ¼ = ¾

Tails1/4

Probability and Inheritance We used the rule of multiplication to find

the probability of a certain genotype. We used the rule of addition to find the

probability of a certain phenotype.

In calculating the chances for various genotypes, each character is considered separately, and then the individual probabilities are multiplied together

Calculate the probability that an F2 seed will be spherical and yellow.

Remember, calculate each trait separately. (create 2 monohybrid squares rather than 1 dihybrid square)

P(yellow,round) = ¾ yellow x ¾ round = 9/16

P(yellow, wrinkled) = ¾ yellow x ¼ wrinkled = 3/16P(green, round) = ¼ green x ¾ round = 3/16P(green,wrinkled) = ¼ green x ¼ wrinkled = 1/16

A 9:3:3:1 ratio!!

For any gene with a dominant allele A and recessiveallele a, what proportions of the offspring from anAA x Aa cross are expected to be homozygous dominant, homozygous recessive, and heterozygous?

Two organisms, with genotypes BbDD and BBDd are mated. Assuming independent assortment of the B/b and D/d genes, write the genotypes of all possible offspring from this cross and use the rules of probability to calculate the chance of each genotype occurring.

Three characters (flower color, seed color, and pod shape) are considered in a cross between two pea plants (PpYyIi x ppYyii).

What fraction of offspring are predicted to be homozygous recessive for at least two of the three characters?

Three characters (flower color, seed color, and pod shape) are considered in a cross between two pea plants (PpYyIi x ppYyii).

What fraction of offspring are predicted to be homozygous recessive for at least two of the three characters?P p

pPp (1/4)

pp (1/4)

pPp (1/4)

pp (1/4)

Pp = ¼ + ¼ = ½pp = ¼ + ¼ = ½

Y y

YYY(1/4)

Yy (1/4)

yYy (1/4)

Yy (1/4)

YY = ¼Yy = ¼ + ¼ = ½yy = ¼

I i

iIi (1/4)

ii (1/4)

iIi (1/4)

ii (1/4)Ii = ¼ + ¼ = ½

ii = ¼ + ¼ = ½

Inheritance patterns are often more complex than predicted by simple Mendelian genetics

Extension on Mendel

The relationship between genotype and phenotype is rarely as simple as in the pea plant characters Mendel studied Many heritable characters are not

determined by only 1 gene with 2 alleles.

However, the basic principles of segregation and independent assortment apply even to more complex patterns of inheritance

Extending Mendelian Genetics for a Single Gene

Inheritance of characters by a single gene may deviate from simple Mendelian patterns in the following situations: When alleles are not completely

dominant or recessive When a gene has more than two

alleles When a gene produces multiple

phenotypes

Degrees of Dominance

1. Complete dominance occurs when phenotypes of the heterozygote and dominant homozygote are identical

2. In incomplete dominance, the phenotype of F1 hybrids is somewhere between the phenotypes of the two parental varieties

3. In codominance, two dominant alleles affect the phenotype in separate, distinguishable ways

Fig. 14-10-1

Red

P Generation

Gametes

WhiteCRCR CWCW

CR CW

Fig. 14-10-2

Red

P Generation

Gametes

WhiteCRCR CWCW

CR CW

F1 GenerationPinkCRCW

CR CWGametes 1/21/2

Fig. 14-10-3

Red

P Generation

Gametes

WhiteCRCR CWCW

CR CW

F1 GenerationPinkCRCW

CR CWGametes 1/21/2

F2 Generation

Sperm

Eggs

CR

CR

CW

CW

CRCR CRCW

CRCW CWCW

1/21/2

1/2

1/2

Frequency of Dominant Alleles

Dominant alleles are not necessarily more common in populations than recessive alleles For example, one baby out of 400 in the

United States is born with extra fingers or toes▪ The allele for this unusual trait is dominant to

the allele for the more common trait of five digits per appendage▪ In this example, the recessive allele is far more

prevalent than the population’s dominant allele

Multiple Alleles

Most genes exist in populations in more than 2 allelic forms

For example, blood typesThe 4 blood types are: Type A Type B Type AB Type O

Multiple Alleles: Blood Types

the 4 phenotypes of the ABO

blood group in humans are

determined by 3 alleles for

the enzyme (I) that attaches

A or B carbohydrates to red

blood cells: IA, IB, and i. A alleles = Carbohydrate A

B alleles = Carbohydrate B

i alleles = no carbohydrates

IA

IB

i

A

B

none(a) The three alleles for the ABO blood groups and their associated carbohydrates

Allele Carbohydrate

GenotypeRed blood cell

appearancePhenotype

(blood group)

IAIA or IA i A

BIBIB or IB i

IAIB AB

ii O

(b) Blood group genotypes and phenotypes

Blood types is also an example of codominance.

Pleiotropy

Most genes have multiple phenotypic effects a property called pleiotropy For example, pleiotropic alleles are

responsible for the multiple symptoms of certain hereditary diseases, such as cystic fibrosis and sickle-cell disease

Extending Mendelian Genetics for Two or More Genes

Some traits may be determined by two or more genes

Epistasis

In epistasis, a gene at one locus alters the phenotypic expression of a gene at a 2nd locus For example, in mice and many other

mammals, coat color depends on two genes▪ One gene determines the pigment color

(BB/Bb = black & bb = brown)▪ The other gene determines whether the pigment

will be deposited in the hair(CC/Cc = color & cc = no color)

Fig. 14-12

BbCc BbCc

Sperm

EggsBC bC Bc bc

BC

bC

Bc

bc

BBCC

1/41/4

1/41/4

1/4

1/4

1/4

1/4

BbCC BBCc BbCc

BbCC bbCC BbCc bbCc

BBCc BbCc

BbCc bbCc

BBcc Bbcc

Bbcc bbcc

9 : 3 : 4

Polygenic Inheritance

Quantitative characters are those that vary in the population along a continuum/spectrum Quantitative variation usually indicates

polygenic inheritance, an additive effect of two or more genes on a single phenotype

Fig. 14-13

Eggs

Sperm

Phenotypes:

Number ofdark-skin alleles: 0 1 2 3 4 5 6

1/646/64

15/6420/64

15/646/64

1/64

1/8

1/8

1/8

1/8

1/8

1/8

1/8

1/8

1/81/8

1/81/8

1/81/8

1/81/8

AaBbCc AaBbCc

Skin color in humans is an example of polygenic inheritance

Nature and Nurture: The Environmental Impact on Phenotype

Another departure from Mendelian genetics arises when the phenotype for a character depends on environment AND genotype The norm of reaction is the phenotypic

range of a genotype influenced by the environment

Fig. 14-14

For example, hydrangea flowers of the same genotype range from blue-violet to pink, depending on soil acidity

Nature and Nurture

An organism’s phenotype includes its: physical appearance internal anatomy physiology behavior

An organism’s phenotype reflects its overall genotype and unique environmental history

Gene Linkage

Some genes do not sort independently They are often inherited together

because they are on the same chromosome.

Gene Linkage

New allele combinations can be produced if chromosomes cross-over during meiosis Recombinant

chromosomes and gametes are produced

Sex-Linkage

Females: XX Males: XY

Some genes are found only on the X chromosome. Because males are heterogametic (X

and Y) and hemizygous (only 1 X), whatever genes are on the X chromosome will be expressed

Sex Linkage – Color blindness The gene for seeing color has 2

alleles: B and b. The loci for this gene is on the X chromosome

Genotype Phenotype

XBXB Color

XBXbColor / carrier for color blindness

XbXb Color-blind

Genotype Phenotype

XBY Color

XbY Color-blind

Mendelian Genetics and Humans

Humans are not good subjects for genetic research Generation time is too long Parents produce relatively few

offspring Breeding experiments are

unacceptable

However, basic Mendelian genetics endures as the foundation of human genetics

Pedigree Analysis

A pedigree is a family tree that describes the interrelationships of parents and children across generations

Pedigree analysis allows us to figure out whether an allele controlling a particular phenotype is dominant or recessive.

KeyMale

Female

AffectedmaleAffectedfemale

Mating

Offspring, inbirth order(first-born on left)

1st generation(grandparents)

2nd generation(parents, aunts,and uncles)

3rd generation(two sisters)

Ww ww ww Ww

Ww ww wwWw Ww ww

ww

Ww

WWor

Widow’s peak No widow’s peak(a) Is a widow’s peak a dominant or recessive trait?

1st generation(grandparents)

2nd generation(parents, aunts,and uncles)

3rd generation(two sisters)

Ff Ff Ff

Ff FfFfFF or ff ff

ff

ff

ff FForFf

Attached earlobe Free earlobe

(b) Is an attached earlobe a dominant or recessive trait?

Dominant or Recessive?

Dominant trait:Every affected individual (G2) has

an affected parent (G1)About ½ of offspring (G3) are

affected

Fig. 14-15a

KeyMale

Female

AffectedmaleAffectedfemale

Mating

Offspring, inbirth order(first-born on left)

Fig. 14-15b

1st generation(grandparents)

2nd generation(parents, aunts,and uncles)

3rd generation(two sisters)

Widow’s peak No widow’s peak

(a) Is a widow’s peak a dominant or recessive trait?

Ww ww

Ww Wwww ww

ww

wwWw

Ww

wwWW

Wwor

Dominant or Recessive?

Recessive trait:Affected people have parents that

are not affected (skip generations)

Fig. 14-15c

Attached earlobe

1st generation(grandparents)

2nd generation(parents, aunts,and uncles)

3rd generation(two sisters)

Free earlobe

(b) Is an attached earlobe a dominant or recessive trait?

Ff Ff

Ff Ff Ff

ff Ff

ff ff ff

ff

FF or

orFF

Ff

Pedigree Analysis

Pedigrees can also be used to make predictions about future offspring

We can use the multiplication and addition rules to predict the probability of specific phenotypes

The Hardy-Weinberg TheoremBiology 11 EnrichedTuesday, December 18th, 2012

The Hardy-Weinberg Theorem The Hardy-Weinberg Equilibrium is a

mathematical theory that describes, in detail, the conditions that must be met for evolution to not occur (for allele frequencies to remain the same) Thus, it is a null hypothesis with which

natural populations (that are NEVER at H-W equilibrium) can be compared to.

Useful model to measure if forces are acting on a population▪ Measuring evolutionary change

H-W Equilibrium

For a population to NOT evolve, the following conditions MUST be met:1. Mating is random2. Large population3. No movement in to or out of

population4. No mutation5. No natural selection

H-W Equilibrium

If any of the 5 conditions for maintaining a Hardy-Weinberg equilibrium are not met, then evolution must be occurring.

Of course, none of these conditions is ever permanently met in any known natural population of organisms: Mutations occur at a slow but steady rate in all known

populations. Many organisms, especially animals, enter (immigration)

and leave (emigration) populations. Most populations are not large enough to be unaffected

by random changes in allele frequencies. Survival is virtually never random. Reproduction in organisms that can choose their mates

is also virtually never random.

H-W Equilibrium

Therefore, according to the Hardy-Weinberg Equilibrium Law, evolution (defined as changes in allele frequencies over time) must be occurring in virtually every population of living organisms.

In other words, “Evolution is as ubiquitous and inescapable as gravity.”

H-W Equilibrium

Hardy-Weinberg Theorem: Assumes 2 alleles (B,b)▪ Frequency of the dominant allele (B) = p▪ Frequency of the recessive allele (b) = q

Frequencies in a gene pool must add up to 1 so:

p + q = 1

p + q = 1

B

B BB

Bb

Bb

b

b bb

p = B alleleq = b allele

p + q = 1

H-W Equilibrium

If we break down frequencies of individual genotypes, then: Frequency of homozygous dominant = p x p = p2

Frequency of homozygous recessive = q x q = q2

Frequency of heterozygous = (p + q) + (q + p) = 2pq

Frequencies of individuals must add up to 1:

p2 + 2pq + q2 = 1

p2 + 2pq + q2 = 1

Homozygous

dominant

Homozygous

recessiveHeterozygous

H-W formulas

Alleles in a gene pool: p + q = 1

Individuals: p2 + 2pq + q2

= 1 bbBbBB

BB

B b

Bb bb

What are the genotype frequencies?What are the genotype frequencies?

Using Hardy-Weinberg Equation

q2 (bb): q (b): p (B):

q2 (bb): q (b): p (B):

population: 100 cats84 black, 16 whiteHow many of each allele?

population: 100 cats84 black, 16 whiteHow many of each allele?

bbBbBB

p2=.36p2=.36 2pq=.482pq=.48 q2=.16q2=.16

Must assume population is in H-W equilibrium!

Must assume population is in H-W equilibrium!

Using Hardy-Weinberg Equation

The following 4 examples will allow you to practice solving HW Equilibrium questions.

q2 q p p2 2pq

p + q = 1p2 + 2pq + q2 = 1

In a population of pigs color is determined by one gene. If the black allele (b) is recessive and the white allele (B) is dominant, what is the frequency of the black allele in this population?

q2 q p p2 2pq

p + q = 1q2 + 2pq + q2 = 1

In a population of 1000 fruit flies, 640 have red eyes and the remainder have sepia eyes. The sepia eye trait is recessive to red eyes. How many individuals would you expect to be homozygous for red eye color?

q2 q p p2 2pq

p + q = 1p2 + 2pq + q2 = 1

In a population of squirrels, the allele that causes bushy tail (B) is dominant, while the allele that causes bald tail (b) is recessive. If 91% of the squirrels have a bushy tail, what is the frequency of the dominant allele?

q2 q p p2 2pq

p + q = 1p2 + 2pq + q2 = 1

In the U.S. 1 out of 10,000 babies are born with Phenylketonuria, a recessive disorder that results in mental retardation if untreated. Approximately what percent of the population are heterozygous carriers of the recessive PKU allele?

Using Hardy-Weinberg equation

bbBbBB

p2=.36p2=.36 2pq=.482pq=.48 q2=.16q2=.16

Assuming H-W equilibrium

Assuming H-W equilibrium

Sampled data Sampled data bbBbBB

p2=.74p2=.74 2pq=.102pq=.10 q2=.16q2=.16

How do you explain the data?

How do you explain the data?

p2=.20p2=.20 2pq=.642pq=.64 q2=.16q2=.16

How do you explain the data?

How do you explain the data?

Null hypothesis Null hypothesis

Application of HW Theorem:

Sickle cell anemia inherit a mutation in gene coding for

hemoglobin▪ oxygen-carrying blood protein▪ recessive allele = HsHs / normal allele = Hb

low oxygen levels causes RBC to sickle breakdown of RBC clogging small blood vessels damage to organs

often lethal

Sickle cell frequency

High frequency of heterozygotes 1 in 5 in Central Africans = HbHs

unusual for allele with severe detrimental effects in homozygotes▪ 1 in 100 = HsHs

▪ usually die before reproductive age

Why is the Hs allele maintained at such high levels in African populations?Why is the Hs allele maintained at such high levels in African populations?

Suggests some selective advantage of being heterozygous…Suggests some selective advantage of being heterozygous…

Malaria Single-celled eukaryote parasite (Plasmodium) spends part of its life cycle in red blood cells

Single-celled eukaryote parasite (Plasmodium) spends part of its life cycle in red blood cells

1

2

3

Heterozygote Advantage In tropical Africa, where malaria is common:

homozygous dominant (normal) : HbHb

▪ die or reduced reproduction from malaria

homozygous recessive: HsHs

▪ die or reduced reproduction from sickle cell anemia

heterozygote carriers are relatively free of both: HbHs

▪ survive & reproduce more, more common in population

Hypothesis:In malaria-infected cells, the O2 level is lowered enough to cause sickling which kills the cell & destroys the parasite.

Hypothesis:In malaria-infected cells, the O2 level is lowered enough to cause sickling which kills the cell & destroys the parasite.

Frequency of sickle cell allele & distribution of malaria