Mendelian Genetics

The laws of probability govern Mendelian inheritance

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

• The multiplication rule states that the probability that two or more independent events will occur together is the product of their individual probabilities

• Probability in a monohybrid cross can be determined using this rule

Segregation ofalleles into eggs

Segregation ofalleles into sperm

Sperm

Eggs

1/2

1/2

1/21/2

1/41/4

1/41/4

Rr Rr

R

R

RR

R

R

r

r

r

r r

r

Punnett Square

Monohybrid Cross

The rule of addition

• States that the probability that any one of two or more exclusive events will occur is calculated by adding together their individual probabilities

Each box in thisdihybrid cross hasa 1/16 chance of occurring.Add them upfor chancesof any phenotype

Dihybrid cross - The traits are: long tail (s), short tail (S), brown hair (B) and white hair (b)

Solving Complex Genetics Problems with the Rules of Probability

• We can apply the rules of probability to predict the outcome of crosses involving multiple characters

• A dihybrid or other multicharacter cross is equivalent to two or more independent monohybrid crosses occurring simultaneously

• In calculating the chances for various genotypes from such crosses each character first is considered separately and then the individual probabilities are multiplied together

Trihybrid Cross of PpYyRr x Ppyyrr

Chance of at least two recessive traits

ppyyRr

ppYyrr

Ppyyrr

PPyyrrppyyrr

1/4 (probability of pp) 1/2 (yy) 1/2 (Rr) 1/4 1/2 1/2 1/2 1/2 1/2 1/4 1/2 1/2 1/4 1/2 1/2

1/16

1/16 2/16

1/16

1/16

6/16 or 3/8

Summary of Basic Mendelian Genetics

• We cannot predict with certainty the genotype or phenotype of any particular seed from the F2 generation of a dihybrid cross, but we can predict the probabilities that it will fit a specific genotype of phenotype.

• Mendel’s experiments succeeded because he counted so many offspring and was able to discern this statistical feature of inheritance and had a keen sense of the rules of chance.

• Mendel’s laws of independent assortment and segregation explain heritable variation in terms of alternative forms of genes that are passed along according to simple rules of probability.

Extending Mendelian Genetics

• The inheritance of characters by a single gene may deviate from simple Mendelian patterns

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

• The relationship between genotype and phenotype is rarely simple

• But we can extend Mendelian principles to patterns of inheritance more complex than Mendel described

The Spectrum of Dominance

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

• In incomplete dominance the phenotype of F1 hybrids is somewhere between the phenotypes of the two parental varieties

Red and White Snapdragons

Incomplete Dominance

P Generation

Red White

Gametes

CWCWCRCR

CR CW

Incomplete Dominance

P Generation

F1 Generation

1/21/2

Red White

Gametes

Pink

Gametes

CWCWCRCR

CR CW

CRCW

CR CW

Incomplete Dominance

P Generation

F1 Generation

F2 Generation

1/21/2

1/21/2

1/2

1/2

Red White

Gametes

Pink

Gametes

Sperm

Eggs

CWCWCRCR

CR CW

CRCW

CR CW

CWCR

CR

CW

CRCR CRCW

CRCW CWCW

The Spectrum of Dominance

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

• The human blood group MN is an example of codominance

MN Blood Groups

The Relation Between Dominance and Phenotype

• Dominant and recessive alleles

– Do not really “interact”

– Lead to synthesis of different proteins that produce a phenotype

Tay-Sachs Disease

• Humans with Tay-Sachs disease produce a non-functioning enzyme to metabolize gangliosides (a lipid) which then accumulate in the brain, harming brain cells, and ultimately leading to death. Tay-Sachs most common in Ashkenazic Jews (from Central Europe)

• Children with two Tay-Sachs alleles have the disease.

• Heterozygotes with one working allele and homozygotes with two working alleles are “normal” at the organismal level, but heterozygotes produce less functional enzymes.

• However, both the Tay-Sachs and functional alleles produce equal numbers of enzyme molecules, codominant at the molecular level.

Tay-Sachs Disease

Frequency of Dominant Alleles

• Dominant alleles are not necessarily more common in populations than recessive alleles

• Polydactyly is a dominant trait – Antonio Alfonseca

• 399 out of 400 people have 5 digits

Dominance/recessiveness relationships

• Range from complete dominance through various degrees of incomplete dominance to codominance

• Reflect the mechanisms by which specific alleles are expressed in the phenotype and do not involve the ability of one allele to subdue another at the level of DNA

Multiple Alleles

Carbohydrate

Allele

(a) The three alleles for the ABO blood groups and their carbohydrates

(b) Blood group genotypes and phenotypes

Genotype

Red blood cellappearance

Phenotype(blood group)

A

A

B

B AB

none

O

IA IB i

iiIAIBIAIA or IAi IBIB or IBi

Pleiotropy – gene affects more than one phenotypic trait

Sickle-cell Anemia

Pleiotropy - Phenotypic traits affected by sickle-cell anemia

• Sickled red-blood cells

• Anemia

• Heart failure

• Brain damage

• Spleen damage

• Rheumatism

• Kidney failure

Coat color in Labrador Retrievers

Sperm

Eggs

9 : 3 : 4

1/41/4

1/41/4

1/4

1/4

1/4

1/4

BbEe BbEe

BE

BE

bE

bE

Be

Be

be

be

BBEE BbEE BBEe BbEe

BbEE bbEE BbEe bbEe

BBEe BbEe BBee Bbee

BbEe bbEe Bbee bbee

Epistasis – a gene at one locus alters the phenotypic expression of a gene at another locus

PolygenicTrait, Quantative Characters – Human height in 175 students at Connecticut Agricultural College

Eggs

Sperm

Phenotypes:

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

1/81/8

1/81/8

1/81/8

1/81/8

1/8

1/8

1/8

1/8

1/8

1/8

1/8

1/8

1/646/64

15/6420/64

15/646/64

1/64

AaBbCc AaBbCc

PolygenicTrait, Quantative Characters –How human skin color might work

Figure 14.UN03

Complete dominanceof one allele

Relationship amongalleles of a single gene

Description Example

Incomplete dominanceof either allele

Codominance

Multiple alleles

Pleiotropy

Heterozygous phenotypesame as that of homo-zygous dominant

Heterozygous phenotypeintermediate betweenthe two homozygousphenotypes

Both phenotypesexpressed inheterozygotes

In the whole population,some genes have morethan two alleles

One gene is able to affectmultiple phenotypiccharacters

ABO blood group alleles

Sickle-cell disease

PP Pp

CRCR CRCW CWCW

IAIB

IA, IB, i

Figure 14.UN04

Epistasis

Polygenic inheritance

Relationship amongtwo or more genes Description Example

The phenotypicexpression of onegene affects thatof another

A single phenotypiccharacter is affectedby two or more genes

9 : 3 : 4

BbEe BbEe

BEBE

bE

bE

Be

Be

be

be

AaBbCc AaBbCc