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