Probability, Mendel, and Extensions to Mendel

Probability, Mendel, and 

Extensions to Mendel 

Set up and work probability problems 

Medelian and non-mendelian modes of 

inheritance and their significane 

The F 1 and F 2 Offspring of a Cross between Pure Lines 

Introduction to Rules of Probability 

Genotypic ration VS Phenotypic Ratio 

Copyright © 2008 Pearson Education Inc., publishing as Pearson Benjamin Cummings/Addison-Wesley 

monohybrid 

cross 

1

Practice Problem 

• A homozygous yellow corn is crossed with a homozygous purple 

corn. The F1 offspring are crossed and produce 139 purple kernels 

and 61 yellow kernels (F2 offspring). 

• What is the genotype of the purple kernels in the P generation 

and the F1 generation? 

• Give a genetic explanation (mode of inheritance) for the 

differences in kernel color. 


Chi-square Test 

• Are the observed data consistent with the data expected under the 

hypothesis being tested? 


• χ 2 = Σ [(o-e) 2 / e] Values are significantly 

different from expected 

2

A Cross between Pure Lines for Two Traits 

F2 offspring genotypes: 

9/16 R–Y– : 3/16 R–yy : 3/16 rrY– : 1/16 rryy 

F2 offspring phenotypes: 9/16 : 3/16 : 3/16 : 1/16 


Hypothesis of independent assortment: 

Alleles of different genes assort independently when gametes form. 

A Cross between Pure Lines for Two Traits 

Are these data are consistent with the 

predictions of independent assortment? 

Mendel’s results 

Conduct a X 2 Test. 


3

Chi-square Test 

• Are the observed data consistent with the data expected under the 

hypothesis being tested? 


• χ 2 = Σ [(o-e) 2 / e] Values are significantly 

different from expected 

Dihybrid cross: Phenotypic ratio 9:3:3:1 

• 9/16 dominant phenotypes at both genes 

(A_B_) 

• 3/16 dominant phenotype at first gene; 

recessive phenotype at second gene 

( A_bb) 

• 3/16 recessive phenotype at first gene; 

dominant phenotype at second gene 

(aaB_) 

• 1/16 recessive phenotypes at both genes 

(aabb) 

4

Dihybrid Cross problem solving 

• Memorize 9:3:3:1 or be able to reproduce it. 

• Not all genetics problems deal with dihybrids! 

• The genotypes may change by the principles 

are the same. 

Practice problems 

• P (dominant phenotype for both traits) 

• AaBBccDd X AAbbCcDd 

give P (AABbccDD offspring) 

•Forkline method for dihybrid 

Variations on Mendel’s Laws: Incomplete Dominance 

Flower color is variable in four-o’clocks. 

origin of ‘blending’ hypothesis? 


5

Variations on Mendel’s Laws: Incomplete Dominance 

Incomplete dominance in flower color 

Parental 

generation 

F1 generation 

F2 generation 


Self-fertilization 

Purple Lavender White 

Incomplete Dominance 

Heterozygote’s phenotype between those of 

the two homozygotes 

Example: Familial hypercholesterolemia 

(FH): normal alleles encode liver receptors 

for LDL cholesterol 

mutant alleles do not produce any receptors 

Phenotype measured by serum cholesterol 

levels. 

Heterozygote has ~ 1/2 the normal number 

of receptors 

Homozygote the mutant allele totally lacks 

the receptor (serum cholesterol level is very 

high) 

Monohybrid cross results in 1:2:1 

genotypic ratio and 1:2:1 phenotypic 

ratio. 

6

Variations on Mendel’s Laws: Co-Dominance 

• Human Blood type 

– I A I A or I A i 

– I B I B or I B i 

– I A I B 

– ii 


Multiple Alleles: the Rule 

• An individual carries two alleles for each 

autosomal gene 

• However, a gene can have multiple alleles in 

the population because its sequence can 

deviate in many ways 

• Different allele combinations can produce 

variations in the phenotype 

• Examples: 

– ABO (3 alleles; four phenotypes); 

– PKU gene (hundreds of alleles; four basic 

phenotypes), 

– CF gene (>1500 alleles!; many phenotypes) 

7

• Multiple Alleles: I A , 

I B , I 0 

• Each person still has 

only 2 alleles. 

• Co‐Dominance: 

Both alleles are 

expressed 

I A I B = type AB 

• Simple Dominant 

and Recessive: Both 

I A and I B are 

dominant to I 0 

ABO Blood Type 

Lethal Alleles 

• Alleles that are incompatible with life. 

• Result in missing or dead genotypic classes. 

• Recessive lethal = 2 copies required for death 

– Cystic fibrosis, sickle cell anemia 

– Homozygous recessive is missing or dies. 

• Dominant lethal = 1 copy required for death 

– Huntington’s disease, achondroplastic dwarfism 

– Heterozygotes and homozygous dominant are 

missing or die (homozygous dominants are typically 

very severely affected and often die early in 

development. 

8

PENETRANCE 

• PENETRANCE = proportion of a genotype 

showing the expected phenotype 

• Non‐penetrant = none show phenotype 

• Complete or 100% penetrance = all relevant 

genotypes express the trait 

• Incompletely penetrant = some show the trait, 

others do not 

• ALL OR NONE EXPRESSION OF A SINGLE GENE 

EXPRESSIVITY 

• EXPRESSIVITY = degree to which a phenotype 

is expressed 

• Variable Expressivity ~ range of phenotypes 

from slight to extreme 

• Variability in expression in different 

individuals 

• Variability in different parts of the same 

individual 

• Example: Polydactyly 

• SEVERITY OR EXTENT OF PHENOTYPIC 

EXPRESSION OF A SINGLE GENE 

9

Huntington’s Disease 

• Dominant lethal 

• Incomplete penetrance: disease is never 

manifested in some carriers. 

• Variable expressivity: appears at variable 

ages from infancy to old age. 

• Remains in populations because death 

typically occurs after reproductive age. 

Gene Interactions 

• > 1 gene pair contributes to the 

phenotype 

• Many, if not most, traits are the 

result of biochemical pathways. 

Each step is controlled by a 

different gene product. 

• Segregation and Independent 

Assortment hold 

• Phenotypic ratios are changed 

from 9:3:3:1 for 2 gene pairs 

• EPISTASIS = phenotypic 

expression of one gene pair hides 

the effect of another, different 

gene pair 

• Examples: 

– albinism (hides the effect of genes for eye color, 

skin color, hair color) 

– Bombay phenotype (hides the effect of ABO 

blood type genes) 

10

Bombay Phenotype 

AB AO 

AB O A B 

• A, B antigens are 

sugars + precursor 

• H gene controls 

synthesis of precursor 

• H = normal, dominant 

allele (can add sugars) 

• h = abnormal, 

recessive allele 

(cannot add A or B 

regardless of 

genotype) 

11

Probability, Mendel, and Extensions to Mendel

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