Phenomena and definitions:

Pleiotropy

Penetrance and Expressivity

Deviations from simple Mendelian phenotypic ratios (3:1, 9:3:3:1, etc.) may result from: incomplete penetrance, incomplete or co-dominance, lethality or reduced viability, epistasis or certain other intergenic interactions, linkage...
 

Intragenic (allelic) interactions:

• *Incomplete dominance:
• heterozygote has "intermediate" phenotype
• typically reflects dose sensitivity/haploinsufficiency
• *Co-dominance:
• distinct contributions from both alleles in the heterozygote
• e.g., A & B alleles of ABO blood type locus

 
* --> Both increase the # of phenotypic classes: 1:2:1 F₂ ratio in a monohybrid cross
 
• Multiple alleles
• # possible genotypes = n(n+1)/2 , where n = # of different alleles
• Allelic series/dominance hierarchies:
• e.g., for 3 alleles of white:  wild-type (w⁺), white-apricot (w^a), and white null (w)
w⁺/w⁺ ,  w⁺/w^a  , and  w⁺/w are all red-eyed
w^a/w^a and  w^a/w have yellowish eyes
w/w have white eyes
--> so, these define the allelic series:  w⁺ > w^a > w
• Complementation tests:

--> used when two mutations (both recessive) have same/similar phenotype
--> same gene or 2 different genes?
• Cross the two mutants (homozyotes) and assess progeny phenotype
• Complementation (i.e., normal progeny) indicates two different genes (each heterozyogous in the F₁)
• Allelic mutations will "fail to complement": both copies will be defective in mutant F₁
• Allelic mutations will also have the same genetic map location - esp. important with dominant mutations

• Lethality:
• Recessive lethal alleles result in inviable homozygotes:
• 1/4 of progeny die when het's are mated
• Viable progeny will have a genotype ratio of 1:2 (homozygous w.t.: heterozygous)
• Phenotype ratio will also be 1:2 if  lethal allele has a dominant (visible) phenotype: e.g., Notch mutation in Drosophila, Agouti-yellow (A^y) mice, Manx (tailless) cats
• Dominant lethals can only be recovered if conditional (e.g., temperature-sensitive)
• Exception: "lethal" human diseases (Huntington's etc) that do not preclude parenthood
• In model sytems, "lethal" means that no adults are recovered

• Multiple loci affecting the same process or trait:
• Additive or interactive phenotypes e.g.:
• skin pigment in corn snakes
• Agouti (A or a) and black/brown (B or b)
• Black/brown (B or b) & non-dilute/dilute (D or d)  (9:3:3:1 in mice b/c "D" is fully dominant)
• Mutations with similar/equivalent phenotypes e.g.:
• Genes in the same pathway with equivalent recessive phenotypes (9:7 ratios)
• Novel phenotypes - e.g., squash shapes (9:6:1)
• Genetic redundancy (e.g., 15:1 ratios)
• Epistasis & Suppression (see handout)
• Recessive epistasis (9:3:4 - e.g., Agouti/black vs. albino) (exception: t.s. "himalayan" allele at albino locus)
• (Duplicate recessive epistasis - 9:7)
• Dominant epistasis (12:3:1 - e.g., White-spotted (W/–) vs. dark/light purple (D/– or d/d)
• (Duplicate dominant epistasis - 15:1)
• Mutant epistasis and pathway analysis
• Epistasis vs. suppression

 
• Gene interactions (epistasis etc.) & independent assortment are distinct phenomena:  interacting genes that are linked will give very different ratios than those covered here

Genetic crosses & progeny ratios are used to distinguish between/among various behaviours (non-complementation, incomplete dominance, lethality, epistasis, linkage, etc.)
 
 

Chi-square:

• Useful for data sets with discrete (discontinuous) variables, where the sample is distributed among specific categories (e.g., Mendelian traits)
• Measures how far the actual distribution diverges from the "expected" values (i.e., those most probable under the hypothesis being tested)
• For every category, the deviation (difference between the observed and expected value) is squared and then divided by the expected value
• Chi-square is simply the sum of all these squared, normalized deviations:
 
X² = SUM (O-E)²/E
(- E must be > 4 for all categories)

What is the source of the experimental deviation, as measured in the X² value? Assuming the experiment was designed correctly, there are at least two general possibilities:

a) random "sampling error" (and a valid hypothesis)

b) a flawed or false hypothesis

While statistical methods alone can't prove the hypothesis, they can be used to estimate the likelihood that the observed deviation would result from random sampling variations alone. For a given chi-square value, this involves:

1) Determining the "degrees of freedom" ( = # of categories minus 1)

2) Finding the probability (P) , or range of probabilities, on a chi-square table

• When P < 0.05, the experimental deviation is "significant", and the data are generally considered to be inconsistent with the hypothesis. *

• When p < 0.01, the deviation is "highly significant", and the hypothesis can be rejected with even greater confidence.*

* Rejecting a true hypothesis is known as a "Type I" error. Setting the "cut off" for rejection at p = 0.05 or 0.01 means that Type I errors will occur with a frequency of 5 % or 1 %, respectively.

The "failure to reject" a hypothesis occurs when experimental data are "consistent" with it (e.g., when p > 0.05). This does not necessarily mean that the hypothesis is correct, but it may be considered valid unless or until other grounds for rejecting it are found.