Genetics Study Notes: Sep 12

Mendelian Genetics and Phenotypic Ratios

Mouse Coat Color Crosses

Genetic crosses can be used to predict the phenotypic ratios of offspring based on parental genotypes. In this example, the cross involves two mice with genotypes AYaBb and Aabb, focusing on two genes affecting coat color.

• Product Law: The probability of independent events occurring together is the product of their individual probabilities.

• Punnett Squares: Used to visualize possible genotypes from a cross.

• Phenotypic Ratio Calculation:

  • No ghost mice (lethal genotype), so total possible offspring = 16.

  • 1/2 of mice will be white.

  • 1/2 will have coat color determined by Agouti genotype:

    • 1/2 × 1/2 = 1/4 yellow

    • 1/2 × 1/4 = 1/8 agouti

    • 1/2 × 1/4 = 1/8 black

  • Final ratio: 8 white : 4 yellow : 2 agouti : 2 black

• Example: Predicting coat color in mouse offspring using Punnett squares and product law.

X-Linked Inheritance

X-Linked Recessive Diseases

X-linked recessive inheritance affects males and females differently due to the presence of one X chromosome in males and two in females.

• Carrier Mother: A female with one normal and one mutant allele on her X chromosomes.

• Hemizygous: Males have only one X chromosome, so they are hemizygous for X-linked genes (only one copy).

• Inheritance Pattern:

  • Carrier mothers can pass the mutant allele to sons (who will be affected) or daughters (who will be carriers).

  • Unaffected fathers cannot pass X-linked traits to sons.

• Example: Pedigree analysis showing affected sons, carrier daughters, and unaffected individuals.

Statistical Analysis in Genetics

Chi-Square Analysis

The chi-square test is used to determine whether observed results deviate significantly from expected results in genetic crosses.

• Purpose: Test the fit between observed and expected phenotypic ratios.

• Null Hypothesis (H0): The observed segregation ratio fits the expected ratio.

• Formula:

$\chi^2 = \sum \frac{(O - E)^2}{E}$

• O: Observed number in each category

• E: Expected number in each category

Sample Problem: Pea Shape

Plants with the wild-type allele (R) produce round peas; those with two recessive alleles (r) produce wrinkled peas. A cross of Rr × Rr is expected to yield a 3:1 ratio of round to wrinkled peas.

• Punnett Square:

	R	r
R	RR	Rr
r	Rr	rr

• Expected Ratio: 3 round : 1 wrinkled

• Observed: 78 round, 42 wrinkled (total 120)

• Expected: 90 round, 30 wrinkled

• Chi-square calculation:

$\chi^2 = \frac{(-12)^2}{90} + \frac{12^2}{30} = \frac{144}{90} + \frac{144}{30} = 1.6 + 4.8 = 6.4$

• Degrees of Freedom (df): Number of categories minus one ($n-1$). Here, $2-1=1$.

• Critical Value: For $df=1$ and $p=0.05$, $\chi^2_{crit}=3.84$.

• Interpretation: $\chi^2_{exp}=6.4 > 3.84$, so $p < 0.05$; reject the null hypothesis.

• Conclusion: The observed data do not fit the expected 3:1 ratio.

Probability Table for Chi-Square

Used to determine the significance of the calculated chi-square value.

Degrees of Freedom (df)	p = 0.05	p = 0.01	p = 0.001
1	3.84	6.64	10.83
2	5.99	9.21	13.82
3	7.81	11.34	16.27
4	9.49	13.28	18.47

• Standard cutoff for statistical significance: $p = 0.05$

• If $p < 0.05$, reject the null hypothesis; if $p \geq 0.05$, fail to reject the null hypothesis.

Applications in Genetics

Genetic Testing

Genetic testing is used to analyze DNA and identify genetic variants associated with traits or diseases. Commercial services (e.g., Embark) can provide information about ancestry, health risks, and inherited traits in animals and humans.

• Example: Genetic testing in dogs to determine breed composition and health risks.

Summary Table: Key Concepts

Concept	Definition	Example/Application
Mendelian Ratio	Expected ratio of phenotypes from a genetic cross	3:1 ratio in Rr x Rr pea cross
Chi-Square Test	Statistical test for goodness-of-fit	Testing if observed pea phenotypes match expected ratio
X-Linked Inheritance	Inheritance of genes on the X chromosome	X-linked recessive diseases in humans
Genetic Testing	Analysis of DNA for traits or diseases	Embark dog DNA test

Additional info: These notes expand on the original slides by providing full academic context, definitions, and examples for each concept, ensuring a self-contained study guide for Genetics students.