Genetics: Probability Rules and Pedigree Analysis

Probability Rules in Genetics

• Product Rule (AND Rule):

  • Used for independent events where both Event $1$ AND Event $2$ occur.

  • Probability of (Event $1$ AND Event $2$) = P(Event $1$) $*$ P(Event $2$).

  • Example: Rolling a $4$ on a red die (1/6) AND a $3$ on a gray die (1/6) = $(1/6) * (1/6) = 1/36$.

• Sum Rule (OR Rule):

  • Used for mutually exclusive events where Event $1$ OR Event $2$ occurs.

  • Probability of (Event $1$ OR Event $2$) = P(Event $1$) $+$ P(Event $2$).

  • Example: Rolling ($4$ on red AND $3$ on gray) OR ($3$ on red AND $4$ on gray) = $(1/36) + (1/36) = 2/36 = 1/18$.

Branch Diagrams for Complex Crosses

• Simplifies analysis of multiple traits without large Punnett squares.

• Break down complex crosses into single-gene Punnett squares.

• Example: Predicting gender and eye color in F1 generation.

  • Gender: $1/2$ female, $1/2$ male.

  • Eye Color (heterozygous x heterozygous): $3/4$ wild type, $1/4$ vermillion.

  • Combine probabilities using the Product Rule (e.g., probability of male AND wild type eyes = $(1/2) * (3/4) = 3/8$).

• Total probabilities of all outcomes should sum to $1$.

Pedigree Analysis

• Examines family histories to infer inheritance patterns and genotypes.

• Symbols:

  • Square: Male

  • Circle: Female

  • Filled symbol: Affected individual

  • Unfilled symbol: Unaffected individual

  • Horizontal line: Mating

  • Vertical line: Descent

• Key Assumption for Rare Traits:

  • Individuals marrying into the family (outside the pedigree) are assumed to be homozygous dominant for the trait, unless empirical data (their children) proves otherwise.

  • This initial assumption can be adjusted based on offspring phenotypes.

• Inferring Inheritance Patterns:

  • Recessive Traits: Often