Exam Review: Heritability

Exam Preparation Notes

Heritability Equations

• Equations for variance, covariance, and correlation will be provided.
• Focus on using these equations to calculate different types of heritability.
• Understand the slope of the regression line and its meaning in terms of narrow-sense heritability.

Types of Heritability

• Broad-sense heritability:
  • Measured one way.
• Narrow-sense heritability:
  • Measured two ways (plus a third method not covered in class).
• Heritability equation (definition) will not be provided.

Review of Heritability Measurements

Broad-Sense Heritability

• Definition: Proportion of total phenotypic variation in a population due to all genetic contributions.
• Calculated by comparing overall genetic variance to overall phenotypic variance.
• Uses clones to estimate.

Clonal Experiments:

• Clones have identical genotypes, so $V_G = 0$ (genetic variance is zero).
• Total variance in phenotype of clones ($V<em>P$) is due to environment ($V</em>E$).
• $V<em>P = V</em>E$ for clones.
• For a heterogeneous population (non-clones), $V<em>P = V</em>G + V_E$.
• Broad-sense heritability: $H^2 = frac{V<em>G}{V</em>T}$, where $V_T$ denotes total variance.

Narrow-Sense Heritability (Mother-Daughter Correlation)

• Measured by correlating the weight (or trait) of mothers and daughters.
• Correlation reflects how similar mothers and daughters look relative to the population average.

Calculation:

• Calculate the observed correlation (R observed) between mothers and daughters.
  • $Covariance = \frac{\sum (x<em>i - \bar{x})(y</em>i - \bar{y})}{n-1}$ (where $x<em>i$ is individual mom, $\bar{x}$ is mean for moms, $y</em>i$ is individual daughter, $\bar{y}$ is mean for daughters)
  • Calculate correlation as $r = \frac{Cov(x,y)}{\sigma<em>x \sigma</em>y}$ (covariance divided by the product of the standard deviations).
• Divide by the expected amount of correlation (R expected).
  • For mothers and daughters, $R_{expected} = 0.5$ because they share half their genes.
• Narrow-sense heritability: $h^2 = \frac{R<em>{observed}}{R</em>{expected}}$.

Narrow-Sense Heritability (Selection Experiment - Not Covered)

• Measure response to selection to estimate heritability.
• $R = h^2S$ where:
  • $S$ is the strength of selection (difference between breeding individuals and the average).
  • $R$ is the response to selection (how much the trait evolves).
• Higher heritability means a greater response to selection.
• Can solve for $h^2$ if $R$ and $S$ are known, $h^2 = R/S$.

Narrow-Sense Heritability (Parent-Offspring Regression)

• Uses regression analysis to calculate narrow-sense heritability.
• $h^2$ represents how much of the total phenotypic variation is due to additive genetic components.
  • X-axis: Mid-parent value (average of mother and father for a trait).
  • Y-axis: Mid-offspring value (average of all children for that trait).
• Each data point represents a family unit.
• Perform a linear regression: $y = mx + b$.
• The slope (m) is the measure of narrow-sense heritability.

Interpreting the Slope:

• Slope of zero: No relationship between parent and offspring traits; offspring are average size regardless of parents.
  • $h^2 = 0$, all offspring are the population average size, regardless of parental size.
  • B (y-intercept) represents the average in the population.
  • Environment determines offspring height, not genetics.
• Slope of one: Perfect prediction of offspring trait based on parents.
  • $h^2 = 1$, offspring size can be perfectly predicted by parental size.
  • Traits are 100% determined by genes from parents.
• Slope between zero and one: Partial prediction; some influence of genetics.
  • 0 < h^2 < 1; some predictability of offspring size from parental size, with some uncertainty.
  • Example: $y = 0.75x + 68$ cm, heritability is 75%.
  • The steeper the line, we get more spread as we go across. Flatter lines cluster around the mean.

Assignment: Class Data Analysis

1. Calculate mid-parent values from the Excel spreadsheet.
2. Plot mid-parent height against mid-offspring height.
3. Perform a linear regression.
4. The slope of the regression line is the estimated narrow-sense heritability.

Comparison with Mid-Friend Data

• Plot mid-friend height against mid-offspring height.
• Expect a flat line because there's no genetic relation between friends and offspring.
• Cumulative data shows a slight positive slope, possibly due to self-aggregation or heightism.