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 (VP) is due to environment (VE).
  • VP = VE for clones.
  • For a heterogeneous population (non-clones), VP = VG + V_E.
  • Broad-sense heritability: H^2 = frac{VG}{VT}, 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 (xi - \bar{x})(yi - \bar{y})}{n-1} (where xi is individual mom, \bar{x} is mean for moms, yi is individual daughter, \bar{y} is mean for daughters)
    • Calculate correlation as r = \frac{Cov(x,y)}{\sigmax \sigmay} (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{observed}}{R{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.