Topic 11: Heritability of Quantitative Traits

BS2470/BS5470 Evolution Heritability of Quantitative Traits

Instructor: Dr. Megan Higgie

Key Questions:

  • How do we estimate how much genetic variation is due to genes vs. environment?

  • What is heritability and what are the two types?

  • How can we use quantitative genetic models to predict evolutionary change in traits even when we do not know the specific genetic basis for these traits?

1. RECAP: PARTITIONING PHENOTYPIC VARIANCE

Phenotypic Variance ($VP$): The observed phenotypic variance can be partitioned as follows: VP = VG + VE

Where:

  • $V_P$: Observed phenotypic variance, representing the total variability in a trait observed in a population.

  • $V_G$: Variance due to genes, which encompasses the genetic diversity contributing to phenotypic differences.

  • $V_E$: Variance due to environment, including all external factors influencing the expression of traits, such as nutrition, climate, and social interactions.

Note: For simplicity, variance due to gene-environment interaction ($V_{G imes E}$), which occurs when the effect of genes on phenotypes depends on the environment, is ignored at this point.

2. Genetic Variance ($V_G$)

Composition of Genetic Variance:

Genetic variance is further made up of:

VG = VA + VD + VI

Where:

  • $V_A$: Additive variance (the additive effects of alleles), which represents the cumulative effect of individual alleles on the phenotype.

  • $V_D$: Dominance variance (interactions of alleles within a locus), reflecting how different alleles at the same locus may mask or enhance each other's effects.

  • $V_I$: Epistatic variance (interactions of alleles across loci), capturing the complexities of how genes at different loci interact to influence phenotypes.

Quantitative Genetic Model Assumption:

  • The model assumes independence of genes and environment; the best genes may not necessarily be found in the best environment and vice versa.

  • Additionally, it assumes there's no Gene-Environment interaction (GxE), which can complicate the analysis of phenotypic variation.

3. Understanding the Contributions to Phenotypes

After analysis, we gain:

  • Insight into the contributions of genetics versus environment to a phenotype, allowing us to understand the underlying mechanisms of trait expression even without specific knowledge of the genetic loci involved.

    Required data: Known relatives from a studied population along with their phenotypic information, enabling statistical models to analyze this data and derive meaningful conclusions about heritability and genetic influence.

4. HERITABILITY

Definition of Heritability:

Heritability is defined as the proportion of phenotypic variation in a trait attributable to genetic factors in a specific population and environment. The formula for heritability is given as the ratio of genetic variance to phenotypic variance:

H^2 = \frac{VG}{VP} = \frac{VG}{VG + V_E}

Heritability metrics range from 0 to 1:

  • A heritability of 0 indicates that all phenotypic variance is due to environmental factors, suggesting that genetics plays no role in the trait expression.

  • A heritability of 1 indicates that all phenotypic variance is due to genetic factors, suggesting a complete absence of environmental influence.

4.1 Types of Heritability

  1. Broad-Sense Heritability ($H^2$):

    • Measures the total genetic variance relative to phenotypic variance, capturing all genetic contributions, including additive, dominance, and epistatic relationships.

    • Example Metrics:

      • Very high broad-sense heritability (>80%) is observed in traits like height, fingerprint ridge count, and certain complex disorders such as schizophrenia, indicating strong genetic influences.

      • High broad-sense heritability (50-80%) for traits like chest circumference and IQ suggests significant but not exclusive genetic contributions.

      • Moderate heritability (20-50%) for traits like anxiety disorders and major depression indicates a more complex interplay between genetics and environmental influences.

  2. Narrow-Sense Heritability ($h^2$):

    • Assesses the proportion of phenotypic variance explained specifically by additive genetic variation, crucial for understanding the inheritance of traits subject to natural or artificial selection.

    • Measured by:

      h^2 = \frac{VA}{VP} = \frac{VA}{VA + VD + VI + V_E}

    • Narrow-sense heritability is particularly relevant in discussions of selection and adaptation, as selection acts directly on the additive genetic variance present in a population.

4.2 Comparison of Heritability

  • Broad-Sense ($H^2$): Relevant for understanding the overall impact of genetics on trait variability, encompassing all genetic components, and is not limited by environmental influences on traits.

  • Narrow-Sense ($h^2$): Directly reflects the potential for evolutionary change and is crucial in selective breeding programs, as it indicates the extent to which traits can be passed on to subsequent generations.

5. ESTIMATING HERITABILITY

Estimating $H^2$ vs. $h^2$: Different family relationships provide insights into components of genetic variation:

  • Family Relationships Studied:

    • Some relationships estimate both $V*A$ and $VD$, capturing the broad genetic influence, while others focus exclusively on $VA$, which is foundational for effective selection.

    • In human studies, estimating $H^2$ is often practical due to ethical considerations and the inability to conduct controlled breeding experiments.

    • For non-human organisms, controlled breeding can yield precise estimates of $h^2$, offering a clearer view of selective potential.

5.1 Family Relationship Framework

TABLE: Relationships and Estimated Variances

Relationship Type

Estimated Variance Contributions

Full siblings

Estimates $VA$ and $VD$

Half siblings

Focus on estimating $V_A$

Parent-offspring

Directly estimates $h^2$

Note: Certain family relationships can complicate the measure of $h^2$, introducing biases caused by correlations in environmental variance, such as when parents and offspring grow up in similar environments, potentially skewing the data.

6. NARROW-SENSE HERITABILITY

Narrow-sense heritability assesses the portion of phenotypic variance attributed purely to additive genetic variation ($VA$). This is critical for understanding how traits may change under selection pressures. The estimated relationship is represented as follows: h^2 = \frac{VA}{V_P}

Where population response to selection is dependent on the magnitude of additive genetic variance and its heritable nature.

6.1 Estimation of Narrow-Sense Heritability

  • The regression formula can be used to estimate $h^2$ through various methods, typically involving parent-offspring assessments.

  • For a single parent-offspring regression:

    Y = a + r X, where $r$ (slope) represents half of $h^2$:

    h^2 = 2r

  • For mean parent-offspring regression, the established relationship holds as:

    h^2 = r

6.2 Example of Estimation

  • A straightforward approach using regression slope to derive heritability can yield valuable insights from averaged data. For instance, if the regression slope for a single parent to offspring relationship among females is $r = 0.4$, then the estimation of heritability gives us $h^2 = 2 \times 0.4 = 0.8$, indicating high heritable potential for the trait studied.

7. RESPONSE TO SELECTION

Key Ingredients Needed:

For a successful response to selection, two essential ingredients must be present:

  • Additive Genetic Variation ($V_A$), which allows offspring to resemble their parents, indicated by an $h^2 >> 0$, suggesting the trait has a genetic basis that can be inherited.

  • Selection: The presence of selective pressure is critical for driving evolutionary change; without it, observed traits remain stable within populations.

7.1 Breeder’s Equation

Equation for Predicting Selection:

The Breeder’s Equation formalizes the prediction of response to selection:

R = h^2 S

Where:

  • $R$: Response to selection, representing the mean change in trait values relative to the base population from which the selection was made.

  • $h^2$: Narrow-sense heritability.

  • $S$: Selection differential, defined as the difference in the mean traits between individuals selected for breeding and the average traits in the base population.

7.2 Magnitude of Response to Selection

  1. Response to selection is influenced proportionally by both $S$ and $h^2$. The longer-term responses to selection highlight the importance of higher heritability for observable changes in traits, emphasizing the role of genetic variance.

8. HERITABILITY OF TRAIT VARIATION AND SELECTION

To illustrate the principles of heritability, Darwin's medium ground finch provides a classic example of selection during adverse environmental conditions:

  • Scenario: Before a severe drought in 1976, the average beak depth of the finches was measured at 9.4 mm, and post-drought, the average beak depth increased to 10.1 mm. Given that the heritability ($h^2$) for beak depth was estimated at 0.8, selection pressures favored birds with deeper beaks, as these individuals were more capable of successfully foraging for food during challenging conditions, thereby enhancing their survival and reproductive success.

8.1 Example Calculation in Ground Finches

Using the Breeder's equation, we can assess the selection differential following the drought:

R = 10.1 mm - 9.4 mm = 0.7 mm

  • Rearranging yields $S$:

    S = \frac{R}{h^2} = \frac{0.7 mm}{0.8} = 0.875 mm

9. ADDITIONAL EXAMPLES OF SELECTION RESPONSES

Case Study in Maize Kernels: This case demonstrates the effects of artificial selection on provitamin A content in maize.

The population's average provitamin A content before selection was 1.25 µg/g, while the mean of the selected plants showed an increase to 1.63 µg/g. The average provitamin A content of offspring from these selected maize plants was recorded at 1.44 µg/g. From this data, the narrow-sense heritability can be calculated:

h^2 = \frac{R}{S} = \frac{0.19 µg/g}{0.38 µg/g} = 0.5

In this scenario, it is insightful to note that under sustained selective pressures, the additive genetic variance ($V_A$) and hence $h^2$ may decrease as desirable alleles become fixed in the population due to selection, illustrating heritability as a population-specific property rather than an inherent characteristic of a trait.

10. KEY POINTS

  • Heritability Definitions: Essential to separate genetic contributions from environmental factors to understand phenotypic variation in traits.

  • Types: Understanding the distinction between broad-sense ($H^2$) for total genetic variance and narrow-sense ($h^2$) for additive contributions is crucial, as the latter directly informs breeding and selection practices.

  • Estimation Techniques: Various family relationship structures provide critical insights for estimating heritability, requiring consideration of potential environmental variances that could skew results.

  • Regression Coefficients: Quantitative measures derived from parent-offspring relationships provide actionable heritability estimates that can influence selection strategies for traits in both natural and agricultural contexts.

11. FURTHER READING

  1. Griffiths et al., Introduction to Genetic Analysis, Chapter 19.

  2. Bergstrom & Dugatkin, Evolution, Chapter 9.

  3. Explore primary literature for in-depth examples and methodologies in genetic analysis and heritability assessment.