How To Calculate Narrow Sense Heritability

Unlocking the secrets of inheritance often leads us down the path of understanding how much of a trait is actually passed down from parents to offspring. This is where narrow-sense heritability comes in, a crucial concept in genetics and breeding, allowing us to predict the response to selection in a population.

What is Narrow-Sense Heritability?

Narrow-sense heritability, denoted as h², is the proportion of phenotypic variance (observable differences among individuals) that is due to additive genetic variance. In simpler terms, it tells us how much of the variation we see in a trait is due to genes that are passed down directly from parents to offspring and contribute to the trait's expression in a predictable, additive manner. This is extremely important for breeders because it determines how effectively they can improve a trait through selective breeding.

• Phenotypic Variance (Vp): The total variation observed in a trait within a population. This includes genetic and environmental influences.
• Additive Genetic Variance (Va): The portion of genetic variance due to the additive effects of genes. This is the variance that responds to selection.

The formula for narrow-sense heritability is:

h² = Va / Vp

Why is Narrow-Sense Heritability Important?

Understanding narrow-sense heritability is vital for several reasons:

• Predicting Response to Selection: Breeders use h² to predict how much a trait will improve in the next generation if they select individuals with superior traits to become parents.
• Designing Breeding Programs: It helps in choosing the most effective breeding strategies. For example, traits with high h² can be improved through simple mass selection, while traits with low h² might require more sophisticated breeding methods.
• Understanding Evolutionary Potential: In evolutionary biology, h² indicates the potential for a population to evolve in response to natural selection acting on a particular trait.
• Managing Genetic Conditions: In human and animal health, understanding the heritability of certain conditions can inform risk assessment and prevention strategies.

Methods to Calculate Narrow-Sense Heritability

Calculating narrow-sense heritability involves several approaches, each with its assumptions and limitations. Here are some common methods:

1. Parent-Offspring Regression

Parent-offspring regression is a classic method that examines the relationship between the phenotype of parents and the phenotype of their offspring. The slope of the regression line provides an estimate of the narrow-sense heritability.

Steps:

1. Collect Data: Gather phenotypic data for the trait of interest from both parents and their offspring. It is essential to have accurate and representative data for both generations.
2. Calculate Mid-Parent Value: For each offspring, calculate the average phenotype of its parents. This is the mid-parent value. If only one parent's data is available, you can use single-parent regression, but this is generally less accurate.
3. Plot the Data: Create a scatter plot with the mid-parent value on the x-axis and the offspring phenotype on the y-axis.
4. Perform Regression Analysis: Calculate the regression line that best fits the data points. The equation of the regression line is y = bx + a, where y is the offspring phenotype, x is the mid-parent value, b is the slope, and a is the y-intercept.
5. Estimate Heritability: The slope (b) of the regression line is an estimate of the narrow-sense heritability (h²).

Formula:

h² = b (slope of the regression line)

Example:

Suppose you are studying plant height in a population of flowers. You measure the height of several parent plants and the average height of their offspring. After plotting the data and performing regression analysis, you find that the slope of the regression line is 0.6. This indicates that the narrow-sense heritability of plant height is 0.6, meaning that 60% of the variation in plant height is due to additive genetic effects.

Assumptions and Limitations:

• No Environmental Correlation: This method assumes that there is no correlation between the environment of the parents and the environment of the offspring. If parents and offspring share similar environments, the estimate of h² will be inflated.
• Random Mating: It is assumed that mating is random within the population. Non-random mating can bias the estimate.
• No Epigenetic Effects: The method assumes that there are no epigenetic effects (changes in gene expression that are not due to changes in DNA sequence) that are passed from parents to offspring.
• Accurate Phenotyping: Accurate measurement of the phenotype in both parents and offspring is crucial.

2. Realized Heritability

Realized heritability is calculated based on the observed response to selection in a breeding program. It quantifies how much the mean of a trait changes after one generation of selection.

Steps:

1. Select Superior Individuals: Choose individuals with superior phenotypes for the trait of interest to become parents.
2. Measure Selection Differential (S): Calculate the difference between the mean phenotype of the selected parents and the mean phenotype of the entire population before selection. This is the selection differential.
3. Measure Response to Selection (R): Calculate the difference between the mean phenotype of the offspring of the selected parents and the mean phenotype of the entire population before selection. This is the response to selection.
4. Estimate Heritability: Divide the response to selection (R) by the selection differential (S) to estimate the narrow-sense heritability (h²).

Formula:

h² = R / S

Example:

Suppose you are breeding cows for milk production. The average milk production in the entire herd is 10,000 liters per year. You select the top 10% of cows with an average milk production of 12,000 liters per year to be the parents of the next generation. The selection differential (S) is 12,000 - 10,000 = 2,000 liters.

The offspring of the selected cows have an average milk production of 11,500 liters per year. The response to selection (R) is 11,500 - 10,000 = 1,500 liters.

The realized heritability is h² = R / S = 1,500 / 2,000 = 0.75. This indicates that 75% of the improvement in milk production is due to additive genetic effects.

Assumptions and Limitations:

• Accurate Measurement: Accurate measurement of the selection differential and the response to selection is crucial.
• No Environmental Change: The environment must be consistent between the generation of selection and the generation of response. Changes in the environment can confound the estimate of h².
• Representative Sample: The selected parents must be a representative sample of the genetic variation for the trait in the population.
• No Genetic Drift: The population size must be large enough to avoid significant genetic drift, which can alter the allele frequencies and bias the estimate.

3. Variance Components Analysis (Using ANOVA)

Variance components analysis is a statistical method used to partition the total phenotypic variance into different components, including additive genetic variance, dominance variance, environmental variance, and error variance. Analysis of Variance (ANOVA) is a common statistical technique used in this method.

Steps:

1. Design an Experiment: Set up an experiment with multiple families (full-sibs or half-sibs) and multiple individuals within each family. The experimental design should allow for the partitioning of variance.
2. Collect Data: Measure the phenotype of the trait of interest for all individuals in the experiment.
3. Perform ANOVA: Conduct an ANOVA to partition the total phenotypic variance into variance components due to family effects, environmental effects, and error.
4. Estimate Variance Components: Estimate the variance components for each source of variation.
5. Calculate Narrow-Sense Heritability: Use the variance components to estimate the narrow-sense heritability.

Formulas:

The exact formulas for calculating h² depend on the experimental design. Here are some common scenarios:

• Full-Sib Design: In a full-sib design, individuals within a family share both parents.

  • Vf = Variance among families
  • Ve = Variance within families (environmental variance + error)
  • Vp = Vf + Ve
  • h² = 2 * Vf / Vp (Assuming no common environmental effects)

• Half-Sib Design: In a half-sib design, individuals within a family share only one parent.

  • Vf = Variance among families
  • Ve = Variance within families (environmental variance + error)
  • Vp = Vf + Ve
  • h² = 4 * Vf / Vp (Assuming no common environmental effects)

Example:

Suppose you are studying body weight in a population of pigs. You set up an experiment with 20 families of half-sibs, with 10 pigs in each family. You measure the body weight of each pig and perform an ANOVA.

The ANOVA results show that the variance among families (Vf) is 10 kg², and the variance within families (Ve) is 30 kg².

The total phenotypic variance (Vp) is Vp = Vf + Ve = 10 + 30 = 40 kg².

The narrow-sense heritability is h² = 4 * Vf / Vp = 4 * 10 / 40 = 1.0. This indicates that the narrow-sense heritability of body weight is 1.0, meaning that all of the variation in body weight is due to additive genetic effects. This is an idealized example, and in practice, heritability estimates are rarely this high.

Assumptions and Limitations:

• Random Assignment: Individuals must be randomly assigned to families and environments.
• No Genotype-Environment Interaction: The method assumes that there is no genotype-environment interaction, meaning that the effect of the genotype on the phenotype is the same in all environments.
• Balanced Design: A balanced experimental design (equal number of individuals in each family) is preferred for accurate estimation of variance components.
• Large Sample Size: A large sample size is needed to accurately estimate the variance components.

4. Twin Studies (Human Genetics)

Twin studies are a common method for estimating heritability in human genetics. By comparing the similarity of traits in monozygotic (identical) twins and dizygotic (fraternal) twins, researchers can estimate the relative contributions of genetic and environmental factors to phenotypic variation.

Steps:

1. Collect Data: Gather phenotypic data for the trait of interest from both monozygotic (MZ) and dizygotic (DZ) twins.
2. Calculate Correlations: Calculate the correlation coefficient for the trait in MZ twins (rMZ) and DZ twins (rDZ).
3. Estimate Heritability: Use the correlations to estimate the narrow-sense heritability.

Formulas:

• h² = 2 * (rMZ - rDZ)

Example:

Suppose you are studying the heritability of IQ in humans. You collect IQ data from a large sample of MZ and DZ twins. The correlation coefficient for IQ in MZ twins (rMZ) is 0.85, and the correlation coefficient for IQ in DZ twins (rDZ) is 0.60.

The narrow-sense heritability is h² = 2 * (rMZ - rDZ) = 2 * (0.85 - 0.60) = 0.50. This indicates that 50% of the variation in IQ is due to additive genetic effects.

Assumptions and Limitations:

• Equal Environments: The method assumes that MZ and DZ twins share similar environments. If MZ twins experience more similar environments than DZ twins, the estimate of h² will be inflated.
• No Gene-Environment Interaction: The method assumes that there is no gene-environment interaction.
• Random Mating: It is assumed that mating is random within the population.
• Representativeness: The twin sample must be representative of the general population.

5. Molecular Methods (Genomic Heritability)

With the advent of high-throughput genotyping technologies, it is now possible to estimate heritability using molecular data. This approach, known as genomic heritability, uses genome-wide association studies (GWAS) to estimate the proportion of phenotypic variance explained by measured genetic variants (SNPs).

Steps:

1. Collect Genotypic and Phenotypic Data: Collect both genotypic data (SNP genotypes) and phenotypic data for the trait of interest from a large sample of individuals.
2. Perform GWAS: Conduct a genome-wide association study (GWAS) to identify SNPs that are associated with the trait.
3. Estimate Variance Explained by SNPs: Estimate the proportion of phenotypic variance explained by the identified SNPs.
4. Calculate Genomic Heritability: Sum the variance explained by all SNPs to estimate the genomic heritability.

Formula:

• h²g = Σ (Variance explained by each SNP)

Example:

Suppose you are studying the heritability of height in humans. You collect genotypic data (SNP genotypes) and height data from a large sample of individuals and perform a GWAS. The GWAS identifies thousands of SNPs that are associated with height.

After estimating the variance explained by each SNP, you find that the total variance explained by all SNPs is 0.40. This indicates that the genomic heritability of height is 0.40, meaning that 40% of the variation in height is explained by the measured SNPs.

Assumptions and Limitations:

• Accurate Genotyping: Accurate genotyping is crucial for accurate estimation of genomic heritability.
• SNP Coverage: The SNPs used in the analysis must adequately capture the genetic variation for the trait.
• Linkage Disequilibrium (LD): The method assumes that the SNPs are in linkage disequilibrium (LD) with the causal variants.
• Sample Size: A large sample size is needed to accurately estimate the variance explained by each SNP.
• Missing Heritability: Genomic heritability estimates often fall short of the heritability estimates obtained from twin studies. This discrepancy is known as the "missing heritability" problem.

Factors Affecting Heritability Estimates

Several factors can affect heritability estimates:

• Population: Heritability estimates are specific to the population in which they are measured. They can vary across different populations due to differences in allele frequencies and environmental conditions.
• Environment: Environmental variation can influence heritability estimates. In environments with high levels of variation, the proportion of phenotypic variance due to genetic factors may be lower, resulting in lower heritability estimates.
• Measurement Error: Errors in measuring the phenotype can reduce the accuracy of heritability estimates.
• Gene-Environment Interaction: Gene-environment interaction occurs when the effect of a gene on the phenotype depends on the environment. This can complicate the estimation of heritability.
• Gene-Environment Correlation: Gene-environment correlation occurs when individuals with certain genotypes are more likely to experience certain environments. This can also complicate the estimation of heritability.

Practical Applications of Narrow-Sense Heritability

Narrow-sense heritability has numerous practical applications in various fields:

• Agriculture: In plant and animal breeding, h² is used to predict the response to selection and design effective breeding programs. Traits with high h² can be improved through simple selection methods, while traits with low h² may require more complex breeding strategies.
• Human Genetics: In human genetics, h² is used to understand the genetic basis of complex traits and diseases. This information can inform risk assessment, prevention strategies, and personalized medicine approaches.
• Evolutionary Biology: In evolutionary biology, h² indicates the potential for a population to evolve in response to natural selection. Traits with high h² are more likely to evolve rapidly.
• Conservation Biology: In conservation biology, h² can be used to assess the genetic diversity and adaptive potential of endangered species.

Conclusion

Calculating narrow-sense heritability is a fundamental step in understanding the genetic architecture of traits and predicting the response to selection. Whether using parent-offspring regression, realized heritability, variance components analysis, twin studies, or molecular methods, each approach provides valuable insights into the relative contributions of genetic and environmental factors. Accurate estimation of h² is crucial for effective breeding programs, understanding the genetic basis of diseases, and predicting evolutionary potential. As genotyping technologies continue to advance and statistical methods become more sophisticated, our ability to estimate and utilize heritability will only continue to grow.