How To Calculate Broad Sense Heritability

Broad sense heritability is a crucial concept in genetics and breeding, helping us understand the proportion of phenotypic variation in a population that is attributable to genetic variation. In simpler terms, it tells us how much of the differences we see among individuals are due to their genes versus environmental factors. Calculating broad sense heritability is essential for making informed decisions in agriculture, animal breeding, and even human genetics. This detailed guide will walk you through the process step by step, providing the necessary context, formulas, and examples to ensure you grasp the concept thoroughly.

Introduction to Broad Sense Heritability

Before diving into the calculations, it's essential to understand the fundamental concepts. Broad sense heritability, denoted as H², is a measure of the total genetic variance contributing to the phenotypic variance. Phenotypic variance (Vp) represents the total variation observed in a trait within a population. This variation can be attributed to genetic variance (Vg) and environmental variance (Ve).

The formula for phenotypic variance is:

Vp = Vg + Ve

Where:

• Vp is the phenotypic variance
• Vg is the genetic variance
• Ve is the environmental variance

Broad sense heritability is then calculated as the ratio of genetic variance to phenotypic variance:

H² = Vg / Vp

This value ranges from 0 to 1, where:

• 0 indicates that all phenotypic variation is due to environmental factors.
• 1 indicates that all phenotypic variation is due to genetic factors.

Understanding these foundational concepts is crucial before delving into the calculation methods.

Steps to Calculate Broad Sense Heritability

Calculating broad sense heritability involves several key steps. Here’s a detailed breakdown to help you through the process:

1. Data Collection:

   • Gather phenotypic data for the trait of interest from a population.
   • Ensure the data is accurate and representative of the population you are studying.

2. Estimating Phenotypic Variance (Vp):

   • Calculate the total phenotypic variance using the standard statistical formula:

   Vp = Σ (xi - μ)² / (n - 1)

   Where: * xi is each individual phenotypic value * μ is the population mean * n is the number of individuals in the population

3. Estimating Genetic Variance (Vg):

   • This step often requires specific experimental designs or data from related individuals.
   • Common methods include using ANOVA (Analysis of Variance) in designed experiments or analyzing parent-offspring data.

4. Estimating Environmental Variance (Ve):

   • Environmental variance is often estimated using genetically identical individuals (e.g., clones or inbred lines).
   • In such cases, any observed phenotypic variance is assumed to be due to environmental factors.

5. Calculating Broad Sense Heritability (H²):

   • Once you have estimates for Vg and Vp, use the formula:

   H² = Vg / Vp

   • Interpret the resulting value to understand the proportion of phenotypic variance attributable to genetic factors.

Let’s delve deeper into each of these steps with detailed explanations and examples.

Step 1: Data Collection

The first step in calculating broad sense heritability is to collect accurate and representative phenotypic data. This involves measuring the trait of interest in a population. For example, if you are studying plant height, you would measure the height of multiple plants in your population.

• Accuracy: Ensure that your measurements are precise and consistent. Use calibrated instruments and standardized procedures.
• Representative Sample: The sample should accurately represent the population you are studying. Avoid biases in your sampling method.
• Sample Size: A larger sample size generally leads to more accurate estimates of variance components.

Step 2: Estimating Phenotypic Variance (Vp)

Phenotypic variance (Vp) represents the total variation observed in the trait within the population. To calculate Vp, use the following formula:

Vp = Σ (xi - μ)² / (n - 1)

Example: Suppose you have the following plant heights (in cm) for 10 plants: 15, 18, 20, 22, 25, 16, 19, 21, 23, 24.

1. Calculate the mean (μ): μ = (15 + 18 + 20 + 22 + 25 + 16 + 19 + 21 + 23 + 24) / 10 = 20.3 cm

2. Calculate the squared differences from the mean (xi - μ)²:

   • (15 - 20.3)² = 28.09
   • (18 - 20.3)² = 5.29
   • (20 - 20.3)² = 0.09
   • (22 - 20.3)² = 2.89
   • (25 - 20.3)² = 22.09
   • (16 - 20.3)² = 18.49
   • (19 - 20.3)² = 1.69
   • (21 - 20.3)² = 0.49
   • (23 - 20.3)² = 7.29
   • (24 - 20.3)² = 13.69

3. Sum the squared differences: Σ (xi - μ)² = 28.09 + 5.29 + 0.09 + 2.89 + 22.09 + 18.49 + 1.69 + 0.49 + 7.29 + 13.69 = 99.00

4. Calculate the phenotypic variance: Vp = 99.00 / (10 - 1) = 99.00 / 9 = 11.00 cm²

Thus, the phenotypic variance for plant height in this example is 11.00 cm².

Step 3: Estimating Genetic Variance (Vg)

Estimating genetic variance is more complex and often requires specific experimental designs. Here are a few common methods:

• ANOVA in Designed Experiments:

  • Analysis of Variance (ANOVA) can be used in designed experiments (e.g., randomized block designs) to partition the total variance into genetic and environmental components.
  • In this approach, you grow different genotypes (e.g., different varieties of a crop) in multiple replicates and use ANOVA to estimate the variance due to genotype (Vg) and the variance due to error (Ve).
  • The genetic variance is then estimated from the mean squares of the ANOVA table.

• Using Inbred Lines or Clones:

  • If you have access to genetically identical individuals (e.g., clones or inbred lines), you can estimate environmental variance (Ve) by measuring the phenotypic variance among these individuals. The assumption is that all the variation among genetically identical individuals is due to environmental factors.
  • Genetic variance (Vg) can then be estimated by subtracting Ve from the total phenotypic variance (Vp).

• Parent-Offspring Regression:

  • This method involves measuring the trait of interest in parents and their offspring.
  • The slope of the regression line of offspring values on parent values provides an estimate of the heritability.
  • This method estimates narrow-sense heritability, which is a component of broad-sense heritability.

Example using ANOVA:

Suppose you conduct an experiment with 5 different genotypes of corn, each grown in 4 replicates in a randomized block design. The ANOVA table provides the following mean squares:

To estimate the genetic variance (Vg), you use the following formula:

Vg = (MSG - MSE) / r

Where:

• MSG is the mean square for genotype
• MSE is the mean square for error
• r is the number of replicates

In this example: Vg = (25 - 5) / 4 = 20 / 4 = 5

Thus, the estimated genetic variance is 5.

Step 4: Estimating Environmental Variance (Ve)

Environmental variance (Ve) represents the variation in phenotype due to environmental factors. Estimating Ve often involves using genetically identical individuals.

• Using Clones or Inbred Lines:
  • Grow multiple clones or inbred lines in a common environment.
  • Measure the phenotypic variance among these individuals.
  • This variance is assumed to be entirely due to environmental factors, so Ve is equal to this variance.

Example using Inbred Lines:

Suppose you grow 20 plants from an inbred line and measure their heights. The phenotypic variance among these plants is 3. Since these plants are genetically identical, you assume that Ve = 3.

In cases where genetically identical individuals are not available, environmental variance can be estimated indirectly by subtracting the genetic variance from the total phenotypic variance:

Ve = Vp - Vg

Step 5: Calculating Broad Sense Heritability (H²)

Once you have estimates for Vg and Vp, you can calculate broad sense heritability using the formula:

H² = Vg / Vp

Example:

Using the values from the previous examples:

• Vp = 11.00 (from Step 2)
• Vg = 5 (from Step 3)

H² = 5 / 11.00 ≈ 0.45

This means that approximately 45% of the phenotypic variation in plant height is due to genetic factors, while the remaining 55% is due to environmental factors.

Interpreting Broad Sense Heritability

The value of H² ranges from 0 to 1 and provides insights into the relative importance of genetic and environmental factors in determining the phenotype.

• H² close to 0: Indicates that most of the phenotypic variation is due to environmental factors. Selection for the trait may be less effective because the environment plays a dominant role.
• H² close to 1: Indicates that most of the phenotypic variation is due to genetic factors. Selection for the trait is likely to be effective because the genetic component is strong.
• Intermediate H² values: Suggest that both genetic and environmental factors contribute significantly to the phenotypic variation.

It's important to remember that broad sense heritability is a population-specific measure and can change depending on the environment and the genetic composition of the population.

Factors Affecting Broad Sense Heritability

Several factors can influence the value of broad sense heritability:

• Genetic Diversity: A population with high genetic diversity is likely to have a higher genetic variance (Vg), which can increase heritability.
• Environmental Variation: Increased environmental variation can increase the phenotypic variance (Vp) without affecting the genetic variance (Vg), thus reducing heritability.
• Population Structure: The genetic relatedness of individuals within the population can affect the estimation of genetic variance.
• Measurement Error: Inaccurate measurements can inflate the phenotypic variance (Vp), leading to an underestimation of heritability.

Importance of Broad Sense Heritability

Broad sense heritability is a valuable tool in various fields:

• Plant and Animal Breeding: It helps breeders predict the potential response to selection. Traits with high heritability are easier to improve through selective breeding.
• Genetics Research: It provides insights into the genetic architecture of traits and the relative importance of genetic versus environmental factors.
• Conservation Biology: It can inform conservation efforts by helping to understand the genetic basis of adaptive traits.
• Human Genetics: While broad sense heritability has limitations in human genetics due to ethical constraints, it can still provide insights into the genetic contributions to complex traits.

Limitations of Broad Sense Heritability

While broad sense heritability is a useful concept, it has several limitations:

• Overestimation of Genetic Contribution: Broad sense heritability includes all types of genetic variance (additive, dominance, and epistatic), which can overestimate the proportion of variation that is heritable in the narrow sense (i.e., the additive genetic variance that responds to selection).
• Population-Specific: Heritability estimates are specific to the population and environment in which they were measured. They cannot be generalized to other populations or environments.
• Environmental Effects: Heritability estimates do not provide information about the specific environmental factors that influence the trait.
• Non-Additive Genetic Effects: Broad sense heritability does not distinguish between different types of genetic effects, such as additive, dominance, and epistasis. This can be a limitation when trying to predict the response to selection.

Advanced Methods for Estimating Heritability

More advanced methods exist for estimating heritability, which can address some of the limitations of the basic approach. These include:

• Restricted Maximum Likelihood (REML): This statistical method is used to estimate variance components in mixed models, which can account for complex experimental designs and relatedness among individuals.
• Genomic Relationship Matrix (GRM): This method uses genome-wide genetic markers to estimate the genetic relatedness among individuals, which can improve the accuracy of heritability estimates.
• Quantitative Trait Locus (QTL) Mapping: This approach identifies specific regions of the genome that are associated with variation in the trait of interest, providing insights into the genetic architecture of the trait.

Practical Examples of Calculating Broad Sense Heritability

To further illustrate the calculation of broad sense heritability, here are a few more practical examples:

Example 1: Crop Yield

Suppose you are studying the yield of a wheat variety. You collect yield data (in kg per plot) from 20 plots and obtain the following results:

• Phenotypic Variance (Vp) = 2.5 kg²
• Genetic Variance (Vg) = 1.8 kg²

Calculate the broad sense heritability:

H² = Vg / Vp = 1.8 / 2.5 = 0.72

Interpretation: Approximately 72% of the variation in wheat yield is due to genetic factors. This suggests that selection for higher yield could be effective.

Example 2: Milk Production in Dairy Cows

You are studying milk production in a herd of dairy cows. You have data on milk yield (in liters per lactation) for 50 cows and estimate the following:

• Phenotypic Variance (Vp) = 5000 L²
• Environmental Variance (Ve) = 3000 L²

First, calculate the genetic variance:

Vg = Vp - Ve = 5000 - 3000 = 2000 L²

Now, calculate the broad sense heritability:

H² = Vg / Vp = 2000 / 5000 = 0.40

Interpretation: About 40% of the variation in milk production is due to genetic factors, while 60% is due to environmental factors such as nutrition and management practices.

Example 3: Disease Resistance in Plants

You are evaluating disease resistance in a population of tomato plants. You score each plant on a scale from 1 to 5, where 1 is highly susceptible and 5 is highly resistant. After analyzing the data, you find:

• Phenotypic Variance (Vp) = 1.2
• Genetic Variance (Vg) = 0.9

Calculate the broad sense heritability:

H² = Vg / Vp = 0.9 / 1.2 = 0.75

Interpretation: 75% of the variation in disease resistance is due to genetic factors. This indicates that selecting for disease-resistant plants would likely be successful.

Conclusion

Calculating broad sense heritability is a fundamental step in understanding the genetic basis of phenotypic variation. By carefully collecting data, estimating variance components, and interpreting the results, you can gain valuable insights into the relative importance of genetic and environmental factors. While broad sense heritability has limitations, it remains a useful tool for breeders, geneticists, and conservation biologists. By understanding the principles and methods outlined in this guide, you can effectively calculate and interpret broad sense heritability in your own research and applications. Advanced methods can provide even more refined estimates, but the basic principles remain essential for any study of quantitative traits.