Describe the different methods to estimate heritability in animals.

Understanding Heritability

Heritability (often denoted as h²) is a critical parameter for animal breeders, indicating the extent to which genetic variation contributes to the observed phenotypic variation in a trait. It is expressed as a ratio of genetic variance (V_G) to total phenotypic variance (V_P), where V_P includes both genetic and environmental variances (V_P = V_G + V_E). While broad-sense heritability (H²) considers all genetic variance (additive, dominance, and epistatic), narrow-sense heritability (h²) focuses specifically on additive genetic variance (V_A). Narrow-sense heritability is particularly important in animal breeding because additive genetic variance is the component that can be directly passed from parents to offspring, making it the primary determinant of response to selection.

Methods to Estimate Heritability

The estimation of heritability relies on analyzing the resemblance among genetically related individuals within a population. Different statistical methods are employed based on the type and availability of data, as well as the genetic relationships among the sampled animals.

1. Regression Methods (Parent-Offspring Regression)

These methods assess the relationship between the performance of parents and their offspring. The slope of the regression line indicates the heritability.

• Offspring-on-One-Parent Regression:

  In this method, the phenotypic values of offspring are regressed on the phenotypic values of one parent (e.g., sire or dam). The regression coefficient (b_OP) estimates half of the narrow-sense heritability (h²), i.e., b_OP = 0.5h². This method is straightforward but requires data across two generations.

  Formula: $h^2 = 2 \times b_{OP}$

• Offspring-on-Mid-Parent Regression:

  Here, the offspring's phenotypic value is regressed on the average phenotypic value of both parents (mid-parent value). The regression coefficient (b_OMP) directly estimates the narrow-sense heritability (h²), i.e., b_OMP = h².

  Formula: $h^2 = b_{OMP}$

Advantages: Relatively simple to understand and calculate, robust against selection of parents [2].

Disadvantages: Requires data from at least two generations and does not fully utilize all genetic relationships within a pedigree. Confounding with maternal effects can be an issue if only dam data is used.

2. Correlation Methods (Intra-class Correlation)

These methods utilize the correlation between relatives to estimate variance components, from which heritability is derived.

• Half-Sib Correlation (Sire or Dam Families):

  This is a widely used method, particularly with paternal half-sibs (offspring sharing the same sire but different dams). The intra-class correlation among paternal half-sibs provides an estimate of one-fourth of the additive genetic variance. By estimating the sire variance component (V_S) and total phenotypic variance (V_P), heritability can be calculated.

  Formula: $h^2 = \frac{4 \times V_S}{V_P}$

  Advantages: Less confounded by common environmental effects compared to full-sib correlations. Widely applicable in livestock populations where a single sire may produce many offspring.

  Disadvantages: Requires accurate pedigree information and sufficient family sizes.

• Full-Sib Correlation:

  This method uses the correlation among full-sibs (offspring sharing both parents). The intra-class correlation among full-sibs estimates half of the additive genetic variance plus one-fourth of the dominance variance. Therefore, it estimates broad-sense heritability, or a value between narrow-sense and broad-sense heritability, making it potentially confounded by common environmental effects and dominance variance.

  Formula: $h^2 = \frac{2 \times (V_S + V_D)}{V_P}$ (where $V_S$ and $V_D$ are sire and dam variance components, estimating additive and dominance effects)

  Advantages: Can be used when parent information is limited.

  Disadvantages: Highly susceptible to confounding by common environmental effects shared by full-sibs (e.g., common maternal environment), leading to overestimation of genetic effects.

• Twin Data Analysis:

  This method is primarily used for estimating broad-sense heritability, especially in humans but also sometimes in animal models involving monozygotic (identical) and dizygotic (fraternal) twins. By comparing the phenotypic correlation between identical twins (sharing 100% of their genes) and fraternal twins (sharing 50% of their genes, on average), the genetic and environmental contributions can be separated.

  Formula for Broad-Sense Heritability (Falconer's Formula): $H^2 = 2 \times (r_{MZ} - r_{DZ})$, where $r_{MZ}$ is the correlation for monozygotic twins and $r_{DZ}$ is for dizygotic twins.

  Advantages: Powerful for disentangling genetic and environmental influences.

  Disadvantages: Availability of twin data, especially monozygotic twins, is limited in most animal populations. Assumptions about equal environmental sharing for both twin types can be violated.

3. Variance Component Estimation (ANOVA and Mixed Models)

These sophisticated statistical methods partition the total phenotypic variance into its genetic and environmental components.

• Analysis of Variance (ANOVA):

  In balanced data sets (equal numbers of individuals per family), ANOVA can be used to estimate variance components. By analyzing mean squares for different sources of variation (e.g., between sires, between dams, within families), genetic and environmental variance components can be derived. This is often used in conjunction with half-sib or full-sib family structures.

  Advantages: Conceptually straightforward for balanced data.

  Disadvantages: Less efficient and potentially biased with unbalanced data, which is common in real-world animal breeding programs.

• Restricted Maximum Likelihood (REML) / Animal Model:

  REML is the most widely used and statistically robust method for estimating variance components, particularly in complex pedigrees and unbalanced data sets. It simultaneously estimates fixed effects (e.g., sex, age, herd-year) and random effects (e.g., additive genetic effects, environmental effects) by maximizing the likelihood of the observed data, while accounting for the loss of degrees of freedom due to estimating fixed effects. The "animal model" is a specific mixed linear model where each animal's additive genetic value is treated as a random effect, allowing for the inclusion of all known pedigree relationships to build an 'A-matrix' (additive relationship matrix).

  Advantages:

  • Provides unbiased estimates of variance components and heritability even with unbalanced data and selection.
  • Utilizes all available pedigree information, maximizing the accuracy of estimates.
  • Can incorporate complex fixed and random effects, accounting for various environmental and genetic factors.

  Disadvantages: Computationally intensive, especially for large datasets. Requires specialized statistical software (e.g., ASREML, WOMBAT, BLUPF90).

• Bayesian Methods:

  Similar to REML, Bayesian methods estimate variance components and genetic parameters by incorporating prior information about the parameters along with the observed data. They provide a posterior distribution of the parameters, offering a more complete picture of uncertainty. Markov Chain Monte Carlo (MCMC) techniques are commonly used for sampling from these distributions.

  Advantages: Can handle complex models and provide full probability distributions for parameters. Useful for incorporating prior knowledge.

  Disadvantages: Computationally demanding and requires careful selection of prior distributions.

4. Genomic-Based Methods

With the advent of high-throughput genotyping, methods leveraging genomic information have become increasingly important.

• Genomic Relationship Matrix (GRM) based methods:

  Instead of relying solely on pedigree-based relationships, these methods construct a Genomic Relationship Matrix (GRM) from high-density SNP (Single Nucleotide Polymorphism) markers. The GRM captures actual genetic similarities between individuals more accurately than pedigree, especially for distantly related individuals or when pedigree records are incomplete. These GRMs are then incorporated into mixed models (similar to REML) to estimate 'genomic heritability' (h²g).

  Advantages: More precise estimates of genetic relationships, increased accuracy of breeding value estimation, ability to estimate heritability in populations without extensive pedigree records.

  Disadvantages: Requires dense SNP chip data, which can be expensive.

• SNP-based Heritability Enrichment Analysis:

  This involves analyzing the proportion of heritability explained by specific SNP subsets. It helps in understanding the genetic architecture of complex traits by identifying genomic regions or functional variants that contribute significantly to a trait's heritability [14]. Models like VanRaden, GCTA, and LDAK are used to analyze heritability enrichment based on SNP data.

  Advantages: Provides insights into the genomic architecture and potential causal variants of traits.

  Disadvantages: Complex modeling, sensitive to assumptions about linkage disequilibrium and minor allele frequency [14].

Method Category	Key Principle	Primary Use	Considerations
Regression	Resemblance between parents and offspring	Estimating narrow-sense heritability (h²)	Requires two generations, sensitive to maternal effects if not accounted for.
Correlation	Resemblance among relatives (half-sibs, full-sibs, twins)	Estimating h² (half-sibs) or H² (full-sibs, twins)	Requires good pedigree, full-sib method confounded by common environment.
Variance Components (REML/Animal Model)	Partitioning phenotypic variance using pedigree relationships	Unbiased estimates of h² in complex, unbalanced pedigrees	Computationally intensive, requires specialized software.
Genomic Methods (GRM)	Using actual genomic similarities (SNPs)	More accurate h² and genomic breeding values	Requires high-throughput genotyping, expensive.