Animal Breeding Calculators
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Heritability (h²)
h² = V_A / V_P
V_A = additive genetic variance; V_P = total phenotypic variance. h² ranges 0–1. High h² (> 0.5): trait responds well to selection (e.g., milk fat % in dairy cattle: h² ≈ 0.5). Low h² (< 0.2): strong environmental influence; less response to selection (e.g., litter size in pigs: h² ≈ 0.1). h² is population and environment specific.
Breeder's Equation (Genetic Gain)
ΔG = i × h × σ_A / L
i = selection intensity (standardized); h = square root of heritability; σ_A = additive genetic standard deviation; L = generation interval (years). To maximize ΔG: increase i (more stringent selection), use high-h² traits, reduce generation interval (genomic selection enables early selection without waiting for progeny).
Estimated Breeding Value (EBV)
EBV = 2 × (deviation of progeny mean from population mean). Best Linear Unbiased Prediction (BLUP) estimates EBVs using all phenotypic information from the animal and its relatives, accounting for environmental effects. Genomic EBV (GEBV) uses genome-wide SNP genotypes to predict breeding values with higher accuracy at earlier ages.
Selection Methods
- Mass selection: Select based on individual phenotype — effective for high-h² traits
- Family selection: Select based on family mean — useful for low-h² traits
- Genomic selection: Train prediction equations on reference population with genotypes + phenotypes; apply to genotyped candidates without phenotype data
Glossary
Frequently Asked Questions
Heritability (h²) = additive genetic variance / total phenotypic variance (V_A/V_P). It quantifies the proportion of phenotypic differences between individuals attributable to additive genetic differences. High h² (>0.5) means selection is effective — high-performing animals reliably pass their advantages to offspring. Low h² (<0.2) means the trait is strongly influenced by environment — individual performance is a poor predictor of genetic merit. Heritability is not fixed — it depends on the population and environment in which it is measured.
EBV is the estimated additive genetic merit of an individual relative to the population average, predicted from phenotypic records of the animal and its relatives using BLUP (Best Linear Unbiased Prediction). EBV = 2 × (mean progeny performance − population mean). Positive EBV means the animal is expected to pass above-average performance to its offspring; negative EBV means below-average. Genomic EBVs (GEBVs) use dense SNP marker data to estimate breeding values more accurately at younger ages, without waiting for progeny to be tested.
Genomic selection uses genome-wide SNP genotypes (~50,000 or more markers) to predict breeding values. Steps: (1) Establish a reference population with both genotypes and high-accuracy phenotypes/EBVs. (2) Estimate marker effects using statistical methods (GBLUP, Bayesian models). (3) Genotype selection candidates and sum their marker effects to obtain genomic EBV (GEBV). Advantages: higher accuracy at younger ages; shorter generation interval; evaluate animals before phenotype is expressed (e.g., predict dairy bull breeding value before daughters calve). Has transformed dairy cattle, pig, and poultry breeding since ~2009.
Genetic gain per year ΔG/year = (i × h × σ_A) / L. Four levers: (1) Selection intensity (i) — select a smaller fraction of candidates; higher i but requires larger candidate population. (2) Heritability (h = √h²) — focus on traits with higher h² or improve trait measurement to reduce environmental variance. (3) Genetic standard deviation (σ_A) — genetic variation must exist; crosses between divergent breeds initially increases σ_A. (4) Generation interval (L, years) — shorter L = faster gain; genomic selection has dramatically reduced L in dairy cattle from ~7 years to ~2 years.