Chapter 9 Heritability and Repeatability

Chapter 9 Heritability and Repeatability σ 2 BV h 2 = σ 2 P r = σ 2 PA σ 2 P I. Heritability II. Repeatability III. Ways to Improve Heritability and Repeatability

Chapter 9 Heritability and Repeatability Learning Objective: To understand the concept of heritability and repeatability and to apply this knowledge to opportunistic selection and culling practices for traits of economic importance.

I. Heritability (A population parameter) Definitions: Heritability (h 2 ) A measure of the strength of the relationship between performance (phenotypic values) and breeding values for a trait in a population. Mathematically, heritability is the square of the correlation between phenotypic values and breeding values. (This is the Narrow-sense definition.) Heritability (In the Broad Sense, H 2 ) A measure of the strength of the relationship between performance (phenotypic values) and genotypic values for a trait in a population. (This is the Broadsense definition.) N.B. There is no such word as inheritability.

Heritability (h 2 ) : Definitions (cont.) Extent that observed phenotypic differences in a trait are due to inheritance (BV). Degree to which offspring resemble their parents in performance for a specific trait. For example, if a trait is highly heritable, a parent tends to breed as good as it Repro/ Health Production Yield h 2 Low (<20%) Moderate (20 to 40%) High (>40%)

A common misunderstanding of heritability: If Heritability is high, this does NOT mean that there is a higher probability or chance that a parent will transmit its genes to its offspring (or vice versa if low). The terms: ability, probability or the chances instead reflect aspects of Mendelian sampling events (segregation, recombination, and independent assortment).

Problem #1. h 2 = 2b The only basis for resemblance between a sire and his offspring is ½ his Breeding Value.

Problem #2. h 2 = 2b

Source: Lukefahr and Jacobson. 1998. JWM 62(1):262-268.

Heritability is presented here as a regression coefficient, redefined as the predicted change in breeding value (offspring) per unit change in phenotypic value (mid-parent).

The Importance of Heritability: Heritability is critically important to selection for quantitative (polygenic) traits. When heritability is low, phenotypic values generally reveal little about underlying breeding values. Accuracy of selection (BV prediction) is poor, and as a result, the rate of genetic change is expected to be slow. Instead, a better approach is to better manage the environment to increase performance. However, for lowly heritable traits, selection accuracy CAN be good if an animal s own performance record is included with relative s and (or) progeny records, which go into a large-scale genetic evaluation. When heritability is high, an animal s performance (phenotypic value) is generally a good indicator of its breeding value, and genetic change due to selection

Heritability and Prediction A Mathematical Example: Predict a sow s BV for number of pigs weaned (NW), based on her first litter record of 12 piglets (μ=10 piglets, set to 0). Heritability is low, only 0.10. ^ ^ ^ BV NW i = μ NW + b BV NW.PNW(P NW μ P NW) {b BV NW.PNW = h 2 NW} = 0 + 0.10 (12-10) = 0 + 0.10 (+2) = 0 + 0.20 = 0.20 (2 vs. 0.20!!!) and EPD = 0.10 Rarely is such a simple formula used because: 1) More than 1 record 2) Other permanent effects (GCV, E p ) 3) Records from relatives are available 4) Traits are correlated (r g ) 5) Common environmental effects (season or year of birth, age of dam, herd or ranch location)

N.B. Like heritability, repeatability ranges from 0 to II. Repeatability Definitions: Repeatability (r) A measure of the strength of the relationship between repeated records (repeated phenotypic values) for a trait in a population. Examples include milk yield, racing and show performance, litter size, fleece or wool weight. Repeatability (r) A measure of the strength (consistency, reliability) of the relationship between single performance records (phenotypic values) and producing abilities (PA) for a trait in a population. {PA = G + Ep} Repeatability (r) Is the correlation between repeated records for a trait for animals in a population.

Alternative Definitions of Repeatability: σ 2 PA σ 2 BV + σ 2 GCV + σ 2 Ep σ 2 BV r = = h 2 = σ 2 P σ 2 P σ 2 P In general, r > h 2 (because PA = BV + GCV and E p ) Besides BV, most polygenic traits that are repeatable are also influenced by GCV and/or E p. For example, weaning weight in beef calves: r = 0.40 and h 2 = 0.25 (Genetics literature) Racing performance in Quarter Horses: r = 0.32 and h 2 = 0.24 Wilham and Wilson, 1991) Antler points in mature White-tailed deer: r = 0.48 and h 2 = 0.39 (Lukefahr and Jacobson, 1998)

REPEATABILITY ESTIMATION FOR LITTER SIZE BORN IN SWINE: Excel demonstration:

Repeatability and Prediction: - An application Most Probable Producing Ability (MPPA) Link: Leachman s Eleanor Cow# n _ (C) Pre- Rank MPPA Ratio * Rank 1 3 476 4 450.7 112.7 3 2 5 492 3 470.8 117.7 1 3 1 560 1 464.0 116.0 2 4 1 500 2 440.0 110.0 4 n b 1 0.400 2 0.571 3 0.667 4 0.727 5 0.769 10 0.870 20 0.930 _ MPPA = H + b (C - H); {b = nr/(1+(n-1)r)}; b = weight factor _ {H = 400 lbs, r = 0.40} * Ratio = (450.7/400) x 100 = 112.7

I. The following horses were evaluated for racing performance (speed in seconds) based on multiple ¼-mile racing records, as follows: _ n b Horse (n) (C) b PA 1 5 19.45 2 8 19.29 3 4 18.80 4 0.653 5 0.702 8 0.790 ^ 1) Calculate b and PA values for all three horses. Formula: PA = b(c - H) _ (Use r = 0.32; H = 20 seconds) b = nr 1 + (n-1)r 2) Due to business expenses, if you had to cull one of the three horses, justify in adequate detail the basis for your decision. 3) Are many records necessary to have good accuracy of PA prediction for this trait? Explain your answer.

II. The following white-tailed bucks were evaluated for total number of antler points based on annual records, as follows: No. of Records Buck average _ Buck (n) (C) Rank b PA Re-Rank 1 3 10.3 2 5 7.5 3 1 9.0 4 2 7.5 1) Calculate b and PA values for all four bucks. Formula: PA = H + b(c - H) (Use r = 0.48; H = 8.0 points) n b 1 0.480 2 0.649 3 0.735 4 0.787 5 0.822 b = nr 1 + (n-1)r 2) If you had to harvest (cull) one of the four bucks, justify the basis for your decision. 3) How does PA accuracy improve with each additional record? That is, what is the basis or concept which explains the enhanced accuracy?

III. Ways to Improve Heritability and Repeatability Predict BV as accurately as possible to minimize mistakes in replacement selection. Predict PA as accurately as possible to minimize mistakes in culling. Emphasize environmental uniformity through good management (i.e., manage all animals as consistently as possible to minimize environmental variation or bias). Provide codes on data recording sheets for different contemporary management groups (e.g., creep feed and pastures) to avoid bias. Use mathematical adjustments for known environmental effects (e.g., WW ADJ ), which reduces total phenotypic variance and also avoids bias. All of these strategies involve improving accuracy and minimizing bias.

Adjusted 205-day WW Formula*: (WW BW) Age x 205 + BW + AOD WW and BW = Actual weaning and birth weights. If BW is unknown, then a 72.5 standard weight can be used. * According to Beef Improvement Federation (BIF, 2015).

Age-of-Dam Correction Factors for Weaning Weight in Beef Cattle* WW Adjustment (lb) Age of Dam BW Males Females 2 +8 +60 +54 3 +5 +40 +36 4 +2 +20 +18 5-10 0 0 0 11+ +3 +20 +18 * According to Beef Improvement Federation (BIF, 2014).

III. The following five male calves have phenotypic records for birth weight (BW) and weaning weight (WW). However, age of calf and dam varied at time of weaning, as shown below. Calf BW WW Age Age Adjusted WW Re- # (lb) (lb) Rank (days) of Dam (lb) Rank 1 55 430 5 180 2 2 60 524 2 205 7 3 50 492 3 200 3 4 65 623 1 230 9 5 55 431 4 182 4 THE FORMULA: WW = ((( WW - BW ) X 205 ) + BW ) + AOD ADJ days 1) Prior to conducting a genetic evaluation, which calf would be the best candidate for replacement selection?