Course: Advanced Animal Breeding

1. Course: Advanced Animal Breeding MS program in Animal Production Faculty of Graduate Studies An-najah National University Instructor: Dr. Jihad Abdallah Covariance between Relatives and Estimation of Genetic Parameters

2. Genetic Covariance Between Relatives rPQ = coefficient of additive relationship uPQ = fACfBD + fADfBC = ¼ (rACrBD + rADrBC) A B C D P Q

3. Environmental covariance • Individuals reared together share the same environment (common environment) which may cause individuals to resemble each other for entirely non-genetic reasons (Environmental covariance). • This covariance between members of the same group increases the variance among group means. The extra variance caused by environmental covariance is called the common environmental variance (VEc) • Sources of environmental covariance may include maternal effects, diet, climatic conditions, disease exposure and herd effects.

4. Maternal effects • A maternal effect can be defined as any environmental influence that the mother confers on the phenotype of her offspring. • Maternal effects increases the covariance among members sharing the same mother. For example offspring of the same mother resemble each other in body weight because they share the same milk supply. • Also maternal effects may increase the covariance between offspring and their mother for the same trait. (phenotypic value of the mother for the studied character influence the value of the offspring for the same character). For example, large mothers give more milk causing their offspring to grow better.

5. The maternal component is an environmental influence of the mother on her offspring. • But mothers may differ in maternal effect because of genetic factors. • Maternal effects of the mother may be controlled by nuclear genes that influence maternal performance or/and cytoplasmic genes transmitted by mitochondrial DNA.

6. The covariance between relatives may be increased if nuclear genetic maternal effects are considered. w is the mother of x and z is the mother of y

7. Estimation of heritability • There are several methods for estimation of heritability: • Regression methods • ANOVA (nested and half-sib designs) • BLUP/REML

8. Regression Methods • Offspring-parent regression: Heritability is estimated by the regression of the phenotype of one offspring (or the mean of all offspring) on the phenotype of one parent. • COV(O,P) = ½ VA • In this case: h2 = 2 (regression coefficient). • Standard error (h2) = 2 (standard error of the regression coefficient)

9. 2. Offspring – Midparent regression: • Heritability is estimated by regressing the phenotype of the offspring on the midparent value (mean phenotype of both parents). • In this case: h2= regression coefficient SE (h2) = SE (regression coefficient)

11. Linear model: Regression coefficient Intercept

12. The standard error of the regression coefficient is: Where:

13. Testing the significance of the heritability estimate H0: h2 = 0 H1: h2 > 0 The test statistic is: If tcal is larger than ttab, then h2 is significantly larger than 0

14. ATTENTION: the estimate of heritability from the regression of offspring on the dam (mother) may be biased upward due to maternal effects  therefore, the estimate is generally larger than that obtained from the regression of offspring on sire (father).

15. Regression on dam’s phenotype h2 = 2 (0.18539)=0.37 Standard error (h2) = 2(0.08372) = 0.1674

16. Regression on dam’s phenotype h2 = 2 (0.22542) = 0.451 Standard error (h2) = 2(0.15522) = 0.31 Regression on midparent h2 = 0.33023 Standard error (h2) = (0.11882)

17. Analysis of Variance (ANOVA) 1. Half-sib design: Sire 1 Sire 2 Sire s .………………………….. Dam 1 Dam 2 …..Dam n1 Dam 1 Dam 2 …..Dam nS daughter 1 daughter 2 …..daughter n1 daughter 1 daughter 2 …..daughter ns

18. The linear model for the half-sib design: i = 1, ……….., s j = 1, ………, ni Yij : observation (phenotype) on the jth daughter of the ith sire µ : overall mean of all individuals Si : random effect of ith sire with mean 0 and variance S2 . Eij: residual (containing uncontrolled environmental and genetic effects) with mean 0 and variance E2 .

19. For a balanced half-sib design(equal number of progeny per sire),λ = number of progeny per sire

22. Example (Becker, 1975) 27331

27. 2. Nested-design (Full-sib/half sib design) : s males (sires) each mated to a number of dams each of which has a number of offspring

29. Value of the kth offspring from the jth dam mated to sire i Effect of sire i Effect of dam j mated to sire i Overall mean Residual:Within-family deviation of kth offspring from the mean of the ij-th family Nested ANOVA model: yijk = m + Si + Dij+ Eijk i = 1, 2, ……..s , (s is the number of sires) j = 1, 2, ……..di (di is the number of dams mated to sire i) k = 1, 2,…......nij (nij is number of progeny of sire i and dam j)

30. s2S = between-sire variance = variance in sire family means s2D = variance among dams within sires = variance of dam means for the same sire s2E = within-family variance s2T = s2S + s2D + s2E

32. If the design is balanced (equal number of dams per sire and equal number of progeny per dam), then λ1 = λ2 = number of progeny per dam λ3 = number of progeny per sire

33. Estimation of variance components Estimation of the genetic and environmental components of variance (assuming no maternal and common environmental effects):

34. Therefore, we can estimate heritability as: Standard error of the heritability estimate

42. Estimation using BLUP/REML

44. Heritability is estimated using ML or REML

45. Estimation of repeatability • Can be estimated when repeated observations are taken on the same animal for the same trait • It is estimated by the intra-class correlation

46. The design: animal 1 animal 2 animal s .………………………….. record 1 record 2 …..record n1 record 1 record 2 …..record nS Y11 Y12 ….. Y1n1 Ys1 Ys2 ….. Ysn1

47. The linear model: i = 1, ……….., s j = 1, ………, ni Yij :jthobservation (phenotype) on the ith animal µ : overall mean of all individuals βi : random effect of ith animal with mean 0 and variance b2 Eij: residual (containing temporary environmental effects) with mean 0 and variance E2 .

48. For a balanced (equal number of records per animal),λ = number of records per animal