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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. Genetic Covariance Between Relatives.

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Course advanced animal breeding

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


Genetic covariance between relatives
Genetic Covariance Between Relatives

rPQ = coefficient of additive relationship

uPQ = fACfBD + fADfBC

= ¼ (rACrBD + rADrBC)

A B C D

P

Q


Environmental covariance
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.


Maternal effects
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.


Course advanced animal breeding

  • 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.


Course advanced animal breeding

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


Estimation of heritability
Estimation of heritability genetic maternal effects are considered.

  • There are several methods for estimation of heritability:

  • Regression methods

  • ANOVA (nested and half-sib designs)

  • BLUP/REML


Regression methods
Regression Methods genetic maternal effects are considered.

  • 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)


Course advanced animal breeding

2. genetic maternal effects are considered.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)


Course advanced animal breeding

Linear model: genetic maternal effects are considered.

Regression coefficient

Intercept


Course advanced animal breeding

The genetic maternal effects are considered.standard error of the regression coefficient is:

Where:


Testing the significance of the heritability estimate
Testing the significance of the heritability estimate genetic maternal effects are considered.

H0: h2 = 0

H1: h2 > 0

The test statistic is:

If tcal is larger than ttab, then h2 is significantly larger than 0


Course advanced animal breeding

  • ATTENTION: genetic maternal effects are considered. 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).


Course advanced animal breeding

Regression on dam’s phenotype genetic maternal effects are considered.

h2 = 2 (0.18539)=0.37

Standard error (h2) = 2(0.08372) = 0.1674


Course advanced animal breeding

Regression on dam’s phenotype genetic maternal effects are considered.

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)


Course advanced animal breeding

Analysis of Variance (ANOVA) genetic maternal effects are considered.

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


Course advanced animal breeding

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 .


Course advanced animal breeding

For a balanced half-sib design genetic maternal effects are considered.(equal number of progeny per sire),λ = number of progeny per sire


Course advanced animal breeding

Example (Becker, 1975) genetic maternal effects are considered.

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Course advanced animal breeding

2. genetic maternal effects are considered.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


Course advanced animal breeding

Value of the k genetic maternal effects are considered.th 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)


Course advanced animal breeding

s genetic maternal effects are considered.2S = 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


Course advanced animal breeding

If the design is balanced ( genetic maternal effects are considered.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


Course advanced animal breeding

Estimation of variance components genetic maternal effects are considered.

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


Course advanced animal breeding

Therefore, we can estimate heritability as: genetic maternal effects are considered.

Standard error of the heritability estimate


Estimation using blup reml
Estimation using BLUP/REML genetic maternal effects are considered.


Course advanced animal breeding

Heritability is estimated using ML or REML genetic maternal effects are considered.


Estimation of repeatability
Estimation of repeatability genetic maternal effects are considered.

  • Can be estimated when repeated observations are taken on the same animal for the same trait

  • It is estimated by the intra-class correlation


Course advanced animal breeding

The design: genetic maternal effects are considered.

animal 1

animal 2

animal s

.…………………………..

record 1 record 2 …..record n1

record 1 record 2 …..record nS

Y11 Y12 ….. Y1n1

Ys1 Ys2 ….. Ysn1


Course advanced animal breeding

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 .


Course advanced animal breeding

For a balanced genetic maternal effects are considered.(equal number of records per animal),λ = number of records per animal


Course advanced animal breeding

Example (Agarwall and Agarwall) genetic maternal effects are considered.

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Course advanced animal breeding

Type 1 Analysis of Variance genetic maternal effects are considered.

Sum of

Source DF Squares Mean Square

ANIMAL 3 230296 76765

Error 14 182517 13037

Corrected Total 17 412813 .

Type 1 Analysis of Variance

Source Expected Mean Square

ANIMAL Var(Error) + 4.4815 Var(ANIMAL)

Error Var(Error)

Corrected Total .

Type 1 Estimates

Variance Component Estimate

Var(ANIMAL) 14220.4

Var(Error) 13036.9