ANIMAL GENETICS BREEDING UNIT II Principles of Animal
ANIMAL GENETICS & BREEDING UNIT – II Principles of Animal & Population Genetics Lecture – 8 Resemblance Between Relatives Dr K G Mandal Department of Animal Genetics & Breeding Bihar Veterinary College, Patna Bihar Animal Sciences University, Patna
Resemblance Between Relatives • Who are the relatives? ü In terms of genetics, those who share some genes in common due to common ancestry. Example: Direct relatives Parent – offspring Grand Parent – grand son Collateral relatives Half-sibs Full-sibs Cousin brother - sister
v Resemblance? • It means look alike or similarity. • Hence, resemblance between relatives means similarity between related individuals. • Related individuals look alike because they share common genes & common environment. • More common genes they have and share more common environment, they will be more resemble to each other.
• Different sort of relatives will show different degrees of resemblance – more closely relatives will show more resemblance. • Resemblance between relatives is the property of metric characters.
Objectives • Helps in grouping of relatives according to their family. • Helps in partitioning component of variance. observational • The degree of resemblance provides the methods of estimating the amount of additive genetic variance (VA). • Provides the heritability. methods to estimate
• Measurement of degree of resemblance between relatives rests on partitioning the observed phenotypic variance into components corresponding to the grouping of individuals into family of half-sibs, full-sibs and parent-offspring.
• Types of variance: Causal components of variance ‘V’ Example : VP = VG + VE = VA + VD + VI + VE Observational components of variance ‘б 2 ‘ б 2 P = б 2 G + б 2 E = б 2 A + б 2 D + б 2 I + б 2 E The observed components of variance can be estimated directly from observed phenotypic values and for this reason they are called as observational components of variance.
• Relatives are correlated to each other due to presence of common genes. • The amount of correlation depends on the degree of relationship. • Correlation between relatives resemblance between relatives. is the • Covariance is used to measure the correlation between relatives. • The degree of resemblance between relatives is the amount of covariance measured as a proportion of the total phenotypic variance.
Measurement of Covariance Full-sibs: • The observed phenotypic variance is partitioned into two components : between groups (б 2 B) & within groups (б 2 W) • The degree of resemblance between full-sibs is termed as intra-class correlation and denoted as ‘t’. t = б 2 B/ (б 2 B + б 2 W) = Co. V(FS)/ б 2 P (observed phenotypic Variance)
Parent - Offspring relationship: • In case of parent-offspring relationship, the grouping of observation is made into pairs rather than groups. (i) One parent with one offspring (ii) One parent with mean of several offspring (iii) Mid-parent with one offspring (iv)Mid-parent with mean of several offspring • The resemblance between parent-offspring is obtained through the estimation of covariance.
• The degree of resemblance between parentoffspring is expressed as regression of offspring on parent, bop = Cov. OP/ б 2 P • Both genetic and environmental sources of variance contribute to the co-variances of relatives, the co-variances of phenotypic values being sum of the genetic and environmental co-variances.
Methods to estimate Genetic Covariance 1. Direct relatives: • The co-variances of offspring with parent is computed from the sum of cross products, and the degree of resemblance is expressed as the regression of offspring on parent, thus bop = Cov. OP / б 2 P Where, б 2 P = variance of parent Cov. OP = covariance of offspring & parent
(i) Offspring and one parent: • Cov. OP = ∑Genotypic value of parent x Mean value of progeny = ∑Genotypic value of parent x ½ of its breeding value = ∑ G ½A = ∑ (A + D) ½A since, G = A + D = ½∑A 2 + ½∑AD = ½VA + ½Cov. AD = ½VA since, Cov. AD = zero
• The degree of resemblance between offspring and one parent is the regression of offspring on one parent, then bop = Cov OP / б 2 P = ½VA/VP (ii) Offspring and mid-parent: • Covariance of the mean of offspring and mean of both the parents : • Let ‘o’ = the mean value of progeny, P 1 & P 2 = the values of two parents, P‾ = ½(P 1 + P 2) = mid-parental value
• Sum of cross product, ∑ OP = ½(∑OP 1 + ∑OP 2) Cov. OP = ½(Cov. OP 1 + Cov. OP 2) Assume that P 1 & P 2 have same variance, then, Cov. OP = ½(Cov. OP + Cov. OP) = ½x 2 Cov. OP = ½VA
• Though the covariance of both the parents are same but observed phenotypic variances are not the same. • Let phenotypic values of P 1 & P 2 as M 1 & M 2 respectively. Then, P = ½(M 1 + M 2) P 2 = [½(M 1 + M 2)]2 = ¼(M 12 + M 22 + 2 M 1 M 2) б 2 P = ¼(б 2 M 1 + б 2 M 2 + 2 Cov. M 1 M 2) = ¼(б 2 M 1 + б 2 M 2)
Assume that variance of both the parents are equal. Then, б 2 P = ¼x 2 б 2 M = ½б 2 M = ½VP • The degree of resemblance between offspring and mid-parent, bop = Cov. OP/б 2 P = ½ VA/ ½ VP = VA/VP
2. Collateral Relatives: • In case of collateral relatives (HS and FS), the total observed phenotypic variance (б 2 P) is partitioned into between group component of variance ( б 2 B) and within group component of variance ( б 2 W). That is, б 2 P = б 2 B + б 2 W б 2 B ≈ covariance between groups б 2 w = variance of individuals within the group
(i) Degree of resemblance between HS: • HS groups constitute the sire family, since sire becomes the common parent. • Cov(HS) = variance of half of the BV of common parent. Cov(HS) = (½A)2 = ¼A 2 = ¼ б 2 A Thus, Cov(HS) = б 2 S = ¼ б 2 A
Degree of resemblance between HS, t = б 2 B/(б 2 B + б 2 W) = б 2 S/(б 2 S + б 2 W) = Cov(HS)/ б 2 P = ¼VA/VP
(ii) Degree of resemblance between FS: In FS, both parents are common. Mean genotypic value of FS = mean BV of both the parents. Let A & A‘ be the BV of parents respectively. Then, covariance of BV is the variance of ½(A + A’) = [½(A + A’)]2 = ¼(A 2 + A‘ 2 + 2 Co. VAA‘) = ¼(VA + VA) = ¼x 2 VA = ½VA
• Variance of dominance deviation of two parents is = ¼VD • Genetic Covariance of FS, Cov(FS) = ½VA + ¼VD • Degree of resemblance between FS is the correlation between FS, i. e. , Cov(FS)/VP t = (½VA + ¼VD)/VP Cov(FS) – 2 Cov(HS) = ½VA + ¼VD – 2(¼VA) = ½VA + ¼VD - ½VA = ¼VD
Phenotypic resemblance between relatives Relatives Covariance Degree of resemblance Regression (b) Or correlation (r) Offspring & one parent Cov OP = ½VA Cov OP / б 2 P bop = Offspring & mid-parent Cov. OP = ½VA Cov. OP/б 2 P bop = VA/VP Half sibs Cov(HS) = ¼VA Cov(HS)/ б 2 P Full sibs Cov(FS) = ½VA + ¼VD Cov(FS)/VP ½VA/VP t = ¼VA/VP t = (½VA + ¼VD)/ VP
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