This document discusses several topics related to estimating heritability and genetic parameters in livestock populations, including: 1) Factors that can affect heritability estimates such as population, location, method of estimation, and data set size. 2) Methods for estimating heritability including paternal half-sib analysis, repeatability, and genetic and phenotypic correlations. 3) The relationship between heritability, repeatability, and variance components. 4) Software tools that are commonly used for genetic data handling and analysis, including LSMLMW and DFREML.

1. Things to be Remembered
 Heritability is estimated for the traits and not for the
Individuals
 It may vary from population to population ----(each
population has different genetic make up)
 It may vary from location to location -----(each
location has different populations and environment)
 It may differ due to method of estimation ----(in
each method different sources of information are
used ignoring others)
 It may vary due to the size of data set ----with large
data set the estimates are more precise

2. Some environmental factors affecting milk yield
Measurements such as milk yield in dairy cattle
are affected by influences such as
Age of the cow at calving
Year and Season of the calving
Preceding dry period
Frequency of milking
Length of lactation
Lactation number
Corrections are made to eliminate these effects

3. Paternal Half-sib Analysis
 Sires are very important and must be known.
 Data on half-sibs are analyzed to estimate intra sire
correlation (t).
 Half sibs have only one forth of their genes in common
 Paternal half sibs used _____a few maternal half sibs in
a set
 The intra sire correlation (t) between paternal half sibs
can be computed as a ratio of the components of
variance.
t = S
2
S
2 + e
2

4. Half-sib correlation
Since half sibs have only one forth of their
genes in common, the S
2 represents A
2 /4.
h2 is computed by multiplying the half sib
correlation “t” by four.
h2= 4 (t)

5. 1 2 3 4 5
S. O.
Variation
D. F. Sum of
squares
Mean Squares Expected Mean
Squares
Between
sires
s –1  Si
2 – T2
n N
3/2 e
2 + kS
2
Within
sires
(ni-
1)
(Total) –
(Between
Sires)
3/2 e
2
Total N –1  Xij
2 – T2
N
Analysis of variance to partition
the variance components

6. REPEATABILITY
 The concept of repeatability is closely allied
to the concept of heritability
 The traits expressed several times during an
animal’s lifetime
Wool yield, weaning weights of lambs for sheep
and milk yield in dairy cattle
 It determines the upper limit of heritability
 May be defined as the correlation between
repeated records
 Regression of past performance on future
performance

7. Repeatability and Heritability
R = (A
2) + (D
2) + (I
2) + (PE
2)
(A
2) + (D
2) + (I
2) + (TE
2) +(PE
2)
H2 = (A
2) + (D
2) + (I
2)
(A
2) + (D
2) + (I
2) + (TE
2) +(PE
2)
h2 = (A
2) _____
(A
2) + (D
2) + (I
2) + (TE
2) +(PE
2)

8. Repeatability
Neither the genes nor the gene combinations
influence the successive expressions of a trait
Repeatability can be computed as the regression
of subsequent performance on past performance.
In may be derived from an analysis of variance
as an intra-class correlation among records or
observations of traits on the same individual.
Knowledge of repeatability estimates for various
traits may be used in selecting for future
performance.

9. Repeatability
 When the repeatability estimate for a trait is high,
culling on the basis of the first record should be
effective in improving the overall record of the
flock in future
 Offspring from the superior individuals should be
given preference when selection is made for
replacement stock.
 Repeatability estimates give an indication of how
many records should be obtained on an individual
before culling
 Used to estimate the probable producing ability of
individuals with repeated observations

10. Av. repeatability estimates for various
traits in dairy cattle
Traits # Studies Average Range
milk yield 17 0.54 0.30 - 0.71
Lactation length 12 0.25 0.09 - 0.53
Dry period 7 0.28 0.01 - 0.34
Calving interval 22 0.29 0.07 - 0.50
Service period 5 0.11 0.08 - 0.34
Services/concep 2 0.07 0.07 - 0.09

11. Analysis of variance for a trait measured
several times on the same individual
SOV df S Sq M Sq Exp M Sq
B C n –1 (Ci)2/m – CF BC/df W
2+ mB
2
W C n (m-1) TSS – BCS WC/df W
2
Total N-1 Xi2- CF

12. w
2 is a measure of the within-animal variance
B
2 is a measure of the between-animal
variance
which estimates all the genetic variance and
the portion of the environmental variance
peculiar to the individual
n = the number of animals/cows
m = the number of times each trait is
measured
N = total number of observations

13. SumXi = (X1+X2+X3……….Xn)
CF = (Xi)2 /N
TSS = Xi2- CF
Bet SS = (Cow)2/n - CF
Within SS= TSS – Bet. SS
Bet. MS = (Bet. SS)/D.F
Within MS = (Within SS)/D.F

14. Milk production records for repeatability estimation
Cow 1 Cow 2 Cow 3
Xi X2 Xi X2 Xi X2
1 6 36 5 25 5 25
2 5 25 4 16 8 64
3 3 9 2 4 4 16
4 4 16 4 16 6 36
 18 86 15 61 23 141

15. ANOVA for repeatability estimation
SOV DF S Sq M Sq Exp M Sq
B C 2 8.1667 4.0833 W
2+ mB
2
W C 9 18.500 2.055 W
2
Total 11 26.667

16. In Terms of Variance Components
T
2 = w
2 + B
2
Repeatability
B
2
R =  w
2 +  B
2
Cow Var (B
2) = 0.507
Repeatability = 0.198

17. Milk production records for repeatability estimation
Cow 1 Cow 2 Cow 3
Xi Xi Xi
1 1025 1125 1450
2 1120 1295 1652
3 1130 1350 985
4 1025 1248 1036
5 990 1540 1125

18. Milk production records for repeatability
estimation
Cow 1 Cow 2 Cow 3
Xi Xi Xi
1 1221 689 1465
2 1698 1400 1358
3 1989 1358 1087
4 1345 1424 1354

19. Milk production records for Heritability estimation
S1 S2 S3
Xi Xi Xi
1 980 1652 1569
2 1025 1568 1254
3 985 1920 1789
4 1090 1867 2546
5 1254 2154 1560
6 1568 2650 1294
7 1520 2145 1550
8 1234 2014 1397

20. Milk production records for Heritability estimation
S1 S2 S3
Xi Xi Xi
1 874 1654 1569
2 987 1587 1254
3 851 1895 1789
4 1024 1897 2546
5 1279 2045 1560
6 1230 2563 1294
7 1428 1987 1550
8 1158 1985 1397

21. Correlations
 Many characteristics among animals are not
independent.
 High wool weight is associated with long staple length
 Higher age at first calving with high milk yield
 Knowledge of the direction and degree of such
associations is important in formulating efficient
breeding/mating plans
 Not only the degree but also the direction of such
associations may change under selection programmes.

22. Correlations
• The environmental component of the correlation
results from the environment shared by the two
traits, for example sheep raised on poor pasture
or rangelands may get poor nutrition and their
live weights and wool yield are both affected.
These effects are not passed on to the next
generation.

23. Phenotypic Correlation
The phenotypic correlation between any two
traits has both genetic as well as environmental
components.
Statistically significant correlation means that
there is a high probability of an association
between the traits under consideration, of the
magnitude indicated by the sample value.
Tables are available which give the probability
of occurrence of correlations of a given
magnitude for a given number of pairs

24. Genetic correlation
 The genetic cause of correlation is chiefly pleotropy,
means that the same gene may affect more than one
trait
 It may also be due to the linkage of genes on the same
chromosome with the degree of association dependent
upon the distance between the two loci.
 Such associations might decrease in every generation,
as the linked genes would break up.
 If the gene is segregating it causes simultaneous
variation in the characters it affects.
 For example, genes that increase growth rate increase
both stature and weight, so they tend to cause
correlation between the two traits.

25. Genetic Correlations
 Genes that increase fatness, however, influence weight
without influencing stature, and are therefore, not a
cause of correlation.
 The degree of correlation arising from pleotropy
expresses the extent to which two characters are
influenced by the same genes.
 Some genes may increase both characters, while others
increase one and decrease the other; the former tend to
cause positive correlation, the latter a negative one.
 It means that selection for one trait will influence the
other correlated trait as a correlated response.

26. Genetic Correlations
The genetic correlation expresses the extent to
which two measurements reflect what is
genetically the same character.
Estimates of genetic correlations are strongly
influenced by gene frequencies, so they may
differ markedly in different populations

27. Phenotypic and Genetic correlations in a herd
of Sahiwal cattle
Traits correlated Pheno. Genet.
FLMY & 1st Lact. Length 0.353 0.483
FLMY & first C. I 0.394 0.457
FLMY & first dry period 0.354 0.493
FLMY & lifetime milk yield 0.022 0.005
AFC & first lactation length 0.148 0.993
AFC & first service period 0.295 0.502
AFC & lifetime milk yield -0.527 -0.999
AFC & herd life 0.322 0.441
AFC & FLMY 0.667 0.605
AFC & longevity 0.017 -0.06

28. Use of Computer in data handling and analysis
  Microsoft Excel
  Q. Pro
• Software Used
 Harvey’s Least Squares Maximum Likelihood
(LSMLMW) (1987, 1988, 1990)
W. R. Harvey (US)
Environmental effects
Genetic parameters based on Sire model

29. Software Used
• Derivative Free Restricted Maximum Likelihood
(DFREML) (1991,1997,1998,2000)
• o K. Meyer (UK)
• o Basically for variance components estimation
• o Heritability, Repeatability, Genetic correlations
• o Estimation of Breeding Values
• Based on BLUP using Individual Animal Model
• Most modern, utilizing all available information