POPULATION GENETICS

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POPULATION GENETICS

• Quantitative traits and evaluation of phenotypic
  variance.
• Heritability of quantitative traits
• Ing. Radovan KASARDA, PhD.

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Estimation of Heritability

• Method parent offspring h2OP
• similarity (kinship) between parents and
  offspring
• according to Wright (1920) relationship
  coefficient is 0,5
• comparison of relatives between groups
• h2 is twice of rXY resp. regress coefficient bYX..

Principle of calculation
Pair X Y X2 Y2 X.Y
1 production of mother production of daughter
n
S X S Y SX2 SY2 SX.Y
To calculate rXY resp. bYX estimate semi-values
A, B, C.
variance of X variance of Y
covariance between X and Y
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Estimation of Heritability

• Method parent offspring h2OP

than
In case data are divided by fathers, calculate
partial Ai, Bi, Ci separatelly for each father
and sumarize it.
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Estimation of Heritability

• Method parent offspring h2OP

With use of ANOVA
Father Variance s2 Covariance ni ni .s2i ni.covXY
1 710 77 20 14200 1540
2 520 154 30 15600 4620
3 800 100 30 24000 3000
4 400 20 20 8000 400
1 640 128 40 25600 5120
2 700 70 10 7000 700
4 530 78 20 10600 1560
2 480 35 20 9600 700
3 550 90 30 16500 2700
4 640 64 30 19200 1920
S 250 150300 22260
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Method half-sibs - ANOVA

• half-sibs have one common parent (father)
• use of genetic similarity between half-sibs
  (0,25)
• universal method
• Conditions of use
• groups of half-sibs in same conditions (min. 3 in
  group)
• group based by father (min. 3 fathers) (p)
• in group min. 3 measurements (ni)
• i.e. min. 9 measurements in total (n)

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ANOVA initial informations
Father i Daughter j Prod. kg Yij Yi. Yi.2/ni Y2ij
1 1 5 25
2 20 400
3 30 Siyij 55 1008,33 900
2 1 30 900
2 20 400
3 30 Siyij 80 2133,33 900
3 1 30 900
2 25 625
3 35 Siyij 90 2700 1225
S p 3 ni3 n 9 Y.. 225 Y.. 225 Y2i.5841,66 Si Sj Y2ij 6275
s2e
s2g
s2e
s2g
s2e
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ANOVA One Way
S DF MS s2
fgp -1 MSgSgfg
fen - p MSeSefe
S F MS s2
216,666 2 108,333 12,037
433,33 6 72,222 72,222
h24.ri
s2P s2g s2e 84,259 ri 0,143 h2 0,57
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ANOVA full-sibs

• in populations of multiparous animals (pigs,
  poultry,..)
• high genetic similarity of full-sibs (0,5), whose
  should under equal conditions show equal
  phenotype
• difficult for segmentation
• in group variability of environment
• between groups variability depended on diverse
  genetics of mothers
• between classes variability deperded on diverse
  genetics of fathers
• s2P s2F s2M s2E

• two-factorial ANOVA is used
• i father j mother k progeny

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ANOVA initial informations
Father i Mother j Daughter k Trait Yijk Yij. Yi.. Y2i../ni Yij.2/nij Y2ijk
1 1 1
2
3
2 1
2
3
3 1
2
3
S p mi nj SY... SY2i../ni Si Sj Y2ij/nij Si Sj Sk Y2ijk
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ANOVA two factorial
S DF MS s2
fFp -1 MSFSFfF
fMm - p MSMSMfM
fen - m MSeSefe
k1 average of daughter per mother k2
average of mother per father k3 average of
daugh. per father
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ANOVA two factorial
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ANOVA Half-sibs

• Exercise Calculate heritability

p8 Yi. Yi.2/ni Y2ij
1 75,94 288,3430 288,6938
2 75,50 285,0112 285,7600
3 79,33 314,6611 315,2639
4 77,98 304,0430 304,6091
5 73,65 271,2151 271,7600
6 76,38 291,6943 292,1326
7 75,34 283,8047 284,1924
8 75,33 283,7295 284,1279
ni20 SY.. SY2i. /ni Si Sj Y2ij
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ANOVA Full-sibs

• Exercise
• p 10 m 130 n 1955
• MSF391,3 k115,00
• MSM37,50 k215,40
• MSE6,40 k3193,00

• Calculate
• s2F h2F
• s2M h2M
• s2E h2FM
• s2P

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Non-parametric estimates of heritability

• very good elaborated
• used if less information is known
• low number of observation, ranking evaluation
• could resuld in non-realistic estimates
• only informative results of h2
• analyses of influence of genotypes on traits
• Estimates by Young
• estimates using Spearman correlation coeficients
• estimates based on realised heritability

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Non-parametric estimates of heritability

• Estimates by Young

above-average mothers below-average
mothers above-average daughters below-average
daughters

• Estimates using Spearmann rank-order correlation
  coefficient

mother rank 5,5 5,5 10
daughter rank 9 8 4
d 3,5 2,5 6
h2 rS
d absolute difference between mother and
daughter ranking

• Calculate heritability

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Non-parametric estimates of heritability

• estimates based on realised heritability
• by division of pop. on better () resp. worser
  (-) half

O offspring P - parents

• according to realized selection

- realized genetic gain - selection difference
(di.s)
- difference of selected offspring from average
of off. generation - difference of selected
parents from average of parental generation