1
00:00:01,562 --> 00:00:03,685
The topic of this lecture is a genetic

2
00:00:03,685 --> 00:00:05,016
parameters in animal breeding.

3
00:00:06,296 --> 00:00:08,620
The lecture is part of module 3,

4
00:00:08,940 --> 00:00:09,822
Animal Breeding.

5
00:00:10,350 --> 00:00:12,833
The creation of this presentation was

6
00:00:12,833 --> 00:00:15,077
supported by the Erasmus plus KA2

7
00:00:15,765 --> 00:00:18,409
grant, if the project ISAGREED,

8
00:00:18,889 --> 00:00:20,064
innovation of content

9
00:00:20,779 --> 00:00:23,103
and structure of study programs in the

10
00:00:23,103 --> 00:00:25,080
field of management of animal genetics

11
00:00:25,794 --> 00:00:28,357
and food resources using digitalization.

12
00:00:30,568 --> 00:00:33,372
Genetic parameters are statistical values

13
00:00:33,773 --> 00:00:35,192
that define the genetic

14
00:00:35,743 --> 00:00:38,467
potential and the heritability of traits

15
00:00:38,627 --> 00:00:40,128
in a population of animals.

16
00:00:40,917 --> 00:00:43,561
Heritability is expressed as a population

17
00:00:43,561 --> 00:00:44,843
statistical parameter

18
00:00:45,611 --> 00:00:48,576
as the heritability coefficient. This

19
00:00:48,576 --> 00:00:50,098
coefficient measures

20
00:00:50,225 --> 00:00:52,148
the proportion of total phenotypic

21
00:00:52,148 --> 00:00:54,872
variability in a trait that can be

22
00:00:54,872 --> 00:00:55,593
attributed

23
00:00:55,560 --> 00:00:58,364
to genetic variability. This

24
00:00:58,364 --> 00:01:00,192
proportion can range from zero

25
00:01:00,334 --> 00:01:03,259
to 1. Another genetic

26
00:01:03,259 --> 00:01:05,208
parameter is genetic correlations,

27
00:01:05,790 --> 00:01:08,634
which quantify the extent to which genes

28
00:01:08,634 --> 00:01:10,224
influencing 1 trait

29
00:01:10,684 --> 00:01:13,168
simultaneously affect another

30
00:01:13,168 --> 00:01:15,240
trait. The value of genetic

31
00:01:15,578 --> 00:01:18,022
correlations range from -1 to

32
00:01:18,182 --> 00:01:20,256
+1. Positive genetic

33
00:01:20,593 --> 00:01:23,237
correlations indicate that improvement

34
00:01:23,357 --> 00:01:25,272
in one trait will lead to improvement

35
00:01:25,808 --> 00:01:28,692
in another trait. Negative

36
00:01:28,772 --> 00:01:30,288
genetic correlations indicate

37
00:01:30,582 --> 00:01:33,066
a trait of between traits, where

38
00:01:33,066 --> 00:01:35,304
improvement in one trait may lead to

39
00:01:35,516 --> 00:01:37,760
a decrease in another.

40
00:01:39,362 --> 00:01:40,320
The last genetic parameter

41
00:01:40,931 --> 00:01:43,335
is repeatability coefficient R,

42
00:01:43,936 --> 00:01:45,338
which estimates the genetic

43
00:01:46,026 --> 00:01:48,109
in repeated traits through an

44
00:01:48,109 --> 00:01:49,872
individual's lifetimes.

45
00:01:52,803 --> 00:01:54,966
Methods for estimating genetic

46
00:01:54,966 --> 00:01:55,928
parameters

47
00:01:56,295 --> 00:01:58,859
Require knowledge of phenotypic values

48
00:01:59,140 --> 00:02:00,384
which are measured for production

49
00:02:00,749 --> 00:02:03,473
traits and quantification of kinship

50
00:02:03,473 --> 00:02:05,400
relationships which determine

51
00:02:05,603 --> 00:02:08,127
shared gene proportions. These

52
00:02:08,127 --> 00:02:10,576
relationships can be determined using

53
00:02:10,858 --> 00:02:13,422
pedigree data or currently using

54
00:02:13,582 --> 00:02:14,544
genomic data.

55
00:02:15,552 --> 00:02:18,477
How do we estimate them?We must use

56
00:02:18,477 --> 00:02:20,680
statistical methods, particularly

57
00:02:20,647 --> 00:02:22,970
linear models such as regression

58
00:02:22,970 --> 00:02:25,454
analysis, analysis of variants.

59
00:02:25,902 --> 00:02:27,945
Covariance analysis and correlation

60
00:02:27,945 --> 00:02:30,480
analysis. The goal is

61
00:02:30,596 --> 00:02:32,919
always to estimate the genetic and

62
00:02:32,999 --> 00:02:35,723
environmental components of variance.

63
00:02:36,492 --> 00:02:38,975
This genetic variance further divided

64
00:02:39,055 --> 00:02:40,512
into 3 main components

65
00:02:41,106 --> 00:02:43,910
where the additive genetic variance is of

66
00:02:43,910 --> 00:02:45,272
most interest.

67
00:02:49,004 --> 00:02:50,544
Among the oldest methods

68
00:02:51,215 --> 00:02:53,819
for estimating genetic parameters is the

69
00:02:53,819 --> 00:02:55,381
analysis of variance.

70
00:02:55,588 --> 00:02:58,152
Using least square method, balanced

71
00:02:58,152 --> 00:03:00,516
data is advantageous for this method.

72
00:03:00,923 --> 00:03:03,167
But for unbalanced data, modified

73
00:03:03,167 --> 00:03:05,410
Henderson's method must be used, which

74
00:03:05,410 --> 00:03:05,592
are included

75
00:03:06,178 --> 00:03:08,742
in various software packages like SAS,

76
00:03:08,942 --> 00:03:10,505
RRAY, et cetera.

77
00:03:12,875 --> 00:03:15,624
In practice, maximum likelihood methods

78
00:03:16,127 --> 00:03:18,771
or its various REML variants

79
00:03:19,412 --> 00:03:20,640
are more commonly used

80
00:03:21,142 --> 00:03:23,866
as they provide the best estimates. Even

81
00:03:23,866 --> 00:03:25,468
for unbalanced data,

82
00:03:26,877 --> 00:03:29,762
Bayesian methods are still

83
00:03:29,762 --> 00:03:31,411
used in researchareas.

84
00:03:37,948 --> 00:03:40,832
We will describe the use of utilityvalues

85
00:03:40,959 --> 00:03:42,962
in families to estimate heritability.

86
00:03:43,764 --> 00:03:45,720
Phenotypic variances between families

87
00:03:46,455 --> 00:03:48,698
and within families are always

88
00:03:48,698 --> 00:03:50,736
calculated if the variance

89
00:03:51,229 --> 00:03:53,712
between families is low. Then the

90
00:03:53,712 --> 00:03:55,752
variance within families is high.

91
00:03:56,724 --> 00:03:59,448
In this case, a high variability value is

92
00:03:59,448 --> 00:04:00,768
calculated from these

93
00:04:01,178 --> 00:04:04,142
traits. Conversely, if the

94
00:04:04,142 --> 00:04:05,744
variance within families

95
00:04:05,872 --> 00:04:08,596
is high and the variance between families

96
00:04:08,596 --> 00:04:10,800
is low, then the low heritability

97
00:04:11,006 --> 00:04:13,931
value is estimated. This is because

98
00:04:13,931 --> 00:04:15,816
the variance of within families

99
00:04:16,782 --> 00:04:19,426
or among individuals within the family.

100
00:04:19,907 --> 00:04:20,832
is more influenced

101
00:04:20,835 --> 00:04:23,719
by environmental variances. On

102
00:04:23,719 --> 00:04:25,562
the other hand, the variances between

103
00:04:25,562 --> 00:04:26,283
families

104
00:04:26,411 --> 00:04:29,054
is more influenced by genetic variances.

105
00:04:29,856 --> 00:04:30,817
It follows

106
00:04:31,185 --> 00:04:33,388
the rule that

107
00:04:33,388 --> 00:04:35,832
total variance

108
00:04:36,239 --> 00:04:38,603
of trait in population is caused by

109
00:04:38,603 --> 00:04:40,896
variance between families, which is

110
00:04:40,973 --> 00:04:42,816
the same as the covariance within

111
00:04:42,816 --> 00:04:45,380
families and variance within

112
00:04:45,380 --> 00:04:46,021
families.

113
00:04:55,649 --> 00:04:55,944
The SCEM

114
00:04:56,337 --> 00:04:58,821
of such an experiment can be seen in the

115
00:04:58,821 --> 00:05:01,040
following picture. We have three

116
00:05:01,272 --> 00:05:04,116
families, where each family consists of

117
00:05:04,116 --> 00:05:05,976
father who has many offspring

118
00:05:06,527 --> 00:05:09,091
with multiple mothers. Herotypic

119
00:05:09,091 --> 00:05:10,992
values are measured in these

120
00:05:11,060 --> 00:05:13,905
offspring. We can assess the variability

121
00:05:13,905 --> 00:05:16,388
within offspring along with thevariability

122
00:05:16,355 --> 00:05:19,039
between groups of related individuals

123
00:05:19,039 --> 00:05:21,203
according to fathers or

124
00:05:21,170 --> 00:05:22,812
according to fathers and mothers

125
00:05:22,812 --> 00:05:25,576
simultaneously. We can get

126
00:05:25,576 --> 00:05:26,057
group

127
00:05:26,104 --> 00:05:28,828
half SIPs with 25% common

128
00:05:28,828 --> 00:05:31,152
genes or we

129
00:05:31,199 --> 00:05:34,083
can also assess groups of full

130
00:05:34,083 --> 00:05:36,854
SIPs with 50%genes.

131
00:05:39,178 --> 00:05:41,088
This model is best applied using

132
00:05:41,228 --> 00:05:44,112
analysis of variants. Analysis

133
00:05:44,152 --> 00:05:46,104
of variants can detect important sources,

134
00:05:47,003 --> 00:05:49,527
effects that contribute to differences

135
00:05:49,527 --> 00:05:50,889
between individuals.

136
00:05:51,577 --> 00:05:54,542
In our case,Those will be the parents

137
00:05:55,183 --> 00:05:55,743
father.

138
00:05:56,912 --> 00:05:59,636
their contribution to the total variance.

139
00:06:00,237 --> 00:06:01,152
The main ways

140
00:06:01,606 --> 00:06:03,770
to determine this variance is to derive

141
00:06:03,770 --> 00:06:06,093
the sum of square of deviations

142
00:06:06,260 --> 00:06:09,024
from the mean and degrees of freedom.

143
00:06:09,906 --> 00:06:10,987
It is important

144
00:06:11,555 --> 00:06:13,438
to have individuals in groups with the

145
00:06:13,478 --> 00:06:16,200
same degree of relatedness. For example,

146
00:06:16,650 --> 00:06:19,374
group of half-sips according to

147
00:06:19,374 --> 00:06:21,216
father or the parent-child

148
00:06:21,905 --> 00:06:24,709
relationship. It holds that

149
00:06:24,709 --> 00:06:26,232
covarianceor similarity

150
00:06:26,759 --> 00:06:28,522
between family members,

151
00:06:29,723 --> 00:06:31,248
is equal to the variance

152
00:06:31,453 --> 00:06:33,777
component between groups.

153
00:06:36,180 --> 00:06:38,551
Ifwe use the model of the half-SIPs

154
00:06:38,631 --> 00:06:41,114
families, then the variance between

155
00:06:41,114 --> 00:06:41,836
half-SIPs

156
00:06:41,803 --> 00:06:44,607
families by pattern now is

157
00:06:44,647 --> 00:06:46,296
equal to the covariance between

158
00:06:46,336 --> 00:06:48,740
the half-SIPs, which is equal to

159
00:06:48,740 --> 00:06:51,312
quarter to additive genetic variance.

160
00:06:52,392 --> 00:06:54,636
The variance in half-shapes families is

161
00:06:54,636 --> 00:06:56,328
equal to residual variances,

162
00:06:57,086 --> 00:06:58,929
which is generally referred to as

163
00:06:58,929 --> 00:07:00,451
environmental variances.

164
00:07:01,700 --> 00:07:04,344
The heritability is then equal to

165
00:07:04,585 --> 00:07:06,360
the ratio of additive genetic

166
00:07:06,394 --> 00:07:08,718
variance to the total phenotypic

167
00:07:08,718 --> 00:07:11,202
variances, which is equal to 4

168
00:07:11,202 --> 00:07:11,843
times

169
00:07:11,970 --> 00:07:14,454
to paternal variance or the variance

170
00:07:14,614 --> 00:07:16,136
between half-shapes families

171
00:07:16,423 --> 00:07:18,426
to the total phenotypic variance.

172
00:07:21,391 --> 00:07:24,322
Wecan see the simplified design of the

173
00:07:24,322 --> 00:07:25,805
experiment in this family.

174
00:07:26,613 --> 00:07:29,417
father has one offspring with one mother.

175
00:07:30,458 --> 00:07:31,580
Therefore, we

176
00:07:31,547 --> 00:07:33,630
evaluate the variability between

177
00:07:34,111 --> 00:07:36,617
offspring by groups according

178
00:07:37,123 --> 00:07:39,686
to fathers. Then it naturally

179
00:07:39,686 --> 00:07:41,472
follows that the additive genetic

180
00:07:42,057 --> 00:07:44,941
is equal to four times the paternal

181
00:07:44,941 --> 00:07:46,624
variance, SIRE

182
00:07:46,751 --> 00:07:49,235
variance. We can estimate the

183
00:07:49,235 --> 00:07:51,558
paternal SARE variance using

184
00:07:51,525 --> 00:07:53,288
analysis of variance.

185
00:07:56,332 --> 00:07:59,103
Thismodel is called the paternal model or

186
00:07:59,103 --> 00:08:01,507
SARE model. It is one-factor

187
00:08:01,507 --> 00:08:02,148
analysis

188
00:08:02,115 --> 00:08:04,759
of variance where the only fixed effect

189
00:08:04,839 --> 00:08:06,552
in the equation is the effect of

190
00:08:06,569 --> 00:08:09,533
fathers. It is assumed that

191
00:08:09,533 --> 00:08:11,649
fathers and mothers are unrelated,

192
00:08:12,785 --> 00:08:15,429
randomly paired, and not affected by

193
00:08:15,429 --> 00:08:16,070
selection.

194
00:08:16,678 --> 00:08:18,400
Another assumption is that we have a

195
00:08:18,400 --> 00:08:21,084
balancer design. This means that the

196
00:08:21,165 --> 00:08:21,601
P fathers

197
00:08:22,494 --> 00:08:25,218
are paired with N mothers and they have

198
00:08:25,618 --> 00:08:26,617
one offspring.

199
00:08:33,404 --> 00:08:35,807
In the resulting table of the new

200
00:08:35,888 --> 00:08:36,649
paternal model,

201
00:08:37,217 --> 00:08:40,101
we see three rows. The last row is

202
00:08:40,101 --> 00:08:41,665
the total phenotypic variance.

203
00:08:42,391 --> 00:08:45,236
The first and the second rowsExpress the

204
00:08:45,236 --> 00:08:46,681
estimation of variance between

205
00:08:47,326 --> 00:08:50,010
and within families. The

206
00:08:50,010 --> 00:08:51,697
degrees of freedom DF

207
00:08:52,100 --> 00:08:54,744
formulas for calculating sum of square or

208
00:08:54,744 --> 00:08:56,713
deviations from the mean according

209
00:08:57,195 --> 00:08:59,518
to the source of variability and the

210
00:08:59,518 --> 00:09:01,080
calculation of the mean square of

211
00:09:01,080 --> 00:09:01,729
variance as

212
00:09:02,369 --> 00:09:05,254
the ratio sum of squares and

213
00:09:05,334 --> 00:09:06,745
degrees of freedom are expressed

214
00:09:07,103 --> 00:09:10,028
here. Statistics and here

215
00:09:10,188 --> 00:09:11,761
and it is and in the last

216
00:09:12,078 --> 00:09:14,562
column. The genetic part begins.

217
00:09:15,363 --> 00:09:16,777
The environmental variance

218
00:09:17,974 --> 00:09:20,457
is directly equal to the variance within

219
00:09:20,858 --> 00:09:23,629
families,residual variances.

220
00:09:24,751 --> 00:09:26,809
In the variance between families, between

221
00:09:26,921 --> 00:09:28,884
groups according to fathers,

222
00:09:29,445 --> 00:09:31,768
MSA includes genetic

223
00:09:31,768 --> 00:09:32,570
variance.

224
00:09:34,940 --> 00:09:36,703
The variance among fathers,

225
00:09:37,872 --> 00:09:40,435
is equal to the residual variance plus.

226
00:09:40,836 --> 00:09:41,857
N0 times

227
00:09:42,005 --> 00:09:44,969
the genetic variances. N0 is the

228
00:09:44,969 --> 00:09:46,873
weighted number of offspring per

229
00:09:46,939 --> 00:09:49,743
father. Because the residual

230
00:09:49,743 --> 00:09:51,987
variance is directly equal to

231
00:09:51,954 --> 00:09:54,518
the within family variances, we can

232
00:09:54,518 --> 00:09:57,001
directly calculate genetic variance asthe

233
00:09:56,968 --> 00:09:59,732
difference between MSA, it is

234
00:09:59,772 --> 00:10:01,936
paternal variance, minus

235
00:10:02,864 --> 00:10:05,188
residual variance, divided by

236
00:10:05,268 --> 00:10:05,909
N0.

237
00:10:07,158 --> 00:10:09,801
Furthermore,We calculate the intraclass

238
00:10:09,801 --> 00:10:11,965
correlation coefficient, rho,

239
00:10:12,412 --> 00:10:14,696
as the ratio of genetic variance to the

240
00:10:14,696 --> 00:10:16,418
total phenotypic variance.

241
00:10:17,467 --> 00:10:20,191
The estimate of heritability coefficient

242
00:10:20,632 --> 00:10:21,985
is obtained by multiplying

243
00:10:22,441 --> 00:10:24,765
this intraclass correlation coefficient

244
00:10:25,085 --> 00:10:27,008
by four,

245
00:10:27,296 --> 00:10:29,219
because we calculate genetic variance

246
00:10:29,459 --> 00:10:32,063
based on half sip groups. And

247
00:10:32,030 --> 00:10:34,514
we know that half sip have a

248
00:10:34,634 --> 00:10:36,797
quarter genetic resemblance.

249
00:10:40,610 --> 00:10:42,049
For correct interpretation

250
00:10:42,059 --> 00:10:44,863
of heritability estimate results,

251
00:10:45,464 --> 00:10:47,065
it is unnecessary to calculate

252
00:10:47,194 --> 00:10:49,838
its standard error. Its value,

253
00:10:50,118 --> 00:10:52,081
SVC, from the formula

254
00:10:52,448 --> 00:10:55,373
depends mainly on the number of half-CB

255
00:10:55,373 --> 00:10:57,097
groups, P, and the weighted

256
00:10:57,463 --> 00:10:59,947
number of offsprings per father.

257
00:11:03,559 --> 00:11:05,522
What is the importance of estimating

258
00:11:05,522 --> 00:11:06,403
heritability?

259
00:11:07,172 --> 00:11:09,655
An estimated high heritability suggests

260
00:11:09,655 --> 00:11:11,899
that the phenotypic variance of the trait

261
00:11:12,059 --> 00:11:14,990
inthe population is largely influenced by

262
00:11:14,990 --> 00:11:17,434
genetic variability. Breeding

263
00:11:17,401 --> 00:11:20,165
programs can focus on traits with

264
00:11:20,165 --> 00:11:22,177
high heritability and thus achieve

265
00:11:22,455 --> 00:11:24,939
faster genetic progress, genetic gain.

266
00:11:27,182 --> 00:11:29,553
Inconclusion, understanding genetic

267
00:11:29,553 --> 00:11:32,209
parameters is crucial for efficient

268
00:11:32,484 --> 00:11:34,888
animal breeding. Heritability

269
00:11:35,369 --> 00:11:37,372
genetic correlation, and

270
00:11:37,379 --> 00:11:39,903
advancements such as GWAS and

271
00:11:39,903 --> 00:11:42,241
genomic selection allow targeted

272
00:11:42,433 --> 00:11:44,837
improvement of traits to increase

273
00:11:44,837 --> 00:11:47,257
productivity and profitability in animal

274
00:11:47,448 --> 00:11:48,169
production.

275
00:11:50,012 --> 00:11:51,534
Thanks for your attention.