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From the perspective of quantitative genetics, why do you get the bride price when you get married
2022-07-05 23:09:00 【Analysis of breeding data】
Betrothal money , It's the money the man gave the woman when he got married . There are two points :
- money
- The man gives the woman
It is said that :“ Father defeat , A setback ; Mother frustration , A nest of frustration ”, It means that a father affects his children , It is a single influence , And the mother affects her children , It is affected by nesting .
because , From a genetic point of view , Children inherit half of their parents' genetic material , But because it is the mother's cytoplasm ( Such as mitochondria ) It also carries genetic material , So mothers pass on more genetic material to their offspring than fathers . therefore , Want to improve the family's genes and personality , Men find a good woman to mate with , Find a better man to mate with than a woman , The impact is greater . Think of it here. , Suddenly I feel married , A lot of betrothal gifts to the woman , It's understandable .
Mother has great influence on offspring , Not just from a genetic point of view ( raw ), And the role of the environment ( Education ), There is also the interaction between genetics and environment ( fertility ). From the perspective of quantitative genetics :
Elementary formula :
Individual performance = Genetic material + Environmental Science ( error )
Advanced formula :
Individual performance = Father's genetic material + Mother's genetic material + Environmental Science ( error )
Further advanced formula :
Individual performance = Father's genetic material + Mother's genetic material + Maternal genetic effects ( Such as mitochondrial genetics )+ Maternal permanent environmental effects ( Such as parenting environment )+ Environmental Science ( error )
In the formula above , Mother provided three :
- Mother's genetic material
- Maternal genetic effects ( Such as mitochondrial genetics )
- Maternal environmental effects ( Such as parenting environment )
Individual permanent environmental effects
, Maternal genetic effects
, Maternal permanent environmental effects
, When building the model , Know it but don't know why , Otherwise One bottle is less than half a bottle
The state of is obviously not the quality that a data analyst should have .
1. Several concepts
- Individual permanent environmental effects (Individual permanent environmental effect), Also known as permanent environmental effects , In general, when an individual has a duplicate value, it can be partitioned out , For example, chickens lay eggs , Piglets, etc .
- Maternal genetic effects (Maternal genetic effect), In general, we call the individual additive genetic effect , Because it takes into account the relationship matrix between individuals (A perhaps G perhaps H matrix ), If the matrix is a random factor , Also consider the relationship matrix , It's called maternal genetic effect .
- Maternal environmental effects (Maternal permanent environmental effect), Also known as the maternal permanent environmental effect , As a random factor in analysis , But don't think about the relationship matrix .
2. There are two kinds of maternal effects
The first one is : Maternal genetic effects , There are also two maternal genetic effects , One is to consider the covariance of maternal genetic effect and individual additive effect , One is not to consider , But the default is to consider .
The second kind : Maternal environmental effects , It doesn't take into account the relationship matrix , The model as a random factor .
3. The first one is : Maternal genetic effects
3.1 Consider maternal genetic effects and individual additive effects covariance
Model writing :
y = X b + Z a + Z m g + e y = Xb + Za + Zm_g + e y=Xb+Za+Zmg+e
here :
- Xb Is a fixed factor
- Za Is a random factor , Individual additive effect
- Zm_g Is a random factor , Maternal genetic effects
- e For the residuals
Variance covariance structure :
G = V a r [ a m g ] = [ A σ a 2 A σ a m A σ a m A σ m g 2 ] G = Var\begin{bmatrix} a\\m_g \end{bmatrix} = \begin{bmatrix} A\sigma_a^2 & A\sigma_{am} \\ A\sigma_{am} & A\sigma_{m_g}^2\end{bmatrix} G=Var[amg]=[Aσa2AσamAσamAσmg2]
here A For the relationship matrix , We can see that additive and maternal covariance exist , And both additive and maternal factors need to be considered A matrix .
Example data + Sample code + Sample results
Data and code :
# Load package
# devtools::install_github("dengfei2013/learnasreml")
library(learnasreml)
# asreml It's commercial software , Need to buy , Please contact :http://www.vsnc.com.cn/
library(asreml)
data("animalmodel.dat")
data("animalmodel.ped")
head(animalmodel.dat)
head(animalmodel.ped)
# m1 The animal model of unisexuality
dat = animalmodel.dat
ped = animalmodel.ped
dat[dat==0] = NA
str(dat)
# Calculate the inverse relationship matrix
ainv = ainverse(ped)
# m1 The animal model of unisexuality + Maternal genetic effects + Additive effects interact with maternal genetic effects
m1 = asreml(BWT ~ SEX + BYEAR, random= ~ str(~vm(ANIMAL,ainv) + vm(MOTHER,ainv), ~us(2):vm(ANIMAL,ainv)),
residual = ~ idv(units),data = dat)
summary(m1)$varcomp
vpredict(m1,h2 ~ V1/(V1+2*V2+V3+V4))
Be careful , there V2 Is the additive and the covariance of the matrix , Because there are two covariances , So when calculating heritability, the denominator should be 2*V2
result :
> summary(m1)$varcomp
component std.error z.ratio bound %ch
vm(ANIMAL, ainv)+vm(MOTHER, ainv)!us(2)_1:1 1.66469827 0.9069349 1.8355213 P 0.0
vm(ANIMAL, ainv)+vm(MOTHER, ainv)!us(2)_2:1 0.01602755 0.4968458 0.0322586 P 0.8
vm(ANIMAL, ainv)+vm(MOTHER, ainv)!us(2)_2:2 1.35818328 0.4194201 3.2382408 P 0.0
units!units 2.19186868 0.6632651 3.3046644 P 0.0
units!R 1.00000000 NA NA F 0.0
> vpredict(m1,h2 ~ V1/(V1+2*V2+V3+V4))
Estimate SE
h2 0.3172785 0.1965149
It can be seen from the results :
- Additive variance components :1.665
- Additive and maternal covariance components :0.016
- Components of maternal genetic variance :1.35
- Residual variance components :2.19
The heritability calculated is 0.317
3.2 Regardless of maternal genetic effects and individual additive effects covariance
Here are two ways to write , The first is to use diag function , Regardless of covariance . The second is to separate additive and maternal genetic effects .
Model writing :
y = X b + Z a + Z m g + e y = Xb + Za + Zm_g + e y=Xb+Za+Zmg+e
here :
- Xb Is a fixed factor
- Za Is a random factor , Individual additive effect
- Zm_g Is a random factor , Maternal genetic effects
- e For the residuals
Variance covariance structure :
G = V a r [ a m g ] = [ A σ a 2 0 0 A σ m g 2 ] G = Var\begin{bmatrix} a\\m_g \end{bmatrix} = \begin{bmatrix} A\sigma_a^2 & 0\\ 0 & A\sigma_{m_g}^2\end{bmatrix} G=Var[amg]=[Aσa200Aσmg2]
here A For the relationship matrix , It can be seen that , Regardless of additive and maternal covariance , And both additive and maternal factors need to be considered A matrix .
Example data + Sample code + Sample results
here , take us
Turn into diag
, That is, we don't consider covariance .
m2.1 = asreml(BWT ~ SEX + BYEAR, random= ~ str(~vm(ANIMAL,ainv) + vm(MOTHER,ainv), ~diag(2):vm(ANIMAL,ainv)),
residual = ~ idv(units),data = dat)
summary(m2.1)$varcomp
vpredict(m2.1,h2 ~ V1/(V1+V2+V3))
result :
> summary(m2.1)$varcomp
component std.error z.ratio bound %ch
vm(ANIMAL, ainv)+vm(MOTHER, ainv)!diag(2)_1 1.689122 0.5291361 3.192225 P 0.0
vm(ANIMAL, ainv)+vm(MOTHER, ainv)!diag(2)_2 1.366709 0.3151848 4.336215 P 0.1
units!units 2.174346 0.3932961 5.528523 P 0.0
units!R 1.000000 NA NA F 0.0
> vpredict(m2.1,h2 ~ V1/(V1+V2+V3))
Estimate SE
h2 0.3229569 0.09621066
It can be seen from the results :
- Additive variance components :1.68
- Components of maternal genetic variance :1.36
- Residual variance components :2.17
The heritability calculated is 0.32
Another way of writing :
It can be written in a similar way to additive variance components , Direct use vm
function , This kind of writing is relatively simple , But the covariance of additive and maternal genetic effects is not considered .
# m2 The animal model of unisexuality + Maternal genetic effects
m2.2 = asreml(BWT ~ SEX + BYEAR, random= ~ vm(ANIMAL,ainv) + vm(MOTHER,ainv),
residual = ~ idv(units),data = dat)
summary(m2.2)$varcomp
vpredict(m2.2,h2 ~ V1/(V1+V2+V3))
> summary(m2.2)$varcomp
component std.error z.ratio bound %ch
vm(ANIMAL, ainv) 1.689188 0.5292161 3.191868 P 0
vm(MOTHER, ainv) 1.366777 0.3153196 4.334578 P 0
units!units 2.174264 0.3932864 5.528448 P 0
units!R 1.000000 NA NA F 0
> vpredict(m2.2,h2 ~ V1/(V1+V2+V3))
Estimate SE
h2 0.3229663 0.09621819
You can see that the results are exactly the same .
4. The second kind : Maternal environmental effects
Model writing :
y = X b + Z a + Z m + e y = Xb + Za + Zm + e y=Xb+Za+Zm+e
here :
- Xb Is a fixed factor
- Za Is a random factor , Individual additive effect
- Zm Is a random factor , Maternal environmental effects
- e For the residuals
Variance covariance structure :
G = V a r [ a m g ] = [ A σ a 2 0 0 I σ m g 2 ] G = Var\begin{bmatrix} a\\m_g \end{bmatrix} = \begin{bmatrix} A\sigma_a^2 & 0\\ 0 & I\sigma_{m_g}^2\end{bmatrix} G=Var[amg]=[Aσa200Iσmg2]
here A For the relationship matrix , It can be seen that , Regardless of additive and maternal covariance , And additivity and consideration A matrix , The mother doesn't think about A matrix .
The maternal environmental effect here , Regardless of the kinship matrix , Take it as a random factor .
# m3 The animal model of unisexuality + Maternal environmental effects
m3 = asreml(BWT ~ SEX + BYEAR, random= ~ vm(ANIMAL,ainv) + MOTHER,
residual = ~ idv(units),data = dat)
summary(m3)$varcomp
vpredict(m3,h2 ~ V1/(V1+V2+V3))
result :
> summary(m3)$varcomp
component std.error z.ratio bound %ch
MOTHER 1.104038 0.2398000 4.603997 P 0
vm(ANIMAL, ainv) 2.277785 0.4970861 4.582274 P 0
units!units 1.656900 0.3734446 4.436803 P 0
units!R 1.000000 NA NA F 0
> vpredict(m3,h2 ~ V1/(V1+V2+V3))
Estimate SE
h2 0.2191107 0.04364284
5. Both maternal genetic effects and maternal environmental effects are considered
This model , It is the most complete model considering maternal effect , He includes
- Maternal genetic effects
- Additive and maternal genetic effect covariance
- Maternal permanent environmental effects
Model writing :
y = X b + Z 1 a + Z 2 m g + Z 3 m e + e y = Xb + Z_1a + Z_2m_g +Z_3m_e + e y=Xb+Z1a+Z2mg+Z3me+e
here :
- Xb Is a fixed factor
- Za Is a random factor , Individual additive effect
- Zm_g Is a random factor , Maternal genetic effects
- Zm Is a random factor , Maternal environmental effects
- e For the residuals
Variance covariance structure :
G = V a r [ a m g m e ] = [ A σ a 2 A σ a m 0 A σ a m A σ m g 2 0 0 0 I σ m e 2 ] G = Var\begin{bmatrix} a\\m_g \\m_e \end{bmatrix} = \begin{bmatrix} A\sigma_a^2 & A\sigma_{am} & 0 \\ A\sigma_{am} & A\sigma_{m_g}^2 & 0 \\0 & 0 & I\sigma_{m_e}^2\end{bmatrix} G=Var⎣⎡amgme⎦⎤=⎣⎡Aσa2Aσam0AσamAσmg2000Iσme2⎦⎤
# m4 The animal model of unisexuality + Maternal genetic effects + Additive effects interact with maternal genetic effects + Maternal environmental effects
m4 = asreml(BWT ~ SEX + BYEAR, random= ~ str(~vm(ANIMAL,ainv) + vm(MOTHER,ainv), ~us(2):vm(ANIMAL,ainv)) + MOTHER,
residual = ~ idv(units),data = dat)
summary(m4)$varcomp
vpredict(m4,h2 ~ V1/(V1+2*V2+V3+V4+V5))
result :
> summary(m4)$varcomp
component std.error z.ratio bound %ch
vm(ANIMAL, ainv)+vm(MOTHER, ainv)!us(2)_1:1 1.688055506 0.9091111 1.85681974 P 0.0
vm(ANIMAL, ainv)+vm(MOTHER, ainv)!us(2)_2:1 0.006385884 0.4954503 0.01288905 P 4.0
vm(ANIMAL, ainv)+vm(MOTHER, ainv)!us(2)_2:2 1.057027088 0.4405431 2.39937292 P 0.1
MOTHER 0.497693182 0.3694028 1.34729116 P 0.6
units!units 2.157268745 0.6628453 3.25455845 P 0.0
units!R 1.000000000 NA NA F 0.0
> vpredict(m4,h2 ~ V1/(V1+2*V2+V3+V4+V5))
Estimate SE
h2 0.3118627 0.1907149
6. Model filtering : The optimal model LRT test
Whether to consider the permanent environmental effect of the mother :m4 VS m1
Whether to consider additive effect and maternal genetic effect covariance :m1 VS m2.1
# LRT test
lrt.asreml(m4,m1,boundary = T)
lrt.asreml(m1,m2.1,boundary = T)
You can see , The maternal permanent environmental effect and covariance are not significant , There can be no .
Which model is the best ? Use BIC Judge :
summary(m1)$bic
summary(m2.1)$bic
summary(m3)$bic
summary(m4)$bic
You can see ,m3 Of BIC Minimum , Its model is : Only additive effects and maternal permanent environmental effects are considered .
7. Application of genomic selection maternal genetic effects ?
GBLUP perhaps SSGBLUP( One step ) Are the benefits of , Models that can be used in traditional animal models , Genome selection can be done with . Some traits are analyzed , The repeatability model needs to be considered , Maternal inheritance , The mother environment, etc , The analysis will be more accurate .
8. What is the relationship between the above variance components and maternal genetic size ?
We inherit more from the mother than from the father , It also needs data support , For specific traits , Like IQ IQ, For example, height , Such as weight and so on , Which of these traits have greater influence , Which effects are small , We need to use the method of population genetic evaluation to calculate , Then we can draw a conclusion . We are not fortune tellers , We use scientific methods to evaluate and predict .
9. reference
Lawrence R. Schaeffer, Linear Models and Animal Breeding, 2010
A R Gilmour, ASReml User Guide Release 4.1 Structural Specification, 2015
D G Butler, ASReml-R Reference Manual Version, 2018
Finally finished , hurriedly Three companies , give the thumbs-up , Looking at , Hair circle of friends .
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