General and Specific Combining Abilities Facundo Muñoz 2017-04-14 breedR version: 0.12.1

Contents In a factorial design (either complete or not) the General Combining Ability (GCA) of a parent is its Breeding Value, while the Specific Combinig Ability (SCA) of a mating is the additional genetic value due to the interaction between those particular genotypes. We propose two alternative ways of getting BLUPs for the GCAs. While for the SCAs we will simply use an unstructured random effect with one level for each observed mating. We illustrate the methods with the following simulated data. Note that in this example the males and females are different individuals (and thus, they have different codes). However, monoic species can be set up as diallels, which simply means that some or all of the codes (and GCAs) will be shared. Otherwise, the methods still apply. Note also that while the GCAs are sampled using the base population’s additive-genetic variance, the intra-family breeding values are sampled with half-that variance. This is standard theory. ## Setup library(breedR) library(ggplot2) set.seed(123) ## Simulation parameters n.parents <- c(male = 15L, female = 10L) n.matings <- 100 n.replicates <- 40 mu = 10 # Intercept sigma2_g <- 6 # Genetic variance of the base population sigma2_s <- 1 # Variance of the SCA sigma2_e <- 1 # Residual variance ## Generate all crosses and sample a subset parents.codes <- list(male = seq.int(n.parents['male']), female = n.parents['male'] + seq.int(n.parents['female'])) matings <- expand.grid(parents.codes) matings <- matings[sample(prod(n.parents), n.matings),] rownames(matings) <- with(matings, paste(male, female, sep = 'x')) ## Simulated values GCA = sapply(do.call('c', parents.codes), function(x) rnorm(1, mean = 0, sd = sqrt(sigma2_g))) SCA = sapply(rownames(matings), function(x) rnorm(1, mean = 0, sd = sqrt(sigma2_s))) ## Expected phenotype per family eta.family <- mu + SCA + (GCA[matings$male] + GCA[matings$female])/2 ## Realised Breeding Values in the progeny

1

## (intra-family variance = half genetic variance) n.progeny <- n.replicates*n.matings eta.realised <- eta.family + rnorm(n.progeny, sd = sqrt(sigma2_g/2)) dat <- data.frame(Id = max(sapply(parents.codes, max)) + seq.int(n.progeny), rep = rep(seq.int(n.replicates), each = n.matings), matings, eta.realised, y = eta.realised + rnorm(n.progeny, sd = sqrt(sigma2_e))) ## Define variable for the non-additive SCA dat <- transform(dat, SCA = factor(paste(male, female, sep = 'x'), levels = rownames(matings))) ## Printing simulated setting print(table(dat[, c('male', 'female')]), zero.print = "") ## female ## male 16 17 18 19 20 21 22 23 24 25 ## 1 40 40 40 40 40 40 ## 2 40 40 40 40 40 40 ## 3 40 40 40 40 40 40 40 40 ## 4 40 40 40 40 40 40 ## 5 40 40 40 40 40 40 40 ## 6 40 40 40 40 40 ## 7 40 40 40 40 40 40 40 ## 8 40 40 40 40 40 40 40 40 ## 9 40 40 40 40 40 40 ## 10 40 40 40 40 40 40 40 40 40 ## 11 40 40 40 40 40 40 40 40 ## 12 40 40 40 40 40 40 ## 13 40 40 40 40 ## 14 40 40 40 40 40 40 40 40 ## 15 40 40 40 40 40 40 str(dat) ## 'data.frame': ## $ Id : ## $ rep : ## $ male : ## $ female : ## $ eta.realised: ## $ y : ## $ SCA :

4000 obs. of 7 variables: int 26 27 28 29 30 31 32 33 34 35 ... int 1 1 1 1 1 1 1 1 1 1 ... int 14 13 1 10 3 7 2 8 4 5 ... int 18 23 20 24 25 16 21 24 21 20 ... num 7.94 10.6 12.14 10.33 8.17 ... num 8.73 11.6 12.52 11.44 7.2 ... Factor w/ 100 levels "14x18","13x23",..: 1 2 3 4 5 6 7 8 9 10 ...

Method 1: using unstructured random effects The first method uses two independent unstructured random effects for the GCAs of the mother and the father trees respectively. Note that remlf90 will estimate two independent variances for these effects, while in reality they are the same. However, we currently do not have a way to specify that in breedR. It will be possible soon, when we

2

implement the generic model. Therefore, this approach is currently sub-efficient. Furthermore, the female and male effects represent actually half of the Breeding Value contributed by both parents. So their variance is a quarter of the base population’s additive-genetic variance. We will then use four times the mean of both estimates as an estimate of the additive-genetic variance. ## Note that I would like to estimate only **one** GCA effect ## However, currently I need to specify two independent random effects with ## two independent variances, which account in reality for the same thing res <- remlf90(y ~ 1, random = ~ male + female + SCA, dat = transform(dat, male = factor(male), female = factor(female))) ## Using default initial variances given by default_initial_variance() ## See ?breedR.getOption. ## Here, the effects 'female' and 'male' are both estimating GCA/2 ## therefore, their variances are Var(GCA)/4 = sigma_g/4 ## So, a point estimator for sigma_g would be: (sigma_g.est <- 4 * mean(res$var[c('female', 'male'), 1])) ## [1] 5.5054 ## while the BLUPs PGCA <- c(ranef(res)$male, ranef(res)$female) ## Check fit qplot(dat$eta, fitted(res)) + geom_abline(intercept=0, slope=1) 15.0

fitted(res)

12.5

10.0

7.5

5

10

15

dat$eta qplot(GCA, PGCA) + geom_abline(intercept=0, slope=1)

3

2

PGCA

1

0

−1

−2 −6

−3

0

3

GCA qplot(SCA, ranef(res)$SCA) + geom_abline(intercept=0, slope=1) 3

ranef(res)$SCA

2

1

0

−1

−2

−1

0

1

2

3

SCA summary(res) ## ## ## ## ## ## ## ## ## ## ## ## ## ##

Formula: y ~ 0 + Intercept + male + female + SCA Data: transform(dat, male = factor(male), female = factor(female)) AIC BIC logLik 17152 17177 -8572 Parameters of special components:

Variance components: Estimated variances male 1.0514 female 1.7013 SCA 0.9908 Residual 3.9535

S.E. 0.46682 0.86324 0.17669 0.08953

4

## ## Fixed effects: ## value s.e. ## Intercept 10.05 0.5018

Method 2: using the implicit pedigree With this approach we estimate directly the genetic variance of the base population, and predict the Breeding Values of all individuals, including the parents (i.e. the GCAs). The SCAs are again fitted as an unstructured random effect. res.add <- remlf90(y ~ 1, random = ~ SCA, genetic = list(model = 'add_animal', pedigree = dat[, c('Id', 'male', 'female')], id = 'Id'), dat = dat) ## Using default initial variances given by default_initial_variance() ## See ?breedR.getOption. # Check fit qplot(dat$eta, fitted(res.add)) + geom_abline(intercept=0, slope=1)

fitted(res.add)

15

10

5

5

10

15

dat$eta # Predicted GCAs for the parents PGCA.add <- ranef(res.add)$genetic[do.call('c', parents.codes)] qplot(GCA, PGCA.add) + geom_abline(intercept=0, slope=1)

5

4

PGCA.add

2

0

−2

−4 −6

−3

0

3

GCA # Predicted SCAs for the families qplot(SCA, ranef(res.add)$SCA) + geom_abline(intercept=0, slope=1)

ranef(res.add)$SCA

3

2

1

0

−1

−2

−1

0

1

2

3

SCA summary(res) ## ## ## ## ## ## ## ## ## ## ## ## ##

Formula: y ~ 0 + Intercept + male + female + SCA Data: transform(dat, male = factor(male), female = factor(female)) AIC BIC logLik 17152 17177 -8572 Parameters of special components:

Variance components: Estimated variances S.E. male 1.0514 0.46682 female 1.7013 0.86324 SCA 0.9908 0.17669

6

## Residual 3.9535 0.08953 ## ## Fixed effects: ## value s.e. ## Intercept 10.05 0.5018

Final remarks • You can derive point estimates of Heritabilities using the resulting variance estimates • The GCA and SCA BLUPs can be extracted with the ranef expressions above • Note that the log-likelihood of both models is exactly the same, while AIC penalizes slightly the first approach because it has one extra parameter.

7

General and Specific Combining Abilities - GitHub

an unstructured random effect with one level for each observed mating. We illustrate the methods with the following simulated data. Note that in this example the ...

622KB Sizes 1 Downloads 308 Views

Recommend Documents

Repeatabilty of general and specific combining ... - Semantic Scholar
Keyword: Potato, combining ability, clone, yield. ... estimated using the computer software SPAR1. A ... MP/90-94 was the best specific combiner for dry.

Repeatabilty of general and specific combining ... - Semantic Scholar
Keyword: Potato, combining ability, clone, yield. ... estimated using the computer software SPAR1. A ... MP/90-94 was the best specific combiner for dry.

Small target detection combining regional stability and ... - GitHub
Nov 9, 2016 - School of Computer Science and Engineering, Nanjing University of Science and ... are also proposed in recent years [14, 15, 20]. ... In Section 2, we present the small target detection model ...... Wei Zhu received the BE degree in sof

Domain-specific and domain-general changes in childrens ...
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. Domain-specific and domain-general changes in childrens development of number comparison.pdf. Domain-specifi

computational abilities
quential memory also emergent properties and collective in origin? This paperexamines a .... rons like a conventional digital computer. There is no evidence.

(virtio-peer) GENERAL OVERVIE - GitHub
sed rings and Queue Data reside in physical memory ranges calle ... The driver must consider the Desc Table, Avail Ring and Queue Data area of the receiveq ...

Approaches and Abilities FAE.pdf
Picking a lock (Cleverly Skilled). Page 3 of 5. Approaches and Abilities FAE.pdf. Approaches and Abilities FAE.pdf. Open. Extract. Open with. Sign In. Main menu.

General-to-specific modeling in Stata
A command is presented, written in Stata and Mata, that implements this algorithm for various data types ... Keywords: st0365, genspec, model selection, general to specific, statistical analysis, specification tests ..... research agenda, even when t

computational abilities
The analysis of networks with strong backward coupling proved intractable. ..... This same analysis shows that the system generally fails in a "soft" fashion, with.

14.6 OVERALL MAX GENERAL DESCRIPTION 28.9 ... - GitHub
OLED EXPANSION. TITLE. DIMENSION IN MM. UNLESS NOTED. GO. TOLERANCES. USED ON. NEXT ASSY. SIZE. 2:1. 1 OF 4. 2016-03-31. DATE.

White matter microstructures underlying mathematical abilities in ...
using ROQS [15], an analysis package developed by the. second two authors ROQS segments white matter structures. on the basis of a user-defined seed voxel ...

now hiring! - Abilities In Motion
wholesale supply company in the U.S. and the industry leader in supply chain ... Apply today by visiting www.weselectthebest.com/locations/robesonia-pa.

now hiring! - Abilities in Motion
We offer an attractive starting pay rate, with aggressive pay increases every six months from hire. ➢ Starting rate of $14.18/hour. ➢ Increases every 6 months.

non-scholastic abilities
In the medical profession- which deals with human touch- these aspects of learning become ... IT skills: Computer, internet. 4. ... Balance of home and career.

employment and transition workshop for veterans - Abilities in Motion
Join us for our first Veteran Employment and Transition Workshop. THURSDAY ... Information about Job Opportunities at Wegmans Stores in the Region.

The Effects of Cognitive and Noncognitive Abilities on ...
3.5 The Measurement System and Identification of the Model .... model. Let Ip denote the latent utility associated with the decision p (p = 1 (Single with No Child),.

Combining Coregularization and Consensus-based ...
Jul 19, 2010 - Self-Training for Multilingual Text Categorization. Massih-Reza .... text classification. Section 4 describes the boosting-based algorithm we developed to obtain the language-specific clas- sifiers. In Section 5, we present experimenta

Combining Intelligent Agents and Animation
tures - Funge's cognitive architecture and the recent SAC concept. Addi- tionally it puts emphasis on strong design and provides easy co-operation of different ...

Alkhateeb_COMM14_MIMO Precoding and Combining Solutions for ...
Alkhateeb_COMM14_MIMO Precoding and Combining Solutions for Millimeter-Wave Systems.pdf. Alkhateeb_COMM14_MIMO Precoding and Combining ...

Combining GPS and photogrammetric measurements ...
Mobile Multi-Sensor Systems Research Group. Department of ... ity and ease of implementation; however, a more fundamental fusion of the GPS data into the.

Alkhateeb_COMM14_MIMO Precoding and Combining Solutions for ...
Alkhateeb_COMM14_MIMO Precoding and Combining Solutions for Millimeter-Wave Systems.pdf. Alkhateeb_COMM14_MIMO Precoding and Combining ...

Autistic Patients' Exceptional Visual Abilities ... -
is also manager of the Specialized Autism Clinic at Rivière-des-Prairies Hospital, ... Western Reserve University in Cleveland, Ohio, and pediatric neurologist at ...