Core of functions to build gaussian kernel, arc-cosine and GBLUP with additive, dominance effects and considering environmental information Last Update: 08 Jan 2020
- 1. Overview
- 2. Data sets
- 3. Environmental Typing
- 4. Kernel Methods
- 5. Statistical Models
- 6. Genomic Prediction
- 7. Variance Components
- 8. Suggested Literature
- 9. Authorship and Acknowledgments
- History and Updates
This page was developed to provide genomic prediction codes using environmental data, dominance effects and reaction norms. We also provide codes for building kernels such as GBLUP, Gaussian Kernel and Deep Kernel. The base article for these codes is the paper of Costa-Neto et al. (submitted to Heredity journal in May 2020). All codes are free and any questions, suggestions or criticism to improve the codes please look for the authors of this page. Thank you very much!
452 tropical maize single-crosses provided by Helix Sementes®, Brazil. Hybrids were obtained from crosses between 128 inbred lines and were evaluated for grain yield (GY) and plant height (PH). Field trials were carried out using a randomized complete block design with two replicates each, allocated across five sites for GY and three for PH during the growing season of 2015.
Inbred lines were genotyped via the Affymetrix® Axiom® Maize Genotyping Array (Unterseer et al. 2014) with 660K SNP markers. Quality control for SNPs was made based on call rate (CR), in which all markers with any missing data point were excluded, and minor allele frequency (MAF) procedures, in which markers with a low level of polymorphism (MAF < 0.05) were removed. Hybrid genotypes were scored by an allelic combination of homozygous markers of parental lines. After quality control, 37,625 SNP were used to compare the imputation methods.
Check the CIMMYT DATA VERSE Repository for the full genotypic and phenotypic data
906 maize single-crosses obtained from a full dial- lel, according to Griffing’s method 4, divided into two heterotic groups, flint and dent, with 34 and 15 lines, respec- tively. Moreover, each heterotic group has a representative line, frequently used as the tester in our breeding program.
The experimental scheme used to evaluate the hybrids was an augmented block design (unreplicated trial) consisted of small blocks, each with 16 unique hybrids and two checks. Trials were carried out in Anhembi (22°50′51′′S, 48°01′06′′W, 466 m) and Piracicaba, at São Paulo State, Brazil (22°42′23′′S, 47°38′14′′W, 535 m), during the second growing season of 2016 and 2017, cultivated between January to June. In both sites and years, the hybrids were evaluated under two nitrogen (N) levels, low (LN) with 30 kg N ha−1, and normal (NN) with 100 kg N ha−1.
The genotyping of the 49 tropical inbred lines was per- formed by Affymetrix® platform, containing about 614,000 SNPs (Unterseer et al. 2014). Then, markers with low call rate (< 95%), minor allele frequency (MAF < 0.05) and heterozygous loci on at least one individual were removed. The missing markers were imputed using the snpReady R package. Finally, the resulting 146,365 SNPs high-quality polymorphic SNPs were used to build the artificial hybrids genomic matrix, deduced by combining the genotypes from its two parents.
Check the Mendeley Repository for the full genotypic and phenotypic data
Both data sets can download in R.Data and RDS format direct here and Mendeley Repository. To download this data, you have to click in 'download' and save in our computer diretory.
Then, to import and read the file in R you must to use the readRDS() function (more detail below). To download every dataset (USP and Helix), please use the following file.
The environmental typing (envirotyping) pipeline were conducted using the functions of the EnvRtype R package. This package has functions for supporting the collection of environmental data get_weather(), processing environmental data processWTH() and build of the W matrix of envirotype covariables W.matrix(). Finally, this package helps the construction of the genomic x envirotyping kinships using get_kernels() functions, which easily can run into a Bayesian Genomic-enabled Prediction framework implemented in BGGE package. Bellow we present a brief example of the use of both packages to run a genomic prediction considering reaction norms. This package can be installed as:
library(devtools)
install_github('allogamous/EnvRtype') # current version: 0.1.6 (December 14th 2020)
Environmental data were obtained from NASA POWER data base using the function get_weather() based on the geographic coordinates and planting dates for each environment:
require(EnvRtype)
# an example using 4 environments from USP set
lat = c(-22.875,-22.705,-22.875,-22.705) # latitude coordinates
lon = c(-47.997,-47.637,-47.997,-47.637) # longitude coordinates
env = c("E1","E2","E3","E4") # environmental ID
plant.date = c("2016-01-26","2016-01-21","2017-01-12","2017-01-10")
harv.date = c('2016-08-01',"2016-07-14","2017-07-25","2017-07-15")
df.clim <- get_weather(env.id = env,lat = lat,lon = lon,start.day = plant.date,end.day = harv.date,country = 'BRA')
head(df.clim) # data set of weather data
Additional environmental variables describing ecophysiological processes (e.g., evapotranspiration, effect of temperature on radiation use efficiency) were computed using the function processWTH():
df.clim <- processWTH(env.data = df.clim,Tbase1 = 8,Tbase2 = 45,Topt1 = 30,Topt2 = 37) # computing thermal-related, radition and atmospheric process
Then, it's possible to create an environmental covariable matrix W, with q environments and k combinations of time intervals (e.g., phenologycal stages) x quantiles (distribution of the environmental data) x environmental factor, as follows:
id.var <- names(df.clim)[c(10:16,22,24:28,30:31)] # names of the variables
W <-W_matrix(env.data = df.clim,var.id = id.var,statistic = 'quantile',by.interval = TRUE,time.window = c(0,14,35,65,90,120))
Below are the codes for three types of kernel methods. We use these methods to model additive (A), dominance (D) and environmental (W) effects. On this page we will make the codes available, especially for obtaining the D effects, but we will exemplify the kernels using only the A effects. To run D and W just replace the matrix A with the respective D and W. To run the following examples, please download the genotypic, phenotypic and environmental data here. To run HELIX, for example, use M and S from Molecular_HELIX.RData as A_matrix and D_matrix, respectively (same for Molecular_USP.RData).
Obtaining dominance effects is given by:
source('https://raw.githubusercontent.com/gcostaneto/KernelMethods/master/Dominance_Matrix.R') # codes for dominance effects
D_matrix <- S.matrix(M = M)
dim(D_matrix) # genotypes x markers
Relationship Kernels based on the Genomic Best Linear Unbiased Predictior (GBLUP) can be implemented as:
source('https://raw.githubusercontent.com/gcostaneto/KernelMethods/master/GBLUP_Kernel.R') # codes for GB kernel
K_A <- GB_Kernel(X = A_matrix,is.center = FALSE) # Genomic relationship for A effects
K_D <- GB_Kernel(X = D_matrix,is.center = TRUE) # Genomic relationship for D effects
# list of matrixs
K_G = list(A = K_A, D = K_D) # A + D model
K_A = list(A = K_A) # A model
require(EnvRtype)
K_W <- list(W=env_kernel(env.data = as.matrix(W))[[2]]) # W matrix
Relationship Kernels based on Gaussian Kernel (GK) can be implemented as:
source('https://raw.githubusercontent.com/gcostaneto/KernelMethods/master/Gaussian_Kernel.R') # codes for GK kernel
K_G <- GK_Kernel(X = list(A=A_matrix,D=D_matrix)) # list for each kernel
K_A <- list(A = K_G$A) # A model
require(EnvRtype)
K_W <- list(W=env_kernel(env.data = as.matrix(W),gaussian = TRUE)[[2]]) # W matrix for GK
Relationship Kernels based on Deep Kernels (DK) cab be implemented based on the arc-cosine method presented in genomic prediction by Cuevas et al (2019) and Crossa et al (2019). Firstly, a base arc-cosine kernel are computed using the molecular matrix data (coded as additive = (0,1,2) or dominance) or environmental data (per environment or per genotype-environment combinations).
Using the function get_GC1 we can compute the base arc-cosine kernel as:
source('https://raw.githubusercontent.com/gcostaneto/KernelMethods/master/DeepKernels.R')
# basic Ark-cosine kernels (1)
K_A <- get_GC1(M = list(A=A_matrix)) # K_A 1
# or build it together (this facilitate the second stage of DK analysis)
K_G <- get_GC1(M = list(A=A_matrix, D=D_matrix))
K_W <- get_GC1(M = list(W=W)) # K_E 1
Then, using the function opt_AK we can compute the base arc-cosine kernels according to a certain model structure:
# opmization of Deep Kernel
# Step 1: built your kernel model using get_kernel from EnvRtype
M1 <-get_kernel(K_G = K_A,K_E = NULL, env = 'env',gid='gid',y='value',data = phenoGE,model = 'MM')
# Step 2: now optmize it using opt_AK function
y = phenoGE$value # phenotypic records with NAs
training <- 1:length(y) # here you put the training set. As example, we use all data and 3 hidden layers (nl = 10)
M1. <- opt_AK(K = M1,y = y,tr = training,nl = 3)
# use the superheat to compare the modifications.
# Example: e
require(superheat)
superheat(M1$KG_G$Kernel, row.dendrogram = T,col.dendrogram = T ) # AK1 kernel for G
superheat(M1.$KG_G$Kernel,row.dendrogram = T,col.dendrogram = T ) # AK optmized for G
details about the models (MM, EMM, MDs and RNMM) are given in the next section.
Five genomic prediction models were presented using the function get_kernels from EnvRtype package.
require(Envtype) # or source('https://raw.githubusercontent.com/allogamous/EnvRtype/master/R/getGEenriched.R')
M1 <-get_kernel(K_G = K_A,K_E = NULL, env = 'env',gid='gid',y='value',data = phenoGE,model = 'MM')
M2 <-get_kernel(K_G = K_G,K_E = NULL, env = 'env',gid='gid',y='value',data = phenoGE,model = 'MM')
M3 <-get_kernel(K_G = K_G,K_E = NULL, env = 'env',gid='gid',y='value',data = phenoGE,model = 'MDs')
M4 <-get_kernel(K_G = K_G,K_E = K_W, env = 'env',gid='gid',y='value',data = phenoGE,model = 'EMM')
M5 <-get_kernel(K_G = K_G,K_E = K_W, env = 'env',gid='gid',y='value',data = phenoGE,model = 'RNMM')
Genomic predictions were performed using the Bayesian Genotype plus Genotype × Environment (BGGE) package (Granato et al. 2018) fitted to 10,000 iterations with the first 1,000 cycles removed as burn-in with thinning equal to 2. To run the following examples, please download the genotypic, phenotypic and environmental data here. To run HELIX, for example, use M and S from Molecular_HELIX.RData as A_matrix and D_matrix, respectively (same for Molecular_USP.RData). Then, run the previous examples (kernels section).
In the EnvRtype package, now is availble a function named kernel_model() that runs the same algorithm from BGGE, but with some advantages such as already computes and organizes the variance components with their respective confidence intervals. If you want to use another package, you can use the functions to create the different kernel methods and use this relationship matrix in another functions. For DK, you can use M <- opt_AK(K = K,y = y,tr = training,nl = 10,package = 'other'), in which K is list of kernels (genomic and enviromic) and the argument 'package' denotes that your kernels will be processed to run in another packages. By default package = 'BGGE', which means that this output can be run in BGGE and EnvRtype.
# example: Using model 5 com DK
# to run this example, download the file https://github.com/gcostaneto/KernelMethods/blob/master/example.RData
# and use this source:
source('https://raw.githubusercontent.com/gcostaneto/KernelMethods/master/DeepKernels.R') # codes for DK
source('https://raw.githubusercontent.com/gcostaneto/KernelMethods/master/Dominance_Matrix.R') # codes for dominance effects
require(EnvRtype) # or source('https://raw.githubusercontent.com/allogamous/EnvRtype/master/R/met_kernel_model.R')
D_matrix <- S.matrix(M = M)
A_matrix <- M # coded as aa = 0, Aa = 1 and AA = 2
Step 2: Compute the basic DK for each effect (A = additive effects, D = dominance, W = environmental data)
K_G <- get_GC1(M = list(A=A_matrix, D=D_matrix))
K_W <- get_GC1(M = list(W=W)) # K_E 1
require(Envtype) # or source('https://raw.githubusercontent.com/allogamous/EnvRtype/master/R/getGEenriched.R')
y = phenoGE$value # phenotypic records with NAs
training <- 1:length(y) # here you put the training set. As example, we use all data and 3 hidden layers (nl = 10)
M5 <-get_kernel(K_G = K_G,K_E = K_W, env = 'env',gid='gid',y='value',data = phenoGE,model = 'RNMM')
M5 <- opt_AK(K = M5,y = y,tr = training,nl = 10)
ne <- as.vector(table(phenoGE$env)) # number of genotypes per environment
y <- phenoGE$yield # phenotypic observations
Z_E <- model.matrix(~0+env,phenoGE) # design matrix for environments
# Using BGGE
require(BGGE)
fit <- BGGE(y = y, K = M5, XF= Z_E, ne = ne,ite = 10E3, burn = 10E2, thin = 2, verbose = TRUE)
# Using EnvRtype (novel)
fit <- kernel_model(y = 'value',env = 'env',gid = 'gid',data = phenoGE,
random = M5,fixed = Z_E,ite=10E3,burnin = 10E2,thin=2)
OBS: for running CV schemes, you need to put the Step 3 inside of each fold. For GB and GK kernels, the M5 ca be computed using the get_kernels() function as explained in Statistical Models section.
Variance components can be extracted using the function Vcomp.BGGE provided in this link or using the following source code:
source('https://raw.githubusercontent.com/gcostaneto/KernelMethods/master/VarianceComponents.R')
Vcomp.BGGE(fit) # for using BGGE
If you are using the kernel_model() function from EnvRtype, this is obtaiend as fit$VarComp, already computed on the fit object.
# Using EnvRtype (novel)
fit <- kernel_model(y = 'value',env = 'env',gid = 'gid',data = phenoGE,
random = M5,fixed = Z_E,ite=10E3,burnin = 10E2,thin=2)
fit$VarComp
-
Costa-Neto, G, Galli G, Carvalho, H F, Fritsche-Neto R, Crossa J (2020). EnvRtype: A package to interplay enviromics and quantitative genomics. available at biorxv
-
Costa-Neto G, Fritsche-Neto R, Crossa J (2020). Nonlinear kernels, dominance, and envirotyping data increase the accuracy of genome-based prediction in multi-environment trials. Heredity (Edinb). http://dx.doi.org/10.1038/s41437-020-00353-1
-
Crossa J, Martini JWR, Gianola D, et al (2019) Deep Kernel and Deep Learning for Genome-Based Prediction of Single Traits in Multienvironment Breeding Trials. Front Genet 10:1–13. https://doi.org/10.3389/fgene.2019.01168
-
Cuevas J, Montesinos-López O, Juliana P, et al (2019) Deep Kernel for genomic and near infrared predictions in multi-environment breeding trials. G3 Genes, Genomes, Genet 9:2913–2924. https://doi.org/10.1534/g3.119.400493
-
Granato I, Cuevas J, Luna-vázquez F, et al (2018) BGGE : A New Package for Genomic-Enabled Prediction Incorporating Genotype x Environment Interaction Models. 8:3039–3047. https://doi.org/10.1534/g3.118.200435
-
Morota G, Gianola D (2014) Kernel-based whole-genome prediction of complex traits: A review. Front Genet 5:. https://doi.org/10.3389/fgene.2014.00363
-
Pérez-Elizalde S, Cuevas J, Pérez-Rodríguez P, Crossa J (2015) Selection of the Bandwidth Parameter in a Bayesian Kernel Regression Model for Genomic-Enabled Prediction. J Agric Biol Environ Stat 20:512–532. https://doi.org/10.1007/s13253-015-0229-y
-
Jarquín D, Crossa J, Lacaze X, et al (2014) A reaction norm model for genomic selection using high-dimensional genomic and environmental data. Theor Appl Genet 127:595–607. https://doi.org/10.1007/s00122-013-2243-1
-
Vitezica ZG, Varona L, Legarra A (2013) On the additive and dominant variance and covariance of individuals within the genomic selection scope. Genetics 195:1223–1230. https://doi.org/10.1534/genetics.113.155176
-
Pérez-Rodríguez P, Gianola D, González-Camacho JM, et al (2012) Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat. G3 Genes, Genomes, Genet. https://doi.org/10.1534/g3.112.003665
-
VanRaden PM (2008) Efficient methods to compute genomic predictions. J Dairy Sci 91:4414–4423. https://doi.org/10.3168/jds.2007-0980
For any questions, suggestions or corrections, please contact the author of this tutorial at Germano Costa neto germano.cneto@usp.br
We thank prof. Jaime Cuevas for his availability for Deep Kernel codes. For more details on this subject, contact him or look for more information in Cuevas et al. (2019).
We thank CIMMYT and the University of São Paulo (USP) for their support in the development of the project.
The theories exposed on this page are presented in the work of Costa Neto et al (2020) and were developed under the authorship of Germano Costa Neto, Jose Crossa and Roberto Fritsche Neto.