Simulation of Pleiotropic, Linked and Epistatic Phenotypes.

simplePHENOTYPES

Contents

• Installation
• Load Sample Data set
• Single Trait
• Multiple Traits: Pleiotropy Architecture
• Multiple Traits: Partial Pleiotropy Architecture
• Multiple Traits: Spurious Pleiotropy Architecture
• Multiple Traits: Partial Pleiotropy Architecture with other useful parameters
• Using Multiple Marker Data Files
• Contact

This short tutorial presents some of the possible genetic settings one could simulate, but it certainly does not explore all the possibilities. For more information on specific input parameters, please check the help documentation (?create_phenotypes).

Installation

In order to install simplePHENOTYPES, the following r packages will also be installed:

• From Bioconductor:
  • SNPRelate
  • gdsfmt
• From CRAN:
  • mvtnorm
  • lqmm
  • data.table

setRepositories(ind = 1:2)
devtools::install_github("samuelbfernandes/simplePHENOTYPES", build_vignettes = TRUE)

Load Sample Data set

Note that the data set used in all vignettes is already in numeric format. In addition to the numeric format, simplePHENOTYPES’ parameter geno_obj also takes an R object in HapMap format as input. Other input options are VCF, GDS, and Plink bed/ped. These last formats should be loaded from file with geno_file or geno_path.

library(simplePHENOTYPES)
data("SNP55K_maize282_maf04")
SNP55K_maize282_maf04[1:8, 1:10]

Single Trait

The simplest option is the simulation of univariate traits. In the example below, we are simulating ten single trait experiments with a heritability of 0.7. In this setting, the simulated trait is controlled by one large-effect QTN (big_add_QTN_effect = 0.9) and two small effect QTNs. The additive effects of these last two QTNs follow a geometric series starting with 0.2. Thus, the effect size of the first of these two QTNs is 0.2, and the effect size of the second is 0.2². Results are being saved at a temporary directory (home_dir = tempdir()). Please see help files (?create_phenotypes) to see which default values are being used.

create_phenotypes(
  geno_obj = SNP55K_maize282_maf04,
  add_QTN_num = 3,
  add_effect = 0.2,
  big_add_QTN_effect = 0.9,
  rep = 10,
  h2 = 0.7,
  model = "A",
  home_dir = tempdir())

Multiple Traits: Pleiotropy Architecture

simplePHENOTYPES provides three multi-trait simulation scenarios: pleiotropy, partial pleiotropy, and spurious pleiotropy. In this example, we are simulating three (ntraits = 3) pleiotropic (architecture = "pleiotropic") trait controlled by three additive and four dominance QTNs. The effect size of the largest-effect additive QTN is 0.3 for all traits (big_add_QTN_effect = c(0.3, 0.3, 0.3)), while the additive and dominance effect sizes are 0.04, 0.2, and 0.1 for each trait, respectively. Heritability for trait_1 is 0.2, while the heritability of the two correlated traits is 0.4. Each replicate is being recorded in a different file (output_format = "multi-file") in a folder named “Results_Pleiotropic”. In this setting, we do not specify the correlation between traits; instead, the observed (realized) correlation is an artifact of different allelic effects for each trait. The same QTNs are used to generate phenotypes in all ten replications (vary_QTN = FALSE)(default); alternatively, we could select different QTNs in each replicate using vary_QTN = TRUE. As mentioned above, the first QTN of each trait will get the effect provided by big_add_QTN_effect; all other QTNs will have the effect size assigned by add_effect and dom_effect. The vector add_effect contains one allelic effect for each trait, and a geometric series (default) is being used to generate allelic effects for each one of the two additive QTNs (add_QTN_num = 3) and three dominance QTNs (dom_QTN_num = 4). All results will be saved to file, and a data.frame with all phenotypes will be assigned to an object called “test1” (to_r = TRUE).

 test1 <-  create_phenotypes(
    geno_obj = SNP55K_maize282_maf04,
    add_QTN_num = 3,
    dom_QTN_num = 4,
    big_add_QTN_effect = c(0.3, 0.3, 0.3),
    h2 = c(0.2, 0.4, 0.4),
    add_effect = c(0.04,0.2,0.1),
    dom_effect = c(0.04,0.2,0.1),
    ntraits = 3,
    rep = 10,
    vary_QTN = FALSE,
    output_format = "multi-file",
    architecture = "pleiotropic",
    output_dir = "Results_Pleiotropic",
    to_r = TRUE,
    seed = 10,
    model = "AD",
    sim_method = "geometric",
  home_dir = tempdir()
  )

Optionally, we may input a list of allelic effects (sim_method = "custom"). In the example below, a geometric series (custom_geometric) is being assigned and should generate the same simulated data as the previous example (all.equal(test1, test2)). Notice that since big_add_QTN_effect is non-NULL, we only need to provide effects for two out of the three simulated additive QTNs. On the other hand, all four dominance QTN must have an effect assigned on the custom_geometric_d list. Importantly, the allelic effects are assigned to each trait based on the order they appear in the list and not based on the names, i.e., ‘trait_1’, ‘trait_2’, and ‘trait_3’.

 custom_geometric_a <- list(trait_1 = c(0.04, 0.0016),
                         trait_2 = c(0.2, 0.04),
                         trait_3 = c(0.1, 0.01))
 custom_geometric_d <- list(trait_1 = c(0.04, 0.0016, 6.4e-05, 2.56e-06),
                         trait_2 = c(0.2, 0.04, 0.008, 0.0016),
                         trait_3 = c(0.1, 0.01, 0.001, 1e-04))

 test2 <-  create_phenotypes(
   geno_obj = SNP55K_maize282_maf04,
   add_QTN_num = 3,
   dom_QTN_num = 4,
   big_add_QTN_effect = c(0.3, 0.3, 0.3),
   h2 = c(0.2,0.4, 0.4),
   add_effect = custom_geometric_a,
   dom_effect = custom_geometric_d,
   ntraits = 3,
   rep = 10,
   vary_QTN = FALSE,
   output_format = "multi-file",
   architecture = "pleiotropic",
   output_dir = "Results_Pleiotropic",
   to_r = T,
   sim_method = "custom",
   seed = 10,
   model = "AD",
  home_dir = tempdir()
 )
 
 all.equal(test1, test2)

Multiple Traits: Partial Pleiotropy Architecture

In this example, we simulate 20 replicates of three partially pleiotropic traits (architecture = "partially"), which are respectively controlled by seven, 13, and four QTNs. All QTNs will have additive effects that follow a geometric series, where the effect size of the i^th QTN is add_effect^i. For instance, trait_2 is controlled by three pleiotropic additive QTNs and ten trait-specific additive QTNs; consequently, the first pleiotropic additive QTN will have an additive effect of 0.33 and the 13^th trait-specific additive QTN will have an effect of 0.33¹³. Correlation among traits is assigned to be equal to the cor_matrix object. All 20 replicates of these three simulated traits will be saved in one file, specifically in a long format and with an additional column named “Rep”. Results will be saved in a directory called “Results_Partially”. In this example, the genotype file will also be saved in numeric format.

cor_matrix <- matrix(c(   1, 0.3, -0.9,
                        0.3,   1,  -0.5,
                       -0.9, -0.5,    1 ), 3)

sim_results <- create_phenotypes(
  geno_obj = SNP55K_maize282_maf04,
  ntraits = 3,
  pleio_a = 3,
  pleio_e = 2,
  same_add_dom_QTN = TRUE,
  degree_of_dom = 0.5,
  trait_spec_a_QTN_num = c(4, 10, 1),
  trait_spec_e_QTN_num = c(3, 2, 5),
  h2 = c(0.2, 0.4, 0.8),
  add_effect = c(0.5, 0.33, 0.2),
  epi_effect = c(0.3, 0.3, 0.3),
  epi_interaction = 2,
  cor = cor_matrix,
  rep = 20,
  output_dir = "Results_Partially",
  output_format = "long",
  architecture = "partially",
  out_geno = "numeric",
  to_r = TRUE,
  model = "AE",
  home_dir = tempdir()
)

Multiple Traits: Spurious Pleiotropy Architecture

Another architecture implemented is Spurious Pleiotropy. In this case, we have two options: direct or indirect LD (type_of_ld = "indirect"). In the example below, we simulate a case of indirect LD with five replicates of two traits controlled by three additive QTNs each. For each QTN, a marker is first selected (intermediate marker), and then two separate markers (one upstream and another downstream) are picked to be QTNs for each of the two traits. This QTN selection is based on an r² threshold of at most 0.8 (ld_max=0.8) with the intermediate marker. The three QTNs will have additive effects that follow a geometric series, where the effect size of the i^th QTN is 0.02ⁱ for one trait and 0.05ⁱ for the other trait. Starting seed number is 200, and output phenotypes are saved in one file, but in a “wide” format with each replicate of two traits being added as additional columns. Plink fam, bim, and bed files are also saved at Results_LD.

create_phenotypes(
  geno_obj = SNP55K_maize282_maf04,
  add_QTN_num = 3,
  h2 = c(0.2, 0.4),
  add_effect = c(0.02, 0.05),
  rep = 5,
  seed = 200,
  output_format = "wide",
  architecture = "LD",
  output_dir = "Results_LD",
  out_geno = "plink",
  remove_QTN = TRUE,
  ld_max =0.8,
  ld_min =0.2,
  model = "A",
  ld_method = "composite",
  type_of_ld = "indirect",
  home_dir = tempdir()
)

Multiple Traits: Partial Pleiotropy Architecture with other useful parameters

The example below simulates five replicates of three traits. In each replicate, different SNPs are selected to be the QTNs for each experiment (vary_QTN = TRUE). These traits are controlled by three pleiotropic (pleio = 3) additive and dominance QTNs (same_add_dom_QTN = TRUE and degree_of_dom = 1); two pleiotropic epistatic QTNs (pleio_e = 2); four, ten and one trait-specific additive and dominance QTNs (trait_spec_a_QTN_num = c(4, 10, 1)); and two, one and five epistatic trait-specific epistatic QTNs (trait_spec_e_QTN_num = c(2, 1, 5)). In addition to the default parameters, each genetic architecture may be simulated with many auxiliary features. For instance, we may be interested in outputting the amount of variance explained by each simulated QTN (QTN_variance = TRUE) or setting a residual correlation between traits (cor_res = residual) and thus, change the default option of independent residuals. Notice that in this example, the heritability is a 2x3 matrix (h2 = heritability). Each column of the matrix “heritability” will be assigned to a different trait. In this case, simplePHENOTYPES will loop over each row of h2, keeping all other variables constant. Since rep = 5 and nrow(h2) = 2, ten experiments will be simulated and saved in separate files. Simulated results will be saved as “.fam” files used as GEMMA input. Simultaneously, one genotypic file without the QTNs for the simulated traits will be saved for each replication. Due to the option vary_QTN = TRUE, each experiment will be simulated with different QTNs; thus, if we opt for remove_QTN = TRUE, many potentially large files will be saved in the output_dir folder. By default, simplePHENOTYPES will ask us if all these files should be saved. To avoid this question, we may use warning_file_saver = FALSE. In the present example, ten plink bed files (which is also the input for GEMMA) are saved. Genotypic files for rep one will be named SNP55K_maize282_maf04_noQTN_rep_1.bed, SNP55K_maize282_maf04_noQTN_rep_1.bim, and SNP55K_maize282_maf04_noQTN_rep_1.fam, whereas the phenotypic file will be saved as Simulated_Data__Rep1_Herit_0.2_0.8_0.7.fam. Importantly, the file SNP55K_maize282_maf04_noQTN_rep_1.fam does not contain the phenotypic data and needs to be replaced by Simulated_Data__Rep1_Herit_0.2_0.8_0.7.fam prior to its use by GEMMA or other software that uses bed files. A parameter particularly useful, especially when simulating dominance, is constraints. Here we only “include” heterozygote SNPs to be used as QTNs ( constraints = list(maf_above = 0.3, maf_below = 0.44, hets = "include")). Optionally, we may “remove” all the heterozygotes from consideration. The other constrain options used here are to select only QTNs with minor allele frequency between 0.3 and 0.44.

residual <- matrix(c(1, 0.1,-0.2,
                     0.1, 1,-0.1,-0.2,-0.1, 1), 3)
heritability <- matrix(c(0.2, 0.4, 0.8,
                         0.6, 0.7, 0.2), 2)
create_phenotypes(
  geno_obj = SNP55K_maize282_maf04,
  pleio_a = 3,
  pleio_e = 2,
  same_add_dom_QTN = TRUE,
  degree_of_dom = 1,
  trait_spec_a_QTN_num = c(4, 10, 1),
  trait_spec_e_QTN_num = c(2, 1, 5),
  epi_effect = c(0.01, 0.4, 0.2),
  add_effect = c(0.3, 0.2, 0.5),
  h2 = heritability,
  ntraits = 3,
  rep = 5,
  vary_QTN = TRUE,
  warning_file_saver = FALSE,
  output_dir = "Results_Partially_ADE",
  output_format = "gemma",
  architecture = "partially",
  model = "ADE",
  QTN_variance = TRUE,
  remove_QTN = TRUE,
  home_dir = tempdir(),
  constraints = list(
    maf_above = 0.3,
    maf_below = 0.44,
    hets = "include"
  ),
  cor_res = residual
)

Using Selected Markers to be QTN

As of the version 1.2.15, it is also possible to select what markers will be used as QTNS. The arguments QTN_list takes a lists of additive, dominance or epistatic QTNs. In the example below, the SNP ss196523212 is selected to be the additive QTN. Another argument that is exemplified below is epi_interaction. It defines the number of markers to be involved in an epistatic interaction. The parameter out_geno is defining that the marker data used in the simulation will be exported as plink BED files.

QTN_list <- list()
QTN_list$add[[1]] <- c("ss196523212")
QTN_list$dom[[1]] <- c("ss196510214", "ss196472187")
QTN_list$epi[[1]] <- c("ss196530605", "ss196475446")
create_phenotypes(
  geno_obj = SNP55K_maize282_maf04,
  add_QTN_num = 1,
  dom_QTN_num = 2,
  epi_QTN_num = 1,
  epi_interaction = 2,
  h2 = c(0.92, 0.4) ,
  add_effect = c(0.90, 0.2),
  dom_effect = c(0.01, 0.3),
  epi_effect = c(-0.3, 0.7),
  ntraits = 2,
  QTN_list = QTN_list,
  rep = 1,
  output_format = "gemma",
  out_geno = "BED",
  output_dir = "output_data",
  model = "ADE",
  home_dir = getwd()
)

Using Multiple Marker Data Files

If files are saved by chromosome, they can be read directly into create_phenotypes using options geno_path (recommendation: consider having all marker data files in a separate folder). If multiple files are saved in the same folder as the marker data, the parameter prefix might be used to select only the marker data. For example, if your data is saved as “WGS_chrm_1.hmp.txt”, …, “WGS_chrm_10.hmp.txt”, one would use prefix = "WGS_chrm_" .

create_phenotypes(
  geno_path = "PATH/TO/FILE",
  prefix = "WGS_chrm_",
  add_QTN_num = 3,
  h2 = 0.2,
  add_effect = 0.02,
  rep = 5,
  seed = 200,
  output_format = "gemma",
  output_dir = "Results",
  model = "ADE",
  home_dir = tempdir()
)

Contact

Questions, suggestions, and bug reports are welcome and appreciated. Please use GitHub issues for bug reports and the simplePHENOTYPES forum for questions and discussions: https://groups.google.com/forum/#!forum/simplephenotypes

Author: Samuel B Fernandes and Alexander E Lipka

Contact: [email protected] or [email protected]

Institution: University of Illinois at Urbana-Champaign.