Comparison: Mandala vs Sommer

Side-by-side analysis for quantitative genetics applications

Overview

This tutorial compares the mandala package with the popular sommer package for analyzing agricultural field trials. Most examples use the same dataset in both packages and fit directly comparable models; where the package workflows differ, the comparison focuses on the closest practical analysis in each package and highlights where Mandala adds field-trial-specific workflow helpers.

What you’ll learn

Key differences between Mandala and Sommer
Side-by-side analysis of comparable MET, GBLUP, and GxE workflows
Variance component estimation comparison
Heritability calculation methods for multi-environment data
When to use each package

Background

Sommer Package

Purpose: Mixed models for plant breeding and quantitative genetics
Key Features:
- Multivariate and univariate mixed models
- Flexible covariance structures and relationship matrices
- Genomic prediction and broader quantitative-genetics workflows
- G×E modeling, including reduced-rank / FA-style structures
- Spatial modeling, including 2D spline support
Primary Use: Quantitative genetics, genomic prediction, and flexible mixed-model analysis for breeding data

Mandala Package

Purpose: Mixed-model analysis for agricultural field trials
Key Features:
- Streamlined workflow for standard field-trial designs
- Direct spatial formula terms and built-in diagnostics
- Genomic prediction helpers for GBLUP workflows
- Dedicated factor-analytic G×E workflow with post-fit visualization
- Unified heritability estimation
Primary Use: Field-trial analysis, variety testing, and genomic prediction within breeding trial workflows

Loading Packages

library(mandala)
library(sommer)
library(dplyr)
library(ggplot2)
library(tidyr)

get_sommer_vc <- function(varcomp, term) {
  hits <- which(startsWith(rownames(varcomp), paste0(term, ".")) | rownames(varcomp) == term)
  if (length(hits) != 1L) {
    stop("Expected exactly one Sommer variance component for term: ", term)
  }
  varcomp[hits, "VarComp"]
}

get_mandala_vc <- function(varcomp, term) {
  hits <- which(varcomp$component == term)
  if (length(hits) != 1L) {
    stop("Expected exactly one Mandala variance component for term: ", term)
  }
  varcomp$estimate[hits]
}

Example 1: Multi-Environment Trial

Data Setup

set.seed(456)
n_genotypes <- 20
n_envs <- 3
n_blocks <- 3

met_data <- expand.grid(
  genotype = factor(paste0("G", sprintf("%02d", 1:n_genotypes))),
  env = factor(paste0("E", 1:n_envs)),
  block = factor(paste0("B", 1:n_blocks))
)

# True variance components
true_var_g <- 500
true_var_gxe <- 200
true_var_error <- 400

# Simulate
met_data$yield <- 6000 +
  rnorm(n_genotypes, 0, sqrt(true_var_g))[as.numeric(met_data$genotype)] +
  rnorm(n_envs, 0, 300)[as.numeric(met_data$env)]

# Add GxE
gxe <- matrix(rnorm(n_genotypes * n_envs, 0, sqrt(true_var_gxe)), 
              n_genotypes, n_envs)
met_data$yield <- met_data$yield + 
  gxe[cbind(as.numeric(met_data$genotype), as.numeric(met_data$env))]

# Add block(env) and error
met_data$env_block <- factor(paste0(met_data$env, "_", met_data$block))
met_data$yield <- met_data$yield + 
  rnorm(n_envs * n_blocks, 0, 50)[as.numeric(met_data$env_block)] +
  rnorm(nrow(met_data), 0, sqrt(true_var_error))

head(met_data)

  genotype env block    yield env_block
1      G01  E1    B1 5861.335     E1_B1
2      G02  E1    B1 5902.917     E1_B1
3      G03  E1    B1 5880.556     E1_B1
4      G04  E1    B1 5822.048     E1_B1
5      G05  E1    B1 5856.848     E1_B1
6      G06  E1    B1 5885.062     E1_B1

Mandala MET Analysis

mandala_met <- mandala(
  fixed  = yield ~ env,
  random = ~ genotype + genotype:env + env:block,
  data   = met_data,
  verbose = FALSE
)

# Variance components
mandala_met_vc <- mandala_met$varcomp
print("Mandala MET Variance Components:")

[1] "Mandala MET Variance Components:"

print(mandala_met_vc)

     component  estimate std.error  z.ratio bound %ch
1     genotype  500.1421 192.81468 2.593900     P  NA
2 genotype:env  128.0159  65.26314 1.961534     P  NA
3    env:block 1347.2889 790.33649 1.704703     P  NA
4     R.sigma2  432.1032  57.23323 7.549865     P  NA

# Extract components
var_g_mandala_met <- get_mandala_vc(mandala_met_vc, "genotype")
var_gxe_mandala_met <- get_mandala_vc(mandala_met_vc, "genotype:env")
var_e_mandala_met <- get_mandala_vc(mandala_met_vc, "R.sigma2")

# Entry-mean heritability across environments
h2_met_mandala <- var_g_mandala_met /
  (var_g_mandala_met + var_gxe_mandala_met / n_envs + var_e_mandala_met / (n_envs * n_blocks))
cat("\nMandala Entry-mean heritability:", round(h2_met_mandala, 3), "\n")


Mandala Entry-mean heritability: 0.847

Sommer MET Analysis

sommer_met <- mmer(
  fixed  = yield ~ env,
  random = ~ genotype + genotype:env + env:block,
  data   = met_data,
  verbose = FALSE
)

# Variance components
met_vc <- summary(sommer_met)$varcomp
print("Sommer MET Variance Components:")

[1] "Sommer MET Variance Components:"

print(met_vc)

                           VarComp VarCompSE   Zratio Constraint
genotype.yield-yield      500.1213 192.74417 2.594742   Positive
genotype:env.yield-yield  127.6429  65.18364 1.958205   Positive
env:block.yield-yield    1347.2640 790.20255 1.704960   Positive
units.yield-yield         432.1280  57.23833 7.549626   Positive

# Extract components
var_g <- get_sommer_vc(met_vc, "genotype")
var_gxe <- get_sommer_vc(met_vc, "genotype:env")
var_e <- get_sommer_vc(met_vc, "units")

# Entry-mean heritability across environments
h2_met <- var_g / (var_g + var_gxe/n_envs + var_e/(n_envs * n_blocks))
cat("\nEntry-mean heritability:", round(h2_met, 3), "\n")


Entry-mean heritability: 0.847

MET Comparison

tibble(
  package = c("Mandala", "Sommer"),
  genotype_variance = c(var_g_mandala_met, var_g),
  gxe_variance = c(var_gxe_mandala_met, var_gxe),
  residual_variance = c(var_e_mandala_met, var_e),
  entry_mean_h2 = c(h2_met_mandala, h2_met)
)

# A tibble: 2 × 5
  package genotype_variance gxe_variance residual_variance entry_mean_h2
  <chr>               <dbl>        <dbl>             <dbl>         <dbl>
1 Mandala              500.         128.              432.         0.847
2 Sommer               500.         128.              432.         0.847

Example 2: Spatial Analysis

This direct comparison starts with the same row and column random-effects adjustment in both packages. For spline-based spatial modeling, Sommer also provides spl2Dc() via mmes(), while Mandala also supports dedicated ar1() and pspline2D(...) spatial formula terms.

set.seed(789)
n_rows <- 10
n_cols <- 10

spatial_data <- data.frame(
  row = rep(1:n_rows, each = n_cols),
  col = rep(1:n_cols, times = n_rows),
  genotype = factor(sample(paste0("G", 1:25), n_rows * n_cols, replace = TRUE))
)

# Add spatial trend + genotype effects + error
gen_eff <- setNames(rnorm(25, 0, 300), paste0("G", 1:25))
spatial_data$yield <- 5000 + 
  gen_eff[spatial_data$genotype] +
  30 * spatial_data$row - 20 * spatial_data$col +
  rnorm(nrow(spatial_data), 0, 200)

Visualize Field Pattern

ggplot(spatial_data, aes(x = col, y = row, fill = yield)) +
  geom_tile() +
  scale_fill_gradient2(low = "#2E6B8A", mid = "#FAF8F5", high = "#9B5B5B",
                       midpoint = mean(spatial_data$yield)) +
  coord_equal() +
  theme_minimal() +
  labs(title = "Field Map - Spatial Trend Visible",
       x = "Column", y = "Row")

Sommer with Row-Column Effects

spatial_data$row_f <- factor(spatial_data$row)
spatial_data$col_f <- factor(spatial_data$col)

sommer_spatial <- mmer(
  fixed = yield ~ 1,
  random = ~ genotype + row_f + col_f,
  data = spatial_data,
  verbose = FALSE
)

print(summary(sommer_spatial)$varcomp)

                        VarComp VarCompSE    Zratio Constraint
genotype.yield-yield 62242.1591 22296.159 2.7916091   Positive
row_f.yield-yield    11391.4155  8201.081 1.3890139   Positive
col_f.yield-yield      490.7583  3227.847 0.1520389   Positive
units.yield-yield    47209.7972  8710.007 5.4201793   Positive

Mandala with the Same Row-Column Effects

mandala_spatial <- mandala(
  fixed  = yield ~ 1,
  random = ~ genotype + row_f + col_f,
  data   = spatial_data,
  verbose = FALSE
)

print(mandala_spatial$varcomp)

  component   estimate std.error   z.ratio bound %ch
1  genotype 62235.6785 22303.624 2.7903842     P  NA
2     row_f 11381.7313  8197.537 1.3884331     P  NA
3     col_f   500.9914  3232.146 0.1550027     P  NA
4  R.sigma2 47234.6463  8718.454 5.4177778     P  NA

Spatial Comparison

sommer_spatial_vc <- summary(sommer_spatial)$varcomp
mandala_spatial_vc <- mandala_spatial$varcomp

tibble(
  package = c("Mandala", "Sommer"),
  genotype_variance = c(get_mandala_vc(mandala_spatial_vc, "genotype"),
                        get_sommer_vc(sommer_spatial_vc, "genotype")),
  row_variance = c(get_mandala_vc(mandala_spatial_vc, "row_f"),
                   get_sommer_vc(sommer_spatial_vc, "row_f")),
  col_variance = c(get_mandala_vc(mandala_spatial_vc, "col_f"),
                   get_sommer_vc(sommer_spatial_vc, "col_f")),
  residual_variance = c(get_mandala_vc(mandala_spatial_vc, "R.sigma2"),
                        get_sommer_vc(sommer_spatial_vc, "units"))
)

# A tibble: 2 × 5
  package genotype_variance row_variance col_variance residual_variance
  <chr>               <dbl>        <dbl>        <dbl>             <dbl>
1 Mandala            62236.       11382.         501.            47235.
2 Sommer             62242.       11391.         491.            47210.

If field rows and columns are expected to be correlated rather than independent, Mandala can replace row_f + col_f with ar1(row_f) + ar1(col_f) directly inside the formula.

Example 3: Genomic Prediction (GBLUP)

Both packages support GBLUP with relationship matrices. To make the comparison meaningful, the phenotype below is simulated from marker-derived genomic signal, so a positive cross-validation result is expected.

Data Setup

set.seed(123)
n_geno <- 50
n_markers <- 200
geno_ids <- paste0("G", 1:n_geno)

# Simulate marker data and build a GRM
M <- matrix(rbinom(n_geno * n_markers, 2, 0.5), n_geno, n_markers)
M_centered <- scale(M, center = TRUE, scale = FALSE)
G <- tcrossprod(M_centered) / n_markers
diag(G) <- diag(G) + 1e-6
rownames(G) <- colnames(G) <- geno_ids

# Simulate phenotype with genomic signal driven by marker effects
qtl_idx <- 1:20
marker_effects <- rnorm(length(qtl_idx), 0, 1)
genomic_signal <- as.numeric(M_centered[, qtl_idx, drop = FALSE] %*% marker_effects)
genomic_signal <- as.numeric(scale(genomic_signal))

gblup_data <- data.frame(
  geno = factor(geno_ids, levels = geno_ids),
  yield = 5000 + 180 * genomic_signal + rnorm(n_geno, 0, 120)
)

head(gblup_data)

  geno    yield
1   G1 4836.758
2   G2 4893.197
3   G3 5053.719
4   G4 4755.437
5   G5 4813.896
6   G6 4727.007

Sommer GBLUP

# Sommer GBLUP
sommer_gblup <- mmer(
  fixed = yield ~ 1,
  random = ~ vsr(geno, Gu = G),
  data = gblup_data,
  verbose = FALSE
)

# Extract GEBVs
gebvs_sommer <- tibble(
  geno = names(sommer_gblup$U$`u:geno`$yield),
  gebv = unname(sommer_gblup$U$`u:geno`$yield)
)
head(gebvs_sommer)

# A tibble: 6 × 2
  geno    gebv
  <chr>  <dbl>
1 G1    -148. 
2 G2     -89.0
3 G3      52.9
4 G4    -215. 
5 G5    -165. 
6 G6    -250.

Mandala GBLUP

# Mandala high-level GBLUP wrapper
invisible(capture.output(
  mandala_gp_fit <- mandala_gp(
    fixed     = yield ~ 1,
    random    = ~ GM(geno, Gmat),
    gen_col   = "geno",
    data      = gblup_data,
    GRM       = G,
    verbose   = FALSE
  )
))

gebvs_mandala <- mandala_gp_fit$gebv %>%
  transmute(geno = id, gebv)
head(gebvs_mandala)

  geno       gebv
1   G1 -147.41641
2  G10 -447.29152
3  G11 -268.57688
4  G12  -69.64077
5  G13  157.34041
6  G14  -85.00044

# Built-in cross-validation helper
invisible(capture.output(
  cv_results <- mandala_gp_cv(
    fixed     = yield ~ 1,
    random    = ~ GM(geno, Gmat),
    gen_col   = "geno",
    data      = gblup_data,
    GRM       = G,
    k_folds   = 5,
    n_reps    = 3,
    verbose   = FALSE
  )
))
mean(cv_results$by_fold$pred_ability)

[1] 0.365165

GBLUP Comparison

gblup_compare <- inner_join(
  gebvs_sommer %>% rename(sommer_gebv = gebv),
  gebvs_mandala %>% rename(mandala_gebv = gebv),
  by = "geno"
)

cat(sprintf("GEBV correlation: %.4f\n", cor(gblup_compare$sommer_gebv, gblup_compare$mandala_gebv)))

GEBV correlation: 1.0000

cat(sprintf("GEBV RMSE: %.4f\n", sqrt(mean((gblup_compare$sommer_gebv - gblup_compare$mandala_gebv)^2))))

GEBV RMSE: 0.3476

head(gblup_compare)

# A tibble: 6 × 3
  geno  sommer_gebv mandala_gebv
  <chr>       <dbl>        <dbl>
1 G1         -148.        -147. 
2 G2          -89.0        -88.7
3 G3           52.9         52.8
4 G4         -215.        -214. 
5 G5         -165.        -165. 
6 G6         -250.        -249.

Example 4: Structured G×E Models

Mandala provides a dedicated factor-analytic G×E workflow for field-trial analysis. Sommer can also fit reduced-rank or FA-style G×E structures through the newer mmes() variance-structure machinery, but that workflow is more manual. This tutorial uses a diagonal G×E Sommer example as a simpler baseline and then shows Mandala’s higher-level FA() workflow.

Sommer Diagonal G×E Model

# Sommer diagonal G×E structure
sommer_diag <- mmer(
  fixed = yield ~ env,
  random = ~ vsr(dsr(env), geno),  # Diagonal G×E
  data = met_data,
  verbose = FALSE
)

Sommer can also fit reduced-rank or FA-style structures with mmes() and vsm(rrm(...), ism(...)), but that requires a more manual specification than the diagonal mmer() example shown here.

Mandala Factor-Analytic G×E Model

# Mandala provides dedicated FA() syntax
fa_model <- mandala(
  fixed  = yield ~ env + geno,
  random = ~ FA(geno, env, k = 2) + by(env):ar1(row) + by(env):ar1(col),
  data   = met_data,
  verbose = FALSE
)

# Built-in visualization
fa_biplot(fa_model)

fa_biplot(fa_model, type = "which_won_where")

fa_heatmap(fa_model)

# Extract environment correlations
fa_env_cor(fa_model)

             E1           E2           E3
E1 1.000000e+00 2.253465e-14 2.253464e-14
E2 2.253465e-14 1.000000e+00 4.506688e-14
E3 2.253464e-14 4.506688e-14 1.000000e+00

# Reliability estimates
fa_reliability(fa_model)

   geno env         blup       se      pev  var_env reliability
1   G01  E1   7.76446633 18.21492 197370.6 4437.611           0
2   G02  E1  -0.67666849 18.21514 197375.4 4437.611           0
3   G03  E1   4.18935571 18.22352 197557.0 4437.611           0
4   G04  E1  -8.59831775 18.22352 197557.0 4437.611           0
5   G05  E1  16.10555048 18.22500 197589.2 4437.611           0
6   G06  E1  20.26744882 18.22500 197589.2 4437.611           0
7   G07  E1  -4.37516375 18.20491 197153.7 4437.611           0
8   G08  E1   4.25653605 18.20491 197153.7 4437.611           0
9   G09  E1 -11.14964159 18.20287 197109.6 4437.611           0
10  G10  E1  -4.84037536 18.20287 197109.6 4437.611           0
11  G11  E1 -16.58236399 18.20287 197109.6 4437.611           0
12  G12  E1 -11.03960703 18.20287 197109.6 4437.611           0
13  G13  E1   2.70244363 18.20491 197153.7 4437.611           0
14  G14  E1   5.34808793 18.20491 197153.7 4437.611           0
15  G15  E1  -5.37377101 18.22500 197589.2 4437.611           0
16  G16  E1 -10.41954420 18.22500 197589.2 4437.611           0
17  G17  E1  -8.32977427 18.22352 197557.0 4437.611           0
18  G18  E1  11.35664246 18.22352 197557.0 4437.611           0
19  G19  E1  16.05904086 18.21514 197375.4 4437.611           0
20  G20  E1  -6.62142511 18.21514 197375.4 4437.611           0
21  G01  E2  -6.25531319 18.21494 197371.0 4437.612           0
22  G02  E2  18.70842985 18.21516 197375.8 4437.612           0
23  G03  E2  -2.93347984 18.22353 197557.4 4437.612           0
24  G04  E2   6.07621387 18.22353 197557.4 4437.612           0
25  G05  E2   9.22922326 18.22502 197589.6 4437.612           0
26  G06  E2  -6.33608228 18.22502 197589.6 4437.612           0
27  G07  E2   8.80883117 18.20492 197154.1 4437.612           0
28  G08  E2  -4.27426303 18.20492 197154.1 4437.612           0
29  G09  E2   6.88270781 18.20288 197109.9 4437.612           0
30  G10  E2  13.13581743 18.20288 197109.9 4437.612           0
31  G11  E2  -1.04068785 18.20288 197109.9 4437.612           0
32  G12  E2   3.00428774 18.20288 197109.9 4437.612           0
33  G13  E2   1.37390772 18.20492 197154.1 4437.612           0
34  G14  E2 -14.24390095 18.20492 197154.1 4437.612           0
35  G15  E2  14.45490564 18.22502 197589.6 4437.612           0
36  G16  E2   6.97489333 18.22502 197589.6 4437.612           0
37  G17  E2  -3.85278747 18.22353 197557.4 4437.612           0
38  G18  E2 -10.94551802 18.22353 197557.4 4437.612           0
39  G19  E2 -24.03085888 18.21516 197375.8 4437.612           0
40  G20  E2 -14.73905417 18.21516 197375.8 4437.612           0
41  G01  E3  -1.47438396 18.21494 197371.0 4437.613           0
42  G02  E3 -18.03152530 18.21516 197375.8 4437.613           0
43  G03  E3  -1.25562123 18.22353 197557.4 4437.613           0
44  G04  E3   2.52211745 18.22353 197557.4 4437.613           0
45  G05  E3 -25.33490690 18.22502 197589.6 4437.613           0
46  G06  E3 -13.93141203 18.22502 197589.6 4437.613           0
47  G07  E3  -4.43353401 18.20492 197154.1 4437.613           0
48  G08  E3   0.01778946 18.20492 197154.1 4437.613           0
49  G09  E3   4.26719175 18.20288 197109.9 4437.613           0
50  G10  E3  -8.29534210 18.20288 197109.9 4437.613           0
51  G11  E3  17.62316620 18.20288 197109.9 4437.613           0
52  G12  E3   8.03570324 18.20288 197109.9 4437.613           0
53  G13  E3  -4.07605301 18.20492 197154.1 4437.613           0
54  G14  E3   8.89603214 18.20492 197154.1 4437.613           0
55  G15  E3  -9.08117538 18.22502 197589.6 4437.613           0
56  G16  E3   3.44500408 18.22502 197589.6 4437.613           0
57  G17  E3  12.18295168 18.22353 197557.4 4437.613           0
58  G18  E3  -0.41108424 18.22353 197557.4 4437.613           0
59  G19  E3   7.97205696 18.21516 197375.8 4437.613           0
60  G20  E3  21.36083776 18.21516 197375.8 4437.613           0

fa_reliability_by_env(fa_model)

  env mean_reliability  n
1  E1                0 20
2  E2                0 20
3  E3                0 20

# Factor scores and loadings
fa_geno_scores(fa_model)

   geno         FA1         FA2            method
1   G01 -0.07430727  1.35320989 svd_from_ge_blups
2   G02  3.14463984 -1.08623221 svd_from_ge_blups
3   G03  0.03808185  0.70707267 svd_from_ge_blups
4   G04 -0.06862734 -1.45418159 svd_from_ge_blups
5   G05  3.68993234  1.62516399 svd_from_ge_blups
6   G06  1.54176417  3.00198635 svd_from_ge_blups
7   G07  0.95292860 -1.04470064 svd_from_ge_blups
8   G08 -0.18483763  0.78738085 svd_from_ge_blups
9   G09 -0.26119695 -1.83256024 svd_from_ge_blups
10  G10  1.64008687 -1.33650882 svd_from_ge_blups
11  G11 -2.33703499 -2.12434220 svd_from_ge_blups
12  G12 -0.91706031 -1.61135520 svd_from_ge_blups
13  G13  0.58893280  0.28200084 svd_from_ge_blups
14  G14 -1.76554018  1.46230897 svd_from_ge_blups
15  G15  1.79864126 -1.47693761 svd_from_ge_blups
16  G16 -0.15029916 -1.74150272 svd_from_ge_blups
17  G17 -1.74939550 -0.88961294 svd_from_ge_blups
18  G18 -0.41393083  2.07633652 svd_from_ge_blups
19  G19 -2.06327526  3.39200925 svd_from_ge_blups
20  G20 -3.40822723 -0.08473759 svd_from_ge_blups

fa_env_loadings(fa_model)

     FA1          FA2
E1 1e-05 0.000000e+00
E2 1e-05 9.999469e-06
E3 1e-05 9.999464e-06

Key Differences Summary

Aspect	Mandala	Sommer
Syntax	Simple formula interface	More verbose
Heritability	Built-in `h2_estimates()`	Manual calculation
Spatial models	AR1, P-spline formula terms, variograms	Row/column effects, custom covariance, `spl2Dc()` via `mmes()`
GBLUP	`GM()` + `mandala_gp()`	`vsr(Gu=)`
Structured G×E	Dedicated `FA()` workflow with biplots/heatmaps	Diagonal and FA-style reduced-rank structures via `mmer()` / `mmes()`, with more manual setup
Two-stage workflows	Dedicated stage 1 / stage 2 helpers for breeding-trial workflows	Possible, but assembled manually from `mmes()` fits
Cross-validation	`mandala_gp_cv()`	Manual
Multi-trait (multivariate)	No	Yes
Built-in visualization	FA plots, heatmaps, variograms	More manual

When to Use Each

Use Mandala when:

Standard field trial designs
Field-trial spatial modeling with direct ar1() or pspline2D(...) terms
Single-trait GBLUP workflows with built-in cross-validation
Factor-analytic G×E with visualization
Built-in two-stage MET and genomic workflows
You want BLUEs, BLUPs, heritability, spatial adjustment, and G×E outputs in one field-trial-oriented workflow
Quick heritability estimates

Use Sommer when:

Multi-trait genomic prediction
Complex custom covariance structures
Reduced-rank / FA-style G×E with manual specification
Spatial modeling through mmer() / mmes() when you want lower-level control
Broader genetics workflows beyond Mandala’s current scope
Already established sommer workflows

Additional Resources

Sommer: https://cran.r-project.org/package=sommer
Mandala: https://listoagriculture.com/products

Session Information

sessionInfo()

R version 4.5.2 (2025-10-31)
Platform: aarch64-apple-darwin20
Running under: macOS Tahoe 26.1

Matrix products: default
BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] C.UTF-8/C.UTF-8/C.UTF-8/C/C.UTF-8/C.UTF-8

time zone: America/New_York
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] tidyr_1.3.1    ggplot2_4.0.0  dplyr_1.1.4    sommer_4.4.4   enhancer_1.1.0
[6] crayon_1.5.3   MASS_7.3-65    Matrix_1.7-4   mandala_1.1.0 

loaded via a namespace (and not attached):
 [1] gtable_0.3.6       jsonlite_2.0.0     compiler_4.5.2     tidyselect_1.2.1  
 [5] Rcpp_1.1.0         splines2_0.5.4     scales_1.4.0       yaml_2.3.10       
 [9] fastmap_1.2.0      lattice_0.22-7     R6_2.6.1           patchwork_1.3.2   
[13] labeling_0.4.3     generics_0.1.4     knitr_1.50         htmlwidgets_1.6.4 
[17] ggrepel_0.9.6      tibble_3.3.0       pillar_1.11.1      RColorBrewer_1.1-3
[21] rlang_1.1.6        utf8_1.2.6         xfun_0.54          S7_0.2.0          
[25] cli_3.6.5          withr_3.0.2        magrittr_2.0.4     digest_0.6.37     
[29] grid_4.5.2         lifecycle_1.0.4    ggdendro_0.2.0     vctrs_0.6.5       
[33] evaluate_1.0.5     glue_1.8.0         farver_2.1.2       purrr_1.1.0       
[37] rmarkdown_2.30     tools_4.5.2        pkgconfig_2.0.3    htmltools_0.5.8.1