Quick Reference

Common tasks at a glance

A concise reference for common tasks when analyzing field trial data with the mandala package.

Basic Model Syntax

Simple RCBD

model <- mandala(
  fixed  = yield ~ genotype,
  random = ~ block,
  data   = field_data
)

Alpha-Lattice Design

model <- mandala(
  fixed  = yield ~ genotype,
  random = ~ rep + rep:incomplete_block,
  data   = field_data
)

Multi-Environment Trial

model <- mandala(
  fixed  = yield ~ genotype + env + genotype:env,
  random = ~ env:block,
  data   = field_data
)

Spatial Model

model <- mandala(
  fixed  = yield ~ genotype,
  random = ~ block,
  data   = field_data,
  R_formula = ~ ar1(row):ar1(col)
)

---

Extracting Results

Variance Components

var_comps <- summary(model)$varcomp
print(var_comps)

Heritability

h2 <- h2_estimates(
  random_mod = model_random,
  fixed_mod  = model_fixed,
  genotype   = "genotype"
)

BLUEs (Fixed Effects)

blues <- model$BLUEs
head(blues)

BLUPs (Random Effects)

blups <- mandala_predict(model, classify_term = "genotype")
head(blups)

---

Package Comparison

Mandala vs Sommer vs lme4

Syntax	Mandala	Sommer	lme4
Model fit	mandala()	mmer()	lmer()
Variance components	$varcomp	summary()$varcomp	VarCorr()
BLUPs	mandala_predict()	randef()	ranef()

---

Common Experimental Designs

1. RCBD

Effect	Type
Genotype	Fixed
Block	Random

yield ~ genotype + (1|block)

2. Alpha-Lattice

Effect	Type
Genotype	Fixed
Rep	Random
Incomplete Block(Rep)	Random

yield ~ genotype + (1|rep) + (1|rep:incomplete_block)

3. Row-Column

Effect	Type
Genotype	Fixed
Row	Random
Column	Random

yield ~ genotype + (1|row) + (1|col)

4. Multi-Environment Trial

Effect	Type
Genotype	Fixed
Environment	Fixed
G×E	Fixed
Block(Env)	Random

yield ~ genotype + env + genotype:env + (1|env:block)

---

Heritability Formulas

Plot Basis

\[h^2 = \frac{\sigma^2_g}{\sigma^2_g + \sigma^2_e}\]

Entry-Mean Basis (Single Environment)

\[h^2 = \frac{\sigma^2_g}{\sigma^2_g + \sigma^2_e/r}\]

Where r = number of replications

Across Multiple Environments

\[h^2 = \frac{\sigma^2_g}{\sigma^2_g + \sigma^2_{g \times e}/e + \sigma^2_e/(e \times r)}\]

Where e = environments, r = reps per environment

---

Data Preparation Checklist

• Factors are properly coded as factors
• Numeric variables are properly coded as numeric
• Missing values are coded as NA
• No duplicate observations
• Column names have no special characters
• Experimental design is correctly specified

---

Model Checking

Check Convergence

summary(model)
# Look for warnings

Examine Residuals

plot(fitted(model), residuals(model))
abline(h = 0, col = "red")

Check Normality

qqnorm(residuals(model))
qqline(residuals(model))

---

Common Issues

Issue	Solution
Model doesn’t converge	Check for missing data, verify design
Negative variance estimates	Simplify model, check data structure
Very low heritability	Check data quality, model specification

---

Visualization Templates

Genotype Performance

library(ggplot2)

blues %>%
  ggplot(aes(x = reorder(genotype, estimate), y = estimate)) +
  geom_point(size = 3) +
  geom_errorbar(aes(ymin = lower_ci, ymax = upper_ci), width = 0.2) +
  coord_flip() +
  theme_minimal() +
  labs(x = "Genotype", y = "Estimated Yield")

G×E Interaction

gxe_data %>%
  ggplot(aes(x = environment, y = mean_yield, 
             group = genotype, color = genotype)) +
  geom_line() +
  geom_point(size = 2) +
  theme_minimal()

Field Heatmap

field_data %>%
  ggplot(aes(x = col, y = row, fill = yield)) +
  geom_tile() +
  scale_fill_viridis_c() +
  theme_minimal()

---

Resources

• Mandala: https://listoagriculture.com/products
• Sommer: https://cran.r-project.org/package=sommer
• lme4: https://cran.r-project.org/package=lme4

Key References

• Piepho et al. (2003) - BLUP in plant breeding
• Gilmour et al. (1997) - Spatial analysis
• Smith et al. (2005) - Variety trials