3) Example of DBV-SBV models for species mixtures in a tester-based design
Preamble
Dependencies:
Simulate data
Simulate the genotypes
Set the dimensions
levSpecies <- c("S1", "S2")
nbGenos <- c("S1" = 500, "S2" = 500)
levGenos <- list(
"S1" = sprintf(
fmt = paste0("gS1_%0", floor(log10(nbGenos["S1"])) + 1, "i"),
1:nbGenos["S1"]
),
"S2" = sprintf(
fmt = paste0("gS2_%0", floor(log10(nbGenos["S2"])) + 1, "i"),
1:nbGenos["S2"]
)
)
nbSnps <- c("S1" = 1000, "S2" = 1000)
levSnps <- list(
"S1" = sprintf(
fmt = paste0("sS1_%0", floor(log10(nbSnps["S1"])) + 1, "i"),
1:nbSnps["S1"]
),
"S2" = sprintf(
fmt = paste0("sS2_%0", floor(log10(nbSnps["S2"])) + 1, "i"),
1:nbSnps["S2"]
)
)SNP genotypes
nb_pops <- 10
weak_div_pops <- diag(nb_pops)
weak_div_pops[upper.tri(weak_div_pops)] <- 0.9
weak_div_pops[lower.tri(weak_div_pops)] <- weak_div_pops[upper.tri(weak_div_pops)]
snpGenos <- lapply(levSpecies, function(species) {
tmp <- rep(nbGenos[species] / nb_pops, nb_pops - 1)
tmp <- c(tmp, nbGenos[species] - sum(tmp))
simulGenosDoseStruct(
nb_genos = tmp,
nb_snps = nbSnps[species],
div_pops = weak_div_pops,
geno_IDs = levGenos[[species]],
snp_IDs = levSnps[[species]]
)
})
names(snpGenos) <- levSpecies
sapply(snpGenos, dim)
## S1 S2
## [1,] 500 500
## [2,] 1000 1000
snpGenos$S1[1:3, 1:4]
## sS1_0001 sS1_0002 sS1_0003 sS1_0004
## gS1_001 0 1 1 1
## gS1_002 1 1 2 1
## gS1_003 1 0 1 1
table(snpGenos$S1)
##
## 0 1 2
## 154493 200572 144935Additive genetic relationships
For simplicity, the first estimator of VanRaden (2008) is used, that assumes linkage equilibrium and Hard-Weinberg equilibrium.
snpAFs <- lapply(snpGenos, function(M) {
colSums(M) / (2 * nrow(M))
})
GRMs_vr <- lapply(levSpecies, function(species) {
GRM <- estimGRM(snpGenos[[species]], snpAFs[[species]])
as.matrix(Matrix::nearPD(GRM)$mat)
})
names(GRMs_vr) <- levSpecies
Simulate the phenotypes
As in Salomon et al (2026), the design will be incomplete (sparse) but balanced, and tester-based, involving:
many genotypes of the first species, the focal one, whose breeding values will be statistically modeled as random, with kinship matrix \(K\);
and a small number of genotypes of the second species, the tester one, whose breeding values will be statistically modeled as fixed.
The yield data are generated according to the following equations:
intercrops: \(Y_{IC} = X_{IC} B_{IC} + Z_{DS_f} BV_f + Z_{D{\times}S} \, DBV{\times}SBV + E_{IC}\)
sole crops:
focal species: \(y_{SC_f} = X_{SC_f} \beta_{SC_f} + Z_{D_f} DBV_f + Z_{D_f} SIGV_f + e_{SC_f}\) where \(\beta_f\) only includes the contrasts for the “block” explanatory factor
tester species: \(y_{SC_t} = X_{SC_t} \beta_{SC_t} + e_{SC_t}\) where \(\beta_t\) includes the contrasts for the “block” and “DBV” explanatory factors (the “SIGV” explanatory factor for the tester species is ignored)
The parameter values correspond to cereal-legume mixtures such as winter wheat and pea, inspired from the papers of Moutier et al (2022) and Haug et al (2023).
nbGenosTrial <- c("S1" = 300, "S2" = 2)
levGenosTrial <- lapply(levSpecies, function(species) {
sample(levGenos[[species]], nbGenosTrial[species])
})
names(levGenosTrial) <- levSpecies
GRMs_vr_trial <- list()
GRMs_vr_trial$S1 <- GRMs_vr$S1[levGenosTrial$S1, levGenosTrial$S1]
GRMs_vr_trial$S2 <- diag(nbGenosTrial["S2"]) # diag because modeled as fixed
dimnames(GRMs_vr_trial$S2) <- list(levGenosTrial$S2, levGenosTrial$S2)
set.seed(12345)
out <- simulDBVSBVinter(GRMs_vr_trial)
names(out)
## [1] "truth" "datW" "datL" "obsMC"
## [5] "sowingDensities" "props"
tmp <- list2env(out, envir = environment())
Indices of plant mixtures
Several indices can be used to compare sole crops and intercrops. Below some of them are computed using the true breeding values, i.e., with neither block effects nor experimental errors, to give an idea of what the simulated data correspond to.
RYT (LER) and RYP
## Reformat and compute
is_mix <- which(datW$type == "IC")
true_RYTs <- list()
true_RYPs <- list()
for (idx in is_mix) {
true_y1_IC <- as.vector(truth$mu[["S1"]]["IC"]) + datW$true_gen_yield_S1[idx]
true_y2_IC <- as.vector(truth$mu[["S2"]]["IC"]) + datW$true_gen_yield_S2[idx]
g1 <- as.character(datW$geno_S1[idx])
g2 <- as.character(datW$geno_S2[idx])
true_y1_SC <- as.vector(truth$mu[["S1"]]["SC"]) +
datW$true_gen_yield_S1[datW$geno_S1 == g1 &
is.na(datW$geno_S2)]
true_y2_SC <- as.vector(truth$mu[["S2"]]["SC"]) +
datW$true_gen_yield_S2[datW$geno_S2 == g2 &
is.na(datW$geno_S1)]
true_y2_SC <- unique(true_y2_SC)
yields <- data.frame(
SCcrop = c(true_y1_SC, true_y2_SC),
intercrop = c(true_y1_IC, true_y2_IC),
row.names = c(g1, g2)
)
tmp <- LER(yields)
mixId <- paste0(g1, "-", g2)
true_RYTs[[mixId]] <- c(
"RY_S1" = as.numeric(tmp$pLER[1]),
"RY_S2" = as.numeric(tmp$pLER[2]),
"RYT" = tmp$LER
)
true_RYPs[[mixId]] <- c(
"RYP_S1" = true_y1_IC /
(props[["S1"]] * true_y1_SC),
"RYP_S2" = true_y2_IC /
(props[["S2"]] * true_y2_SC)
)
}
true_RYTs <- data.frame(
mix = names(true_RYTs),
geno_S1 = sapply(strsplit(names(true_RYTs), "-"), `[`, 1),
geno_S2 = sapply(strsplit(names(true_RYTs), "-"), `[`, 2),
as.data.frame(do.call(rbind, true_RYTs)),
stringsAsFactors = TRUE
)
str(true_RYTs)
## 'data.frame': 300 obs. of 6 variables:
## $ mix : Factor w/ 300 levels "gS1_001-gS2_301",..: 24 210 257 230 285 118 224 267 158 205 ...
## $ geno_S1: Factor w/ 300 levels "gS1_001","gS1_002",..: 24 210 257 230 285 118 224 267 158 205 ...
## $ geno_S2: Factor w/ 2 levels "gS2_191","gS2_301": 1 1 1 1 1 1 1 1 1 1 ...
## $ RY_S1 : num 0.472 0.565 0.452 0.47 0.512 ...
## $ RY_S2 : num 1.028 0.706 1.063 0.862 0.88 ...
## $ RYT : num 1.5 1.27 1.51 1.33 1.39 ...
summary(true_RYTs[, grep("RY_", colnames(true_RYTs))])
## RY_S1 RY_S2
## Min. :0.3419 Min. :0.6585
## 1st Qu.:0.4543 1st Qu.:0.8416
## Median :0.4954 Median :0.8961
## Mean :0.4904 Mean :0.8962
## 3rd Qu.:0.5264 3rd Qu.:0.9470
## Max. :0.6406 Max. :1.1352
summary(true_RYTs[, grep("RYT", colnames(true_RYTs))])
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.235 1.350 1.387 1.387 1.421 1.549
true_RYPs <- data.frame(
mix = names(true_RYPs),
geno_S1 = sapply(strsplit(names(true_RYPs), "-"), `[`, 1),
geno_S2 = sapply(strsplit(names(true_RYPs), "-"), `[`, 2),
as.data.frame(do.call(rbind, true_RYPs)),
stringsAsFactors = TRUE
)
str(true_RYPs)
## 'data.frame': 300 obs. of 5 variables:
## $ mix : Factor w/ 300 levels "gS1_001-gS2_301",..: 24 210 257 230 285 118 224 267 158 205 ...
## $ geno_S1: Factor w/ 300 levels "gS1_001","gS1_002",..: 24 210 257 230 285 118 224 267 158 205 ...
## $ geno_S2: Factor w/ 2 levels "gS2_191","gS2_301": 1 1 1 1 1 1 1 1 1 1 ...
## $ RYP_S1 : num 0.598 0.716 0.572 0.596 0.648 ...
## $ RYP_S2 : num 4.88 3.35 5.05 4.09 4.18 ...
summary(true_RYPs[, grep("RYP", colnames(true_RYPs))])
## RYP_S1 RYP_S2
## Min. :0.4331 Min. :3.128
## 1st Qu.:0.5754 1st Qu.:3.998
## Median :0.6275 Median :4.256
## Mean :0.6212 Mean :4.257
## 3rd Qu.:0.6668 3rd Qu.:4.498
## Max. :0.8115 Max. :5.392
if (FALSE) {
## using the RYT() function
keys <- unique(paste0(datL$focal, " in ", datL$standID))
tmp <- do.call(rbind, strsplit(keys, " in "))
datLavg <- data.frame(
key = keys,
focal = tmp[, 1],
standID = tmp[, 2],
stringsAsFactors = TRUE
)
datLavg$type <- "IC"
datLavg$type[as.character(datLavg$focal) == as.character(datLavg$standID)] <- "SC"
datLavg$focal_species <- "S1"
datLavg$focal_species[grep("^gS2_", datLavg$focal)] <- "S2"
datLavg$prop <- 1
datLavg$prop[datLavg$type == "IC" & datLavg$focal_species == "S1"] <- props["S1"]
datLavg$prop[datLavg$type == "IC" & datLavg$focal_species == "S2"] <- props["S2"]
for (i in 1:nrow(datLavg)) {
idx <- which(datL$focal == datLavg$focal[i] &
datL$standID == datLavg$standID[i])
datLavg$focal_yield[i] <- mean(datL$focal_yield[idx])
}
true_RYTs2 <- RYT(datLavg, "standID", "focal", "prop", "focal_yield")
true_RYTs2 <- droplevels(true_RYTs2[!is.na(true_RYTs2$RYT), ])
true_RYTs2 <- droplevels(true_RYTs2[!duplicated(true_RYTs2$standID), ])
}
## Plot
ggplot(true_RYTs) +
aes(x = RY_S1) +
geom_histogram(color = "white", bins = 30) +
geom_vline(
xintercept = sowingDensities$S1["IC"] /
sowingDensities$S1["SC"],
col = "red", linewidth = 2
) +
labs(
title = "True relative yields (partial land-equivalent ratios) of species 1 for all mixtures",
x = "RY (partial LER) of species 1"
) +
theme_bw()
ggplot(true_RYTs) +
aes(x = RY_S2) +
geom_histogram(color = "white", bins = 30) +
geom_vline(
xintercept = sowingDensities$S2["IC"] /
sowingDensities$S2["SC"],
col = "red", linewidth = 2
) +
labs(
title = "True partial land-equivalent ratio of species 2 for all mixtures",
x = "RY (partial LER) of species 2"
) +
theme_bw()
ggplot(true_RYTs) +
aes(x = geno_S2, y = RYT) +
geom_violin(aes(fill = geno_S2), trim = FALSE, show.legend = FALSE) +
geom_boxplot(width = 0.2) +
labs(
title = "True land-equivalent ratio for all mixtures"
) +
theme_bw()
p <- ggplot(true_RYTs) +
aes(x = RY_S1, y = RY_S2, color = geno_S2)
for (i in seq(0.75, 2, by = 0.25)) {
if (i == 1) {
p <- p + geom_abline(intercept = i, slope = -1, linetype = "solid", color = "black")
} else {
p <- p + geom_abline(intercept = i, slope = -1, linetype = "dotted", color = "black")
}
}
p + geom_abline(intercept = 0, slope = 1, linetype = "dotted", color = "black") +
geom_point(size = 2) +
labs(
title = "True relative yields (RYs, a.k.a. partial LERs)",
x = "relative yield (partial LER) of species 1",
y = "relative yiedl (partial LER) of species 2",
color = "Tester"
) +
## guides(color="none") +
scale_x_continuous(breaks = seq(0, 1.4, by = 0.1)) +
scale_y_continuous(breaks = seq(0, 1.4, by = 0.1)) +
coord_cartesian(xlim = c(0, 1.4), ylim = c(0, 1.4)) +
theme(aspect.ratio = 1) +
theme_bw()
ggplot(true_RYPs) +
aes(x = RYP_S1, y = RYP_S2, color = geno_S2) +
geom_abline(intercept = 0, slope = 1, linetype = "solid", color = "black") +
geom_hline(yintercept = 1) +
geom_vline(xintercept = 1) +
geom_point(size = 2) +
labs(
title = "True relative yields per plant (RYPs)",
x = "RYP of species 1",
y = "RYP of species 2",
color = "Tester"
) +
## guides(color="none") +
scale_x_continuous(breaks = seq(0, 6.5, by = 1)) +
scale_y_continuous(breaks = seq(0, 6.5, by = 1)) +
coord_cartesian(xlim = c(0, 6.5), ylim = c(0, 6.5)) +
theme(aspect.ratio = 1) +
theme_bw()
RYM
## Reformat and compute
tmp <- datW[, c("geno_S1", "geno_S2", "true_yield_S1", "true_yield_S2")]
tmp$ID <- NA
tmp$props <- NA
tmp$true_yield <- NA
## sole crop of species 1:
idx <- which(!is.na(tmp$geno_S1) & is.na(tmp$geno_S2))
tmp$ID[idx] <- as.character(tmp$geno_S1[idx])
tmp$props[idx] <- "1"
tmp$true_yield[idx] <- tmp$true_yield_S1[idx]
## sole crop of species 2:
idx <- which(is.na(tmp$geno_S1) & !is.na(tmp$geno_S2))
tmp$ID[idx] <- as.character(tmp$geno_S2[idx])
tmp$props[idx] <- "1"
tmp$true_yield[idx] <- tmp$true_yield_S2[idx]
## intercrops of species 1 and 2:
idx <- which(!is.na(tmp$geno_S1) & !is.na(tmp$geno_S2))
sep <- "|"
tmp$ID[idx] <- as.character(paste0(
tmp$geno_S1[idx], sep,
tmp$geno_S2[idx]
))
prop1 <- props["S1"]
prop2 <- props["S2"]
stopifnot(prop1 + prop2 == 1)
prop1 <- round(prop1, 2)
prop2 <- 1 - prop1
tmp$props[idx] <- paste0(prop1, sep, prop2)
tmp$true_yield[idx] <- tmp$true_yield_S1[idx] + tmp$true_yield_S2[idx]
stopifnot(all(!is.na(tmp$ID)))
tmp$ID <- factor(tmp$ID)
tmp$props <- factor(tmp$props)
## keep only one yield (the true one) per modality
dupIDs <- table(as.character(tmp$ID))
(dupIDs <- names(dupIDs)[dupIDs > 1])
## [1] "gS2_191" "gS2_301"
for (dupID in dupIDs) {
idx <- which(as.character(tmp$ID) == dupID)
tmp <- droplevels(tmp[-idx[2:length(idx)], ])
}
rm(dupIDs)
tmp <- RYM(tmp,
colIDstand = "ID", colIDcomps = "ID", colProps = "props",
colY = "true_yield", sep = "|"
)
summary(tmp$RYM)
## Min. 1st Qu. Median Mean 3rd Qu. Max. NAs
## 0.8698 0.9740 1.0124 1.0172 1.0524 1.2174 302
## Plot
ggplot(tmp) +
aes(x = RYM) +
geom_histogram(na.rm = TRUE, bins = 30, color = "white") +
geom_vline(xintercept = 1, linewidth = 2) +
geom_vline(xintercept = mean(tmp$RYM, na.rm = TRUE), linewidth = 2, color = "red") +
labs(title = "True relative yields of mixtures (RYMs)") +
theme_bw()
Explore the data
In this section, an exploratory data analysis is done on the data including block effects and experimental errors, so that it can be easily applied on real data, too.
str(datW)
## 'data.frame': 604 obs. of 20 variables:
## $ standID : Factor w/ 602 levels "gS1_001","gS1_001+gS2_301",..: 47 351 567 253 419 471 89 513 459 289 ...
## $ geno_S1 : Factor w/ 300 levels "gS1_001","gS1_002",..: 24 176 284 127 210 236 45 257 230 145 ...
## $ geno_S2 : Factor w/ 2 levels "gS2_191","gS2_301": NA NA NA NA NA NA NA NA NA NA ...
## $ type : Factor w/ 2 levels "SC","IC": 1 1 1 1 1 1 1 1 1 1 ...
## $ type2 : Factor w/ 3 levels "sole_S1","sole_S2",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ block : Factor w/ 2 levels "A","B": 1 1 1 1 1 1 1 1 1 1 ...
## $ x : int 6 23 16 19 29 21 4 23 21 11 ...
## $ y : int 9 6 2 10 4 2 7 3 4 3 ...
## $ plot : Factor w/ 604 levels "10A1","10A10",..: 575 143 61 88 200 119 426 140 121 14 ...
## $ true_gen_yield_S1: num -15.47 2.51 -7.03 -6.73 17.57 ...
## $ true_gen_yield_S2: num NA NA NA NA NA NA NA NA NA NA ...
## $ true_yield_S1 : num 48.6 66.6 57.1 57.4 81.7 ...
## $ true_yield_S2 : num NA NA NA NA NA NA NA NA NA NA ...
## $ true_fix_yield_S1: num 64.1 64.1 64.1 64.1 64.1 ...
## $ true_fix_yield_S2: num NA NA NA NA NA NA NA NA NA NA ...
## $ true_rnd_yield_S1: num -15.47 2.51 -7.03 -6.73 17.57 ...
## $ true_rnd_yield_S2: num NA NA NA NA NA NA NA NA NA NA ...
## $ yield_S1 : num 48.4 64.3 58.5 57.9 81.8 ...
## $ yield_S2 : num NA NA NA NA NA NA NA NA NA NA ...
## $ tot_yield : num 48.4 64.3 58.5 57.9 81.8 ...
tapply(datW$type, datW$block, table)
## $A
##
## SC IC
## 152 150
##
## $B
##
## SC IC
## 152 150ggplot(datL) +
aes(x = block, y = focal_yield) +
geom_violin(aes(fill = block)) +
geom_boxplot(fill = "white", width = 0.2) +
theme_bw() +
facet_grid(focal_species ~ type)
is_mix <- datW$type == "IC"
subDatW <- droplevels(datW[is_mix, ])
ggplot(subDatW) +
aes(x = yield_S1, y = yield_S2, color = geno_S1, shape = geno_S2) +
geom_abline(intercept = seq(0, 200, by = 10), slope = -1, linetype = "dotted", color = "black") +
geom_point(size = 2) +
labs(
title = "Partial yields in intercrop",
x = "species 1 (in qt.ha-1)", y = "species 2 (in qt.ha-1)",
shape = "Tester (species S2)"
) +
guides(color = "none") +
theme_bw()
Yield map
## Add the empty micro-plots:
coords <- data.frame(
x = rep(sort(unique(datW$x)), each = length(unique(datW$y))),
y = sort(unique(datW$y)),
block = "A",
plot = NA
)
coords$block[coords$x >= min(datW$x[datW$block != "A"])] <- "B"
coords$plot <- paste0(coords$x, coords$block, coords$y)
length(idx <- which(!coords$plot %in% as.character(datW$plot)))
## [1] 16
tmp <- as.data.frame(matrix(nrow = length(idx), ncol = ncol(datW)))
colnames(tmp) <- colnames(datW)
tmp[, c("x", "y", "block", "plot")] <- coords[idx, ]
datWSupp <- rbind(
datW,
as.data.frame(tmp)
)
## Plot
xranges <- do.call(rbind, tapply(datW$x, datW$block, range))
p <- ggplot(datWSupp) +
aes(x = x, y = y) +
theme_bw() +
theme(
panel.grid.minor = element_blank(),
panel.grid.major = element_blank()
) +
scale_x_continuous(breaks = sort(unique(datW$x))) +
scale_y_continuous(
breaks = sort(unique(datW$y)),
sec.axis = dup_axis()
) +
guides(x = guide_axis(angle = 90)) +
geom_tile(na.rm = TRUE) +
geom_rect(aes(xmin = x - 0.5, xmax = x + 0.5, ymin = y - 0.5, ymax = y + 0.5),
color = "white"
) +
geom_text(
x = sum(xranges[1, ]) / 2, y = 10.7, label = "Block A",
hjust = 0, color = "black"
) +
geom_text(
x = sum(xranges[2, ]) / 2, y = 10.7, label = "Block B",
hjust = 0, color = "black"
) +
geom_vline(
xintercept = max(datW$x[datW$block == "A"]),
color = "black", linetype = "dashed", linewidth = 1
)
p + aes(fill = type) +
labs(title = "Types of microplots") +
scale_fill_discrete()
scaleCols <- c("#CB2027", "#ffec1b", "#b3e93e", "#60BD68", "#059748")
scaleLim <- range(datW$tot_yield)
p + aes(fill = tot_yield) +
labs(title = "Total yield for each microplot") +
scale_fill_continuous(type = "viridis")
Infer the parameters
Using intercrops only
Prepare the inputs
idxIC <- which(!is.na(datW$geno_S1) & !is.na(datW$geno_S2))
datW_IC <- droplevels(datW[idxIC, ])
listY <- list(Y_IC = datW_IC[, c("yield_S1", "yield_S2")])
listX <- list(X_IC = model.matrix(~ 1 + block + geno_S2, datW_IC,
contrasts.arg = list(
"block" = "contr.sum",
"geno_S2" = "contr.sum"
)
))
listZ <- list(Z_DS_f = model.matrix(~ 0 + geno_S1, datW_IC))
colnames(listZ$Z_DS_f) <- gsub("^geno_S1", "", colnames(listZ$Z_DS_f))
listVCov <- list(K = GRMs_vr_trial$S1[
levels(datW_IC$geno_S1),
levels(datW_IC$geno_S1)
])Fit the model
fitsTmb <- list()
i <- 1
for (REML in c(TRUE, FALSE)) {
print(paste0("fit model with ", ifelse(REML, "REML", "ML"), "..."))
st <- system.time(
fitTmb <- fitDBVSBVinter(listY, listX, listZ, listVCov,
lOptions = list(iter.max = 20),
REML = REML, verbose = 0
)
)
print(st)
fitsTmb[[i]] <- fitTmb
i <- i + 1
break # skip ML to speed-up
}
## [1] "fit model with REML..."
## user system elapsed
## 6.555 10.091 4.775for (i in seq_along(fitsTmb)) {
fitTmb <- fitsTmb[[i]]
p <- ggplot(fitTmb$trace) +
aes(x = iter, y = objfn) +
geom_point() +
geom_line() +
labs(
title = "Optimization convergence",
subtitle = paste0("REML=", fitTmb$REML)
) +
theme_bw()
print(p)
}
Checks
for (i in seq_along(fitsTmb)) {
fitTmb <- fitsTmb[[i]]
print(paste0("REML=", fitTmb$REML))
print("Check fixed effects:")
checks <- data.frame(
species = rep(c("S1", "S2"), each = nrow(truth$B_IC)),
truth = c(truth$B_IC),
estim = c(fitTmb$report$B_IC)
)
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(checks)
print("Check (co)variances of random genetic effects:")
checks <- data.frame(
ID = c("var(DBV)_S1", "var(SBV)_S1", "cor(DBVxSBV)_S1"),
truth = c(
truth$var_DBV["S1"],
truth$var_SBV["S1"],
truth$cor_DBV_SBV["S1"]
),
estim = c(
fitTmb$report$vars_BV_f,
fitTmb$report$Cor_BV[1, 2]
)
)
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(checks)
print("Check (co)variances of residual errors:")
checks <- data.frame(
ID = c("var(err)_IC_S1", "var(err)_IC_S2", "cor(err)"),
truth = c(truth$var_err_IC, truth$cor_err_IC),
estim = c(fitTmb$report$vars_E_IC, fitTmb$report$Cor_E_IC[1, 2])
)
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(checks)
print(fitTmb$sry_sdr[grep("^log_sd|^unconstr_cor", rownames(fitTmb$sry_sdr)), ])
if (FALSE) {
print(paste0(
"AIC = ", round(fitTmb$AIC),
" (k = ", attr(fitTmb$AIC, "k"), ")"
))
}
print("Check random genetic effects of the focal species:")
checks <- data.frame(
type = c(
rep(c("DBV", "SBV"), each = nrow(truth$BV$S1)),
rep("BV_IC", length(truth$BV_IC$S1))
),
truth = c(
truth$BV$S1[levels(datW_IC$geno_S1), ],
truth$BV_IC$S1
),
estim = c(
fitTmb$sry_sdr[grep("^BV_f$", rownames(fitTmb$sry_sdr)), "Estimate"],
fitTmb$report$BV_IC_f[names(truth$BV_IC$S1)]
)
)
checks$type <- factor(checks$type,
levels = c("BV_IC", "DBV", "SBV"))
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(tapply(1:nrow(checks), checks$type, function(idx) {
cor(checks$truth[idx], checks$esti[idx])
}))
p <- ggplot(checks) +
aes(x = estim, y = truth) +
geom_hline(yintercept = 0, linetype = "dotted") +
geom_vline(xintercept = 0, linetype = "dotted") +
geom_abline(slope = 1, intercept = 0, linetype = "dotted") +
geom_point() +
labs(
title = "Results with intercrop-only data",
subtitle = paste0("REML=", fitTmb$REML)
) +
theme_bw() +
facet_wrap(~type)
print(p)
}
## [1] "REML=TRUE"
## [1] "Check fixed effects:"
## species truth estim nBE
## 1 S1 32.0000000 32.2620473 0.8188977
## 2 S1 -0.8791112 -0.9022131 2.6278643
## 3 S1 0.3530473 0.8270258 134.2535499
## 4 S2 27.0000000 26.9249453 -0.2779803
## 5 S2 1.4664826 1.5524331 5.8609969
## 6 S2 -0.9739075 -1.2320781 26.5087312
## [1] "Check (co)variances of random genetic effects:"
## ID truth estim nBE
## 1 var(DBV)_S1 27.040 21.5538769 -20.288917
## 2 var(SBV)_S1 5.408 3.9594092 -26.786073
## 3 cor(DBVxSBV)_S1 -0.900 -0.8837167 -1.809261
## [1] "Check (co)variances of residual errors:"
## ID truth estim nBE
## S1 var(err)_IC_S1 4.577666 12.9479801 182.8512
## S2 var(err)_IC_S2 0.975124 2.3183543 137.7497
## cor(err) -0.200000 -0.6463386 223.1693
## Estimate Std. Error
## log_sd_BV_f 1.5352779 0.1248651
## log_sd_BV_f 0.6880474 0.1257445
## unconstr_cor_DS_f -1.8881935 0.4552946
## log_sd_E_IC 1.2804699 0.1699969
## log_sd_E_IC 0.4204288 0.1752656
## unconstr_cor_E_IC -0.8470454 0.2757618
## [1] "Check random genetic effects of the focal species:"
## BV_IC DBV SBV
## NA 0.9272051 0.9249494
## Warning: Removed 300 rows containing missing values or values outside the scale range
## (`geom_point()`).
Using both sole crops and intercrops
Prepare the inputs
idxIC <- which(!is.na(datW$geno_S1) & !is.na(datW$geno_S2))
datW_IC <- droplevels(datW[idxIC, ])
idxSCf <- which(datL$type == "SC" & datL$focal_species == "S1")
datL_SC_f <- droplevels(datL[idxSCf, ])
idxSCt <- which(datL$type == "SC" & datL$focal_species == "S2")
datL_SC_t <- droplevels(datL[idxSCt, ])
listY <- list()
listY$Y_IC <- datW_IC[, c("yield_S1", "yield_S2")]
listY$y_SC_f <- datL_SC_f$focal_yield
listY$y_SC_t <- datL_SC_t$focal_yield
sapply(listY[-1], length)
## y_SC_f y_SC_t
## 300 4
listX <- list()
listX$X_IC <- model.matrix(~ 1 + block + geno_S2,
data = datW_IC,
contrasts.arg = list(
"block" = "contr.sum",
"geno_S2" = "contr.sum"
)
)
listX$X_SC_f <- model.matrix(~ 1 + block, datL_SC_f,
contrasts.arg = list(block = "contr.sum")
)
listX$X_SC_t <- model.matrix(~ 1 + block + focal, datL_SC_t,
contrasts.arg = list(
block = "contr.sum",
focal = "contr.sum"
)
)
listZ <- list()
listZ$Z_DS_f <- model.matrix(~ 0 + geno_S1, datW_IC)
colnames(listZ$Z_DS_f) <- gsub("^geno_S1", "", colnames(listZ$Z_DS_f))
listZ$Z_D_f <- model.matrix(~ 0 + focal, datL_SC_f)
colnames(listZ$Z_D_f) <- gsub("^focal", "", colnames(listZ$Z_D_f))
listVCov <- list(K = GRMs_vr_trial$S1[
levels(datW_IC$geno_S1),
levels(datW_IC$geno_S1)
])Fit the model
fitsTmb <- list()
i <- 1
for (REML in c(TRUE, FALSE)) {
print(paste0("fit model with ", ifelse(REML, "REML", "ML"), "..."))
st <- system.time(
fitTmb <- fitDBVSBVinter(listY, listX, listZ, listVCov,
lOptions = list(iter.max = 20),
REML = REML, verbose = 0
)
)
print(st)
fitsTmb[[i]] <- fitTmb
i <- i + 1
break # skip ML to speed-up
}
## [1] "fit model with REML..."
## user system elapsed
## 12.037 16.875 8.183for (i in seq_along(fitsTmb)) {
fitTmb <- fitsTmb[[i]]
p <- ggplot(fitTmb$trace) +
aes(x = iter, y = objfn) +
geom_point() +
geom_line() +
labs(
title = "Optimization convergence",
subtitle = paste0("REML=", fitTmb$REML)
) +
theme_bw()
print(p)
}
Checks
for (i in seq_along(fitsTmb)) {
fitTmb <- fitsTmb[[i]]
print(paste0("REML=", fitTmb$REML))
print("Check fixed effects:")
checks <- data.frame(
species = rep(c("S1", "S2"), each = nrow(truth$B_IC)),
truth = c(truth$B_IC),
estim = c(fitTmb$report$B_IC)
)
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(checks)
checks <- data.frame(
species = "S1",
truth = obsMC$blObsContrs$S1[, "SC"],
estim = fitTmb$report$beta_SC_f
)
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(checks)
checks <- data.frame(
species = "S2",
truth = c(
obsMC$blObsContrs$S2[, "SC"],
obsMC$BVObsContrs$S2[-1, "SC", "DBV"]
),
estim = fitTmb$report$beta_SC_t
)
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(checks)
print("Check (co)variances of random genetic effects:")
checks <- data.frame(
ID = c("var(DBV)", "var(SBV)", "var(SIGV)", "cor(DBVxSBV)"),
truth = c(
truth$var_DBV["S1"],
truth$var_SBV["S1"],
truth$var_SIGV["S1"],
truth$cor_DBV_SBV["S1"]
),
estim = c(
fitTmb$report$vars_BV_f,
fitTmb$report$var_SIGV_f,
fitTmb$report$Cor_BV[1, 2]
)
)
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(checks)
print("Check (co)variances of residual errors:")
checks <- data.frame(
ID = c(
"var(err)_S1", "var(err)_S2", "cor(err)",
"var(err)_SC_S1", "var(err)_SC_S2"
),
truth = c(
truth$var_err_IC, truth$cor_err_IC,
truth$var_err_SC
),
estim = c(
fitTmb$report$vars_E_IC, fitTmb$report$Cor_E_IC[1, 2],
fitTmb$report$var_err_SC_f, fitTmb$report$var_err_SC_t
)
)
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(checks)
print(fitTmb$sry_sdr[grep("^log_sd|^unconstr_cor", rownames(fitTmb$sry_sdr)), ])
if (FALSE) {
print(paste0(
"AIC = ", round(fitTmb$AIC),
" (k = ", attr(fitTmb$AIC, "k"), ")"
))
}
print("Check random genetic effects of the focal species:")
checks <- data.frame(
type = c(
rep(c("DBV", "SBV", "SIGV"), each = nrow(truth$BV$S1)),
rep(c("BV_IC", "BV_SC"), each = length(truth$BV_IC$S1))
),
truth = c(
truth$BV$S1[levels(datW_IC$geno_S1), ],
truth$SIGVs$S1[levels(datW_IC$geno_S1)],
truth$BV_IC$S1,
truth$BV_SC$S1
),
estim = c(
fitTmb$sry_sdr[grep("^BV_f$", rownames(fitTmb$sry_sdr)), "Estimate"],
fitTmb$sry_sdr[grep("^SIGV_f$", rownames(fitTmb$sry_sdr)), "Estimate"],
fitTmb$report$BV_IC_f[names(truth$BV_IC$S1)],
fitTmb$report$BV_SC_f[names(truth$BV_SC$S1)]
)
)
checks$type <- factor(checks$type,
levels = c("BV_SC", "BV_IC", "DBV", "SBV", "SIGV"))
checks$nBE <- normBiasError(checks$estim, checks$truth)
print(tapply(1:nrow(checks), checks$type, function(idx) {
cor(checks$truth[idx], checks$esti[idx])
}))
p <- ggplot(checks) +
aes(x = estim, y = truth) +
geom_hline(yintercept = 0, linetype = "dotted") +
geom_vline(xintercept = 0, linetype = "dotted") +
geom_abline(slope = 1, intercept = 0, linetype = "dotted") +
geom_point() +
labs(
title = "Results with both sole-crop and intercrop data",
subtitle = paste0("REML=", fitTmb$REML)
) +
theme_bw() +
facet_wrap(~type)
print(p)
}
## [1] "REML=TRUE"
## [1] "Check fixed effects:"
## species truth estim nBE
## 1 S1 32.0000000 32.2251660 0.7036438
## 2 S1 -0.8791112 -0.9633425 9.5814112
## 3 S1 0.3530473 0.8738495 147.5162918
## 4 S2 27.0000000 26.9415626 -0.2164350
## 5 S2 1.4664826 1.5833567 7.9696924
## 6 S2 -0.9739075 -1.2487199 28.2175034
## species truth estim nBE
## (Intercept) S1 65.2281099 65.0776326 -0.230694
## blockB S1 -0.9027075 -0.6974963 -22.732859
## species truth estim nBE
## (Intercept) S2 31.241459 31.241459 1.137179e-14
## blockB S2 1.112205 1.112205 0.000000e+00
## S2 -1.267077 -1.267077 1.401933e-13
## [1] "Check (co)variances of random genetic effects:"
## ID truth estim nBE
## 1 var(DBV) 27.040 27.7567517 2.6507091
## 2 var(SBV) 5.408 5.1264375 -5.2064078
## 3 var(SIGV) 13.520 22.6288018 67.3727947
## 4 cor(DBVxSBV) -0.900 -0.9024047 0.2671927
## [1] "Check (co)variances of residual errors:"
## ID truth estim nBE
## 1 var(err)_S1 4.577666 6.9309104 51.40709
## 2 var(err)_S2 0.975124 1.2065426 23.73222
## 3 cor(err) -0.200000 -0.3682183 84.10914
## 4 var(err)_SC_S1 17.382857 7.2754008 -58.14612
## 5 var(err)_SC_S2 2.468571 0.4246598 -82.79735
## Estimate Std. Error
## log_sd_BV_f 1.66173956 0.05645749
## log_sd_BV_f 0.81720548 0.06987074
## unconstr_cor_DS_f -2.09428379 0.37468092
## log_sd_E_IC 0.96799559 0.12386395
## log_sd_E_IC 0.09387948 0.17655510
## unconstr_cor_E_IC -0.39604462 0.20200687
## log_sd_SIGV_f 1.55961176 0.13805801
## log_sd_e_SC_f 0.99224945 0.32588006
## log_sd_e_SC_t -0.42823348 2.21598353
## [1] "Check random genetic effects of the focal species:"
## BV_SC BV_IC DBV SBV SIGV
## 0.8905423 NA 0.9352593 0.9325153 0.7216580
## Warning: Removed 300 rows containing missing values or values outside the scale range
## (`geom_point()`).
Reference
See the article for more details:
- Salomon J, Enjalbert J, Flutre T. 2026. Joint modeling of social genetic effects in mono- and pluri-specific groups: case study in intercrops. https://doi.org/10.64898/2026.03.27.714849
Appendix
t1 <- proc.time()
t1 - t0
## user system elapsed
## 28.543 28.836 22.728
print(sessionInfo(), locale = FALSE)
## R version 4.6.0 (2026-04-24)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.4 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] emmeans_2.0.3 plantmix_1.0.2 lme4_2.0-1 Matrix_1.7-5 ggplot2_4.0.3
## [6] knitr_1.51
##
## loaded via a namespace (and not attached):
## [1] sass_0.4.10 generics_0.1.4 lattice_0.22-9 digest_0.6.39
## [5] magrittr_2.0.5 estimability_1.5.1 evaluate_1.0.5 grid_4.6.0
## [9] RColorBrewer_1.1-3 mvtnorm_1.4-1 fastmap_1.2.0 jsonlite_2.0.0
## [13] viridisLite_0.4.3 scales_1.4.0 jquerylib_0.1.4 reformulas_0.4.4
## [17] Rdpack_2.6.6 cli_3.6.6 rlang_1.2.0 rbibutils_2.4.1
## [21] splines_4.6.0 withr_3.0.2 cachem_1.1.0 yaml_2.3.12
## [25] otel_0.2.0 tools_4.6.0 nloptr_2.2.1 minqa_1.2.8
## [29] dplyr_1.2.1 boot_1.3-32 buildtools_1.0.0 vctrs_0.7.3
## [33] R6_2.6.1 lifecycle_1.0.5 MASS_7.3-65 pkgconfig_2.0.3
## [37] pillar_1.11.1 bslib_0.11.0 gtable_0.3.6 glue_1.8.1
## [41] Rcpp_1.1.1-1.1 xfun_0.58 tibble_3.3.1 tidyselect_1.2.1
## [45] sys_3.4.3 farver_2.1.2 htmltools_0.5.9 nlme_3.1-169
## [49] igraph_2.3.2 labeling_0.4.3 rmarkdown_2.31 maketools_1.3.2
## [53] TMB_1.9.21 compiler_4.6.0 S7_0.2.2