RES <- readRDS("data/RES.rds")
D <- RES$D
lgr::get_logger("mlr3")$set_threshold("warn")
# d <- RES$dataIn [1]:
Setup
In [2]:
Benchmark helper function
library(mlr3verse, quietly = TRUE)
mse <- msrs(c("regr.mse"))
if (!interactive())
lgr::get_logger("mlr3")$set_threshold("warn")
get_benchi_table <- function(tasks, nfolds = 5, resamplings = NULL) {
# TODO activate xgboost and ranger for == uncomment things below
set.seed(123)
learners <- lrns(c("regr.featureless", "regr.lm"
# , "regr.xgboost", "regr.ranger"
))
# learners$regr.xgboost$param_set$set_values(
# eta = 0.04,
# nrounds = 300,
# max_depth = 2
# )
benchi <- xfun::cache_rds({
benchmark(benchmark_grid(
tasks,
learners,
if(is.null(resamplings)) rsmp("cv", folds = nfolds) else resamplings
))
},
file = "benchmark.rds",
dir = "cache/",
hash = list(tasks, nfolds)
)
res <- tidyr::pivot_wider(benchi$aggregate(mse),
id_cols = task_id,
names_from = learner_id,
values_from = regr.mse
) |> as.data.frame()
rownames(res) <- res$task_id
res <- res[, -1]
colnames(res) <- gsub("regr.", "", colnames(res))
stopifnot(any(colnames(res) == "featureless"))
res <- 1 - res / res$featureless
res[, -1, drop = FALSE] |> round(3)
}Testing prediction quality using
- Linear models
- Random forests (default parameters)
- XGBoost (with parameter tuning)
Weather Variables:
In [3]:
Code
Weather_vars <- c(
"anavg_temp", "ansum_prec",
"juvdev_prec", "juvdev_sun",
"ansum_sun", "juvdev_temp"
)
# set NA's to 0 but include a column to indicate that
NA_weather <- is.na(D$juvdev_sun)
D[NA_weather, Weather_vars] <- 0
D$NA_weather <- NA_weather
Weather_vars <- c(Weather_vars, "NA_weather")
stopifnot(all(Weather_vars %in% names(D)))
Weather_vars[1] "anavg_temp" "ansum_prec" "juvdev_prec" "juvdev_sun" "ansum_sun"
[6] "juvdev_temp" "NA_weather" In [4]:
Code
P_var_sets <- list(
onlyweather = NULL,
k = "k",
PS = "PS_log",
kPS = c("PS_log", "k", "kPS_log"),
AAE10 = "P_AAE10_log",
CO2 = "P_CO2_log",
AAE10_CO2 = c("P_AAE10_log", "P_CO2_log", "P_AAE10_CO2_loglog"),
AAE10_CO2_kPS = c("P_AAE10_log", "P_CO2_log", "PS_log", "k", "kPS_log"),
CO2_kPS = c("P_CO2_log", "PS_log", "k", "kPS_log")
)
Earth_vars <- c(
"soil_0_20_clay", "soil_0_20_pH_H2O", "soil_0_20_Corg", "soil_0_20_silt"
)In [5]:
Code
Y_vars_yield <- c("Ymain_norm", "Ymain_rel", "annual_P_uptake", "annual_P_balance")
Y_vars_earth <- c("PS_log", "k", "kPS_log", "P_AAE10_log", "P_CO2_log")impute NA’s for Earth variables. impute value with the mean of Site X block
In [6]:
Code
# xtabs(~is.na(D$soil_0_20_silt) + Site + block, D)
for (var in Earth_vars) {
D[[var]] <- ave(D[[var]], D$Site, D$block, FUN = \(x) ifelse(is.na(x), mean(x, na.rm = TRUE), x))
}remove Cadenazzoo since too many crucial data missing
In [7]:
Code
D <- D[D$site != "CAD", ]
D$Site <- droplevels(D$Site)Now check NA’s
In [8]:
Code
sapply(D[, unique(c(Y_vars_yield, Y_vars_earth, Weather_vars, unlist(P_var_sets), Earth_vars))],
\(x) sum(is.na(x)|is.nan(x))) |> cbind() [,1]
Ymain_norm 23
Ymain_rel 117
annual_P_uptake 70
annual_P_balance 55
PS_log 0
k 0
kPS_log 0
P_AAE10_log 0
P_CO2_log 0
anavg_temp 0
ansum_prec 0
juvdev_prec 0
juvdev_sun 0
ansum_sun 0
juvdev_temp 0
NA_weather 0
P_AAE10_CO2_loglog 0
soil_0_20_clay 0
soil_0_20_pH_H2O 0
soil_0_20_Corg 0
soil_0_20_silt 0Predicting Yield variables (with/without Weather data) with Earth-dynamics
With Weather data
In [9]:
Code
P_var_sets$onlyweather
NULL
$k
[1] "k"
$PS
[1] "PS_log"
$kPS
[1] "PS_log" "k" "kPS_log"
$AAE10
[1] "P_AAE10_log"
$CO2
[1] "P_CO2_log"
$AAE10_CO2
[1] "P_AAE10_log" "P_CO2_log" "P_AAE10_CO2_loglog"
$AAE10_CO2_kPS
[1] "P_AAE10_log" "P_CO2_log" "PS_log" "k" "kPS_log"
$CO2_kPS
[1] "P_CO2_log" "PS_log" "k" "kPS_log" Algorithm learns to predict location from weather since we do not do stratified cross-validation (leaving out locations).
In [10]:
Code
Tables_yield_weather <- list()
for(yvar in Y_vars_yield){
ind <- complete.cases(D[,unique(c(yvar ,Weather_vars, unlist(P_var_sets)))])
mytsks <- list()
for (nam in names(P_var_sets)) {
mytsk <- as_task_regr(
D[ind, c(yvar, Weather_vars, P_var_sets[[nam]])],
target = yvar,
id = nam)
mytsks[[nam]] <- mytsk
}
Tables_yield_weather[[yvar]] <- get_benchi_table(mytsks)
}
Tables_yield_weather$Ymain_norm
lm
onlyweather -0.018
k 0.023
PS 0.204
kPS 0.203
AAE10 0.147
CO2 0.231
AAE10_CO2 0.235
AAE10_CO2_kPS 0.220
CO2_kPS 0.246
$Ymain_rel
lm
onlyweather 0.132
k 0.105
PS 0.184
kPS 0.189
AAE10 0.222
CO2 0.210
AAE10_CO2 0.245
AAE10_CO2_kPS 0.238
CO2_kPS 0.157
$annual_P_uptake
lm
onlyweather 0.391
k 0.353
PS 0.446
kPS 0.415
AAE10 0.496
CO2 0.463
AAE10_CO2 0.491
AAE10_CO2_kPS 0.463
CO2_kPS 0.449
$annual_P_balance
lm
onlyweather 0.113
k 0.077
PS 0.627
kPS 0.632
AAE10 0.432
CO2 0.594
AAE10_CO2 0.591
AAE10_CO2_kPS 0.652
CO2_kPS 0.644In [11]:
Code
tmp <- do.call(cbind, lapply(Tables_yield_weather, \(x) x$lm));
rownames(tmp) <- rownames(Tables_yield_weather[[1]])
(Tables_yield_weather_lm <- tmp) Ymain_norm Ymain_rel annual_P_uptake annual_P_balance
onlyweather -0.018 0.132 0.391 0.113
k 0.023 0.105 0.353 0.077
PS 0.204 0.184 0.446 0.627
kPS 0.203 0.189 0.415 0.632
AAE10 0.147 0.222 0.496 0.432
CO2 0.231 0.210 0.463 0.594
AAE10_CO2 0.235 0.245 0.491 0.591
AAE10_CO2_kPS 0.220 0.238 0.463 0.652
CO2_kPS 0.246 0.157 0.449 0.644Without Weather data
In [12]:
Code
P_var_sets_noweather <- P_var_sets[-1]
Tables_yield <- list()
for(yvar in Y_vars_yield){
ind <- complete.cases(D[,unique(c(yvar, unlist(P_var_sets_noweather)))])
mytsks <- list()
for (nam in names(P_var_sets_noweather)) {
mytsk <- as_task_regr(
D[ind,
c(yvar, P_var_sets_noweather[[nam]]
# ,"Site"
)],
target = yvar,
id = nam)
# mytsk$set_col_roles("Site", "group")
mytsks[[nam]] <- mytsk
}
Tables_yield[[yvar]] <- get_benchi_table(mytsks)
}
Tables_yield$Ymain_norm
lm
k 0.021
PS 0.223
kPS 0.215
AAE10 0.109
CO2 0.228
AAE10_CO2 0.232
AAE10_CO2_kPS 0.233
CO2_kPS 0.232
$Ymain_rel
lm
k -0.009
PS 0.051
kPS 0.036
AAE10 0.152
CO2 0.105
AAE10_CO2 0.129
AAE10_CO2_kPS 0.139
CO2_kPS 0.094
$annual_P_uptake
lm
k -0.005
PS 0.034
kPS 0.030
AAE10 0.095
CO2 0.075
AAE10_CO2 0.097
AAE10_CO2_kPS 0.049
CO2_kPS 0.046
$annual_P_balance
lm
k 0.018
PS 0.553
kPS 0.540
AAE10 0.277
CO2 0.500
AAE10_CO2 0.491
AAE10_CO2_kPS 0.562
CO2_kPS 0.561In [13]:
Code
tmp <- do.call(cbind, lapply(Tables_yield, \(x) x$lm));
rownames(tmp) <- rownames(Tables_yield[[1]])
(Tables_yield_lm <- tmp) Ymain_norm Ymain_rel annual_P_uptake annual_P_balance
k 0.021 -0.009 -0.005 0.018
PS 0.223 0.051 0.034 0.553
kPS 0.215 0.036 0.030 0.540
AAE10 0.109 0.152 0.095 0.277
CO2 0.228 0.105 0.075 0.500
AAE10_CO2 0.232 0.129 0.097 0.491
AAE10_CO2_kPS 0.233 0.139 0.049 0.562
CO2_kPS 0.232 0.094 0.046 0.561xgboost & ranger are no good in this setting since only very few variables available
Predicting Earth-dynamics via soil variables (with/without Treatment)
In [14]:
Code
Earth_vars[1] "soil_0_20_clay" "soil_0_20_pH_H2O" "soil_0_20_Corg" "soil_0_20_silt" Code
Y_vars_earth[1] "PS_log" "k" "kPS_log" "P_AAE10_log" "P_CO2_log" In [15]:
Code
D$is.trt0 <- D$Treatment == "P0"
D$is.trt1 <- D$Treatment == "P100"
mytsks_treatment <- list()
mytsks_notreatment <- list()
for(yvar in Y_vars_earth){
ind <- complete.cases(D[,unique(c(yvar, unlist(P_var_sets_noweather)))])
mytsk <- as_task_regr(
D[ind, c(yvar, Earth_vars, "is.trt1", "is.trt0"
# ,"Site"
)],
target = yvar,
id = yvar)
# mytsk$set_col_roles("Site", "group")
mytsks_treatment[[yvar]] <- mytsk
mytsk <- as_task_regr(
D[ind, c(yvar, Earth_vars
# ,"Site"
)],
target = yvar,
id = yvar)
# mytsk$set_col_roles("Site", "group")
mytsks_notreatment[[yvar]] <- mytsk
}
Tables_earth_treatment <- get_benchi_table(mytsks_treatment)
Tables_earth_notreatment <- get_benchi_table(mytsks_notreatment)In [16]:
Tables_earth_treatment lm
PS_log 0.885
k 0.328
kPS_log 0.752
P_AAE10_log 0.824
P_CO2_log 0.792Tables_earth_notreatment lm
PS_log 0.042
k 0.267
kPS_log 0.023
P_AAE10_log 0.365
P_CO2_log 0.025In [17]:
Code
tmp <- rbind(
"soil + treatment" = Tables_earth_treatment[["lm"]],
"only soil" = Tables_earth_notreatment[["lm"]]
)
colnames(tmp) <- rownames(Tables_earth_treatment)
(Tables_earth_lm <- tmp) PS_log k kPS_log P_AAE10_log P_CO2_log
soil + treatment 0.885 0.328 0.752 0.824 0.792
only soil 0.042 0.267 0.023 0.365 0.025In [18]:
Code
saveRDS(list(
Tables_yield = Tables_yield,
Tables_yield_weather = Tables_yield_weather,
Tables_earth_treatment = Tables_earth_treatment,
Tables_earth_notreatment = Tables_earth_notreatment,
Tables_yield_lm = Tables_yield_lm,
Tables_yield_weather_lm = Tables_yield_weather_lm,
Tables_earth_lm = Tables_earth_lm
), "cache/benchmark-tables.rds")In [19]:
Code
cor(D$annual_P_balance, D$PS) # 0.54389[1] NACode
cor(D$fert_P_tot, D$PS) # 0.48236[1] 0.6449276Code
cor(D$annual_P_uptake, D$PS) # 0.070678[1] NAWe did manage to have high predictive power for weather. This could also be due to our regression models recovering location&year from it and hence still overfitting on the test set.
Without Weather data we only managed for annual balance to get some predictive power (30%). Since we the balance is uptake - fert_P, this means that we mostly predicted fert_P. Interestingly PS is best to predict this quantity
Legacy Code
In [20]:
XGBoost - Parameter Tuning
# Get parameter estimates for XGBoost
t <- as_task_regr(
subset(D[complete.cases(D$annual_P_balance),],
select = c("annual_P_balance", P_var_sets$AAE10_CO2_kPS#, Weather_vars
)),
target = "annual_P_balance"
)
l <- lrn("regr.xgboost",
nrounds = 500 # More iterations due to lower learning rate
)
# Create search space
ps <- ps(
max_depth = p_int(2, 4),
eta = p_dbl(0.001, 0.3, tags = "logscale")
)
# Setup tuning
instance <- ti(
task = t,
learner = l,
resampling = rsmp("cv", folds = 3),
measure = msr("regr.mse"),
terminator = trm("none"),
search_space = ps
)
# Grid search
tuner <- mlr3tuning::tnr("grid_search")
tuner$optimize(instance)
instance$resultYmain_rel max_depth eta learner_param_vals x_domain regr.mse
P uptake max_depth eta learner_param_vals x_domain regr.mse
annual_P_balance max_depth eta learner_param_vals x_domain regr.mse
In [21]:
Code
# nlme.coef$kPS_log <- nlme.coef$k * nlme.coef$PS
#
#
# nlme.coef.mrg <- merge(nlme.coef,allP[allP$year>=2017,],by = "uid")
# # add log-transformed versions
# D$kPS_log <- log(D$kPS_log)
# D$PS_log <- log(D$PS)
# D$soil_0_20_P_AAE10_log <- log(D$soil_0_20_P_AAE10)
# D$soil_0_20_P_CO2_log <- log(D$soil_0_20_P_CO2)
#
# D$k
subset(D, select = c("Ymain_rel", P_var_sets$AAE10_CO2_kPS, Weather_vars)) Ymain_rel P_AAE10_log P_CO2_log PS_log k kPS_log
55 72.33 1.8870696 -1.46967597 -2.9145147 0.20191085 -4.514444
56 92.91 1.8870696 -1.46967597 -2.9145147 0.20191085 -4.514444
57 65.60 1.8870696 -1.46967597 -2.9145147 0.20191085 -4.514444
58 NA 1.8870696 -1.46967597 -2.9145147 0.20191085 -4.514444
59 NA 1.8870696 -1.46967597 -2.9145147 0.20191085 -4.514444
60 NA 1.8870696 -1.46967597 -2.9145147 0.20191085 -4.514444
61 84.81 1.8870696 -1.46967597 -2.9145147 0.20191085 -4.514444
62 NA 1.8245493 -1.34707365 -2.6264148 0.23310593 -4.082677
63 106.32 1.8245493 -1.34707365 -2.6264148 0.23310593 -4.082677
64 69.17 1.8245493 -1.34707365 -2.6264148 0.23310593 -4.082677
65 NA 1.8245493 -1.34707365 -2.6264148 0.23310593 -4.082677
66 84.97 1.8245493 -1.34707365 -2.6264148 0.23310593 -4.082677
67 82.00 1.8245493 -1.34707365 -2.6264148 0.23310593 -4.082677
68 NA 1.8245493 -1.34707365 -2.6264148 0.23310593 -4.082677
69 89.08 0.8329091 -1.83258146 -3.3408312 0.15014993 -5.236952
70 81.01 0.8329091 -1.83258146 -3.3408312 0.15014993 -5.236952
71 NA 0.8329091 -1.83258146 -3.3408312 0.15014993 -5.236952
72 66.00 0.8329091 -1.83258146 -3.3408312 0.15014993 -5.236952
73 NA 0.8329091 -1.83258146 -3.3408312 0.15014993 -5.236952
74 74.25 0.8329091 -1.83258146 -3.3408312 0.15014993 -5.236952
75 NA 0.8329091 -1.83258146 -3.3408312 0.15014993 -5.236952
76 79.31 1.8870696 -1.34707365 -3.8896385 0.13492618 -5.892666
77 NA 1.8870696 -1.34707365 -3.8896385 0.13492618 -5.892666
78 74.44 1.8870696 -1.34707365 -3.8896385 0.13492618 -5.892666
79 92.33 1.8870696 -1.34707365 -3.8896385 0.13492618 -5.892666
80 80.85 1.8870696 -1.34707365 -3.8896385 0.13492618 -5.892666
81 NA 1.8870696 -1.34707365 -3.8896385 0.13492618 -5.892666
82 NA 1.8870696 -1.34707365 -3.8896385 0.13492618 -5.892666
83 109.20 3.1045867 -0.38566248 -1.4927360 0.11739091 -3.634982
84 NA 3.1045867 -0.38566248 -1.4927360 0.11739091 -3.634982
85 NA 3.1045867 -0.38566248 -1.4927360 0.11739091 -3.634982
86 NA 3.1045867 -0.38566248 -1.4927360 0.11739091 -3.634982
87 91.61 3.1045867 -0.38566248 -1.4927360 0.11739091 -3.634982
88 63.16 3.1045867 -0.38566248 -1.4927360 0.11739091 -3.634982
89 91.33 3.1045867 -0.38566248 -1.4927360 0.11739091 -3.634982
90 NA 2.8449094 -0.63487827 -2.1350669 0.17309044 -3.889008
91 NA 2.8449094 -0.63487827 -2.1350669 0.17309044 -3.889008
92 NA 2.8449094 -0.63487827 -2.1350669 0.17309044 -3.889008
93 68.61 2.8449094 -0.63487827 -2.1350669 0.17309044 -3.889008
94 73.44 2.8449094 -0.63487827 -2.1350669 0.17309044 -3.889008
95 78.32 2.8449094 -0.63487827 -2.1350669 0.17309044 -3.889008
96 101.92 2.8449094 -0.63487827 -2.1350669 0.17309044 -3.889008
97 80.26 2.4069451 -1.17118298 -2.2181329 0.17801699 -3.944009
98 107.85 2.4069451 -1.17118298 -2.2181329 0.17801699 -3.944009
99 NA 2.4069451 -1.17118298 -2.2181329 0.17801699 -3.944009
100 NA 2.4069451 -1.17118298 -2.2181329 0.17801699 -3.944009
101 72.56 2.4069451 -1.17118298 -2.2181329 0.17801699 -3.944009
102 95.57 2.4069451 -1.17118298 -2.2181329 0.17801699 -3.944009
103 NA 2.4069451 -1.17118298 -2.2181329 0.17801699 -3.944009
104 NA 2.6741486 -0.94160854 -2.2067423 0.17736688 -3.936277
105 52.11 2.6741486 -0.94160854 -2.2067423 0.17736688 -3.936277
106 69.74 2.6741486 -0.94160854 -2.2067423 0.17736688 -3.936277
107 93.51 2.6741486 -0.94160854 -2.2067423 0.17736688 -3.936277
108 NA 2.6741486 -0.94160854 -2.2067423 0.17736688 -3.936277
109 NA 2.6741486 -0.94160854 -2.2067423 0.17736688 -3.936277
110 72.61 2.6741486 -0.94160854 -2.2067423 0.17736688 -3.936277
111 90.42 4.2017031 0.76546784 -0.9083699 0.23219455 -2.368550
112 NA 4.2017031 0.76546784 -0.9083699 0.23219455 -2.368550
113 NA 4.2017031 0.76546784 -0.9083699 0.23219455 -2.368550
114 94.15 4.2017031 0.76546784 -0.9083699 0.23219455 -2.368550
115 90.11 4.2017031 0.76546784 -0.9083699 0.23219455 -2.368550
116 62.97 4.2017031 0.76546784 -0.9083699 0.23219455 -2.368550
117 NA 4.2017031 0.76546784 -0.9083699 0.23219455 -2.368550
118 85.44 3.0540012 -0.51082562 -1.6359640 0.15615814 -3.492850
119 97.94 3.0540012 -0.51082562 -1.6359640 0.15615814 -3.492850
120 NA 3.0540012 -0.51082562 -1.6359640 0.15615814 -3.492850
121 104.41 3.0540012 -0.51082562 -1.6359640 0.15615814 -3.492850
122 81.58 3.0540012 -0.51082562 -1.6359640 0.15615814 -3.492850
123 NA 3.0540012 -0.51082562 -1.6359640 0.15615814 -3.492850
124 NA 3.0540012 -0.51082562 -1.6359640 0.15615814 -3.492850
125 83.33 3.4873751 -0.10536052 -1.3788326 0.17699689 -3.110456
126 NA 3.4873751 -0.10536052 -1.3788326 0.17699689 -3.110456
127 NA 3.4873751 -0.10536052 -1.3788326 0.17699689 -3.110456
128 76.88 3.4873751 -0.10536052 -1.3788326 0.17699689 -3.110456
129 47.89 3.4873751 -0.10536052 -1.3788326 0.17699689 -3.110456
130 NA 3.4873751 -0.10536052 -1.3788326 0.17699689 -3.110456
131 87.03 3.4873751 -0.10536052 -1.3788326 0.17699689 -3.110456
132 125.95 2.8507065 -0.99425227 -3.3238864 0.22062441 -4.835180
133 83.27 2.8507065 -0.99425227 -3.3238864 0.22062441 -4.835180
134 NA 2.8507065 -0.99425227 -3.3238864 0.22062441 -4.835180
135 NA 2.8507065 -0.99425227 -3.3238864 0.22062441 -4.835180
136 66.48 2.8507065 -0.99425227 -3.3238864 0.22062441 -4.835180
137 NA 2.8507065 -0.99425227 -3.3238864 0.22062441 -4.835180
138 132.89 2.8507065 -0.99425227 -3.3238864 0.22062441 -4.835180
139 NA 3.0492730 -1.07880966 -3.2178905 0.18943117 -4.881620
140 75.56 3.0492730 -1.07880966 -3.2178905 0.18943117 -4.881620
141 NA 3.0492730 -1.07880966 -3.2178905 0.18943117 -4.881620
142 117.88 3.0492730 -1.07880966 -3.2178905 0.18943117 -4.881620
143 65.52 3.0492730 -1.07880966 -3.2178905 0.18943117 -4.881620
144 NA 3.0492730 -1.07880966 -3.2178905 0.18943117 -4.881620
145 91.54 3.0492730 -1.07880966 -3.2178905 0.18943117 -4.881620
146 NA 3.1570004 -1.10866262 -3.6548744 0.28439752 -4.912257
147 65.33 3.1570004 -1.10866262 -3.6548744 0.28439752 -4.912257
148 77.26 3.1570004 -1.10866262 -3.6548744 0.28439752 -4.912257
149 NA 3.1570004 -1.10866262 -3.6548744 0.28439752 -4.912257
150 NA 3.1570004 -1.10866262 -3.6548744 0.28439752 -4.912257
151 133.86 3.1570004 -1.10866262 -3.6548744 0.28439752 -4.912257
152 93.11 3.1570004 -1.10866262 -3.6548744 0.28439752 -4.912257
153 NA 2.7972813 -1.27296568 -3.3755708 0.21679430 -4.904377
154 89.10 2.7972813 -1.27296568 -3.3755708 0.21679430 -4.904377
155 54.11 2.7972813 -1.27296568 -3.3755708 0.21679430 -4.904377
156 86.78 2.7972813 -1.27296568 -3.3755708 0.21679430 -4.904377
157 NA 2.7972813 -1.27296568 -3.3755708 0.21679430 -4.904377
158 NA 2.7972813 -1.27296568 -3.3755708 0.21679430 -4.904377
159 126.90 2.7972813 -1.27296568 -3.3755708 0.21679430 -4.904377
160 NA 3.5055574 -0.69314718 -2.3555262 0.34791259 -3.411330
161 87.36 3.5055574 -0.69314718 -2.3555262 0.34791259 -3.411330
162 NA 3.5055574 -0.69314718 -2.3555262 0.34791259 -3.411330
163 109.78 3.5055574 -0.69314718 -2.3555262 0.34791259 -3.411330
164 145.89 3.5055574 -0.69314718 -2.3555262 0.34791259 -3.411330
165 NA 3.5055574 -0.69314718 -2.3555262 0.34791259 -3.411330
166 90.60 3.5055574 -0.69314718 -2.3555262 0.34791259 -3.411330
167 NA 3.4750672 -0.57981850 -2.4402754 0.30702495 -3.621102
168 92.78 3.4750672 -0.57981850 -2.4402754 0.30702495 -3.621102
169 79.12 3.4750672 -0.57981850 -2.4402754 0.30702495 -3.621102
170 94.92 3.4750672 -0.57981850 -2.4402754 0.30702495 -3.621102
171 139.72 3.4750672 -0.57981850 -2.4402754 0.30702495 -3.621102
172 NA 3.4750672 -0.57981850 -2.4402754 0.30702495 -3.621102
173 NA 3.4750672 -0.57981850 -2.4402754 0.30702495 -3.621102
174 77.97 3.6988298 -0.63487827 -2.5704141 0.25060055 -3.954309
175 NA 3.6988298 -0.63487827 -2.5704141 0.25060055 -3.954309
176 92.11 3.6988298 -0.63487827 -2.5704141 0.25060055 -3.954309
177 138.29 3.6988298 -0.63487827 -2.5704141 0.25060055 -3.954309
178 NA 3.6988298 -0.63487827 -2.5704141 0.25060055 -3.954309
179 NA 3.6988298 -0.63487827 -2.5704141 0.25060055 -3.954309
180 87.56 3.6988298 -0.63487827 -2.5704141 0.25060055 -3.954309
181 96.55 3.1267605 -0.79850770 -2.8188200 0.16133292 -4.643105
182 90.00 3.1267605 -0.79850770 -2.8188200 0.16133292 -4.643105
183 NA 3.1267605 -0.79850770 -2.8188200 0.16133292 -4.643105
184 137.97 3.1267605 -0.79850770 -2.8188200 0.16133292 -4.643105
185 NA 3.1267605 -0.79850770 -2.8188200 0.16133292 -4.643105
186 96.80 3.1267605 -0.79850770 -2.8188200 0.16133292 -4.643105
187 NA 3.1267605 -0.79850770 -2.8188200 0.16133292 -4.643105
188 134.81 3.8712010 -0.43078292 -2.0165660 0.29038401 -3.253117
189 58.00 3.8712010 -0.43078292 -2.0165660 0.29038401 -3.253117
190 NA 3.8712010 -0.43078292 -2.0165660 0.29038401 -3.253117
191 NA 3.8712010 -0.43078292 -2.0165660 0.29038401 -3.253117
192 84.67 3.8712010 -0.43078292 -2.0165660 0.29038401 -3.253117
193 88.53 3.8712010 -0.43078292 -2.0165660 0.29038401 -3.253117
194 NA 3.8712010 -0.43078292 -2.0165660 0.29038401 -3.253117
195 NA 3.9039908 -0.38566248 -1.8173600 0.22557569 -3.306459
196 NA 3.9039908 -0.38566248 -1.8173600 0.22557569 -3.306459
197 NA 3.9039908 -0.38566248 -1.8173600 0.22557569 -3.306459
198 117.78 3.9039908 -0.38566248 -1.8173600 0.22557569 -3.306459
199 132.12 3.9039908 -0.38566248 -1.8173600 0.22557569 -3.306459
200 97.18 3.9039908 -0.38566248 -1.8173600 0.22557569 -3.306459
201 92.53 3.9039908 -0.38566248 -1.8173600 0.22557569 -3.306459
202 NA 3.9512437 -0.16251893 -1.6506135 0.13768829 -3.633376
203 NA 3.9512437 -0.16251893 -1.6506135 0.13768829 -3.633376
204 NA 3.9512437 -0.16251893 -1.6506135 0.13768829 -3.633376
205 98.28 3.9512437 -0.16251893 -1.6506135 0.13768829 -3.633376
206 91.44 3.9512437 -0.16251893 -1.6506135 0.13768829 -3.633376
207 137.66 3.9512437 -0.16251893 -1.6506135 0.13768829 -3.633376
208 90.98 3.9512437 -0.16251893 -1.6506135 0.13768829 -3.633376
209 NA 3.8372995 -0.51082562 -1.7109028 0.06500092 -4.444257
210 NA 3.8372995 -0.51082562 -1.7109028 0.06500092 -4.444257
211 NA 3.8372995 -0.51082562 -1.7109028 0.06500092 -4.444257
212 92.34 3.8372995 -0.51082562 -1.7109028 0.06500092 -4.444257
213 132.91 3.8372995 -0.51082562 -1.7109028 0.06500092 -4.444257
214 94.74 3.8372995 -0.51082562 -1.7109028 0.06500092 -4.444257
215 108.89 3.8372995 -0.51082562 -1.7109028 0.06500092 -4.444257
216 NA 2.5649494 -1.46967597 -3.0602039 0.22808615 -4.538236
217 NA 2.5649494 -1.46967597 -3.0602039 0.22808615 -4.538236
218 98.64 2.5649494 -1.46967597 -3.0602039 0.22808615 -4.538236
219 94.74 2.5649494 -1.46967597 -3.0602039 0.22808615 -4.538236
220 98.67 2.5649494 -1.46967597 -3.0602039 0.22808615 -4.538236
221 90.23 2.5649494 -1.46967597 -3.0602039 0.22808615 -4.538236
222 108.37 2.5649494 -1.46967597 -3.0602039 0.22808615 -4.538236
223 82.03 2.6390573 -1.46967597 -2.9064446 0.20616803 -4.485508
224 115.94 2.6390573 -1.46967597 -2.9064446 0.20616803 -4.485508
225 89.10 2.6390573 -1.46967597 -2.9064446 0.20616803 -4.485508
226 NA 2.6390573 -1.46967597 -2.9064446 0.20616803 -4.485508
227 NA 2.6390573 -1.46967597 -2.9064446 0.20616803 -4.485508
228 81.61 2.6390573 -1.46967597 -2.9064446 0.20616803 -4.485508
229 83.91 2.6390573 -1.46967597 -2.9064446 0.20616803 -4.485508
230 92.86 3.2695689 -1.34707365 -2.6081966 0.15273297 -4.487261
231 83.28 3.2695689 -1.34707365 -2.6081966 0.15273297 -4.487261
232 113.04 3.2695689 -1.34707365 -2.6081966 0.15273297 -4.487261
233 93.87 3.2695689 -1.34707365 -2.6081966 0.15273297 -4.487261
234 NA 3.2695689 -1.34707365 -2.6081966 0.15273297 -4.487261
235 NA 3.2695689 -1.34707365 -2.6081966 0.15273297 -4.487261
236 104.22 3.2695689 -1.34707365 -2.6081966 0.15273297 -4.487261
237 110.14 2.2823824 -1.51412773 -2.5903371 0.14899842 -4.494157
238 96.24 2.2823824 -1.51412773 -2.5903371 0.14899842 -4.494157
239 104.70 2.2823824 -1.51412773 -2.5903371 0.14899842 -4.494157
240 NA 2.2823824 -1.51412773 -2.5903371 0.14899842 -4.494157
241 97.49 2.2823824 -1.51412773 -2.5903371 0.14899842 -4.494157
242 91.95 2.2823824 -1.51412773 -2.5903371 0.14899842 -4.494157
243 NA 2.2823824 -1.51412773 -2.5903371 0.14899842 -4.494157
244 NA 3.4843123 -0.56211892 -2.0944336 0.19984180 -3.704663
245 NA 3.4843123 -0.56211892 -2.0944336 0.19984180 -3.704663
246 92.15 3.4843123 -0.56211892 -2.0944336 0.19984180 -3.704663
247 107.57 3.4843123 -0.56211892 -2.0944336 0.19984180 -3.704663
248 98.85 3.4843123 -0.56211892 -2.0944336 0.19984180 -3.704663
249 100.00 3.4843123 -0.56211892 -2.0944336 0.19984180 -3.704663
250 86.47 3.4843123 -0.56211892 -2.0944336 0.19984180 -3.704663
251 96.38 3.3286267 -0.40047757 -1.6439616 0.10705720 -3.878354
252 140.42 3.3286267 -0.40047757 -1.6439616 0.10705720 -3.878354
253 NA 3.3286267 -0.40047757 -1.6439616 0.10705720 -3.878354
254 100.00 3.3286267 -0.40047757 -1.6439616 0.10705720 -3.878354
255 NA 3.3286267 -0.40047757 -1.6439616 0.10705720 -3.878354
256 92.53 3.3286267 -0.40047757 -1.6439616 0.10705720 -3.878354
257 94.92 3.3286267 -0.40047757 -1.6439616 0.10705720 -3.878354
258 NA 3.4339872 -0.67334455 -2.1715576 0.21193823 -3.723018
259 97.18 3.4339872 -0.67334455 -2.1715576 0.21193823 -3.723018
260 96.34 3.4339872 -0.67334455 -2.1715576 0.21193823 -3.723018
261 95.02 3.4339872 -0.67334455 -2.1715576 0.21193823 -3.723018
262 NA 3.4339872 -0.67334455 -2.1715576 0.21193823 -3.723018
263 126.25 3.4339872 -0.67334455 -2.1715576 0.21193823 -3.723018
264 113.27 3.4339872 -0.67334455 -2.1715576 0.21193823 -3.723018
265 NA 3.1484534 -0.67334455 -2.0030331 0.18423357 -3.694584
266 104.28 3.1484534 -0.67334455 -2.0030331 0.18423357 -3.694584
267 NA 3.1484534 -0.67334455 -2.0030331 0.18423357 -3.694584
268 94.25 3.1484534 -0.67334455 -2.0030331 0.18423357 -3.694584
269 102.07 3.1484534 -0.67334455 -2.0030331 0.18423357 -3.694584
270 119.16 3.1484534 -0.67334455 -2.0030331 0.18423357 -3.694584
271 99.28 3.1484534 -0.67334455 -2.0030331 0.18423357 -3.694584
272 108.69 3.6428355 -0.16251893 -1.5511331 0.13120470 -3.582130
273 130.60 3.6428355 -0.16251893 -1.5511331 0.13120470 -3.582130
274 NA 3.6428355 -0.16251893 -1.5511331 0.13120470 -3.582130
275 93.30 3.6428355 -0.16251893 -1.5511331 0.13120470 -3.582130
276 96.66 3.6428355 -0.16251893 -1.5511331 0.13120470 -3.582130
277 100.75 3.6428355 -0.16251893 -1.5511331 0.13120470 -3.582130
278 NA 3.6428355 -0.16251893 -1.5511331 0.13120470 -3.582130
279 NA 3.5174978 -0.09431068 -1.2221855 0.10473925 -3.478467
280 NA 3.5174978 -0.09431068 -1.2221855 0.10473925 -3.478467
281 97.51 3.5174978 -0.09431068 -1.2221855 0.10473925 -3.478467
282 111.65 3.5174978 -0.09431068 -1.2221855 0.10473925 -3.478467
283 128.34 3.5174978 -0.09431068 -1.2221855 0.10473925 -3.478467
284 85.16 3.5174978 -0.09431068 -1.2221855 0.10473925 -3.478467
285 99.69 3.5174978 -0.09431068 -1.2221855 0.10473925 -3.478467
286 130.43 3.5204608 -0.38566248 -1.2647377 0.13141530 -3.294130
287 93.42 3.5204608 -0.38566248 -1.2647377 0.13141530 -3.294130
288 106.17 3.5204608 -0.38566248 -1.2647377 0.13141530 -3.294130
289 NA 3.5204608 -0.38566248 -1.2647377 0.13141530 -3.294130
290 94.44 3.5204608 -0.38566248 -1.2647377 0.13141530 -3.294130
291 NA 3.5204608 -0.38566248 -1.2647377 0.13141530 -3.294130
292 88.06 3.5204608 -0.38566248 -1.2647377 0.13141530 -3.294130
293 NA 4.0621657 -0.05129329 -1.2757306 0.21076772 -2.832729
294 106.02 4.0621657 -0.05129329 -1.2757306 0.21076772 -2.832729
295 100.42 4.0621657 -0.05129329 -1.2757306 0.21076772 -2.832729
296 96.86 4.0621657 -0.05129329 -1.2757306 0.21076772 -2.832729
297 133.49 4.0621657 -0.05129329 -1.2757306 0.21076772 -2.832729
298 94.25 4.0621657 -0.05129329 -1.2757306 0.21076772 -2.832729
299 NA 4.0621657 -0.05129329 -1.2757306 0.21076772 -2.832729
300 NA 2.6810215 -1.77195684 -3.8181685 0.18211399 -5.521291
301 NA 2.6810215 -1.77195684 -3.8181685 0.18211399 -5.521291
302 86.01 2.6810215 -1.77195684 -3.8181685 0.18211399 -5.521291
303 104.08 2.6810215 -1.77195684 -3.8181685 0.18211399 -5.521291
304 69.73 2.6810215 -1.77195684 -3.8181685 0.18211399 -5.521291
305 80.08 2.6810215 -1.77195684 -3.8181685 0.18211399 -5.521291
306 91.63 2.6810215 -1.77195684 -3.8181685 0.18211399 -5.521291
307 66.34 3.0155349 -1.77195684 -3.7414147 0.22288952 -5.242494
308 NA 3.0155349 -1.77195684 -3.7414147 0.22288952 -5.242494
309 NA 3.0155349 -1.77195684 -3.7414147 0.22288952 -5.242494
310 67.05 3.0155349 -1.77195684 -3.7414147 0.22288952 -5.242494
311 61.28 3.0155349 -1.77195684 -3.7414147 0.22288952 -5.242494
312 94.25 3.0155349 -1.77195684 -3.7414147 0.22288952 -5.242494
313 81.18 3.0155349 -1.77195684 -3.7414147 0.22288952 -5.242494
314 98.91 3.5234150 -1.34707365 -3.8931747 0.14517478 -5.822992
315 NA 3.5234150 -1.34707365 -3.8931747 0.14517478 -5.822992
316 75.10 3.5234150 -1.34707365 -3.8931747 0.14517478 -5.822992
317 NA 3.5234150 -1.34707365 -3.8931747 0.14517478 -5.822992
318 110.97 3.5234150 -1.34707365 -3.8931747 0.14517478 -5.822992
319 129.31 3.5234150 -1.34707365 -3.8931747 0.14517478 -5.822992
320 94.92 3.5234150 -1.34707365 -3.8931747 0.14517478 -5.822992
321 88.90 2.8390785 -1.83258146 -3.6735278 0.26166020 -5.014236
322 NA 2.8390785 -1.83258146 -3.6735278 0.26166020 -5.014236
323 64.66 2.8390785 -1.83258146 -3.6735278 0.26166020 -5.014236
324 NA 2.8390785 -1.83258146 -3.6735278 0.26166020 -5.014236
325 65.52 2.8390785 -1.83258146 -3.6735278 0.26166020 -5.014236
326 71.26 2.8390785 -1.83258146 -3.6735278 0.26166020 -5.014236
327 75.85 2.8390785 -1.83258146 -3.6735278 0.26166020 -5.014236
328 100.10 4.2253728 -0.23572233 -2.0697768 0.21782370 -3.593846
329 86.78 4.2253728 -0.23572233 -2.0697768 0.21782370 -3.593846
330 135.27 4.2253728 -0.23572233 -2.0697768 0.21782370 -3.593846
331 NA 4.2253728 -0.23572233 -2.0697768 0.21782370 -3.593846
332 NA 4.2253728 -0.23572233 -2.0697768 0.21782370 -3.593846
333 114.85 4.2253728 -0.23572233 -2.0697768 0.21782370 -3.593846
334 106.63 4.2253728 -0.23572233 -2.0697768 0.21782370 -3.593846
335 99.69 3.9376908 -0.57981850 -2.3967665 0.21384349 -3.939277
336 97.89 3.9376908 -0.57981850 -2.3967665 0.21384349 -3.939277
337 145.25 3.9376908 -0.57981850 -2.3967665 0.21384349 -3.939277
338 NA 3.9376908 -0.57981850 -2.3967665 0.21384349 -3.939277
339 105.43 3.9376908 -0.57981850 -2.3967665 0.21384349 -3.939277
340 109.77 3.9376908 -0.57981850 -2.3967665 0.21384349 -3.939277
341 NA 3.9376908 -0.57981850 -2.3967665 0.21384349 -3.939277
342 NA 3.5582011 -0.99425227 -2.6575735 0.21147919 -4.211202
343 108.05 3.5582011 -0.99425227 -2.6575735 0.21147919 -4.211202
344 88.12 3.5582011 -0.99425227 -2.6575735 0.21147919 -4.211202
345 129.95 3.5582011 -0.99425227 -2.6575735 0.21147919 -4.211202
346 97.83 3.5582011 -0.99425227 -2.6575735 0.21147919 -4.211202
347 108.65 3.5582011 -0.99425227 -2.6575735 0.21147919 -4.211202
348 NA 3.5582011 -0.99425227 -2.6575735 0.21147919 -4.211202
349 109.17 3.7013020 -0.63487827 -2.6521244 0.21152273 -4.205547
350 NA 3.7013020 -0.63487827 -2.6521244 0.21152273 -4.205547
351 81.61 3.7013020 -0.63487827 -2.6521244 0.21152273 -4.205547
352 117.23 3.7013020 -0.63487827 -2.6521244 0.21152273 -4.205547
353 110.24 3.7013020 -0.63487827 -2.6521244 0.21152273 -4.205547
354 102.63 3.7013020 -0.63487827 -2.6521244 0.21152273 -4.205547
355 NA 3.7013020 -0.63487827 -2.6521244 0.21152273 -4.205547
356 89.46 4.3385971 0.07696104 -1.4624073 0.18550740 -3.147068
357 113.99 4.3385971 0.07696104 -1.4624073 0.18550740 -3.147068
358 98.22 4.3385971 0.07696104 -1.4624073 0.18550740 -3.147068
359 NA 4.3385971 0.07696104 -1.4624073 0.18550740 -3.147068
360 106.02 4.3385971 0.07696104 -1.4624073 0.18550740 -3.147068
361 131.88 4.3385971 0.07696104 -1.4624073 0.18550740 -3.147068
362 NA 4.3385971 0.07696104 -1.4624073 0.18550740 -3.147068
363 99.62 4.5174313 0.67803354 -1.2422076 0.13496530 -3.244945
364 103.50 4.5174313 0.67803354 -1.2422076 0.13496530 -3.244945
365 NA 4.5174313 0.67803354 -1.2422076 0.13496530 -3.244945
366 143.00 4.5174313 0.67803354 -1.2422076 0.13496530 -3.244945
367 111.18 4.5174313 0.67803354 -1.2422076 0.13496530 -3.244945
368 113.35 4.5174313 0.67803354 -1.2422076 0.13496530 -3.244945
369 NA 4.5174313 0.67803354 -1.2422076 0.13496530 -3.244945
370 NA 4.2668963 0.11332869 -1.5757798 0.20749743 -3.148416
371 92.89 4.2668963 0.11332869 -1.5757798 0.20749743 -3.148416
372 89.85 4.2668963 0.11332869 -1.5757798 0.20749743 -3.148416
373 114.85 4.2668963 0.11332869 -1.5757798 0.20749743 -3.148416
374 134.86 4.2668963 0.11332869 -1.5757798 0.20749743 -3.148416
375 NA 4.2668963 0.11332869 -1.5757798 0.20749743 -3.148416
376 132.21 4.2668963 0.11332869 -1.5757798 0.20749743 -3.148416
377 NA 4.0656021 0.53649337 -2.1617951 0.28873132 -3.404054
378 128.47 4.0656021 0.53649337 -2.1617951 0.28873132 -3.404054
379 107.89 4.0656021 0.53649337 -2.1617951 0.28873132 -3.404054
380 110.14 4.0656021 0.53649337 -2.1617951 0.28873132 -3.404054
381 NA 4.0656021 0.53649337 -2.1617951 0.28873132 -3.404054
382 81.03 4.0656021 0.53649337 -2.1617951 0.28873132 -3.404054
383 125.60 4.0656021 0.53649337 -2.1617951 0.28873132 -3.404054
anavg_temp ansum_prec juvdev_prec juvdev_sun ansum_sun juvdev_temp
55 10.1 1035.6 0.23 0.22 1960.0 1.37
56 11.2 752.6 -0.36 -0.02 2105.7 0.40
57 11.3 725.8 -0.38 0.42 2019.7 1.00
58 9.5 1029.7 0.23 0.13 1692.1 -0.34
59 10.7 870.9 -0.35 0.18 1886.0 1.10
60 10.5 993.9 -0.25 0.44 1862.4 1.60
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383 FALSEMethods
we used machine learning methods to assess how much information different sets of variables (c.f. P_var_sets) have each on the dependent variable (Puptake, Y-rel, P-balance), how redundant this information is. The machine learning methods to quantify the predictive power of different variable sets are: i) ordinary least squares (OLS) as a baseline; ii) XGBoost (gradient boosting with tree-based models and hyperparameter tuning for learning rate and tree depth) (arxiv:1603.02754); iii) Random Forests (with default parameters) (doi:10.1023/A:1010933404324). Computations were performed using the mlr3 framework (doi:10.21105/joss.01903). Performance was measured as percentage of explained variance on hold-out data via 5-fold cross-validation, calculated as (1 - MSE/Variance(y)), where MSE represents mean squared error.
We tried adjusting for weather variables but it seems that the ML-methods rather reconstruct the site-specific patterns….