diff --git a/exploration/scriptR/Alexis_code_BRT_articleV12.r b/exploration/scriptR/Alexis_code_BRT_articleV12.r
new file mode 100644
index 0000000000000000000000000000000000000000..0bbe1085486badf8794087179c60d301bf4580ad
--- /dev/null
+++ b/exploration/scriptR/Alexis_code_BRT_articleV12.r
@@ -0,0 +1,238 @@
+# # Code article V1.2 avec ajout DDL
+# February 2019
+
+library(dplyr)
+library(tidyr)
+library(stats)
+library(lubridate)
+library(purrr)
+library(suncalc)
+library(furrr)
+library(tictoc)
+library(caret)
+library(readr)
+library(patchwork)
+library(dismo)
+library(gbm)
+library(vioplot)
+library(fields)
+library(gam)
+library(voxel)
+library(aplpack)
+library(scales)
+library(tidyverse)
+
+rm(list=ls())
+
+USER="Alexis"
+
+if(USER=="Alexis"){
+ repertoire_travail<-getwd()
+ repertoire_data<-paste0(repertoire_travail,"/data/input/")
+ repertoire_dataGW<-paste0(repertoire_travail,"/data/GlobalWarming/")
+ repertoire_sorties<-paste0(repertoire_travail,"/data/output/")
+}else{
+ repertoire_travail <- getwd()
+ repertoire_data <- "../data/input/"
+ repertoire_sorties <- "../data/output/"
+}
+
+#----------------------------------------------------------------------------
+#La fonction de contour remasterisée
+load(paste0(repertoire_sorties, "contourGBM.RData"))
+#La fonction de calcul de dayl-length
+load(paste0(repertoire_sorties, "dayLight.RData"))
+#----------------------------------------------------------------------------
+
+
+# Day length -------------------------------------------------------------
+st <- as.Date("2019-01-01")
+en <- as.Date("2019-12-31")
+calendar <- seq.Date(st, en, by = "day")
+
+dayL<-data.frame(date=calendar,
+ site=c(rep("Garonne", 365),rep("Dordogne",365)),
+ DL=c(dayLight(dates=calendar),
+ dayLight(dates=calendar, latitude = 44.8333 , longitude=0.35)))
+
+dayL %>%
+ group_by(site) %>%
+ mutate(deltaDL1=ifelse(row_number() == 1, NaN, DL - lag(DL, 1)),
+ dataLink=format(date, "%d-%m"),
+ jourDeAnnee=lubridate::yday(date)) %>%
+ ungroup() %>%
+ as.data.frame()->dayL
+
+# Day length -------------------------------------------------------------
+
+
+
+# Data env + reproduction -------------------------------------------------------------
+
+envCondition<-read.table(paste0(repertoire_data, "envCondition.csv"),
+ header=TRUE, sep=";") %>%
+ mutate(jourDeAnnee=lubridate::yday(date)) %>%
+ filter(jourDeAnnee %in% c(91:213))->data
+data$date<-as.Date(data$date)
+data$dataLink=base::format(data$date, "%d-%m")
+
+
+repro<-read.table(paste0(repertoire_data,"reproMonitoring.csv"), sep=";", header = T)
+repro$date<-as.Date(repro$date)
+repro$Presence<-as.numeric(repro$Bulls>0)
+
+data<-right_join(x=data, y=repro, by=c("lien", "date"))
+
+# Data env + reproduction -------------------------------------------------------------
+
+data<-left_join(x=data, y=dayL, by=c("dataLink","site"))
+data<-data[,names(data) %in% c("lien", "site", 'date.x', "Temp1",
+ "deltaDL1.y", "Q1", "Presence")]
+
+names(data)<-c("lien", "site", 'date', "Temp1", "Q1", "Presence", "deltaDL1")
+
+# END du data--------------------------------------------------------------
+
+indexes = sample(1:nrow(data),size=0.3*nrow(data))
+trained_data = data[-indexes,]
+test_data = data[indexes,]
+
+
+# ------------------------------------------------------------------------------
+# 1/
+# Le modele BRT presence-absence
+# ------------------------------------------------------------------------------
+
+Variable<-c("Temp1", "Q1", "deltaDL1")
+
+
+brtTempPres<-gbm.step(data=trained_data,
+ gbm.x = Variable, gbm.y = "Presence",
+ family = "bernoulli", tree.complexity = 5,
+ learning.rate = 0.001, bag.fraction = 0.5)
+
+Relative_influence<-as.data.frame(summary(brtTempPres))
+
+# ----------------------------------------------------------------------------
+
+data$Preds<-predict.gbm(brtTempPres, data, n.trees=brtTempPres$gbm.call$best.trees, type="response")
+d <- cbind(data$Presence, data$Preds)
+
+pres <- d[d[,1]==1 , 2]
+abs <- d[d[,1]==0 , 2]
+e.dm<-evaluate(p=pres, a=abs)
+e.dm
+# Check the evaluation results
+str(e.dm)
+# Boxplot of presence and absence suitable values
+# blue are absences, red are presences
+boxplot(e.dm,col=c('blue','red'))
+# Density plot of presence and absence suitable values
+# blue are absences, red are presences
+raster::density(e.dm)#
+tr.b<-threshold(e.dm,'spec_sens')
+# Get the value of the threshold=0.570914
+abline(v=tr.b)
+
+#----------------------------------------------------------------------
+# Parital plot
+
+par(mfrow=c(2,2))
+
+a<-plot.gbm(brtTempPres,
+ i.var=1,
+ return.grid = TRUE, type="link")
+
+
+b<-plot.gbm(brtTempPres,
+ i.var=2,
+ return.grid = TRUE, type="link")
+
+c<-plot.gbm(brtTempPres,
+ i.var=3,
+ return.grid = TRUE, type="link")
+
+a %>%
+ ggplot()+
+ geom_line(aes(x=Temp1, y=y))+
+ xlab("Water temperature (°C)")+
+ ylab("Marginal effect on logit(p)")+
+ theme_bw()->A
+
+b %>%
+ ggplot()+
+ geom_line(aes(x=Q1, y=y))+
+ xlab("Water discharge (log scale; m3/s)")+
+ ylab("Marginal effect on logit(p)")+
+ theme_bw()->B
+
+c %>%
+ ggplot()+
+ geom_line(aes(x=deltaDL1, y=y))+
+ xlab("Day-length difference (hours)")+
+ ylab("Marginal effect on logit(p)")+
+ theme_bw()->C
+
+C+A+B+plot_layout(2,2)
+
+#----------------------------------------------------------------------------
+# 3-d dependanc plots
+
+
+find.int <- gbm.interactions(brtTempPres)
+find.int$interactions
+find.int$rank.list
+
+par(mfrow=c(2,2), mar=c(4,4,1,2))
+
+# Temperature et delta day length
+contourGBM(brtTempPres, 3, 1,perspective = FALSE,
+ smooth = "average", y.label='Water temperature (°C)',
+ x.label="Day-length difference (hours)")
+
+X<-data.frame(x=data$deltaDL1,
+ y=data$Temp1)
+
+aplpack::plothulls(X,fraction=1,add=TRUE, pch="", main="")
+
+points(data$Temp1[data$Presence>0]~data$deltaDL1[data$Presence>0],
+ pch="+",cex=.7)
+
+box()
+
+#-------------------------------------------------------
+
+# Temeprature et debit
+contourGBM(brtTempPres, 1, 2,perspective = FALSE,
+ smooth = "average", x.label='Water temperature (°C)',
+ y.label="Water discharge (log scale; m3/s)")
+
+X<-data.frame(x=data$Temp1,
+ y=data$Q1)
+
+aplpack::plothulls(X,fraction=1,add=TRUE, pch="", main="")
+
+points(data$Q1[data$Presence>0] ~ data$Temp1[data$Presence>0],
+ pch="+",cex=.7)
+
+box()
+#---------------------------------------------------------------
+
+contourGBM(brtTempPres, 3, 2,perspective = FALSE,
+ smooth = "average", x.label="Day-length difference (hours)",
+ y.label="Water discharge (log scale; m3/s)")
+
+X<-data.frame(x=data$deltaDL1,
+ y=data$Q1)
+
+aplpack::plothulls(X,fraction=1,add=TRUE, pch="", main="")
+
+points(data$deltaDL1[data$Presence>0],
+ data$Q1[data$Presence>0],
+ pch="+",cex=.7)
+box()
+
+
+
+
+
diff --git a/exploration/scriptR/BTRarticle.RData b/exploration/scriptR/BTRarticle.RData
new file mode 100755
index 0000000000000000000000000000000000000000..92f88ed6e85f93954751d014c1955102fba35c60
Binary files /dev/null and b/exploration/scriptR/BTRarticle.RData differ
diff --git a/exploration/scriptR/GARDONNE_T.txt b/exploration/scriptR/GARDONNE_T.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d32f553d512dfc0d1c6ad52865929af92381c9ec
--- /dev/null
+++ b/exploration/scriptR/GARDONNE_T.txt
@@ -0,0 +1,21551 @@
+date Temp(°C)
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diff --git a/exploration/scriptR/LAMAGIST_T.txt b/exploration/scriptR/LAMAGIST_T.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ba7085870053d4621ba597fc501f9e9f36756cfd
--- /dev/null
+++ b/exploration/scriptR/LAMAGIST_T.txt
@@ -0,0 +1,21551 @@
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+2017-02-17 7.525
+2017-02-18 7.474
+2017-02-19 6.939
+2017-02-20 6.245
+2017-02-21 10.705
+2017-02-22 9.469
+2017-02-23 7.658
+2017-02-24 7.651
+2017-02-25 6.012
+2017-02-26 6.182
+2017-02-27 11.693
+2017-02-28 8.018
+2017-03-01 10.88
+2017-03-02 11.641
+2017-03-03 11.567
+2017-03-04 7.636
+2017-03-05 8.632
+2017-03-06 11.051
+2017-03-07 8.971
+2017-03-08 12.519
+2017-03-09 11.596
+2017-03-10 10.723
+2017-03-11 13.195
+2017-03-12 11.861
+2017-03-13 12.112
+2017-03-14 10.241
+2017-03-15 9.838
+2017-03-16 11.992
+2017-03-17 11.184
+2017-03-18 10.634
+2017-03-19 8.68
+2017-03-20 11.209
+2017-03-21 9.512
+2017-03-22 9.238
+2017-03-23 7.517
+2017-03-24 6.932
+2017-03-25 10.339
+2017-03-26 11.615
+2017-03-27 12.783
+2017-03-28 13.056
+2017-03-29 13.832
+2017-03-30 15.276
+2017-03-31 13.311
+2017-04-01 10.651
+2017-04-02 11.297
+2017-04-03 12.541
+2017-04-04 13.728
+2017-04-05 11.97
+2017-04-06 11.601
+2017-04-07 12.119
+2017-04-08 15.396
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+2017-04-10 16.276
+2017-04-11 14.55
+2017-04-12 13.446
+2017-04-13 15.031
+2017-04-14 13.239
+2017-04-15 12.084
+2017-04-16 11.916
+2017-04-17 12.458
+2017-04-18 11.878
+2017-04-19 10.731
+2017-04-20 10.215
+2017-04-21 11.419
+2017-04-22 14.058
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+2017-04-25 11.858
+2017-04-26 7.471
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+2017-04-28 8.799
+2017-04-29 11.306
+2017-04-30 11.489
+2017-05-01 10.766
+2017-05-02 13.335
+2017-05-03 13.297
+2017-05-04 14.365
+2017-05-05 15.426
+2017-05-06 15.081
+2017-05-07 14.955
+2017-05-08 14.86
+2017-05-09 14.962
+2017-05-10 15.365
+2017-05-11 15.727
+2017-05-12 17.964
+2017-05-13 16.469
+2017-05-14 17.28
+2017-05-15 19.976
+2017-05-16 22.107
+2017-05-17 20.109
+2017-05-18 13.291
+2017-05-19 12.028
+2017-05-20 13.819
+2017-05-21 16.675
+2017-05-22 19.617
+2017-05-23 16.147
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+2017-05-25 23.5
+2017-05-26 23.198
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+2017-05-28 23.454
+2017-05-29 21.048
+2017-05-30 19.607
+2017-05-31 18.757
+2017-06-01 21.823
+2017-06-02 22.953
+2017-06-03 16.804
+2017-06-04 15.576
+2017-06-05 18.381
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+2017-06-08 20.851
+2017-06-09 20.275
+2017-06-10 23.489
+2017-06-11 25.749
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+2017-06-13 25.542
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+2017-06-19 27.4
+2017-06-20 27.383
+2017-06-21 29.308
+2017-06-22 28.851
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+2017-07-04 22.993
+2017-07-05 25.324
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+2017-07-09 21.257
+2017-07-10 19.592
+2017-07-11 20.868
+2017-07-12 20.353
+2017-07-13 21.209
+2017-07-14 20.89
+2017-07-15 21.719
+2017-07-16 24.005
+2017-07-17 25.675
+2017-07-18 26.402
+2017-07-19 24.425
+2017-07-20 20.369
+2017-07-21 19.461
+2017-07-22 20.407
+2017-07-23 20.74
+2017-07-24 19.788
+2017-07-25 19.795
+2017-07-26 19.523
+2017-07-27 21.367
+2017-07-28 22.405
+2017-07-29 23.774
+2017-07-30 23.494
+2017-07-31 23.382
diff --git a/exploration/scriptR/PatrickPrg.R b/exploration/scriptR/PatrickPrg.R
index 15fbd030b59be2432277ec2fc0070d346467e92d..7d21a0fa8d54ccf6dba4b44bd85afb941e597d23 100644
--- a/exploration/scriptR/PatrickPrg.R
+++ b/exploration/scriptR/PatrickPrg.R
@@ -4,8 +4,8 @@ basins = read.csv("/home/patrick/Documents/workspace/GR3D/data/input/reality/bas
tempData = read.csv("/home/patrick/Documents/workspace/GR3D/data/input/reality/SeasonTempBVFacAtlant1801_2100_newCRU_RCP85.csv", sep = ";")
riverName = "Garonne"
-riverName = "Rhine"
-riverName = "Meuse"
+# riverName = "Rhine"
+# riverName = "Meuse"
surfaceBasin = basins[basins$nomBV == riverName, 'surface']
@@ -50,11 +50,11 @@ temperatureEffect = function(tempWater, TminRep, ToptRep, TmaxRep){
}
-thermalBevertonHolt = function(stock, temperature, juvenileTolerance, surface = 84810) {
+thermalBevertonHolt = function(stock, temperature, juvenileTolerance, surface = 84810, aFecundity = 135000) {
survOptRep = 0.0017
delta_t = 0.33
lambda = 4.1E-4
- a = 135000 # ~fecondité
+ # a ~ fecondité
tempEffect = temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3] )
b = -log(survOptRep * tempEffect)/delta_t
c = lambda/surface
@@ -69,17 +69,17 @@ thermalBevertonHolt = function(stock, temperature, juvenileTolerance, surface =
alpha = (b * exp(-b * delta_t)) / (c * (1 - exp(-b * delta_t)))
alpha[tempEffect == 0] = 0
- beta = b / (a * c * (1 - exp(-b * delta_t)))
+ beta = b / (aFecundity * c * (1 - exp(-b * delta_t)))
recruit = alpha * stock * AlleeEffect / (beta + stock * AlleeEffect)
return(recruit)
}
-stockAtCrash = function(temperature, juvenileTolerance, surface = 84810) {
+stockAtCrash = function(temperature, juvenileTolerance, surface = 84810, aFecundity = 135000) {
survOptRep = 0.0017
delta_t = 0.33
lambda = 4.1E-4
- a = 135000 # ~fecondité
+
tempEffect = temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3])
b = -log(survOptRep * tempEffect) / delta_t
b[b == Inf] = 0
@@ -91,7 +91,7 @@ stockAtCrash = function(temperature, juvenileTolerance, surface = 84810) {
S95 = eta * surface
S50 = S95 / theta
- beta = b / (a * c * (1 - exp(-b * delta_t)))
+ beta = b / (aFecundity * c * (1 - exp(-b * delta_t)))
res = S50 + (S95 - S50) * log(beta * log(19) / (S95 - S50)) / log(19)
res[is.nan(res)] = 0
@@ -99,18 +99,18 @@ stockAtCrash = function(temperature, juvenileTolerance, surface = 84810) {
}
-thermalBevertonHoltWithoutAllee = function(stock, temperature, juvenileTolerance, surface = 84810) {
+thermalBevertonHoltWithoutAllee = function(stock, temperature, juvenileTolerance, surface = 84810, aFecundity = 135000) {
survOptRep = 0.0017
delta_t = 0.33
lambda = 4.1E-4
- a = 135000 # ~fecondité
+
tempEffect = temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3] )
b = -log(survOptRep * tempEffect)/delta_t
c = lambda/surface
alpha = (b * exp(-b * delta_t)) / (c * (1 - exp(-b * delta_t)))
alpha[tempEffect == 0] = 0
- beta = b / (a * c * (1 - exp(-b * delta_t)))
+ beta = b / (aFecundity * c * (1 - exp(-b * delta_t)))
recruit = alpha * stock / (beta + stock )
return(recruit)
@@ -125,50 +125,53 @@ modifiedBevertonHolt = function(stock){
return(alpha * (stock^d) / ((beta^d) + (stock^d)))
}
-survivingRecruit = function(stock, temperature, juvenileTolerance, spawnerTolerance, sigmaZ, surface){
+survivingRecruit = function(stock, temperature, juvenileTolerance, spawnerTolerance, sigmaZ, surface, aFecundity){
survStock = stock * temperatureEffect(temperature, spawnerTolerance[1], spawnerTolerance[2], spawnerTolerance[3])
- recruit = thermalBevertonHolt(survStock, temperature, juvenileTolerance, surface)
+ recruit = thermalBevertonHolt(survStock, temperature, juvenileTolerance, surface, aFecundity)
survRecruit = recruit * exp(-sigmaZ)
return(survRecruit)
}
+spawnerTolerance = c(10, 20, 23) # Rougier 2014
+juvenileTolerance = c(9.8, 20, 26) # Rougier et al 2015
-spawnerTolerance = c(10, 20, 23)
-juvenileTolerance = c(9.8, 20, 26)
+# spawnerTolerance = c(10.7, 17, 25.7) # spawning temperature range Paumier et al 2019
+# juvenileTolerance = c(10.8, 20.8, 29.8) #tolerance temperature range Jatteau 2017
+#
-spawnerTolerance = c(10.7, 17, 25.7) # spawning temperature range Paumier et al 2019
+spawnerTolerance = c(10.7, 17, 25.7) # spawning temperature range Paumier et al 2019
juvenileTolerance = c(10.8, 20.8, 29.8) #tolerance temperature range Jatteau 2017
-Tmin = 8
-spawnerTolerance = c(Tmin, 20, 23)
-juvenileTolerance = c(Tmin, 16, 23)
+# Tmin = 8
+# spawnerTolerance = c(Tmin, 20, 23)
+# juvenileTolerance = c(Tmin, 16, 23)
sigmaZ = 0.4 * 5 # Z * lifespan of female
propFemale = 0.5
-
+aFecundity = 185000
# ================================ stock-recruitment relationship at 1900-1910 SPRING temperature ====
-ymax = 1e7
+ymax = 5e6
S = seq(0, 1e6, 100)
# with spawner mortality according to temperature
survS = S * temperatureEffect(TrefInRiver$Spring, spawnerTolerance[1], spawnerTolerance[2], spawnerTolerance[3])
-plot(S, thermalBevertonHolt(survS, TrefInRiver$Spring, juvenileTolerance, surface = surfaceBasin), type = 'l',
- xlab = 'Stock (female)', ylab = 'R (female and male)', ylim = c(0, ymax) )
-lines(S, thermalBevertonHolt(survS, TrefInRiver$Spring + 2, juvenileTolerance, surface = surfaceBasin), col = 'red')
-lines(S, thermalBevertonHolt(survS, TrefInRiver$Spring - 2, juvenileTolerance, surface = surfaceBasin), col = 'blue')
+plot(S, thermalBevertonHolt(survS, TrefInRiver$Spring, juvenileTolerance, surface = surfaceBasin, aFecundity) * propFemale, type = 'l',
+ xlab = 'Stock (female)', ylab = 'R (female)', ylim = c(0, ymax), main = riverName )
+lines(S, thermalBevertonHolt(survS, TrefInRiver$Spring + 1, juvenileTolerance, surface = surfaceBasin, aFecundity) * propFemale, col = 'red')
+lines(S, thermalBevertonHolt(survS, TrefInRiver$Spring - 1, juvenileTolerance, surface = surfaceBasin, aFecundity) * propFemale, col = 'blue')
# replacement line with prop of female in recruit
-lines(c(0, ymax * exp(-sigmaZ) * propFemale), c(0, ymax), col = 'green', lty = 2)
+lines(c(0, ymax * exp(-sigmaZ)), c(0, ymax), col = 'green', lty = 2)
# =============================== comparison with Rougier et al stock-recruitment relationship for the Garonne River ======
-tempe = TrefInRiver$Spring
-tempe = as.numeric(tempData %>%
- filter(Year > 1991 & Year <= 2009 & NOM == riverName) %>%
- summarize(meanSpring = mean(Spring), meanSummer = mean(summer)) )
-tempe = juvenileTolerance[2]
+#tempe = TrefInRiver$Spring
+#tempe = as.numeric(tempData %>%
+# filter(Year > 1991 & Year <= 2009 & NOM == riverName) %>%
+# summarize(meanSpring = mean(Spring), meanSummer = mean(summer)) )[1]
+#tempe = juvenileTolerance[2]
tempe = 20.2 # Rougier 2014
Stot = seq(0, 2e6, 1e4)
@@ -176,22 +179,24 @@ ymax = 1e7
survS = Stot * temperatureEffect(tempe, spawnerTolerance[1], spawnerTolerance[2], spawnerTolerance[3])
plot(Stot, thermalBevertonHolt(stock = survS * propFemale, temperature = tempe, juvenileTolerance = juvenileTolerance,
- surface = surfaceBasin),
+ surface = surfaceBasin, aFecundity = 135000),
type = 'l', xlab = 'Total stock (2 x female)', ylab = 'R (female and male)', ylim = c(0, ymax) )
# lines(Stot, thermalBevertonHolt(stock = survS, temperature = tempe, juvenileTolerance = juvenileTolerance, surface = surfaceBasin), lty = 3)
-lines(Stot, thermalBevertonHoltWithoutAllee(Stot * propFemale, tempe, juvenileTolerance, surface = surfaceBasin), col = 'blue')
+lines(Stot, thermalBevertonHoltWithoutAllee(Stot * propFemale, tempe, juvenileTolerance, surface = surfaceBasin, aFecundity = 135000), col = 'blue')
## lines(Stot, thermalBevertonHolt(Stot, tempe, juvenileTolerance), lty=2 )
lines(Stot, modifiedBevertonHolt(Stot), col = 'green') # for the Garonne River
# replacement line
lines(c(0, ymax * exp(-sigmaZ)), c(0, ymax), col = 'green', lty = 2)
# ===================================== stock at equilibrium =============================================================
-stocksAtEquilibrium = function(temperature, juvenileTolerance, spawnerTolerance, sigmaZ, surface, propFemale = 0.5) {
+# as coded in GR3D v3
+stocksAtEquilibrium = function(temperature, juvenileTolerance, spawnerTolerance, sigmaZ, surface, propFemale, aFecundity, pHoming) {
# !!!!! stock and recruit consider only females !!!!!!
- objFct = function(stock, temperature, juvenileTolerance, spawnerTolerance, sigmaZ, surface){
- survRecruit = survivingRecruit(stock, temperature, juvenileTolerance, spawnerTolerance, sigmaZ, surface) * propFemale
- return((survRecruit - stock)^2)
+ objFct = function(femaleStock, temperature, juvenileTolerance, spawnerTolerance, sigmaZ, surface, aFecundity, pHoming){
+ survFemaleRecruit = survivingRecruit(femaleStock, temperature, juvenileTolerance, spawnerTolerance, sigmaZ, surface, aFecundity) * propFemale
+ survFemaleRecruit = survFemaleRecruit * pHoming
+ return((survFemaleRecruit - femaleStock)^2)
}
stockatequilibrium = 0
@@ -199,29 +204,37 @@ stocksAtEquilibrium = function(temperature, juvenileTolerance, spawnerTolerance,
# stock at crash before the spawner mortality
tempEffSpawner = temperatureEffect(temperature, spawnerTolerance[1], spawnerTolerance[2], spawnerTolerance[3])
- stockatcrash = ifelse(tempEffSpawner > 0, stockAtCrash(temperature, juvenileTolerance, surface) / tempEffSpawner, 0)
+ stockatcrash = ifelse(tempEffSpawner > 0, stockAtCrash(temperature, juvenileTolerance, surface, aFecundity) / tempEffSpawner, 0)
if (stockatcrash > 0) {
recruitatcrash = thermalBevertonHolt(stockatcrash * tempEffSpawner,
- temperature, juvenileTolerance, surface) * propFemale
+ temperature, juvenileTolerance, surface, aFecundity) * propFemale
sigmaZatcrash = -log(stockatcrash / recruitatcrash)
+ Zhoming = -log(pHoming)
- if (sigmaZ < sigmaZatcrash) {
+ # pHoming is added after the mortatly at sea
+ if ((sigmaZ + Zhoming) < sigmaZatcrash) {
stockattrap = optimise(objFct, c(0, stockatcrash), temperature = temperature, juvenileTolerance = juvenileTolerance, spawnerTolerance = spawnerTolerance,
- sigmaZ = sigmaZ, surface = surface)$minimum
+ sigmaZ = sigmaZ, surface = surface, aFecundity = aFecundity, pHoming = pHoming)$minimum
stockatequilibrium = optimise(objFct, (c(1, 100) * stockatcrash), temperature = temperature, juvenileTolerance = juvenileTolerance, spawnerTolerance = spawnerTolerance,
- sigmaZ = sigmaZ, surface = surface)$minimum
+ sigmaZ = sigmaZ, surface = surface, aFecundity = aFecundity, pHoming = pHoming)$minimum
}
}
return(c(stockatequilibrium, stockattrap, stockatcrash))
}
+# ===== Parameters =================================================
temperature = seq(5,30,.1)
+aFecundity = 135000 * 2
+propFemale = .5
+pHoming = .75
-stocks = as.data.frame(t(sapply(temperature, function(temp) (stocksAtEquilibrium(temp, juvenileTolerance, spawnerTolerance, sigmaZ, surface = surfaceBasin)))))
+# == simulation of spawner mortality, reprpoduction, mortality at sea, homing ==========================================
+stocks = as.data.frame(t(sapply(temperature, function(temp) (stocksAtEquilibrium(temp, juvenileTolerance, spawnerTolerance, sigmaZ, surface = surfaceBasin,
+ propFemale = propFemale, aFecundity = aFecundity, pHoming = pHoming )))))
names(stocks) = c('atEquilibrium', 'atTrap', 'atCrash')
stocks$temperature = temperature
@@ -235,12 +248,10 @@ max(stocks$temperature[stocks$atEquilibrium == 0 & stocks$temperature < 20])
tempe = 14.4
stocks[stocks$temperature == tempe, ]
-
-
S = seq(0, 5e5, 1e3) # only females
recruit = thermalBevertonHolt(S * temperatureEffect(tempe, spawnerTolerance[1], spawnerTolerance[2], spawnerTolerance[3]),
- temperature = tempe, juvenileTolerance = juvenileTolerance, surface = surfaceBasin) * propFemale
+ temperature = tempe, juvenileTolerance = juvenileTolerance, surface = surfaceBasin, aFecundity = aFecundity ) * propFemale * pHoming
plot(S, recruit, type = 'l', xlab = 'Stock (# female)', ylab = 'Recruit (# of female)', main = paste(riverName, surfaceBasin))
lines(c(0, max(recruit) * exp(-sigmaZ)), c(0, max(recruit)), col = 'green', lty = 2)
@@ -257,7 +268,7 @@ points(sAtCrash, thermalBevertonHolt(sAtCrash * temperatureEffect(tempe, spawner
temperature = tempe, juvenileTolerance = juvenileTolerance, surface = surfaceBasin) * propFemale)
-# ==== recruitment according to temperature ===========================
+ # ==== recruitment according to temperature ===========================
# but need to fix a reference stock !
refStock = 1.5e6 / 2 # female !!!
temperature = seq(5,30,.1)
diff --git a/exploration/scriptR/TQ_Dordogne_Garonne.xlsx b/exploration/scriptR/TQ_Dordogne_Garonne.xlsx
new file mode 100644
index 0000000000000000000000000000000000000000..af02837c2281cd89671b16706fbe5e87d9015d72
Binary files /dev/null and b/exploration/scriptR/TQ_Dordogne_Garonne.xlsx differ
diff --git a/exploration/scriptR/allModels.R b/exploration/scriptR/allModels.R
new file mode 100644
index 0000000000000000000000000000000000000000..249b13637aa19a07034847f882cddb2bf8520316
--- /dev/null
+++ b/exploration/scriptR/allModels.R
@@ -0,0 +1,214 @@
+library(openxlsx)
+library(dplyr)
+library(tidyr)
+library(lubridate)
+
+library(insol)
+
+rm(list = ls())
+
+# ===== probability to spawn from BRT Paumier et al
+library(gbm)
+load("BTRarticle.RData")
+
+
+# ===== juvenile survival from Jatteau et al 2017 ===============================================================================
+dailySurvivalEmbryoCoeff = function(temperature, modelSurvivalEmbryoCoeff, parDurationIncubation){
+ sel = is.na(temperature)
+ temperature[sel] = 0
+ duration = (parDurationIncubation[1] * temperature ^ parDurationIncubation[2]) # remove the round() to smooth the curve
+ predict_matrix = model.matrix(~ Temp + I(Temp ^ 2) + I(Temp ^ 3), data = data.frame(Temp = temperature))
+ surv = (1 / (1 + exp(-predict_matrix %*% modelSurvivalEmbryoCoeff))) ^ (1 / duration)
+ surv[sel] = NA
+ return(surv)
+}
+
+cumulativeSurvivalEmbryoCoeff = function(temperature, modelSurvivalEmbryoCoeff){
+ sel = is.na(temperature)
+ temperature[sel] = 0
+ predict_matrix = model.matrix(~ Temp + I(Temp ^ 2) + I(Temp ^ 3), data = data.frame(Temp = temperature))
+ surv = (1 / (1 + exp(-predict_matrix %*% modelSurvivalEmbryoCoeff)))
+ surv[sel] = NA
+ return(surv)
+}
+
+dailySurvivalLarvaeCoeff = function(temperature, modelSurvivalLarvaeCoeff) {
+ sel = is.na(temperature)
+ temperature[sel] = 0
+ pred_matrix = model.matrix(~Temp + I(Temp^2) + I(Temp^3), data = data.frame(Temp = temperature))
+ surv = exp(-1/exp(pred_matrix %*% (modelSurvivalLarvaeCoeff)))
+ surv[sel] = NA
+ return(surv)
+}
+
+computeJuvenileSurvival = function(data, parDurationIncubation, modelSurvivalEmbryoCoeff, modelSurvivalLarvaeCoeff, horizon) {
+
+ data = data %>% select(one_of(c("date", "temperature"))) %>%
+ mutate(temperatureEmbryo = temperature ^ -parDurationIncubation[2]) %>%
+ mutate(dailyEmbryoSurvival = dailySurvivalEmbryoCoeff(temperature, modelSurvivalEmbryoCoeff, parDurationIncubation) ) %>%
+ mutate(dailyLarvalSurvival = dailySurvivalLarvaeCoeff(temperature, modelSurvivalLarvaeCoeff)) %>%
+ mutate(durationIncubation = NA, juvenileSurvival = NA)
+
+ for (t in (1:(nrow(data) - (horizon + 20)))) {
+ # compute duration of incubation
+ if (!is.na(data$temperatureEmbryo[t])) {
+ i = 0
+ while (sum(data$temperatureEmbryo[t:(t + i)]) < parDurationIncubation[1]) {
+ i = i + 1
+ if (is.na(sum(data$temperatureEmbryo[t:(t + i)]))) {
+ i = NA
+ break()
+ }
+ }
+ }
+ durationIncubation = i + 1
+ data$durationIncubation[t] = durationIncubation
+ if (!is.na(durationIncubation)) {
+ # cumulative survival of embryo
+ embryoSurvival = prod(data$dailyEmbryoSurvival[t:(t + durationIncubation - 1)])
+
+ # cumulative survival of larval until horizon days of hatch
+ larvalSurvival = prod(data$dailyLarvalSurvival[(t + durationIncubation):(t + durationIncubation + horizon - 1)])
+
+ # cumulative juvenile survival
+ data$juvenileSurvival[t] = embryoSurvival * larvalSurvival
+ }
+ }
+ return(data)
+}
+
+parDurationIncubation = c(1124.531453, -1.834438)
+modelSurvivalEmbryoCoeff = c(-1.245015E+01, 1.120331E+00 , -7.830614E-03, -6.112982E-04)
+modelSurvivalLarvaeCoeff = c(-1.851093E+00, 5.132855E-01, -1.020347E-02, -7.005887E-05 )
+horizon = 14
+
+
+# ==== Air temperature ===================================================================================================
+# données Safran (mises à disposition par Eric Sauquet)
+safranDordogne = read.csv("GARDONNE_T.txt", sep = " ", skip = 1, header = FALSE, col.names = c("date", "temperature")) %>%
+ mutate(date = as.Date(date), site = "Dordogne") %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3,6,9,12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(lien = paste(site, format(date, "%Y"), season, sep = "_"))
+safranGaronne = read.csv("LAMAGIST_T.txt", sep = " ", skip = 1, header = FALSE, col.names = c("date", "temperature")) %>%
+ mutate( date = as.Date(date), site = "Garonne") %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3,6,9,12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(lien = paste(site, format(date, "%Y"), season, sep = "_"))
+
+# ==== water temperature + probability to spawn from Paumier et al =======================================================
+# données EDF (mis à disposition par Elorri)
+dataDordogne = read.xlsx( xlsxFile = 'TQ_Dordogne_Garonne.xlsx', sheet = "Dordogne_1997_2018", detectDates = TRUE) %>%
+ select(one_of(c("date", "temperature", "debit" ))) %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3,6,9,12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(site = "Dordogne", lien = paste(site, format(date, "%Y"), season, sep = "_")) %>%
+ mutate(dayOfYear = yday(date), DL = daylength(lat = 44.8452, long = 0.4065, jd = dayOfYear, tmz = 1)[,3]) %>%
+ mutate(Temp1 = temperature, Q1 = log(debit)) %>%
+ mutate(deltaT1 = c(NA,diff(Temp1)) , deltaQ1 = c(NA,diff(Q1)), deltaDL1 = c(NA, diff(DL)))
+dataDordogne$pReproduce = predict.gbm(finalBrtPres, dataDordogne, n.trees = finalBrtPres$gbm.call$best.trees, type="response")
+dataDordogne$pReproduce[1] = NA
+dataDordogne$juvenileSurvival = computeJuvenileSurvival(dataDordogne, parDurationIncubation, modelSurvivalEmbryoCoeff, modelSurvivalLarvaeCoeff, horizon)$juvenileSurvival
+head(dataDordogne,5)
+
+dataGaronne = read.xlsx( xlsxFile = 'TQ_Dordogne_Garonne.xlsx', sheet = "Garonne_1976_2018", detectDates = TRUE) %>%
+ rename(date = Date) %>% select(one_of(c("date", "temperature", "debit"))) %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3,6,9,12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(site = "Garonne", lien = paste(site, format(date, "%Y"), season, sep = "_")) %>%
+ mutate(dayOfYear = yday(date), DL = daylength(lat = 44.1167, long = 0.8333, jd = dayOfYear, tmz = 1)[,3]) %>%
+ mutate(Temp1 = temperature, Q1 = log(debit)) %>%
+ mutate(deltaT1 = c(NA,diff(Temp1)) , deltaQ1 = c(NA,diff(Q1)), deltaDL1 = c(NA, diff(DL)))
+dataGaronne$pReproduce = predict.gbm(finalBrtPres, dataGaronne, n.trees = finalBrtPres$gbm.call$best.trees, type="response")
+dataGaronne$pReproduce[1] = NA
+dataGaronne$juvenileSurvival = computeJuvenileSurvival(dataGaronne, parDurationIncubation, modelSurvivalEmbryoCoeff, modelSurvivalLarvaeCoeff, horizon)$juvenileSurvival
+
+head(dataGaronne)
+
+rm(finalBrtPres)
+
+
+# combine data =========================================================================================================
+
+selectedSeason = c("spring", "winter","fall", "summer")
+# selectedSeason = c("spring", "winter")
+# selectedSeason = c("spring")
+dailyWaterTemperature = dataDordogne %>% bind_rows(dataGaronne) %>% filter(season %in% selectedSeason) %>% rename(waterTemperature = temperature)
+waterData = dailyWaterTemperature %>% group_by(lien, season) %>% summarize(meanWaterTemp = mean(waterTemperature))
+
+head(waterData)
+dailyAirTemperature = safranDordogne %>% bind_rows(safranGaronne) %>% filter(season %in% selectedSeason) %>% rename(airTemperature = temperature)
+airData = dailyAirTemperature %>% group_by(lien, season) %>% summarize(meanAirTemp = mean(airTemperature))
+
+myData = waterData %>% left_join(airData, by = c("lien", "season"))
+myDailyData = dailyWaterTemperature %>% left_join(dailyAirTemperature %>% select(one_of(c("date", "airTemperature", "site"))), by = c("date", "site"))
+
+head(myDailyData)
+
+weightedJuvSurvival = myDailyData %>% mutate(pReproduce = replace_na(pReproduce, 0)) %>% group_by(lien, season) %>% summarise(meanWaterTemp = mean(waterTemperature), meanAirTemp = mean(airTemperature),
+ meanSurvival = weighted.mean(x = juvenileSurvival, w = pReproduce, na.rm = TRUE))
+head(weightedJuvSurvival)
+
+temperature = seq(5,30,.1)
+plot(weightedJuvSurvival$meanAirTemp, weightedJuvSurvival$meanSurvival, pch=20, xlim=range(temperature), ylim=c(0,1),
+ col = c("red", "blue", "yellow", "green")[as.factor(weightedJuvSurvival$season)])
+legend("topleft", legend = c("winter", "spring", "summer", "fall"), col = c("red", "blue", "yellow", "green"), lty = -1, pch = 20)
+
+
+embryoSurvival = cumulativeSurvivalEmbryoCoeff(temperature, modelSurvivalEmbryoCoeff)
+larvalSurvival = dailySurvivalLarvaeCoeff(temperature, modelSurvivalLarvaeCoeff)^horizon
+points(weightedJuvSurvivalSplash$meanWaterTemp, weightedJuvSurvivalSplash$meanSurvival, pch = 20, col = 'darkblue')
+
+lines(temperature, embryoSurvival * larvalSurvival, col = 'red')
+lines(temperature, temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3]) * max(embryoSurvival * larvalSurvival), col = "blue")
+#legend("topleft", legend = c("uniform bull", "observed splash", "juvenile tolerance", "temperature effect"),
+# pch = c(20,20,-1,-1), lty = c(0,0, 1,1), col = c('black', 'green', 'red', "blue"))
+
+
+# with fake day of the year ====================================
+myDailyDataFake = myDailyData %>% mutate(fakeDayOfYear = case_when(season == "winter" ~ dayOfYear + 90,
+ season == "spring" ~ dayOfYear,
+ season == "summer" ~ dayOfYear - 91,
+ season == " winter" ~ dayOfYear - 183)) %>%
+ mutate(DL = case_when(site == "Garonne" ~ daylength(lat = 44.1167, long = 0.8333, jd = fakeDayOfYear, tmz = 1)[,3],
+ site == "Dordogne" ~ daylength(lat = 44.8452, long = 0.4065, jd = fakeDayOfYear, tmz = 1)[,3])) %>%
+ mutate(deltaDL1 = c(NA, diff(DL)))
+myDailyDataFake$pReproduceFake = predict.gbm(finalBrtPres, myDailyDataFake, n.trees = finalBrtPres$gbm.call$best.trees, type="response")
+myDailyDataFake$pReproduceFake[1] = NA
+head(myDailyDataFake)
+
+
+
+weightedJuvSurvivalFake = myDailyDataFake %>% mutate(pReproduceFake = replace_na(pReproduceFake, 0)) %>% group_by(lien, season) %>%
+ summarise(meanWaterTemp = mean(waterTemperature), meanAirTemp = mean(airTemperature),
+ meanSurvival = weighted.mean(x = juvenileSurvival, w = pReproduceFake))
+
+
+plot(weightedJuvSurvivalFake$meanAirTemp, weightedJuvSurvivalFake$meanSurvival, pch = 20, xlim = range(temperature), ylim = c(0,1),
+ col = c("red", "blue", "yellow", "green")[as.factor(weightedJuvSurvivalFake$season)])
+legend("topleft", legend = c("winter", "spring", "summer", "fall"), col = c("red", "blue", "yellow", "green"), lty = -1, pch = 20)
+
+
+weightedJuvSurvivalFake %>% filter(season == "summer" & meanSurvival <.45)
+
+myDailyDataFake %>% filter(between(date, as.Date("2003-06-25"), as.Date("2003-07-10")), site == 'Dordogne' )
+
+# calibration ============================================================================================
+objFun = function(par, observationData) {
+ SE = (observationData$meanSurvival - par[4] * Rosso2(observationData$meanAirTemp, par))^2
+ return(sum(SE, na.rm = TRUE))
+}
+
+objFunLehman = function(par, observationData) {
+ SE = (observationData$meanSurvival - par[4] * modifiedLehman(observationData$meanAirTemp, par))^2
+ return(sum(SE, na.rm = TRUE))
+}
+
+data = weightedJuvSurvivalFake %>% drop_na()
+resRosso2 = nlm(objFun, p = c(10,17,25,.6), observationData = data)
+resLehman = nlm(objFunLehman, p = c(10,17,25,.6), observationData = data)
+
+print(resRosso2)
+plot(data$meanAirTemp, data$meanSurvival, pch=20, xlim = range(temperature), ylim=c(0,1),
+ col = c("red", "blue", "yellow", "green")[as.factor(data$season)])
+legend("topleft", legend = c("winter", "spring", "summer", "fall"), col = c("red", "blue", "yellow", "green"), lty = -1, pch = 20)
+# lines(temperature, Rosso2(temperature, juvenileTolerance) * max(embryoSurvival * larvalSurvival), col = "blue", lty =2)
+lines(temperature, Rosso2(temperature, resRosso2$estimate[1:3]) * resRosso2$estimate[4], col = "blue")
+lines(temperature, modifiedLehman(temperature, resLehman$estimate[1:3]) * resLehman$estimate[4], col ='cyan')
+
diff --git a/exploration/scriptR/journVSsaison.R b/exploration/scriptR/journVSsaison.R
index 74692ad7a068a5b70cbc17845fe3dfd396df49a8..c8c7ed9e8b7536f5cdd7f6d6e6a150d5321ff00c 100644
--- a/exploration/scriptR/journVSsaison.R
+++ b/exploration/scriptR/journVSsaison.R
@@ -1,4 +1,5 @@
library(dplyr)
+library(tidyr)
library(survival)
library(lme4)
#library(pracma)
@@ -28,7 +29,7 @@ dailySurvivalLarvae = function(temperature, modelSurvivalLarvae) {
return(surv)
}
-# with lme coeff
+# directly with coeff
dailySurvivalEmbryoCoeff = function(temperature, modelSurvivalEmbryoCoeff, parDurationIncubation){
sel = is.na(temperature)
temperature[sel] = 0
@@ -39,6 +40,16 @@ dailySurvivalEmbryoCoeff = function(temperature, modelSurvivalEmbryoCoeff, parDu
return(surv)
}
+cumulativeSurvivalEmbryoCoeff = function(temperature, modelSurvivalEmbryoCoeff){
+ sel = is.na(temperature)
+ temperature[sel] = 0
+ predict_matrix = model.matrix(~ Temp + I(Temp ^ 2) + I(Temp ^ 3), data = data.frame(Temp = temperature))
+ surv = (1 / (1 + exp(-predict_matrix %*% modelSurvivalEmbryoCoeff)))
+ surv[sel] = NA
+ return(surv)
+}
+
+
dailySurvivalLarvaeCoeff = function(temperature, modelSurvivalLarvaeCoeff) {
sel = is.na(temperature)
temperature[sel] = 0
@@ -54,34 +65,219 @@ modelSurvivalLarvaeCoeff = c(-1.851093E+00, 5.132855E-01, -1.020347E-02, -7.005
horizon = 14
temperature = seq(5,35,.1)
-embryoSurvival = dailySurvivalEmbryoCoeff(temperature, modelSurvivalEmbryoCoeff, parDurationIncubation)
+embryoSurvival = cumulativeSurvivalEmbryoCoeff(temperature, modelSurvivalEmbryoCoeff)
larvalSurvival = dailySurvivalLarvaeCoeff(temperature, modelSurvivalLarvaeCoeff)^horizon
-plot(temperature, embryoSurvival, type = 'l')
-lines(temperature, larvalSurvival)
-
-plot(temperature, embryoSurvival * larvalSurvival, type = 'l')
+plot(temperature, embryoSurvival, type = 'l', col = 'blue')
+lines(temperature, larvalSurvival, col = 'green')
+lines(temperature, embryoSurvival * larvalSurvival, col = 'red' )
+legend("topright", legend = c("embryo", "larval", "cumulative"), col = c('blue', 'green', 'red'), lty = 1)
-temperature = seq(5, 30,.1)
+# duration of hatching
duration = (parDurationIncubation[1] * temperature ^ parDurationIncubation[2])
-plot(temperature, duration, type ='l')
+plot(temperature, duration, type = 'l')
+
+# ===== comparison between Jatteau and Rosso equation =================================
+temperatureEffect = function(tempWater, TminRep, ToptRep, TmaxRep){
+ response = (tempWater - TminRep) * (tempWater - TmaxRep) / ((tempWater - TminRep) * (tempWater - TmaxRep) - (tempWater - ToptRep)^2)
+ response[tempWater <= TminRep | tempWater >= TmaxRep] = 0
+ return(response)
+}
+
+juvenileTolerance = c(10.8, 20.8, 29.8) #tolerance temperature range Jatteau 2017
+plot(temperature, embryoSurvival * larvalSurvival, type = 'l', col = 'red', ylim = c(0,1))
+lines(temperature, temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3] ))
+
+cbind(temperature, embryoSurvival * larvalSurvival)
+
+# new juvenile tolerance range at 1% =============================
+c(9.7, 20.8, 30.7)
+temperature[which.max(embryoSurvival * larvalSurvival)]
+max(temperature[(embryoSurvival * larvalSurvival) <= (0.01 * max(embryoSurvival * larvalSurvival)) & temperature < temperature[which.max(embryoSurvival * larvalSurvival)] ])
+min(temperature[(embryoSurvival * larvalSurvival) <= (0.01 * max(embryoSurvival * larvalSurvival)) & temperature > temperature[which.max(embryoSurvival * larvalSurvival)] ])
+
+# ==== stock recruitment relationship accoring to temperature
+thermalBevertonHolt = function(stock, temperature, juvenileTolerance, surface = 84810, aFecundity = 135000) {
+ survOptRep = 0.0017
+ delta_t = 0.33
+ lambda = 4.1E-4
+ # a ~ fecondité
+ tempEffect = temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3] )
+ b = -log(survOptRep * tempEffect)/delta_t
+ c = lambda/surface
+
+ eta = 2.4
+ theta = 1.9
+ #theta = 1.15
+ S95 = eta * surface
+ S50 = S95 / theta
+
+ AlleeEffect = 1 / (1 + exp(-log(19) * (stock - S50) / (S95 - S50)))
+
+ alpha = (b * exp(-b * delta_t)) / (c * (1 - exp(-b * delta_t)))
+ alpha[tempEffect == 0] = 0
+ beta = b / (aFecundity * c * (1 - exp(-b * delta_t)))
+
+ recruit = alpha * stock * AlleeEffect / (beta + stock * AlleeEffect)
+ return(recruit)
+}
+
+
+
+plot(temperature, (embryoSurvival * larvalSurvival) / (embryoSurvival * larvalSurvival)[temperature == juvenileTolerance[2]] , type = 'l', col = 'red', ylim = c(0,1), ylab = 'suvival / survival(Topt)' )
+lines(temperature, temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3] ), lty = 2)
+lines(temperature, sapply(temperature, function(temp) (thermalBevertonHolt(stock = 84810 * 3, temperature = temp, juvenileTolerance = juvenileTolerance, aFecundity = 135000 * 2))) /
+ thermalBevertonHolt(stock = 84810 * 3, temperature = juvenileTolerance[2] , juvenileTolerance = juvenileTolerance, aFecundity = 135000 * 2))
+legend('topleft', legend = c("Jatteau et al", "GR3D temp effect", "GR3D S-R rel."), lty = c(1,2,1), col = c("red", "black", "black"))
# ==== observed data ========================================================================
envGGD = read.csv("envCondition.csv", sep = ";")
repro = read.csv("reproMonitoring.csv", sep = ";")
-envGGD = envGGD %>% mutate(dateC = as.character(date), date = as.Date(date)) %>% mutate(month = format(date, '%m'))
-repro = repro %>% mutate(dateC = as.character(date), date = as.Date(date)) %>% mutate(month = format(date, '%m'))
+envGGD = envGGD %>% mutate(date = as.Date(date)) %>% mutate(month = format(date, '%m')) %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3, 6, 9, 12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(lien = paste(lien, season, sep = '_'))
+
+
+repro = repro %>% mutate(date = as.Date(date)) %>% mutate(month = format(date, '%m')) %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3, 6, 9, 12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(lien = paste(lien, season, sep = '_'))
+
+
+selectedSeason = c("spring")
+elabData = envGGD %>% select(one_of(c("lien", "date", "season", "Temp1", "juvenileSurvival"))) %>% left_join(select(repro, one_of(c("lien", "date", "Bulls", "BullsRelative"))), by = c("lien", "date")) %>%
+ filter(season %in% selectedSeason)
+
+juvSurvival = elabData %>% group_by(lien) %>% summarise(meanWaterTemp = mean(Temp1), meanSurvival = mean(juvenileSurvival, na.rm = TRUE))
+weightedJuvSurvivalSplash = elabData %>% mutate(Bulls = replace_na(Bulls, 0)) %>% group_by(lien) %>% summarise(meanWaterTemp = mean(Temp1),
+ meanSurvival = weighted.mean(x = juvenileSurvival, w = Bulls, na.rm = TRUE))
+
+plot(juvSurvival$meanWaterTemp, juvSurvival$meanSurvival, pch = 20, xlim = c(10,30), ylim = c(0,1),
+ xlab = ' water temperature', ylab = 'juvenile survival')
+points(weightedJuvSurvivalSplash$meanWaterTemp, weightedJuvSurvivalSplash$meanSurvival, pch = 20, col = 'green')
+
+lines(temperature, embryoSurvival * larvalSurvival, col = 'red')
+lines(temperature, temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3]), col = "blue")
+legend("topleft", legend = c("uniform bull", "observed splash", "juvenile tolerance", "temperature effect"),
+ pch = c(20,20,-1,-1), lty = c(0,0, 1,1), col = c('black', 'green', 'red', "blue"))
+
+# run code to upload SAFRAN data
+weightedJuvSurvival = weightedJuvSurvival %>% left_join(airData, by = 'lien')
+
+
+# ==== water temperature versus air temperature
+library(openxlsx)
+
+# données EDF (mis à disposition par Elorri)
+dataDordogne = read.xlsx( xlsxFile = 'TQ_Dordogne_Garonne.xlsx', sheet = "Dordogne_1997_2018", detectDates = TRUE) %>%
+ select(one_of(c("date", "temperature"))) %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3,6,9,12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(site = "Dordogne", lien = paste(site, format(date, "%Y"), season, sep = "_"))
+dataGaronne = read.xlsx( xlsxFile = 'TQ_Dordogne_Garonne.xlsx', sheet = "Garonne_1976_2018", detectDates = TRUE) %>%
+ rename(date = Date) %>% select(one_of(c("date", "temperature"))) %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3,6,9,12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(site = "Garonne", lien = paste(site, format(date, "%Y"), season, sep = "_"))
+
+# données Safran (mises à disposition par Eric Sauquet)
+safranDordogne = read.csv("GARDONNE_T.txt", sep = " ", skip = 1, header = FALSE, col.names = c("date", "temperature")) %>%
+ mutate(date = as.Date(date), site = "Dordogne") %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3,6,9,12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(lien = paste(site, format(date, "%Y"), season, sep = "_"))
+safranGaronne = read.csv("LAMAGIST_T.txt", sep = " ", skip = 1, header = FALSE, col.names = c("date", "temperature")) %>%
+ mutate( date = as.Date(date), site = "Garonne") %>%
+ mutate(season = cut(as.numeric(format(date, '%m')), breaks = c(0, 3,6,9,12), labels = c("winter", "spring", "summer" , "fall"))) %>%
+ mutate(lien = paste(site, format(date, "%Y"), season, sep = "_"))
+
+# myData
+# selectedSeason = c("spring", "winter","fall", "summer")
+# selectedSeason = c("spring", "winter")
+selectedSeason = c("spring")
+dailyWaterTemperature = dataDordogne %>% bind_rows(dataGaronne) %>% filter(season %in% selectedSeason)
+waterData = dailyWaterTemperature %>% group_by(lien, season) %>% summarize(meanWaterTemp = mean(temperature))
+
+dailyAirTemperature = safranDordogne %>% bind_rows(safranGaronne) %>% filter(season %in% selectedSeason)
+airData = dailyAirTemperature %>% group_by(lien, season) %>% summarize(meanAirTemp = mean(temperature))
+
+myData = waterData %>% left_join(airData, by = c("lien", "season"))
+myDailyData = dailyWaterTemperature %>% rename(waterTemperature = temperature) %>% left_join(dailyAirTemperature %>% rename(airTemperature = temperature), by = c("date"))
+
+# seasonal average
+plot(myData$meanWaterTemp, myData$meanAirTemp, xlab = "seasonal average WATER temperature", ylab = "seasonal average AIR temperature", pch = 20,
+ col = c("red", "blue", "yellow", "green")[as.factor(myData$season)])
+legend("topleft", legend = c("winter", "spring", "summer", "fall"), col = c("red", "blue", "yellow", "green"), lty = 1)
+#text(myData$meanWaterTemp, myData$meanAirTemp, myData$lien, cex=.5, pos=2)
+airWaterLm = lm(meanAirTemp ~ meanWaterTemp , data = myData)
+summary(airWaterLm)
+abline(reg = airWaterLm, col = 'blue')
+abline(coef = c(0,1), lty = 2)
+
+rbind(spawnerTolerance, predict(airWaterLm, newdata = data.frame(meanWaterTemp = spawnerTolerance, season = "spring") ))
+rbind(juvenileTolerance, predict(airWaterLm, newdata = data.frame(meanWaterTemp = juvenileTolerance, season = "spring") ))
+
+# ==== daily values ==================================================================
+# see Santiago, J. M., GarcÃa de Jalón, D., Alonso, C., Solana, J., Ribalaygua, J., Pórtoles, J. & Monjo, R. (2016) Brown trout thermal niche
+# and climate change: expected changes in the distribution of cold-water fish in central Spain. Ecohydrology 9, 514–528.
+# Mohseni, O., Stefan, H. G. & Erickson, T. R. (1998) A nonlinear regression model for weekly stream temperatures.
+# Water Resources Research 34, 2685–2692.
+
+
+plot(myDailyData$waterTemperature, myDailyData$airTemperature, pch = 20, col = 'grey',
+ xlab = "WATER temperature", ylab = "AIR temperature")
+points(myData$meanWaterTemp, myData$meanAirTemp, pch = 20, col = 'blue')
+
+legend("topleft", legend = c( "daily", "seasonal average"), col = c("grey", "blue"), pch = 20)
+abline(coef = c(0,1), lty = 2)
+daylyLm = lm(airTemperature ~ waterTemperature , data = myDailyData)
+summary(daylyLm)
+
+rbind(spawnerTolerance, predict(daylyLm, newdata = data.frame(waterTemperature = spawnerTolerance, season = "spring") ))
+rbind(juvenileTolerance, predict(daylyLm, newdata = data.frame(waterTemperature = juvenileTolerance, season = "spring") ))
+abline(reg = daylyLm, col = 'black')
+
+modifiedMohseni = function(airTemperature, par){
+ mu = par[1] # the estimated minimum stream temperature
+ alpha = par[2] # the estimated maximum stream temperature
+ beta = par[3] # the air temperature at which the rate of change of the stream temperature with respect to the air temperature is at a maximum
+ gamma = par[4] # the value of the rate of change at β.
+ lambda = par[5] # a coefï¬cient representing the resistance of DMST to change with respect to DMAT variation in one day (ΔTa).
+
+ deltaAirTemperature = c(NA, diff(airTemperature))
+ waterTemperature = mu + lambda * deltaAirTemperature + (alpha - mu) / (1 + exp(gamma * (beta - airTemperature)))
+
+ return(waterTemperature)
+}
+
+SSE = function(par, obsAirTemperature, obsWaterTemperature){
+ return(sum((modifiedMohseni(obsAirTemperature, par) - obsWaterTemperature)^2, na.rm = TRUE))
+}
+
+daylyNLM = nlm(f = SSE, p = c(5, 30, 15, .2, .1), obsAirTemperature = myDailyData$airTemperature, obsWaterTemperature = myDailyData$waterTemperature )
+
+daylyLM = lm(waterTemperature ~ airTemperature, data = myDailyData)
+
+hist(modifiedMohseni( myDailyData$airTemperature, par = daylyNLM$estimate ) - myDailyData$waterTemperature, breaks = 50)
+hist(predict.lm(daylyLM, newdata = myDailyData) - myDailyData$waterTemperature, breaks = 50)
+summary(lm(modifiedMohseni( myDailyData$airTemperature, par = daylyNLM$estimate ) ~ myDailyData$waterTemperature))
+summary(daylyLM)
-elabData = envGGD %>% left_join(select(repro, one_of(c("lien", "dateC", "Bulls", "BullsRelative"))), by = c("lien", "dateC")) %>%
- filter(month %in% c('04', '05', '06'))
+plot(myDailyData$airTemperature, myDailyData$waterTemperature, pch = 20, col = 'grey',
+ xlab = "AIR temperature", ylab = "WATER temperature")
-myData = elabData %>% group_by(lien) %>% summarise(meanWaterTemp = mean(Temp1), meanSurvival = mean(juvenileSurvival, na.rm = TRUE))
+# ===== survival according to air or water temperature ==============================
+plot(weightedJuvSurvival$meanWaterTemp, weightedJuvSurvival$meanSurvival, pch = 20, xlim = c(10,30), ylim = c(0,1),
+ xlab = 'temperature', ylab = 'juvenile survival', col = 'green')
+points(weightedJuvSurvival$meanAirTemp, weightedJuvSurvival$meanSurvival, pch = 20, col = 'darkgreen')
+lines(temperature, embryoSurvival * larvalSurvival, col = 'red')
+lines(temperature, temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3]), col = "blue")
+legend("topright", legend = c("water temperature", "air temperature", "juvenile tolerance", "temperature effect"),
+ col = c("green", "darkgreen", 'red', 'blue'), pch = c(20, 20, -1,-1), lty = c(0,0,1,1),, cex = .8)
+plot(juvSurvival$meanWaterTemp, juvSurvival$meanSurvival, pch = 20, xlim = c(10,30), ylim = c(0,1),
+ xlab = ' water temperature', ylab = 'juvenile survival')
+points(weightedJuvSurvival$meanWaterTemp, weightedJuvSurvival$meanSurvival, pch = 20, col = 'green')
-plot(elabData$Temp1, elabData$juvenileSurvival, pch = 20, col = "grey", xlim = c(10,30), ylim = c(0,1),
- xlab = 'water temperature', ylab = 'juvenile survival')
-points(myData$meanWaterTemp, myData$meanSurvival)
-lines(temperature, embryoSurvival * larvalSurvival)
-
\ No newline at end of file
+lines(temperature, embryoSurvival * larvalSurvival, col = 'red')
+lines(temperature, temperatureEffect(temperature, juvenileTolerance[1], juvenileTolerance[2], juvenileTolerance[3]), col = "blue")
+legend("topleft", legend = c("uniform bull", "observed splash", "juvenile tolerance", "temperature effect"),
+ pch = c(20,20,-1,-1), lty = c(0,0, 1,1), col = c('black', 'green', 'red', "blue"))
diff --git a/exploration/scriptR/temperatureEffects.R b/exploration/scriptR/temperatureEffects.R
new file mode 100644
index 0000000000000000000000000000000000000000..0b201eabcf8dfd4e8dba705a970236331264f302
--- /dev/null
+++ b/exploration/scriptR/temperatureEffects.R
@@ -0,0 +1,250 @@
+
+rm(list = ls())
+
+Ratkowsky = function(temperature, par){
+ # Ratkowsky, D. A., McMEEKIN, T. A. & Chandler, R. E. (1983) Model for Bacterial Culture Growth Rate Throughout the Entire
+ # Biokinetic Temperature Range. J. BACTERIOL. 154, 5.
+
+ # see Shi, P.-J., Reddy, G. V. P., Chen, L. & Ge, F. (2016) Comparison of Thermal Performance Equations in Describing Temperature-Dependent
+ # Developmental Rates of Insects: (I) Empirical Models. Annals of the Entomological Society of America 109, 211–215.
+
+ #
+ # Li, W. K. & Dickie, P. M. (1987) Temperature characteristics of photosynthetic and heterotrophic activities: seasonal
+ # variations in temperate microbial plankton. Applied and Environmental Microbiology 53, 2282–2295.
+ # Lowâ€Décarie, E., Boatman, T. G., Bennett, N., Passfield, W., Gavalásâ€Olea, A., Siegel, P. & Geider, R. J. (2017) Predictions
+ # of response to temperature are contingent on model choice and data quality. Ecology and Evolution 7, 10467–10481.
+ # Grimaud, G. M., Mairet, F., Sciandra, A. & Bernard, O. (2017) Modeling the temperature effect on the specific growth rate of
+ # phytoplankton: a review. Reviews in Environmental Science and Bio/Technology 16, 625–645.
+
+
+ Tmin = par[1]
+ Tmax = par[2]
+ a = par[3] # give the extent of change in rate for unit change in temperature below Topt
+ b = par[4] # give the extent of change in rate for unit change in temperature above Topt
+
+ rate = ((a * (temperature - Tmin))^2) * ((1 - exp(b * (temperature - Tmax)))^2)
+
+ rate[!between(temperature, Tmin, Tmax)] = 0
+ return(rate)
+}
+
+
+temperature = seq(0, 35, .1)
+Tmin = 10
+Tmax = 25
+
+temperature = seq(Tmin, Tmax, .1)
+plot(temperature, Ratkowsky(temperature, par = c(Tmin, Tmax, .2, .2)), type = 'l', ylab = 'rate', mmain = 'Ratkowsky')
+lines(temperature, Ratkowsky(temperature, par = c(Tmin, Tmax, .3, .1)), col = 2)
+lines(temperature, Ratkowsky(temperature, par = c(Tmin, Tmax, .1, .3)), col = 3)
+
+modifiedLehman = function(temperature, par){
+ # Svirezhev, Yu. M., Krysanova, V. P. & Voinov, A. A. (1984) Mathematical modelling of a fish pond ecosystem.
+ # Ecological Modelling 21, 315–337.
+
+ Tmin = par[1]
+ Topt = par[2]
+ Tmax = par[3]
+
+ # rate(Tmin or Tmax) = exp(-4.6) = 1 %
+
+ rate = rep(0, length(temperature))
+ rate[temperature < Topt] = exp(-4.6 * ((Topt - temperature[temperature < Topt]) / (Topt - Tmin))^4)
+ rate[temperature >= Topt] = exp(-4.6 * ((temperature[temperature >= Topt] - Topt) / (Tmax - Topt))^4)
+
+ return(rate)
+}
+
+Tmin = 10
+Topt = 20
+Tmax = 30
+
+plot(temperature, modifiedLehman(temperature, par = c(Tmin, Topt, Tmax)), ylab = 'rate', type = 'l', main = ' modified Lehman')
+temperature[which.max(modifiedLehman(temperature, par = c(Tmin, Topt, Tmax)))]
+
+Rosso1 = function(temperature, par){
+ # Rosso, L., Lobry, J. R. & Flandrois, J. P. (1993) An Unexpected Correlation between Cardinal Temperatures of Microbial Growth Highlighted
+ # by a New Model. Journal of Theoretical Biology 162, 447–463.
+ # Rosso, L., Lobry, J. R., Bajard, S. & Flandrois, J. P. (1995) Convenient model to describe the combined effects of temperature
+ # and pH on microbial growth. Applied and Environmental Microbiology 61, 610–616.
+
+ Tmin = par[1]
+ Topt = par[2]
+ Tmax = par[3]
+
+ rate = ((temperature - Tmax) * (temperature - Tmin)^2) /
+ ((Topt - Tmin) * ((Topt - Tmin) * (temperature - Topt) - (Topt - Tmax) * (Topt + Tmin - 2 * temperature)))
+
+ rate[temperature <= Tmin | temperature >= Tmax] = 0
+
+ return(rate)
+}
+
+Rosso2 = function(temperature, par){
+ # with an inflexion point below Topt
+ #
+ # Rosso, L., Lobry, J. R., Bajard, S. & Flandrois, J. P. (1995) Convenient model to describe the combined effects of temperature
+ # and pH on microbial growth. Applied and Environmental Microbiology 61, 610–616.
+ # Grimaud, G. M., Mairet, F., Sciandra, A. & Bernard, O. (2017) Modeling the temperature effect on the specific growth rate of
+ # phytoplankton: a review. Reviews in Environmental Science and Bio/Technology 16, 625–645.
+
+ # Rougier, T., Drouineau, H., Dumoulin, N., Faure, T., Deffuant, G., Rochard, E. & Lambert, P. (2014) The GR3D model, a tool to explore
+ # the Global Repositioning Dynamics of Diadromous fish Distribution. Ecological Modelling 283, 31–44.
+ # Kielbassa, J., Delignette-Muller, M. L., Pont, D. & Charles, S. (2010) Application of a temperature-dependent von Bertalanffy growth
+ # model to bullhead (Cottus gobio). Ecological Modelling 221, 2475–2481.
+
+
+
+ Tmin = par[1]
+ Topt = par[2]
+ Tmax = par[3]
+
+ rate = (temperature - Tmin) * (temperature - Tmax) / ((temperature - Tmin) * (temperature - Tmax) - (temperature - Topt)^2)
+
+ rate[temperature <= Tmin | temperature >= Tmax] = 0
+
+ return(rate)
+}
+
+Tmin = 10
+Topt = 22
+Tmax = 25
+plot(temperature, Rosso2(temperature, par = c(Tmin, Topt, Tmax)), ylab = 'rate', type = 'l')
+lines(temperature, Rosso1(temperature, par = c(Tmin, Topt, Tmax)), col = 2)
+legend("topleft", legend = c("Rosso1 (GR3D)", "Rosso2"), lty = 1, col = c(1,2))
+
+
+Blanchard = function(temperature, par){
+ # Grimaud, G. M., Mairet, F., Sciandra, A. & Bernard, O. (2017) Modeling the temperature effect on the specific growth rate of
+ # phytoplankton: a review. Reviews in Environmental Science and Bio/Technology 16, 625–645.
+
+ Topt = par[1]
+ Tmax = par[2]
+ beta = par[3]
+
+ rate = (((Tmax - temperature) / (Tmax - Topt))^beta) * exp(-beta * (Topt - temperature) / (Tmax - Topt))
+ rate[is.na(rate)] = 0
+ rate[temperature > Tmax] = 0
+ return(rate)
+ }
+
+Topt = 22
+Tmax = 25
+betas = c(1.1, 2, 4)
+plot(temperature, Blanchard(temperature, par = c(Topt, Tmax, betas[1])), ylab = 'rate', type = 'l', main = "Blanchard")
+for (i in (2:length(betas))){
+ lines(temperature, Blanchard(temperature, par = c(Topt, Tmax, betas[i])), col =i)
+}
+legend("topleft", legend = paste0("betas = ", betas), lty = 1, col = 1 : length(betas))
+
+EppleyNorberg = function(temperature, par){
+ # Eppley, R. W. (1972) Temperature and phytoplankton growth in the sea. Fish. bull 70, 1063–1085.
+ # Norberg, J. (2004) Biodiversity and ecosystem functioning: A complex adaptive systems approach.
+ # Limnology and Oceanography 49, 1269–1277.
+ #
+ # Grimaud, G. M., Mairet, F., Sciandra, A. & Bernard, O. (2017) Modeling the temperature effect on the specific growth rate of
+ # phytoplankton: a review. Reviews in Environmental Science and Bio/Technology 16, 625–645.
+
+ w = par[1] # the thermal niche width
+ z = par[2] # the temperature at which the growth rate is equal to the Eppley function and is a proxy of Topt
+ a = par[3] #
+ b = par[4] #
+
+ rate = (1 - ((temperature - z) / w)^2) * a * exp(b * temperature)
+ rate[rate < 0] = 0
+ return(rate)
+}
+
+plot(temperature, EppleyNorberg(temperature, par = c(10, 20 , .6,.06)), type = 'l', ylab = 'rate', main = "EppleyNorberg")
+
+
+modifiedMasterReaction = function(temperature, par){
+ # Corkrey, R., McMeekin, T. A., Bowman, J. P., Ratkowsky, D. A., Olley, J. & Ross, T. (2014) Protein Thermodynamics Can Be Predicted
+ # Directly from Biological Growth Rates. PLoS ONE 9, e96100.
+
+
+ # Grimaud, G. M., Mairet, F., Sciandra, A. & Bernard, O. (2017) Modeling the temperature effect on the specific growth rate of
+ # phytoplankton: a review. Reviews in Environmental Science and Bio/Technology 16, 625–645.
+
+ TinK = temperature + 273.15
+
+ deltaH_star = 4874 # enthalpy change (J/mol amino acid residue)
+ T_H_star = 375.5 # conergence temperaure for enthalpy (K)
+ deltaS_star = 17.0 # entropy change (J / K)
+ T_S_star = 390.9 # convergence temperature fot entropy (K)
+ R = 8.314 # gaz constant (J/ K mol)
+
+ deltaH_A = par[1] # enthalpy activation (J / mol)
+ deltaCp = par[2] # the heat capacity change (J/mol amino acid residue)
+ n = par[3] # the number of amino acid residues
+ c = par[4] # scaling constant
+
+ rate = TinK * exp(c - deltaH_A / (R * TinK)) /
+ (1 + exp(-n * (deltaH_star - TinK * deltaS_star + deltaCp * (TinK - T_H_star - TinK * log(TinK / T_S_star))) / (R * TinK)))
+
+ return(rate)
+}
+
+
+temperature = seq(0,100,.1)
+plot(temperature, modifiedMasterReaction(temperature, par = c(48.6, 49.7, 388, 1)), type = 'l', ylab = 'rate', main = "modifiedMasterReaction",
+ ylim = c(0,1000))
+lines(temperature, modifiedMasterReaction(temperature, par = c(73.3, 59.9, 422, 1)), col = 2)
+lines(temperature, modifiedMasterReaction(temperature, par = c(71.3, 71.4, 180, 1)), col = 3)
+lines(temperature, modifiedMasterReaction(temperature, par = c(96.0, 96.9, 101, 1)), col = 4)
+legend("bottomright", legend = c('psychrophile', "mesophile", "thermophile", "hyperthermophile"), lty = 1 , col = 1:4)
+
+YanHunt = function(temperature, par){
+ # Yan, W. & Hunt, L. A. (1999) An Equation for Modelling the Temperature Response of Plants using only
+ # the Cardinal Temperatures. Annals of Botany 84, 607–614.
+
+ Topt = par[1]
+ Tmax = par[2]
+
+ rate = ((Tmax - temperature) / (Tmax - Topt)) * ((temperature / Topt) ^ (Topt / (Tmax - Topt)))
+ rate[rate < 0] = 0
+ return(rate)
+ }
+
+temperature = seq(3, 35,.1)
+Topt = 22
+Tmax = 30
+plot(temperature, YanHunt(temperature, par = c(Topt, Tmax)), type = 'l', ylab = 'rate', main = "YanHunt")
+
+Arrhenius = function(temperature, par){
+ # Gillooly, J. F., Brown, J. H., West, G. B., Savage, V. M. & Charnov, E. L. (2001) Effects of Size and Temperature on
+ # Metabolic Rate. Science 293, 2248–2251.
+ # Charnov, E. L. & Gillooly, J. F. (2003) Thermal time: Body size, food quality and the 10°C rule. Evolutionary Ecology Research 5, 43–51.
+
+ Ei = par[1] # average activation energy for the rate-limiting enzyme-catalyzed biochemical reactions of metabolism. ~= 0.6 eV
+ tetha0 = par[2]
+ T0 = par[3] + 273.15
+ kB = 8.62E-5 # Boltzmann's constant in eV K-1
+
+ TinK = temperature + 273.15
+
+ rate = tetha0 * exp(Ei * (TinK - T0) / (kB * TinK * T0))
+ return(rate)
+}
+
+modifiedThorntonLessem = function(temperature, par){
+ # Thornton, K. W. & Lessem, A. S. (1978) A temperature algorithm for modifying biological rates. Transactions of the American
+ # Fisheries Society 107, 284–287.
+
+ Tlow01 = par[1] # =~ Tmin
+ Tlow80 = par[2] # lower bound of tolerance range
+ Thigh80 = par[3] # higher bound of tolerance range
+ Thigh99 = par[4] # =~ Tmax
+
+ b = log((1 - .8) / .8)
+ a = log((1 - 0.01)/0.01) - b
+
+ rateLow = 1 / (1 + exp(b - a * (temperature - Tlow80) / (Tlow80 - Tlow01)))
+ rateHigh = 1 / (1 + exp(b + a * (temperature - Thigh80) / (Thigh99 - Thigh80)))
+ return(rateLow + rateHigh - 1)
+}
+
+plot(temperature, modifiedThorntonLessem(temperature, par = c(Tmin, 14, 27, Tmax)), type = 'l', ylab = 'rate', main = "modifiedThorntonLessem")
+temperature[which.max(modifiedThorntonLessem(temperature, par = c(Tmin, 14, 27, Tmax)))]
+
+lines(temperature, modifiedLehman(temperature, par = c(Tmin, 21.3, Tmax)), col = 'red')