Appendix S1
2023-10-28
Loading the required libraries
library(mapSpain)
library(randomForest)
library(ggplot2)
library(ggpubr)
library(mgcViz)
library(forecast)
library(DHARMa)We first prepare the database for the communities and, afterwards, assemble them together to prepare the national database.
comunidad<-read.table("comunidad.txt", header = TRUE, sep = "\t",stringsAsFactors = T)
comunidad<- comunidad[names(comunidad[c(1,2,3)])]# eliminating unnecessary columnsEliminating asturias, Cantabria,Asturias and Murcia (because of insufficient data - see main text)
comunidad<- comunidad[comunidad$community!="Asturias"&comunidad$community!="Cantabria"&comunidad$community!="R.deMurcia"&comunidad$community!="Canarias",]
comunidad$community<- factor(comunidad$community)Creating one dataframe for each community
for (i in levels(comunidad$community)) {
command <- paste0(i, "<-subset(comunidad, community=='", i, "')")
eval(parse(text=command))
}For each community, we replace missing values with the estimated ones from random forest techniques.
This is to identify and replace outliers in the time series of each community
for (i in levels(comunidad$community)) {
command <- paste0(i,"$N[tsoutliers(",i,"$N)$index]<- tsoutliers(",i,"$N)$replacements")
eval(parse(text=command))
}Joining the datasets together again
comunidad<- rbind(Andalucia,Aragon,Baleares,C.Valenciana,CastillalaMancha,CastillayLeon,Cataluna,Extremadura,Galicia,LaRioja,Madrid,Navarra,PaisVasco)
comunidad$RHD<- as.factor(ifelse(comunidad$year<1988,"no RHD",ifelse(comunidad$year<2011,"GI.1","GI.2")))Creating a new national dataset made of the sums of annual Ns from each community (excluding Cantabria, Asturias and Murcia)
nacionalnew<- aggregate(comunidad$N, list(comunidad$year), FUN=mean)
names(nacionalnew)<- c("year","N")National data - GAM analysis
We use GAM analyses on all years of collected data to evaluate the temporal pattern at the national level in the number of hunted rabbits.
gam1 <- gam(N ~ s(year, k=20) , data=nacionalnew, select=T, method="REML")# select=T means that we are using the double penalty approach to do selection. When select=T the p-value refers to the probability that actually there is no effect at all of the predictor on the response variable (flat line).summary(gam1)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 455500 8649 52.67 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 10.21 19 10.94 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.845 Deviance explained = 88.7%
## -REML = 488.63 Scale est. = 2.9173e+09 n = 39simgam2<- simulateResiduals(gam1,plot=T)# OK
gam.check(gam1)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 6 iterations.
## Gradient range [-3.013763e-06,-6.044938e-07]
## (score 488.6339 & scale 2917332364).
## Hessian positive definite, eigenvalue range [3.000395e-06,20.55868].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.0 10.2 1.49 1Creating a new, toy dataframe to make predictions from the model and use them to visualize them. Note there is no data for 2004, because it was not available (see main text).
newdata<- data.frame(year=1980:2018,N=nacionalnew$N)
predizioni<- predict(gam1,newdata = newdata, type="terms",se=T)
newdata$predsgam1<- as.numeric(predizioni$fit)+gam1$coefficients[1]
newdata$predsgam1se<- as.numeric(predizioni$se.fit)
newdata$RHD<- factor(c(rep("no RHD",8),rep("GI.1",23),rep("GI.2",8)))
newdata$RHD<- relevel(newdata$RHD,"no RHD")National yearly numbers of hunted rabbits
This figure (Figure 2 in main text) represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2. outbreaks
# png("Figure2.png",width=480*1.5)
ggplot(newdata, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1-1.96*predsgam1se,ymax=predsgam1+1.96*predsgam1se,fill= RHD),stat="identity",linetype=0,size=5)+
scale_fill_brewer(palette = "BuPu")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdata$year), max(newdata$year), by = 1))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(x="year", y="# hunted rabbits",title="Spain")+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(plot.title = element_text(size = rel(1.8), angle = 00))+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
# dev.off()Communities data - GAM analysis
We use GAM analyses on all years of collected data to evaluate the temporal pattern at level of each community in the number of hunted rabbits.
Andalusia
Andalucia<- comunidad[comunidad$community=="Andalucia",]
gam1and <- gam(N ~ s(year, k=20) , data=Andalucia, select=T, method="REML")
summary(gam1and)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2023011 70096 28.86 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 9.451 19 11.69 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.854 Deviance explained = 89%
## -REML = 566.46 Scale est. = 1.9163e+11 n = 39simgam2and<- simulateResiduals(gam1and,plot=T)# OK
gam.check(gam1and)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-5.364598e-13,2.599589e-06]
## (score 566.4607 & scale 191626541004).
## eigenvalue range [-2.599205e-06,20.323].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.00 9.45 1.48 1Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataAnd<- data.frame(year=sort(unique(Andalucia$year)),N=Andalucia[order(Andalucia$year),]$N)
predizioniAnd<- predict(gam1and,newdataAnd = newdataAnd, type="terms",se=T)
newdataAnd$predsgam1and<- as.numeric(predizioniAnd$fit)+gam1and$coefficients[1]
newdataAnd$predsgam1andse<- as.numeric(predizioniAnd$se.fit)
newdataAnd$RHD<- Andalucia$RHD
newdataAnd$RHD<- relevel(newdataAnd$RHD,"no RHD")Andalusia yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Andalusia.
# png("Figure1and.png",width=480*1.5)
p1<- ggplot(newdataAnd, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1and-1.96*predsgam1andse,ymax=predsgam1and+1.96*predsgam1andse,fill= RHD),stat="identity",linetype=0,size=5)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataAnd$year), max(newdataAnd$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Andalusia")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p1
# dev.off()Aragon
Aragon<- comunidad[comunidad$community=="Aragon",]
gam1ara <- gam(N ~ s(year, k=20) , data=Aragon, select=T, method="REML")
summary(gam1ara)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 182752 5710 32 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 7.416 19 50.81 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.962 Deviance explained = 97%
## -REML = 467.58 Scale est. = 1.2718e+09 n = 39simgam2and<- simulateResiduals(gam1ara,plot=T)# OK
gam.check(gam1ara)#OK
##
## Method: REML Optimizer: outer newton
## full convergence after 11 iterations.
## Gradient range [-3.776319e-08,1.247419e-08]
## (score 467.5842 & scale 1271752878).
## Hessian positive definite, eigenvalue range [0.4193064,19.61939].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.00 7.42 1.16 0.81Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataAra<- data.frame(year=sort(unique(Aragon$year)),N=Aragon[order(Aragon$year),]$N)
predizioniAra<- predict(gam1ara,newdataAra = newdataAra, type="terms",se=T)
newdataAra$predsgam1ara<- as.numeric(predizioniAra$fit)+gam1ara$coefficients[1]
newdataAra$predsgam1arase<- as.numeric(predizioniAra$se.fit)
newdataAra$RHD<- Aragon$RHD
#str(newdataAra$RHD)
newdataAra$RHD<- relevel(newdataAra$RHD,"no RHD")Aragon yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Aragon.
# png("Figure1ara.png",width=480*1.5)
p2<- ggplot(newdataAra, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1ara-1.96*predsgam1arase,ymax=predsgam1ara+1.96*predsgam1arase,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataAra$year), max(newdataAra$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Aragon")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p2
# dev.off()Balearic Islands
Baleares<- comunidad[comunidad$community=="Baleares",]
gam1bal <- gam(N ~ s(year, k=20) , data=Baleares, select=T, method="REML")
summary(gam1bal)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 415756 11530 36.06 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 15.53 19 47.34 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.959 Deviance explained = 97.6%
## -REML = 515.4 Scale est. = 5.1843e+09 n = 39simgam2and<- simulateResiduals(gam1bal,plot=T)# OK
gam.check(gam1bal)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-4.750783e-05,-6.061421e-06]
## (score 515.4009 & scale 5184330900).
## Hessian positive definite, eigenvalue range [4.751164e-05,22.6113].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.0 15.5 1.42 0.98Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataBal<- data.frame(year=sort(unique(Baleares$year)),N=Baleares[order(Baleares$year),]$N)
predizioniBal<- predict(gam1bal,newdataBal = newdataBal, type="terms",se=T)
newdataBal$predsgam1bal<- as.numeric(predizioniBal$fit)+gam1bal$coefficients[1]
newdataBal$predsgam1balse<- as.numeric(predizioniBal$se.fit)
newdataBal$RHD<- Baleares$RHD
newdataBal$RHD<- relevel(newdataBal$RHD,"no RHD")Balearic Islands’ yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Balearic Islands.
# png("Figure1bal.png",width=480*1.5)
p3<- ggplot(newdataBal, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1bal-1.96*predsgam1balse,ymax=predsgam1bal+1.96*predsgam1balse,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataBal$year), max(newdataBal$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Balearic Islands")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p3
# dev.off()Basque Country
PaisVasco<- comunidad[comunidad$community=="PaisVasco",]
gam1pai <- gam(N ~ s(year, k=20) , data=PaisVasco, select=T, method="REML")
summary(gam1pai)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4102.5 142.9 28.71 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 8.172 19 6.837 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.774 Deviance explained = 82.2%
## -REML = 328.64 Scale est. = 7.9621e+05 n = 39simgam2pai<- simulateResiduals(gam1pai,plot=T)# OK
gam.check(gam1pai)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 11 iterations.
## Gradient range [-8.361913e-05,4.423263e-05]
## (score 328.6437 & scale 796211.1).
## Hessian positive definite, eigenvalue range [0.3252916,19.76446].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.00 8.17 1.07 0.66Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataPai<- data.frame(year=sort(unique(PaisVasco$year)),N=PaisVasco[order(PaisVasco$year),]$N)
predizioniPai<- predict(gam1pai,newdataPai = newdataPai, type="terms",se=T)
newdataPai$predsgam1pai<- as.numeric(predizioniPai$fit)+gam1pai$coefficients[1]
newdataPai$predsgam1paise<- as.numeric(predizioniPai$se.fit)
newdataPai$RHD<- PaisVasco$RHD
newdataPai$RHD<- relevel(newdataPai$RHD,"no RHD")Basque Country yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Basque Country.
# png("Figure1pai.png",width=480*1.5)
p13<- ggplot(newdataPai, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1pai-1.96*predsgam1paise,ymax=predsgam1pai+1.96*predsgam1paise,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataPai$year), max(newdataPai$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Basque Country")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p13
# dev.off()Castille La Mancha
CastillalaMancha<- comunidad[comunidad$community=="CastillalaMancha",]
CastillalaMancha<- CastillalaMancha[order(CastillalaMancha$year),]
gam1clm <- gam(N ~ s(year, k=20) , data=CastillalaMancha, select=T, method="REML")
summary(gam1clm)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1484833 45925 32.33 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 6.636 19 7.187 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.782 Deviance explained = 82%
## -REML = 544.5 Scale est. = 8.2254e+10 n = 39simgam2and<- simulateResiduals(gam1clm,plot=T)# OK
gam.check(gam1clm)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 4 iterations.
## Gradient range [-1.045278e-05,5.132807e-05]
## (score 544.5039 & scale 82254084987).
## Hessian positive definite, eigenvalue range [8.165634e-06,19.59717].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.00 6.64 0.85 0.16Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataClm<- data.frame(year=sort(unique(CastillalaMancha$year)),N=CastillalaMancha[order(CastillalaMancha$year),]$N)
predizioniClm<- predict(gam1clm,newdataClm = newdataClm, type="terms",se=T)
newdataClm$predsgam1clm<- as.numeric(predizioniClm$fit)+gam1clm$coefficients[1]
newdataClm$predsgam1clmse<- as.numeric(predizioniClm$se.fit)
newdataClm$RHD<- CastillalaMancha$RHD
newdataClm$RHD<- relevel(newdataClm$RHD,"no RHD")Castille La Mancha yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Castille La Mancha.
# png("Figure1clm.png",width=480*1.5)
p4<- ggplot(newdataClm, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1clm-1.96*predsgam1clmse,ymax=predsgam1clm+1.96*predsgam1clmse,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataClm$year), max(newdataClm$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Castille La Mancha")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p4
# dev.off()Castille and Leon
CastillayLeon<- comunidad[comunidad$community=="CastillayLeon",]
CastillayLeon<- CastillayLeon[order(CastillayLeon$year),]
gam1cyl <- gam(N ~ s(year, k=20) , data=CastillayLeon, select=T, method="REML")
summary(gam1cyl)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 276847 10156 27.26 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 5.694 19 11.14 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.848 Deviance explained = 87.1%
## -REML = 485.37 Scale est. = 4.0227e+09 n = 39simgam2and<- simulateResiduals(gam1cyl,plot=T)# OK
gam.check(gam1cyl)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 9 iterations.
## Gradient range [-6.364965e-06,4.789114e-06]
## (score 485.3667 & scale 4022744860).
## Hessian positive definite, eigenvalue range [0.1925016,19.3626].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.00 5.69 1.02 0.44Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataCyl<- data.frame(year=sort(unique(CastillayLeon$year)),N=CastillayLeon[order(CastillayLeon$year),]$N)
predizioniCyl<- predict(gam1cyl,newdataCyl = newdataCyl, type="terms",se=T)
newdataCyl$predsgam1cyl<- as.numeric(predizioniCyl$fit)+gam1cyl$coefficients[1]
newdataCyl$predsgam1cylse<- as.numeric(predizioniCyl$se.fit)
newdataCyl$RHD<- CastillayLeon$RHD
newdataCyl$RHD<- relevel(newdataCyl$RHD,"no RHD")Castille and Leon yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Castille and Leon.
# png("Figure1cyl.png",width=480*1.5)
p5<- ggplot(newdataCyl, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1cyl-1.96*predsgam1cylse,ymax=predsgam1cyl+1.96*predsgam1cylse,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataCyl$year), max(newdataCyl$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Castille and Leon")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p5
# dev.off()Catalonia
Temporal pattern of ynHR in Cataluna.
Cataluna<- comunidad[comunidad$community=="Cataluna",]
gam1cat <- gam(N ~ s(year, k=20) , data=Cataluna, select=T, method="REML")
summary(gam1cat)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 189551 3214 58.98 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 3.923 19 3.652 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.646 Deviance explained = 68.3%
## -REML = 438.14 Scale est. = 4.028e+08 n = 39simgam2and<- simulateResiduals(gam1cat,plot=T)# OK
gam.check(gam1cat)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 4 iterations.
## Gradient range [-0.0001422475,0.0001665832]
## (score 438.1402 & scale 402797146).
## Hessian positive definite, eigenvalue range [0.0001279724,19.21014].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.00 3.92 0.92 0.22Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataCat<- data.frame(year=sort(unique(Cataluna$year)),N=Cataluna[order(Cataluna$year),]$N)
predizioniCat<- predict(gam1cat,newdataCat = newdataCat, type="terms",se=T)
newdataCat$predsgam1cat<- as.numeric(predizioniCat$fit)+gam1cat$coefficients[1]
newdataCat$predsgam1catse<- as.numeric(predizioniCat$se.fit)
newdataCat$RHD<- Cataluna$RHD
newdataCat$RHD<- relevel(newdataCat$RHD,"no RHD")Catalonia yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Catalonia.
# png("Figure1cat.png",width=480*1.5)
p6<- ggplot(newdataCat, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1cat-1.96*predsgam1catse,ymax=predsgam1cat+1.96*predsgam1catse,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataCat$year), max(newdataCat$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Catalonia")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p6
# dev.off()Extremadura
Extremadura<- comunidad[comunidad$community=="Extremadura",]
gam1ext <- gam(N ~ s(year, k=20) , data=Extremadura, select=T, method="REML")
summary(gam1ext)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 416371 24435 17.04 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 4.496 19 4.595 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.697 Deviance explained = 73.3%
## -REML = 516.32 Scale est. = 2.3286e+10 n = 39simgam2and<- simulateResiduals(gam1ext,plot=T)# OK
gam.check(gam1ext)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 4 iterations.
## Gradient range [-0.0001309699,8.130931e-05]
## (score 516.3195 & scale 23286293815).
## Hessian positive definite, eigenvalue range [0.0001309406,19.27776].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.0 4.5 1.06 0.61Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataExt<- data.frame(year=sort(unique(Extremadura$year)),N=Extremadura[order(Extremadura$year),]$N)
predizioniExt<- predict(gam1ext,newdataExt = newdataExt, type="terms",se=T)
newdataExt$predsgam1ext<- as.numeric(predizioniExt$fit)+gam1ext$coefficients[1]
newdataExt$predsgam1extse<- as.numeric(predizioniExt$se.fit)
newdataExt$RHD<- Extremadura$RHD
newdataExt$RHD<- relevel(newdataExt$RHD,"no RHD")Extremadura yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Extremadura.
# png("Figure1ext.png",width=480*1.5)
p9<- ggplot(newdataExt, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1ext-1.96*predsgam1extse,ymax=predsgam1ext+1.96*predsgam1extse,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataExt$year), max(newdataExt$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Extremadura")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p9
Galicia
Galicia<- comunidad[comunidad$community=="Galicia",]
gam1gal <- gam(N ~ s(year, k=20) , data=Galicia, select=T, method="REML")
summary(gam1gal)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 144480 5240 27.57 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 2.863 19 5.892 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.747 Deviance explained = 76.6%
## -REML = 454.73 Scale est. = 1.0708e+09 n = 39simgam2and<- simulateResiduals(gam1gal,plot=T)# OK
gam.check(gam1gal)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 4 iterations.
## Gradient range [-0.0003050271,0.0002228541]
## (score 454.7262 & scale 1070779005).
## Hessian positive definite, eigenvalue range [2.951103e-05,19.1133].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.00 2.86 1.13 0.73Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataGal<- data.frame(year=sort(unique(Galicia$year)),N=Galicia[order(Galicia$year),]$N)
predizioniGal<- predict(gam1gal,newdataGal = newdataGal, type="terms",se=T)
newdataGal$predsgam1gal<- as.numeric(predizioniGal$fit)+gam1gal$coefficients[1]
newdataGal$predsgam1galse<- as.numeric(predizioniGal$se.fit)
newdataGal$RHD<- Galicia$RHD
newdataGal$RHD<- relevel(newdataGal$RHD,"no RHD")Galicia yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Galicia.
# png("Figure1gal.png",width=480*1.5)
p10<- ggplot(newdataGal, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1gal-1.96*predsgam1galse,ymax=predsgam1gal+1.96*predsgam1galse,fill= RHD),stat="identity",linetype=0,size=15)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataGal$year), max(newdataGal$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Galicia")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p10
# dev.off()La Rioja
LaRioja<- comunidad[comunidad$community=="LaRioja",]
gam1lar <- gam(N ~ s(year, k=20) , data=LaRioja, select=T, method="REML")
summary(gam1lar)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 54235 1619 33.51 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 12.21 19 28.66 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.935 Deviance explained = 95.6%
## -REML = 429.8 Scale est. = 1.0218e+08 n = 39simgam2and<- simulateResiduals(gam1lar,plot=T)# problems
gam.check(gam1lar)# problems
##
## Method: REML Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-1.147485e-06,-1.032252e-07]
## (score 429.7967 & scale 102180507).
## Hessian positive definite, eigenvalue range [8.29943e-07,21.20956].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.0 12.2 1.38 0.98Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataLar<- data.frame(year=sort(unique(LaRioja$year)),N=LaRioja[order(LaRioja$year),]$N)# there is no data for 2004! do not care about the warning message!
predizioniLar<- predict(gam1lar,newdataLar = newdataLar, type="terms",se=T)
newdataLar$predsgam1lar<- as.numeric(predizioniLar$fit)+gam1lar$coefficients[1]
newdataLar$predsgam1larse<- as.numeric(predizioniLar$se.fit)
newdataLar$RHD<- LaRioja$RHD
newdataLar$RHD<- relevel(newdataLar$RHD,"no RHD")La Rioja yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in La Rioja.
# png("Figure1lar.png",width=480*1.5)
p11<- ggplot(newdataLar, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1lar-1.96*predsgam1larse,ymax=predsgam1lar+1.96*predsgam1larse,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataLar$year), max(newdataLar$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="La Rioja")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p11
dev.off()## null device
## 1Madrid
Madrid<- comunidad[comunidad$community=="Madrid",]
gam1mad <- gam(N ~ s(year, k=20) , data=Madrid, select=T, method="REML")
summary(gam1mad)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 356754 5424 65.77 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 13.55 19 23.87 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.923 Deviance explained = 95%
## -REML = 479.51 Scale est. = 1.1474e+09 n = 39simgam2and<- simulateResiduals(gam1mad,plot=T)# OK
gam.check(gam1mad)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 6 iterations.
## Gradient range [-4.928378e-05,-4.231532e-06]
## (score 479.5116 & scale 1147446061).
## Hessian positive definite, eigenvalue range [4.927972e-05,21.62304].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.0 13.5 1.35 0.97Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataMad<- data.frame(year=sort(unique(Madrid$year)),N=Madrid[order(Madrid$year),]$N)# there is no data for 2004! do not care about the warning message!
predizioniMad<- predict(gam1mad,newdataMad = newdataMad, type="terms",se=T)
newdataMad$predsgam1mad<- as.numeric(predizioniMad$fit)+gam1mad$coefficients[1]
newdataMad$predsgam1madse<- as.numeric(predizioniMad$se.fit)
newdataMad$RHD<- Madrid$RHD
newdataMad$RHD<- relevel(newdataMad$RHD,"no RHD")Madrid yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Madrid.
# png("Figure1mad.png",width=480*1.5)
p7<- ggplot(newdataMad, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1mad-1.96*predsgam1madse,ymax=predsgam1mad+1.96*predsgam1madse,fill= RHD),stat="identity",linetype=0,size=15)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataMad$year), max(newdataMad$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Madrid")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p7
# dev.off()Navarra
Navarra<- comunidad[comunidad$community=="Navarra",]
gam1nav <- gam(N ~ s(year, k=20) , data=Navarra, select=T, method="REML")
summary(gam1nav)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 101609 3742 27.16 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 5.654 19 7.758 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.795 Deviance explained = 82.6%
## -REML = 447.26 Scale est. = 5.4596e+08 n = 39simgam2and<- simulateResiduals(gam1nav,plot=T)# OK
gam.check(gam1nav)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 5 iterations.
## Gradient range [-5.559075e-06,5.124794e-06]
## (score 447.265 & scale 545964259).
## Hessian positive definite, eigenvalue range [5.558998e-06,19.46269].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.00 5.65 1.3 0.94Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataNav<- data.frame(year=sort(unique(Navarra$year)),N=Navarra[order(Navarra$year),]$N)
predizioniNav<- predict(gam1nav,newdataNav = newdataNav, type="terms",se=T)
newdataNav$predsgam1nav<- as.numeric(predizioniNav$fit)+gam1nav$coefficients[1]
newdataNav$predsgam1navse<- as.numeric(predizioniNav$se.fit)
newdataNav$RHD<- Navarra$RHD
newdataNav$RHD<- relevel(newdataNav$RHD,"no RHD")Navarra yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Navarra.
# png("Figure1nav.png",width=480*1.5)
p12<- ggplot(newdataNav, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1nav-1.96*predsgam1navse,ymax=predsgam1nav+1.96*predsgam1navse,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataNav$year), max(newdataNav$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Navarra")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p12
# dev.off()Valencian Community
Valencia<- comunidad[comunidad$community=="C.Valenciana",]
gam1val <- gam(N ~ s(year, k=20) , data=Valencia, select=T, method="REML")
summary(gam1val)# summary of results##
## Family: gaussian
## Link function: identity
##
## Formula:
## N ~ s(year, k = 20)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 271192 5956 45.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(year) 3.368 19 7.75 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.795 Deviance explained = 81.3%
## -REML = 461.12 Scale est. = 1.3836e+09 n = 39simgam2and<- simulateResiduals(gam1val,plot=T)# OK
gam.check(gam1val)# OK
##
## Method: REML Optimizer: outer newton
## full convergence after 9 iterations.
## Gradient range [-1.383943e-06,-1.067039e-07]
## (score 461.118 & scale 1383559590).
## Hessian positive definite, eigenvalue range [0.3645777,19.09443].
## Model rank = 20 / 20
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(year) 19.00 3.37 0.99 0.4Creating a new, toy dataframe to make predictions from the model and use them to visualize them.
newdataVal<- data.frame(year=sort(unique(Valencia$year)),N=Valencia[order(Valencia$year),]$N)
predizioniVal<- predict(gam1val,newdataVal = newdataVal, type="terms",se=T)
newdataVal$predsgam1val<- as.numeric(predizioniVal$fit)+gam1val$coefficients[1]
newdataVal$predsgam1valse<- as.numeric(predizioniVal$se.fit)
newdataVal$RHD<- Valencia$RHD
newdataVal$RHD<- relevel(newdataVal$RHD,"no RHD")Valencian Community yearly numbers of hunted rabbits
This figure represents the GAM curve depicting the variation in the number of hunted rabbits between 1980 and 2018 before and after GI.1 and GI.2 outbreaks in Valencian Community.
# png("Figure1val.png",width=480*1.5)
p8<- ggplot(newdataVal, aes(x = year, y = N, fill=RHD))+
geom_smooth(aes(ymin=predsgam1val-1.96*predsgam1valse,ymax=predsgam1val+1.96*predsgam1valse,fill= RHD),stat="identity",linetype=0)+
scale_fill_brewer(palette = "BuGn")+
geom_point()+
scale_x_continuous(breaks = seq(min(newdataVal$year), max(newdataVal$year), by = 1))+
theme(axis.title.y = element_text(size = rel(1.8), angle = 90))+
theme(axis.title.x = element_text(size = rel(1.8), angle = 0))+
theme(axis.text.x = element_text(angle = 45,size=13,vjust = 0.2))+#vjust align the labels under the tick (in the center)+
theme(axis.text.y = element_text(size = rel(1.5), angle = 45, margin = margin(t = 0, r = 10, b = 0, l = 0)))+
theme(axis.text.x = element_text(size = rel(1.5), angle = 45, margin = margin(t = 5, r = 0, b = 0, l = 0)))+
labs(y="# hunted rabbits",title="Valencian Community")+
theme(legend.position = c(0.9,0.9),legend.text = element_text(size = 12),legend.title=element_blank())+
theme(plot.margin = margin(t = 1, r = 1, b = 1, l = 1, unit = "cm"))
p8
# dev.off()National data - GLM analyses of linear trends
As it is often the case for large count data, and according to preliminary analyses on this dataset, the Gaussian distribution fitted the data better than a Poisson or Poisson-related one. For this reason we used GLM with gaussian distribution on log-transformed count (no. of hunted rabbits) data. We considered the eigth years after the outbreak of each variant of RHD.
RHD1<- nacionalnew[nacionalnew$year>1987&nacionalnew$year<1996,]
RHD2<- nacionalnew[nacionalnew$year>2010,]
RHD1$logN<- log(RHD1$N)
RHD2$logN<- log(RHD2$N)
n1<- lm(logN ~ year, data=RHD1)
summary(n1)##
## Call:
## lm(formula = logN ~ year, data = RHD1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.30930 -0.06462 0.02676 0.07141 0.31642
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 299.05329 64.36987 4.646 0.00352 **
## year -0.14371 0.03232 -4.446 0.00435 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2095 on 6 degrees of freedom
## Multiple R-squared: 0.7672, Adjusted R-squared: 0.7284
## F-statistic: 19.77 on 1 and 6 DF, p-value: 0.004347We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.144, P = 0.00435).
n2<- lm(logN ~ year, data=RHD2)
summary(n2)##
## Call:
## lm(formula = logN ~ year, data = RHD2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.07410 -0.05740 0.01675 0.04167 0.07662
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.306794 19.265679 1.158 0.291
## year -0.004618 0.009563 -0.483 0.646
##
## Residual standard error: 0.06198 on 6 degrees of freedom
## Multiple R-squared: 0.0374, Adjusted R-squared: -0.123
## F-statistic: 0.2331 on 1 and 6 DF, p-value: 0.6463Vice versa, we found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = -0.005, P = 0.64632).
Communities data - GLM analyses of linear trends
Using the eigth days after the outbreak of each variant of RHD.
Andalusia
RHDand1<- Andalucia[Andalucia$year>1987&Andalucia$year<1996,]
RHDand1<- RHDand1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDand2)
RHDand2<- Andalucia[Andalucia$year>2010,]
RHDand1$logN<- log(RHDand1$N)
RHDand2$logN<- log(RHDand2$N)
n1and<- lm(logN ~ year, data=RHDand1)
summary(n1and)##
## Call:
## lm(formula = logN ~ year, data = RHDand1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7039 -0.1437 0.0925 0.2077 0.6391
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 509.84823 146.39081 3.483 0.0131 *
## year -0.24876 0.07351 -3.384 0.0148 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4764 on 6 degrees of freedom
## Multiple R-squared: 0.6562, Adjusted R-squared: 0.5989
## F-statistic: 11.45 on 1 and 6 DF, p-value: 0.01478We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.249, P = 0.01478).
n2and<- lm(logN ~ year, data=RHDand2)
summary(n2and)##
## Call:
## lm(formula = logN ~ year, data = RHDand2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.086977 -0.007341 0.003848 0.022685 0.044551
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 124.321294 13.413533 9.268 8.92e-05 ***
## year -0.054685 0.006658 -8.213 0.000176 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04315 on 6 degrees of freedom
## Multiple R-squared: 0.9183, Adjusted R-squared: 0.9047
## F-statistic: 67.45 on 1 and 6 DF, p-value: 0.0001758We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = -0.055, P = 1.8^{-4}).
Aragon
RHDara1<- Aragon[Aragon$year>1987&Aragon$year<1996,]
RHDara1<- RHDara1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDara2)
RHDara2<- Aragon[Aragon$year>2010,]
RHDara1$logN<- log(RHDara1$N)
RHDara2$logN<- log(RHDara2$N)
n1ara<- lm(logN ~ year, data=RHDara1)
summary(n1ara)##
## Call:
## lm(formula = logN ~ year, data = RHDara1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7606 -0.3794 -0.1309 0.2732 1.2584
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 207.2971 207.5357 0.999 0.356
## year -0.0990 0.1042 -0.950 0.379
##
## Residual standard error: 0.6754 on 6 degrees of freedom
## Multiple R-squared: 0.1307, Adjusted R-squared: -0.01413
## F-statistic: 0.9024 on 1 and 6 DF, p-value: 0.3788We found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.099, P = 0.37881).
n2ara<- lm(logN ~ year, data=RHDara2)
summary(n2ara)##
## Call:
## lm(formula = logN ~ year, data = RHDara2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.068401 -0.059385 -0.002427 0.012909 0.162004
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -242.32746 24.92262 -9.723 6.80e-05 ***
## year 0.12678 0.01237 10.247 5.04e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08018 on 6 degrees of freedom
## Multiple R-squared: 0.9459, Adjusted R-squared: 0.9369
## F-statistic: 105 on 1 and 6 DF, p-value: 5.038e-05We found a significant positive linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = 0.127, P = 5^{-5}).
Balearic Islands
RHDbal1<- Baleares[Baleares$year>1987&Baleares$year<1996,]
RHDbal1<- RHDbal1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDbal2)
RHDbal2<- Baleares[Baleares$year>2010,]
RHDbal1$logN<- log(RHDbal1$N)
RHDbal2$logN<- log(RHDbal2$N)
n1bal<- lm(logN ~ year, data=RHDbal1)
summary(n1bal)##
## Call:
## lm(formula = logN ~ year, data = RHDbal1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.3919 -0.1385 -0.0665 0.1401 0.4412
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 495.3966 89.6108 5.528 0.00148 **
## year -0.2424 0.0450 -5.387 0.00168 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2916 on 6 degrees of freedom
## Multiple R-squared: 0.8287, Adjusted R-squared: 0.8001
## F-statistic: 29.02 on 1 and 6 DF, p-value: 0.001685We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.242, P = 0.00168).
n2bal<- lm(logN ~ year, data=RHDbal2)
summary(n2bal)##
## Call:
## lm(formula = logN ~ year, data = RHDbal2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45595 -0.05685 0.04203 0.14448 0.24238
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.10632 75.68969 0.887 0.409
## year -0.02768 0.03757 -0.737 0.489
##
## Residual standard error: 0.2435 on 6 degrees of freedom
## Multiple R-squared: 0.08296, Adjusted R-squared: -0.06988
## F-statistic: 0.5428 on 1 and 6 DF, p-value: 0.4891We found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = -0.028, P = 0.48906).
Basque Country
RHDpai1<- PaisVasco[PaisVasco$year>1987&PaisVasco$year<1996,]
RHDpai1<- RHDpai1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDpai2)
RHDpai2<- PaisVasco[PaisVasco$year>2010,]
RHDpai1$logN<- log(RHDpai1$N)
RHDpai2$logN<- log(RHDpai2$N)
n1pai<- lm(logN ~ year, data=RHDpai1)
summary(n1pai)##
## Call:
## lm(formula = logN ~ year, data = RHDpai1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.29173 -0.14836 0.04382 0.11780 0.23453
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 268.68051 65.18126 4.122 0.00620 **
## year -0.13074 0.03273 -3.995 0.00716 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2121 on 6 degrees of freedom
## Multiple R-squared: 0.7267, Adjusted R-squared: 0.6812
## F-statistic: 15.96 on 1 and 6 DF, p-value: 0.007163We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.131, P = 0.00716).
n2pai<- lm(logN ~ year, data=RHDpai2)
summary(n2pai)##
## Call:
## lm(formula = logN ~ year, data = RHDpai2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3298 -1.0132 -0.1895 0.8177 1.8273
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1448.5738 411.2302 -3.523 0.0125 *
## year 0.7226 0.2041 3.540 0.0122 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.323 on 6 degrees of freedom
## Multiple R-squared: 0.6762, Adjusted R-squared: 0.6222
## F-statistic: 12.53 on 1 and 6 DF, p-value: 0.01222We found a significant positive linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = 0.723, P = 0.01222).
Castille La Mancha
RHDclm1<- CastillalaMancha[CastillalaMancha$year>1987&CastillalaMancha$year<1996,]
RHDclm1<- RHDclm1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDclm2)
RHDclm2<- CastillalaMancha[CastillalaMancha$year>2010,]
RHDclm1$logN<- log(RHDclm1$N)
RHDclm2$logN<- log(RHDclm2$N)
n1clm<- lm(logN ~ year, data=RHDclm1)
summary(n1clm)##
## Call:
## lm(formula = logN ~ year, data = RHDclm1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.26644 -0.13445 -0.01862 0.11230 0.35875
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 195.20806 66.02512 2.957 0.0254 *
## year -0.09119 0.03315 -2.751 0.0333 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2149 on 6 degrees of freedom
## Multiple R-squared: 0.5577, Adjusted R-squared: 0.484
## F-statistic: 7.566 on 1 and 6 DF, p-value: 0.03326We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.091, P = 0.03326).
n2clm<- lm(logN ~ year, data=RHDclm2)
summary(n2clm)##
## Call:
## lm(formula = logN ~ year, data = RHDclm2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.199456 -0.056676 0.000915 0.055791 0.182456
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.039823 39.078138 0.564 0.593
## year -0.003727 0.019398 -0.192 0.854
##
## Residual standard error: 0.1257 on 6 degrees of freedom
## Multiple R-squared: 0.006115, Adjusted R-squared: -0.1595
## F-statistic: 0.03692 on 1 and 6 DF, p-value: 0.854We found a significant positive linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = -0.004, P = 0.85397).
Castille and Leon
RHDcyl1<- CastillayLeon[CastillayLeon$year>1987&CastillayLeon$year<1996,]
RHDcyl1<- RHDcyl1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDcyl2)
RHDcyl2<- CastillayLeon[CastillayLeon$year>2010,]
RHDcyl1$logN<- log(RHDcyl1$N)
RHDcyl2$logN<- log(RHDcyl2$N)
n1cyl<- lm(logN ~ year, data=RHDcyl1)
summary(n1cyl)##
## Call:
## lm(formula = logN ~ year, data = RHDcyl1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.3489 -0.2531 -0.1271 0.1845 0.6310
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 575.8427 114.1221 5.046 0.00234 **
## year -0.2832 0.0573 -4.943 0.00260 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3714 on 6 degrees of freedom
## Multiple R-squared: 0.8028, Adjusted R-squared: 0.77
## F-statistic: 24.43 on 1 and 6 DF, p-value: 0.002597We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.283, P = 0.0026).
n2cyl<- lm(logN ~ year, data=RHDcyl2)
summary(n2cyl)##
## Call:
## lm(formula = logN ~ year, data = RHDcyl2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.256154 -0.056491 0.007184 0.112284 0.167896
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -108.39941 49.45120 -2.192 0.0709 .
## year 0.06003 0.02455 2.446 0.0501 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1591 on 6 degrees of freedom
## Multiple R-squared: 0.4992, Adjusted R-squared: 0.4157
## F-statistic: 5.981 on 1 and 6 DF, p-value: 0.05009We found a marginally significant positive linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = 0.06, P = 0.05009).
Catalonia
RHDcat1<- Cataluna[Cataluna$year>1987&Cataluna$year<1996,]
RHDcat1<- RHDcat1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDcat2)
RHDcat2<- Cataluna[Cataluna$year>2010,]
RHDcat1$logN<- log(RHDcat1$N)
RHDcat2$logN<- log(RHDcat2$N)
n1cat<- lm(logN ~ year, data=RHDcat1)
summary(n1cat)##
## Call:
## lm(formula = logN ~ year, data = RHDcat1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.151111 0.002862 0.027594 0.030554 0.038467
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 128.03924 21.05284 6.082 0.000898 ***
## year -0.05823 0.01057 -5.508 0.001503 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06851 on 6 degrees of freedom
## Multiple R-squared: 0.8349, Adjusted R-squared: 0.8074
## F-statistic: 30.34 on 1 and 6 DF, p-value: 0.001503We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.058, P = 0.0015).
n2cat<- lm(logN ~ year, data=RHDcat2)
summary(n2cat)##
## Call:
## lm(formula = logN ~ year, data = RHDcat2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.184985 -0.068587 -0.002701 0.074970 0.149003
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.058014 38.678873 0.027 0.979
## year 0.005499 0.019200 0.286 0.784
##
## Residual standard error: 0.1244 on 6 degrees of freedom
## Multiple R-squared: 0.01349, Adjusted R-squared: -0.1509
## F-statistic: 0.08204 on 1 and 6 DF, p-value: 0.7842We found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = 0.005, P = 0.78418).
Extremadura
RHDext1<- Extremadura[Extremadura$year>1987&Extremadura$year<1996,]
RHDext1<- RHDext1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDext2)
RHDext2<- Extremadura[Extremadura$year>2010,]
RHDext1$logN<- log(RHDext1$N)
RHDext2$logN<- log(RHDext2$N)
n1ext<- lm(logN ~ year, data=RHDext1)
summary(n1ext)##
## Call:
## lm(formula = logN ~ year, data = RHDext1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.09435 -0.05718 -0.03851 0.02370 0.22717
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -53.89605 34.45306 -1.564 0.1688
## year 0.03383 0.01730 1.955 0.0983 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1121 on 6 degrees of freedom
## Multiple R-squared: 0.3892, Adjusted R-squared: 0.2874
## F-statistic: 3.824 on 1 and 6 DF, p-value: 0.09831We found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = 0.034, P = 0.09831).
n2ext<- lm(logN ~ year, data=RHDext2)
summary(n2ext)##
## Call:
## lm(formula = logN ~ year, data = RHDext2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.243691 -0.112524 -0.004564 0.113688 0.279717
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 366.95948 61.05475 6.010 0.000956 ***
## year -0.17658 0.03031 -5.826 0.001125 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1964 on 6 degrees of freedom
## Multiple R-squared: 0.8498, Adjusted R-squared: 0.8248
## F-statistic: 33.95 on 1 and 6 DF, p-value: 0.001125We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = -0.177, P = 0.00112).
Galicia
RHDgal1<- Galicia[Galicia$year>1987&Galicia$year<1996,]
RHDgal1<- RHDgal1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDgal2)
RHDgal2<- Galicia[Galicia$year>2010,]
RHDgal1$logN<- log(RHDgal1$N)
RHDgal2$logN<- log(RHDgal2$N)
n1gal<- lm(logN ~ year, data=RHDgal1)
summary(n1gal)##
## Call:
## lm(formula = logN ~ year, data = RHDgal1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.14398 -0.06837 -0.05484 0.07470 0.21995
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.639033 39.975196 0.466 0.657
## year -0.003274 0.020073 -0.163 0.876
##
## Residual standard error: 0.1301 on 6 degrees of freedom
## Multiple R-squared: 0.004414, Adjusted R-squared: -0.1615
## F-statistic: 0.0266 on 1 and 6 DF, p-value: 0.8758We found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.003, P = 0.8758).
n2gal<- lm(logN ~ year, data=RHDgal2)
summary(n2gal)##
## Call:
## lm(formula = logN ~ year, data = RHDgal2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.28512 -0.17945 -0.01267 0.07485 0.43648
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 137.31955 82.70364 1.660 0.148
## year -0.06258 0.04105 -1.524 0.178
##
## Residual standard error: 0.2661 on 6 degrees of freedom
## Multiple R-squared: 0.2792, Adjusted R-squared: 0.1591
## F-statistic: 2.324 on 1 and 6 DF, p-value: 0.1782We found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = -0.063, P = 0.17824).
La Rioja
RHDlrj1<- LaRioja[LaRioja$year>1987&LaRioja$year<1996,]
RHDlrj1<- RHDlrj1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDlrj2)
RHDlrj2<- LaRioja[LaRioja$year>2010,]
RHDlrj1$logN<- log(RHDlrj1$N)
RHDlrj2$logN<- log(RHDlrj2$N)
n1lrj<- lm(logN ~ year, data=RHDlrj1)
summary(n1lrj)##
## Call:
## lm(formula = logN ~ year, data = RHDlrj1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.112929 -0.005660 -0.002662 0.010353 0.086652
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.079504 18.745784 0.644 0.543
## year -0.001090 0.009413 -0.116 0.912
##
## Residual standard error: 0.061 on 6 degrees of freedom
## Multiple R-squared: 0.002231, Adjusted R-squared: -0.1641
## F-statistic: 0.01341 on 1 and 6 DF, p-value: 0.9116We found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.001, P = 0.91157).
n2lrj<- lm(logN ~ year, data=RHDlrj2)
summary(n2lrj)##
## Call:
## lm(formula = logN ~ year, data = RHDlrj2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.23375 -0.22404 -0.05275 0.12896 0.49609
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -59.19775 89.52360 -0.661 0.533
## year 0.03500 0.04444 0.788 0.461
##
## Residual standard error: 0.288 on 6 degrees of freedom
## Multiple R-squared: 0.0937, Adjusted R-squared: -0.05734
## F-statistic: 0.6204 on 1 and 6 DF, p-value: 0.4609We found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = 0.035, P = 0.46089).
Madrid
RHDmad1<- CastillayLeon[CastillayLeon$year>1987&CastillayLeon$year<1996,]
RHDmad1<- RHDmad1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDmad2)
RHDmad2<- CastillayLeon[CastillayLeon$year>2010,]
RHDmad1$logN<- log(RHDmad1$N)
RHDmad2$logN<- log(RHDmad2$N)
n1mad<- lm(logN ~ year, data=RHDmad1)
summary(n1mad)##
## Call:
## lm(formula = logN ~ year, data = RHDmad1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.3489 -0.2531 -0.1271 0.1845 0.6310
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 575.8427 114.1221 5.046 0.00234 **
## year -0.2832 0.0573 -4.943 0.00260 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3714 on 6 degrees of freedom
## Multiple R-squared: 0.8028, Adjusted R-squared: 0.77
## F-statistic: 24.43 on 1 and 6 DF, p-value: 0.002597We found a significant negative linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.283, P = 0.0026).
n2mad<- lm(logN ~ year, data=RHDmad2)
summary(n2mad)##
## Call:
## lm(formula = logN ~ year, data = RHDmad2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.256154 -0.056491 0.007184 0.112284 0.167896
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -108.39941 49.45120 -2.192 0.0709 .
## year 0.06003 0.02455 2.446 0.0501 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1591 on 6 degrees of freedom
## Multiple R-squared: 0.4992, Adjusted R-squared: 0.4157
## F-statistic: 5.981 on 1 and 6 DF, p-value: 0.05009We found a marginally significant positive linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = 0.06, P = 0.05009).
Valencian Community
RHDval1<- C.Valenciana[C.Valenciana$year>1987&C.Valenciana$year<1996,]
RHDval1<- RHDval1[1:8,]# cutting out the years after the first eight (same number for which we have info on RHDval2)
RHDval2<- C.Valenciana[C.Valenciana$year>2010,]
RHDval1$logN<- log(RHDval1$N)
RHDval2$logN<- log(RHDval2$N)
n1val<- lm(logN ~ year, data=RHDval1)
summary(n1val)##
## Call:
## lm(formula = logN ~ year, data = RHDval1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08781 -0.06794 0.01583 0.05436 0.08429
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 50.08158 22.56531 2.219 0.0683 .
## year -0.01894 0.01133 -1.672 0.1456
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07343 on 6 degrees of freedom
## Multiple R-squared: 0.3178, Adjusted R-squared: 0.2041
## F-statistic: 2.795 on 1 and 6 DF, p-value: 0.1456We found a non-significant linear trend on the log-scale of the number of yearly hunted rabbits after the GI.1 outbreak (slope = -0.019, P = 0.14557).
n2val<- lm(logN ~ year, data=RHDval2)
summary(n2val)##
## Call:
## lm(formula = logN ~ year, data = RHDval2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.101425 -0.037851 -0.005208 0.029501 0.140244
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -80.79378 27.32568 -2.957 0.0254 *
## year 0.04649 0.01356 3.427 0.0140 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08791 on 6 degrees of freedom
## Multiple R-squared: 0.6619, Adjusted R-squared: 0.6056
## F-statistic: 11.75 on 1 and 6 DF, p-value: 0.01401We found a significant positive linear trend on the log-scale of the number of yearly hunted rabbits after the GI.2 outbreak (slope = 0.046, P = 0.01401).