Script04

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# Script 04 - Time-series-specific analysis.
# Haubrock et al. The invasion curve and dynamics of a European-wide introduced species. 
#
# This script includes the code for the following steps:
#    (1) Data curation and preparation
#    (2) Apply linear models to identify patterns and drivers of the  invasion curve
# 
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(1) Data curation and preparation

#read data
fits<-read.csv("Logistic_fits.csv", sep=",", stringsAsFactors=FALSE)

# merge the final output from Script03 with the time-series specific results from Script01
master_file_2<-merge(fits,master_file,by="site_id") #merge the Dv trend analysis result with S-statistic of the MK trend test resuls

#repeat the "Consideration of explanatory variables" section from Script02
master_file_2$Latitude<-as.numeric(master_file_2$Latitude) # ensure data is numeric
master_file_2$Longitude<-as.numeric(master_file_2$Longitude) # ensure data is numeric
master_file_2$StudyLength.s <- decostand(master_fil_2e$Study_length, "standardize") # standardize accordingly
# the standardization is to be repeated with every environmental variable included. 
# in this works case, this includes: the average temperature over the period, average precipiation over the period, the change in temperature (trends S-statistic), change in precipitation (trends S-statistic),
# years after monitoring started, elevation, elevation drop, slope, ppt, runoff, NH4, NO3, percentage of urban areas in the site's proximity, percentage of open water bodies in the site's proximity
# R², intrinsic growth rate r, initial population sie N0, and carrying capacity K, point of infliction tcrit and point the abundance plateaus tplat.

(2) Model selection

# this step will identify the best fit covariates for the model. 
# exemplary shown on R²
res1 <- glmulti(R.2.s ~ r.s+K.s+N0.s+observations.s+Lat.s+Lon.s+S_Temp.s+S_Prec.s+Mean_temp.s+Mean_prec.s+Elevation.s+Slope.s+Runoff.s+Urban.s+Water.s, 
               data=mydata,
               level=1, method="ML",crit="aicc", confsetsize=128)
print(res1) # inspection
plot(res1) # inspection
top1 <- weightable(res1)
top1 <- top1[top1$aicc <= min(top1$aicc) + 2,]
top1 # extract best fitting covariates

# this step is to be repeated for the intrinsic growth rate r, initial population sie N0, 
# and carrying capacity K, point of infliction tcrit and point the abundance plateaus tplat

(2) Apply linear models to identify patterns and drivers of the  invasion curve

#apply model
fm1 <- lmer(R.2.s ~ 1 + r.s + K.s + observations.s + Lat.s + Elevation.s + Slope.s + Runoff.s+ (1|Country),
             data = mydata,control=lmerControl(optimizer="bobyqa",optCtrl=list(maxfun=100000)))
fm1 # inspection
summary(fm1) # inspection

# this step is to be repeated for the intrinsic growth rate r, initial population sie N0, 
# and carrying capacity K, point of infliction tcrit and point the abundance plateaus tplat