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# Content: 
# 1. Evaluation of analyses in Marin et al 
# 2. Analysis of more extensive dataset including data from both the Kautokeino area and the Karasjok area
#
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#
# 1. Evaluation of analyses in Marin et al
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# 13570_2021_209_MOESM1_ESM.txt gives data from the supplementary material of Marin, A., E. Sjaastad, T. A. 
# Benjaminsen, M. N. M. Sara, and E. J. L. Borgenvik. 2020. 
# Productivity beyond density: A critique of management models for reindeer pastoralism in Norway. 
# Pastoralism 10:9. doi:10.1186/s13570-020-00164-3 

# Variables included
# District - categorical variable that gives the identity code for the reindeer herding districs included in the dataset
# type - categorical variable that distinguish between district regarded as "island"-type or "mainland"-type
# Year - categorical variable for the reindeer production year
# year - numerical variable given as the year of the end of the reindeer production year
# calf - average slaughter weights  of calves for a given district and year
# varit - average slaughter weights  of varit (1-2 year old male reindeer) for a given district and year
# density.end - reindeer density at the end of the reindeer production year  
# density.start - reindeer density at the end of the reindeer production year
#
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options(stringsAsFactors=F)

Marin.dat<-read.table("13570_2021_209_MOESM1_ESM.txt", sep = ",", header=T) # read in the data

# extract the range of years with available varit data
range(Marin.dat$year[!is.na(Marin.dat$varit)])
# [1] 1997 2012    #output from above command giving the range of years

# fitting the linear model to data from mainland districts and all years reported in Marin et al using 
# density estimates from the start of the reindeer herding year
lm.marin.allyrs<-lm(varit~log(density.start), data=Marin.dat, subset=type=="mainland")


round(summary(lm.marin.allyrs)$r.squared,2) # Extract r-squared from fitted model 
# [1] 0.31                    # Higher r-squared value (0.31) than the 0.24 reported in Marin et al (2020)

# fit the same model but using densities at the end of the reindeer herding year as predictor
lm.marin.allyrs2<-lm(varit~log(density.end), data=Marin.dat, subset=type=="mainland")

round(summary(lm.marin.allyrs2)$r.squared,2) # Extract r-squared from fitted model 
# [1] 0.24                    # Same r-squared value as reported in Marin et al (2020) suggesting they 
                              # used densities at the end of the reindeer herding year as predictor 

# fit the same model but data from the subset of years 1998-2000 and densities at the end of the reindeer herding year as predictor
lm.marin.subyrs<-lm(varit~log(density.end), data=Marin.dat, subset=type=="mainland"&year%in%c(1999:2001))

round(summary(lm.marin.subyrs)$r.squared,2) # Extract r-squared from fitted model 
# [1] 0.29                    # Approximately same r-squared value as obtained for the whole dataset, suggest 
                              # no change in r-squared when extending the dataset

# Extract district identity codes included in the dataset
levels(factor(Marin.dat$District))
#  "19"     "19/32T" "20"     "21"     "22"     "23"     "24A"    "24B"    "25"     "26"     "27"     "28"    
#  "29"     "32"     "33"     "33T"    "34"     "35"     "36"     "37"     "39"     "40"     "41"     "42"

# According to Landbruksdirektoratet. 2019. Ressursregnskap for reindriftsnæringen. Reindriftsforvaltningen, Alta. (in Norwegian).
# these are all districts identities associated with the Kautokeino area, and none associated with the Karasjok area.


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#
# 2. Evaluation of more extensive dataset including data from both the Kautokeino area and the Karasjok area
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# 13570_2021_209_MOESM2_ESM.txt gives data on average varit slaughter weigts from the years 1998-2019 extracted 
# as described in the main text.
#
# Variables included
# District - categorical variable that gives the identity code for the reindeer herding districs included in the dataset
# type - categorical variable that distinguish between district regarded as "island"-type or "mainland"-type
# year - numerical variable given as the year of the end of the reindeer production year
# varit - average slaughter weights  of varit (1-2 year old male reindeer) for a given district and year
# n.varit.wt - sample size average varit slaughter weights are based on
# area - area of summer pastures of reindeer district
# N - reindeer population size at the end of the reindeer production year
# density - reindeer density at the end of the reindeer production year (N/area)
#
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# Reading in the data and some data manipulations
varit.dat<-read.table("13570_2021_209_MOESM1_ESM.txt", sep = ",", header=T) # read in the data
varit.dat$log.density<-log(varit.dat$density)  # calculate log(density) and save as variable log.density

# Generate subset index variable coded 0 for observations with a density estimate available, more than 24 varit slaughter weight observations
# mainland districts excluding district 36 and 16A, 16B and 16C
subset.index<-ifelse(is.na(varit.dat$density)|varit.dat$n.varit.wt<25|varit.dat$type=="island"|varit.dat$District%in%c("16A", "16B", "16C","36"), 1, 0)

# Generate subset index variable coded 0 for years 1998-2001 and subset.index = 0 and coded 1 else 
subset.index1 <-ifelse(subset.index==1|varit.dat$year>2001|varit.dat$year==1998, 1, 0)
# Generate subset index variable coded 0 for years 2002-2019 and subset.index = 0 and coded 1 else 
subset.index2 <-ifelse(subset.index==1|varit.dat$year%in%c(1999, 2000, 2001), 1, 0)

mean.logD<-mean(varit.dat$log.density[subset.index==0]) # calculate average log(density) for data used in analyses (subset.index==0) 
varit.dat$center.logD<-varit.dat$log.density-mean.logD  # center estimates of log(density)

# fit the linear model using data from the subset of years 1998-2001 and log(densities) as predictor
lm.varit.subyrs<-lm(varit~log(density), data=varit.dat, subset=subset.index1==0)
round(summary(lm.varit.subyrs)$r.squared,2) # Extract r-squared from fitted model  
# [1] 0.65    # Slightly lower r-squared value than the value (r-squared = 0.70) reported in Ims & Kosmo (2001)
              # much higher value than estimated (r-squared = 0.25) for the 1998-2001 data used in Marin et al. 

# fit the linear model using data from all the years 1998-2019 
lm.varit.allyrs<-lm(varit~log(density), data=varit.dat, subset=subset.index==0)
round(summary(lm.varit.allyrs)$r.squared,2) # Extract r-squared from fitted model  
#[1] 0.47             # Slightly lower r-squared value than the value estimated for 1998-2019 
                      # much higher value than estimated (r-squared = 0.24) for the data used in Marin et al. 


# Figure 1
par(mar=c(5,6,2,2))
plot(varit~density, data=varit.dat, subset=subset.index==0, type="n", xaxt="n", xlab="Reindeer density", ylab="Varit slaughter weight", las=1, cex.lab=1.5, cex.axis=1.5, xlim=c(0,19) )
axis(1, at=c(0:20), labels=F, tcl=-0.5)
axis(1, at=seq(0,20, by=5), labels=T, cex.axis=1.5, tcl=-0.5)
points(varit~density, data=varit.dat, subset=subset.index1==0, pch=16, cex=1.5)
points(varit~density, data=varit.dat, subset=subset.index2==0, pch=1, cex=1.5)
lines(1:19, lm.varit.allyrs$coefficients[1]+lm.varit.allyrs$coefficients[2]*log(1:19), lty=1, lwd=3)

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# Linear mixed model with year and District fitted as random intercepts and log(density) fitted as random slope varying between District
# Model fitted using centered log(density) estimates

library(lme4)
library(MuMIn)

# fit full model
lmm.full<-lmer(varit~center.logD +(center.logD|District)+(1|year), data=varit.dat, subset=subset.index==0)

# Estimates from model 
summary(lmm.full)

# calculate approximate estimates of r-squared for fixed effects r-squared -  R2m, 
# and full model (fixed and random effects) - R2c 
r.squaredGLMM(lmm.full)
#           R2m       R2c
#[1,] 0.3744239 0.8035477

# fit reduced model without random log(density) slopes
lmm.red<-lmer(varit~center.logD +(1|District)+(1|year), data=varit.dat, subset=subset.index==0)

# calculate likelihood ratio test statistic
chistat <- anova(lmm.red, lmm.full)[2,"Chisq"]
# calculate p-value for test of random slopes variance being different from zero
0.5 * pchisq(chistat, 1, lower.tail=FALSE) + 0.5 * pchisq(chistat, 2, lower.tail=FALSE)
# [1] 0.1548859