analysiscode.Rmd

---
title: Environmental Analysis - How do sites differ and does this determine rates
  of clonality?
author: "Amanda Stahlke"
date: "5/13/2020"
output:
  pdf_document: default
  html_document:
    df_print: paged
  word_document: default
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
citation()

library(BiodiversityR)
library(vegan)
 citation("vegan")
library(goeveg)
library(lme4)
library(MuMIn)
  citation("MuMIn")
library(rpart)
library(party)
library(subselect)
library(MASS)

library(dplyr)
library(reshape2)
library(ggplot2)
```

# Import data and subset

```{r prepdata}
gen_env<-na.omit(read.csv("geno_enviro.csv"))
names(gen_env)
#gen_env$BL<-gen_env$bare+gen_env$litter #composite background variable
gen_env$Site<-as.factor(gen_env$Site)
head(gen_env)
```

```{r GNrank}
site_GN_rank <- gen_env %>%
  group_by(Site) %>%
  summarise(unique(GN_Rank))
site_GN_rank 

clone_rate <- gen_env %>%
  group_by(Site) %>%
  summarise(sum(Clone)) %>%
  mutate(clone_rate=1-`sum(Clone)`/15) %>%
  as.data.frame()
merge(clone_rate, site_GN_rank)

stemcts <- gen_env %>%
  # group_by(Site) %>%
  summarise(avg=mean(stem), sd=sd(stem)) %>%
  mutate(avg/(100))

arrange(gen_env, stem) %>%
  dplyr::select(site.plot.subplot, stem)

```

## Create vegetation matrix
Aggregate site variables for the average and standard deviation across a site.

```{r aggregate_and_GNrank}
#####Veg summary
veg_mat<-aggregate(list("grass"=gen_env$grass,"bare"=gen_env$bare,"draba"=gen_env$Ldraba.cvr,"litter"=gen_env$litter, "forb"=gen_env$forb),
                   by=list("Site"=gen_env$Site),FUN=mean)

veg_mat.sd<-aggregate(list("grass"=gen_env$grass,"bare"=gen_env$bare,"draba"=gen_env$Ldraba.cvr,"litter"=gen_env$litter),
                   by=list("Site"=gen_env$Site),FUN=sd)

GN<-read.csv("G_N_bysite.csv")
veg_mat$R_GN<-GN[,"R_GN"]
veg_mat$GN<-GN$site.G.N
veg_mat
```

R_GN is the rank of G/N across sites.
From least to most clonal: Site 1, 6, 3, 5, 2, 4. 
For the following plots, these variables are plotted against the G/N rank. 
I'm not sure how I feel about this because GN isn't uniformly distributed. Sites 3 and 6 have almost the same GN, for example.


```{r vegplotsgrass}
plot(veg_mat$R_GN,veg_mat$grass)
plot(veg_mat$R_GN,veg_mat$bare)
plot(veg_mat$R_GN,veg_mat$litter)
plot(veg_mat$R_GN,veg_mat$forb)
plot(veg_mat$grass,veg_mat$forb)

plot(veg_mat$R_GN,veg_mat$draba,xaxt="n",ylim=c(0,60),ylab="% Draba",xlab="Prevalence of Clones")
plot(veg_mat$R_GN,veg_mat$grass,xaxt="n",ylim=c(0,60),ylab="% Grass", xlab="Prevalence of Clones")
plot(veg_mat$R_GN,veg_mat$bare,xaxt="n",ylim=c(0,60),ylab="% Bare",xlab="Prevalence of Clones")
```

Grass is highly variable across sites. Bare ground seems to best seperate the low and high clonal sites.The most clonal sites have the most bare ground (but it's still only about 10%).

## What are the general site-level differences among measured variables we think are probably important? 

```{r}
 ggplot(data = gen_env, aes(x=canopy)) +
  geom_histogram()

ggplot(data = gen_env, aes(x=Site, y=canopy)) +
  geom_boxplot() + 
  geom_point(alpha=0.3)
 ggsave("canopy_site.jpg")

 ggplot(data = gen_env, aes(x=Site, y=woody)) +
  geom_boxplot() + 
  geom_point(alpha=0.3)
ggsave("woody_site.jpg")

ggplot(data = gen_env, aes(x=Site, y=K)) +
  geom_boxplot() + 
  geom_point(alpha=0.3)
  
ggplot(data = gen_env, aes(x=Site, y=litter)) +
  geom_boxplot() + 
  geom_point(alpha=0.3)
 ggplot(data = gen_env, aes(x=Site, y=grass)) +
  geom_boxplot() + 
  geom_point(alpha=0.3)
 ggsave("grass_site.jpg")
ggplot(data = gen_env, aes(x=Site, y=forb)) +
  geom_boxplot() + 
  geom_point(alpha=0.3)
 ggsave("forb_site.jpg")
ggplot(data = gen_env, aes(x=Site, y=bare)) +
  geom_boxplot() + 
  geom_point(alpha=0.3)
  ggsave("bare_site.jpg")
 ggplot(data = gen_env, aes(x=Site, y=stem)) +
  geom_boxplot() + 
  geom_point(alpha=0.3) 
   ggsave("stem_site.jpg")
ggplot(data = gen_env, aes(x=Site, y=Ldraba.cvr)) +
  geom_boxplot() + 
  geom_point(alpha=0.3) 
   ggsave("Ldraba.cvr_site.jpg")
   
ggplot(data = gen_env, aes(x=Site, y=Sand)) +
  geom_boxplot() + 
  geom_point(alpha=0.3) 
  ggsave("Sand_site.jpg")
   
```


# Correlation among vriables 

Next, look at soil nutrient variables. 
```{r correlation}
cormat <- round(cor(gen_env[,c(6:9,11:dim(gen_env)[2])],  method = "spearman"),2) # drop texture and site

# Get upper triangle of the correlation matrix
  get_upper_tri <- function(cormat){
    cormat[lower.tri(cormat)]<- NA
    return(cormat)
  }
  
upper_tri <- get_upper_tri(cormat)
melted_cormat <- melt(upper_tri, na.rm = TRUE)

ggplot(data = melted_cormat, aes(x=Var1, y=Var2, fill=value)) + 
  geom_tile(color = "white")+
 scale_fill_gradient2(low = "blue", high = "red", mid = "white", 
   midpoint = 0, limit = c(-1,1), space = "Lab", 
   name="Spearman\nCorrelation") +
  theme_minimal()+ 
 theme(axis.text.x = element_text(angle = 45, vjust = 1, 
    hjust = 1))+
 coord_fixed()

melted_cormat %>%
  filter(abs(value) >.5 & value <1) %>%
  arrange(desc(value))

melted_cormat %>%
  filter(Var1 == "Clone" |  Var2 == "Clone") %>%
  arrange(desc(value))

melted_cormat %>%
  filter(Var1 == "stem" |  Var2 == "stem") %>%
  arrange(desc(abs(value)))

melted_cormat %>%
  filter(Var1 == "bare" |  Var2 == "bare") %>%
  arrange(desc(abs(value)))

melted_cormat %>%
  filter(Var1 == "grass" |  Var2 == "grass") %>%
  arrange(desc(abs(value)))

melted_cormat %>%
  filter(Var1 == "forb" |  Var2 == "forb") %>%
  arrange(desc(abs(value)))

melted_cormat %>%
  filter(Var1 == "Sand" |  Var2 == "Sand") %>%
  arrange(desc(abs(value)))

melted_cormat %>%
  filter(Var1 == "canopy" |  Var2 == "canopy") %>%
  arrange(desc(abs(value)))

```

## Drop highly correlated variables for envfact

```{r drop_correlation_envfact}
names(gen_env)
env_fact<-gen_env[,11:dim(gen_env)[2]]
names(env_fact)

fact_drops<-c("Ca","Clay","Cu","Salts", "woody", "bare", "litter")
env_fact<-data.frame(env_fact[,-which(names(env_fact)%in%fact_drops)])
head(env_fact)
```

Drop Ca, Clay, Cu, and Salts

#NMDS of subplots
```{r NMDS}
env.mds<-metaMDS(env_fact, distance = "gower", k=4)
stressplot(env.mds)
```

```{r NMDS2}
env.mds2<-metaMDS(env_fact, distance = "gower", k=4, previous.best = env.mds)
stressplot(env.mds2)
```

*** Solution reached
Non-metric fit is better than linear 

```{r stress_dims}
dim.result <- dimcheckMDS(env_fact,distance="gower",k=8,trymax = 20)
data.frame(dimension = seq_along(dim.result), stress=dim.result)
```
Stress is still barely above .2 at 2 dimensions, might as well show 3 dims. 

```{r NMDS_plot_site, warning=F, message=F}
env.plot<-ordiplot(env.mds,display = "sites",type="n", choices = c(3,2))
ordisymbol(env.plot, gen_env, "Site", legend=TRUE,cex=2,lwd=2,choices = c(3,2))
env.factors<-envfit(env.mds,env_fact, permutations = 999)
plot(env.factors, p.max=0.01)
```

Here, symbols represent the G/N ranking, where 1 is fewest clones and 6 is most. 
```{r NMDS_plot_GNrank, warning=F, message=F}
env.plot<-ordiplot(env.mds,display = "sites",type="n", choices = c(1,2))
ordisymbol(env.plot, gen_env, "GN_Rank", legend=TRUE,cex=2,lwd=2,choices = c(1,2))
env.factors<-envfit(env.mds,env_fact)
plot(env.factors)
```

# Examine multivariate dispersion among sites
Betadispersion - sites. Create a dissimilarity matrix for betdispersion analysis; Looks at multivariate dispersion (variance) among SITES

```{r betadisp}
commax<-vegdist(env_fact, method = "gower")
fum<-with(gen_env,betadisper(commax,Site))
plot(fum)
fum
boxplot(fum) #variation among sampled points
permutest(fum) #-- Difference in multivariate dispersion between sites
plot(TukeyHSD(fum))
```

# Make composite soil variables 
## from soils NMDS

```{r make_soilz_MDS}
soilz<-gen_env[,c("pH","OM","Nitrate","K","S",
                  "Zn","Fe","Mn","Mg","Na","CEC","P")] 

soilz.mds<-metaMDS(soilz,distance = "gower", k=4)
soilz.mds<-metaMDS(soilz,distance = "gower", k=4,
                   previous.best = soilz.mds)

dim.soil.result <- dimcheckMDS(soilz,distance="gower",k=4,trymax = 20)
data.frame(dimension = seq_along(dim.soil.result), stress=dim.soil.result)

## soil variables for multimodel comparison
# soil.nut1<-soilz.mds$points[,"MDS1"]
# soil.nut2<-soilz.mds$points[,"MDS2"]
```


```{r plot_soilz_NMDS}
nut.plot<-ordiplot(soilz.mds,display = "sites",type="n")
ordisymbol(nut.plot, gen_env, "Site", legend=TRUE,cex=2,lwd=2)
nut.factors<-envfit(soilz.mds,soilz)
plot(nut.factors)

```

## Make soil variables from PCoA

```{r envfact_pcoa}

soilz.D <- vegdist(soilz, "gower")
soilz.factors<-envfit(soilz.D, soilz, perm=999)

soilz.pcoa <- cmdscale(env_fact.D,eig=TRUE, k=NROW(soilz)-1)
soilz.plot<-ordiplot(soilz.pcoa,display = "sites",type="n")
ordisymbol(soilz.plot, gen_env, "Site", legend=TRUE,cex=2,lwd=2)
plot(soilz.factors)

eig <- eigenvals(soilz.pcoa)
eig/ sum(eig)
cumsum(eig/ sum(eig)) 


#soil variables for multimodel comparison
soilz.pcoa1<-soilz.pcoa$points[,1]
soilz.pcoa2<-soilz.pcoa$points[,2]

barplot(soilz.pcoa$eig)
cumsum(soilz.pcoa$eig)
```

```{r}
soilz.D <- vegdist(soilz, "gower")
res <- ape::pcoa(soilz.D)
nut.factors<-envfit(soilz.D, soilz, perm=999)

biplot(res, rn=gen_env$Site)
plot(nut.factors, p.max=.05)

#soil variables for multimodel comparison
soil.nut.pcoa1<-res$vectors[,"Axis.1"]
soil.nut.pcoa2<-res$vectors[,"Axis.2"]

barplot(res$values$Relative_eig)
cumsum(res$values$Relative_eig)
cumsum(res$eig)/sum(res$eig)
```

# Do we need to account for site? 
```{r anosim_adonis, cache=TRUE}
env2 <- gen_env[,c(11:ncol(gen_env))]
env2 <- as.matrix(env2)
colnames(env2)

# vegdist(env2, distance = "gower")
anosim <- anosim(env2, grouping = gen_env$Site, distance = "gower", permutations = 9999) 
anosim
plot(anosim)

adonis <- adonis2(env2 ~ gen_env$Site)
adonis
```


# Global model for multi-model comparison; Clone 0,1

glm() fits a generalized linear model and glmer() fits linear mixed effects models
Global model includes Sand, grass, litter, soil, poca nutrients 1, pcoa nutrients 2. glmer allows inclusions of site as a random factor. 

```{r global_glm_glmer}
cl_global_forb_glm <- glm(Clone ~ Sand+grass+forb+canopy+ 
                    soil.nut.pcoa1+soil.nut.pcoa2,
                    data=gen_env,family="binomial",
                    na.action = "na.fail",weights = rep(15,dim(gen_env)[1]))
summary(cl_global_forb_glm)

cl_global_forb_site <- glmer(Clone ~ Sand+grass+forb+canopy+
                  soil.nut.pcoa1 +
                  soil.nut.pcoa2 + (1|gen_env$Site),
                  data=gen_env, family="binomial", 
                  na.action = "na.fail",
                  weights = rep(15,dim(gen_env)[1]))
summary(cl_global_forb_site)

anova(cl_global_forb_site, cl_global_forb_glm)
```

Inclusion of site as random effect impoves AIC. When site was included as a random effect, Sand gains significance. 

```{r reduce_the_model}

cl_redux1_forb_site <- glmer(Clone ~ Sand+grass+forb+
                  soil.nut.pcoa1 +
                  (1|gen_env$Site),
                  data=gen_env, family="binomial", 
                  na.action = "na.fail",
                  weights = rep(15,dim(gen_env)[1]))
summary(cl_redux1_forb_site)

anova( cl_global_forb_site, cl_redux1_forb_site)
```

Any points with extra high influence of the glm? Can't run Cook's distance with the mixed effects model unfortunately. 


```{r cooks_round_1}
cooksd<-cooks.distance(cl_global_forb_glm)
plot(cooksd)
abline(h = 4*mean(cooksd, na.rm=T), col="red")
text(x=1:length(cooksd)+1, y=cooksd, labels=ifelse(cooksd>4*mean(cooksd, na.rm=T),names(cooksd),""), col="red")  # add labels
influential <- as.numeric(names(cooksd)[(cooksd > 4*mean(cooksd, na.rm=T))])

cbind(gen_env[influential, ],soil.nut.pcoa1[influential],soil.nut.pcoa2[influential])

```
Remove these subplots and run again.

```{r remove outliers}
gen_env_pruned <- gen_env[-influential,]
soil.nut.pcoa1_pruned<-res$vectors[-influential,"Axis.1"]
soil.nut.pcoa2_pruned<-res$vectors[-influential,"Axis.2"]

cl_global_glm_pruned<-glm(Clone ~ 
           Sand+grass+forb+canopy+
             soil.nut.pcoa1_pruned+soil.nut.pcoa2_pruned,
           data=gen_env_pruned, family="binomial",
           na.action="na.fail",
           weights = rep(13,dim(gen_env_pruned)[1]))

cl_global_glmer_pruned <- glmer(Clone ~ 
           Sand+grass+forb+canopy+
             soil.nut.pcoa1_pruned + soil.nut.pcoa2_pruned 
           +(1|gen_env_pruned$Site),
           data=gen_env_pruned, 
           family="binomial", 
           na.action = "na.fail",
           weights = rep(13,dim(gen_env_pruned)[1]))

summary(cl_global_glm_pruned)
summary(cl_global_glmer_pruned)

anova(cl_global_glmer_pruned, cl_global_glm_pruned)
```

After removing outlier subplots 1.1.4, 4.3.13, and 5.3.13, soilt.nut.pcoa2 lost significance. Are there outliers in this model? 

```{r cooks_round_2}
cooksd_pruned<-cooks.distance(cl_global_glm_pruned)
plot(cooksd_pruned)
abline(h = 4*mean(cooksd_pruned, na.rm=T), col="red")
text(x=1:length(cooksd_pruned)+1, y=cooksd_pruned,
     labels=ifelse(cooksd_pruned > 4*mean(cooksd_pruned,na.rm=T),
                   names(cooksd_pruned),""), col="red")  # add labels
influential <- as.numeric(names(cooksd_pruned)
                          [(cooksd_pruned > 4*mean(cooksd_pruned,
                                                   na.rm=T))])
cbind(gen_env_pruned[influential,],
      soil.nut.pcoa1_pruned[influential],
      soil.nut.pcoa2_pruned[influential])

```
Yes, but they're from different sites and not all clonal. Leave them in. 

## Does site 4 have an outsized effect? 

```{r drop_4}
drop4 <- which(gen_env$Site == 4)
gen_env_pruned4 <- gen_env[-drop4,]
soil.nut.pcoa1_pruned4 <-res$vectors[-drop4,"Axis.1"]
soil.nut.pcoa2_pruned4 <-res$vectors[-drop4,"Axis.2"]


cl_global_glm_pruned4<-glm(Clone ~
                            Sand+grass+forb+
                            soil.nut.pcoa1_pruned4 + soil.nut.pcoa2_pruned4,
                          data=gen_env_pruned4,
                          family="binomial",
                          na.action="na.fail",
                          weights = rep(15,dim(gen_env_pruned4)[1]))


cl_global_glmer_pruned4<-glmer(Clone ~
                                Sand+grass+forb+
                                soil.nut.pcoa1_pruned4 + soil.nut.pcoa2_pruned4
                              +(1|gen_env_pruned4$Site),
                              data=gen_env_pruned4,
                              family="binomial",
                              na.action = "na.fail",
                              weights = rep(15,dim(gen_env_pruned4)[1]))

summary(cl_global_glm_pruned4)
summary(cl_global_glmer_pruned4)

anova(cl_global_glmer_pruned4, cl_global_glm_pruned4)
```
After dropping site 4, the glmer incorporating site was still a significantly better model.The glmer identfied Sand (p <.001), and grass, forb, and soil.nut1 (p< .001).  

Outliers? 

```{r}
cooksd_pruned <- cooks.distance(cl_global_glm_pruned4)
plot(cooksd_pruned)
abline(h = 4*mean(cooksd_pruned, na.rm=T), col="red")
text(x=1:length(cooksd_pruned)+1, y=cooksd_pruned,
     labels=ifelse(cooksd_pruned > 4*mean(cooksd_pruned,na.rm=T),
                   names(cooksd_pruned),""), col="red")  # add labels
influential <- as.numeric(names(cooksd_pruned)
                          [(cooksd_pruned > 4*mean(cooksd_pruned, na.rm=T) )] )

cbind(gen_env_pruned4[influential,],
      soil.nut.pcoa1_pruned4[influential],
      soil.nut.pcoa1_pruned4[influential])

```
1.1.4, 2.2.9, and 6.3.13 have outsize effect now.  Leave these in and more on. Continue to parse down the glmer without site 4. 

```{r}
cl_redux1_glmer_pruned4<-glmer(Clone ~
                                Sand+grass+forb+
                                soil.nut.pcoa1_pruned4
                              + (1|gen_env_pruned4$Site),
                              data=gen_env_pruned4,
                              family="binomial",
                              na.action = "na.fail",
                              weights = rep(15,dim(gen_env_pruned4)[1]))
summary(cl_redux1_glmer_pruned4)

anova(cl_global_glmer_pruned4, cl_redux1_glmer_pruned4)


cl_redux2_glmer_pruned4<-glmer(Clone ~
                                grass+forb+
                                soil.nut.pcoa1_pruned4
                              +(1|gen_env_pruned4$Site),
                              data=gen_env_pruned4,
                              family="binomial",
                              na.action = "na.fail",
                              weights = rep(15,dim(gen_env_pruned4)[1]))
summary(cl_redux2_glmer_pruned4)

anova(cl_redux1_glmer_pruned4, cl_redux2_glmer_pruned4)
```

Not a significant improvement by removing anything there. Same variables, same directons of effect. 

Sand           2.44e-07 ***
grass          6.61e-11 ***
forb           6.55e-08 ***
soil.nut.pcoa1 1.85e-08 ***

Include site 4 and move on. Decompose soil nutrients as possible: 

## Can we identify individual soil variables that predict subplot clonality? 

```{r}
cl_nutrs_glmer <- glmer(Clone ~
              Sand + forb + grass +
              I(K/100)+ OM + Fe + Zn + S + Mn  
              +  (1|gen_env$Site),
             data=gen_env,family="binomial",
            na.action = "na.fail",
             weights = rep(15,dim(gen_env)[1]))

summary(cl_nutrs_glmer)

dd<-dredge(cl_nutrs_glmer)
importance(subset(dd, delta<4))
importance(subset(dd, delta<=2))

```
Okay! Forb, grass, Sand, OM, and S are all in the top models every time.  

## Re-scale some variables to account for scale of measurement issues. 

```{r rescale_vars}
cl_global_glmer_rescaled <-glmer(Clone ~ 
           I(Sand/100) + I(grass/100) +I(forb/100)+
             soil.nut.pcoa1 +
           +(1|gen_env$Site),
           data=gen_env, 
           family="binomial", 
           na.action = "na.fail",
           weights = rep(15,dim(gen_env)[1]))
summary(cl_global_glmer_rescaled)


cl_nutrs_glmer <- glmer(Clone ~
              I(Sand/100) + I(grass/100) +I(forb/100)+
              OM + S
              +  (1|gen_env$Site),
             data=gen_env,family="binomial",
            na.action = "na.fail",
             weights = rep(15,dim(gen_env)[1]))
summary(cl_nutrs_glmer)

```

OM is highlighy negatively correlated with bare ground. (Check OM variation too.)

## Plot model results
```{r ggcoefstats}
library(ggstatsplot)

# for reproducibility
set.seed(123)

# plot
ggstatsplot::ggcoefstats(
  cl_nutrs_glmer,
  point.args = list(color = "red", shape = 15),
  vline.args = list(color = "#CC79A7", linetype = "dotdash"),
  # stats.label.color = c("#0072B2", "#D55E00", "darkgreen"),
  # title = "Subplot clonality predicted by environmental conditions",
  # ggtheme = hrbrthemes::theme_ipsum_ps(),
  ggstatsplot.layer = FALSE) + # note the order in which the labels are entered
  # +
  ggplot2::scale_y_discrete(labels = c("Sand", "Grass Cover", "Forb Cover", "OM", "S")) +
ggplot2::labs(x = "regression coefficient", y = NULL)
ggsave("subplotclonality_forb_glmer_final.jpg", height = 4.5, width = 6, units = "in", dpi = 300)
```

# Do the same predictors of clonality predict Stem density (1-inf)?
lmer for continuous cariable: count of stems with random effect of site. 

```{r}
stem_global_lmer_rescaled <-lmer(stem ~ 
           I(Sand/100) + I(grass/100) +I(forb/100)+ I(canopy/100)+ 
             soil.nut.pcoa1 +
             soil.nut.pcoa2 +                          
           (1|gen_env$Site),
           data=gen_env, 
           na.action = "na.fail")
summary(stem_global_lmer_rescaled)

stem_global_lm_rescaled <- lm(stem~
                     I(Sand/100) + I(grass/100) +I(forb/100)+I(canopy/100)+ 
                      soil.nut.pcoa1 +
                    soil.nut.pcoa2,
                      data=gen_env)
summary(stem_global_lm_rescaled)

stem_global_lm_rescaled_litter <- lm(stem~
                     I(Sand/100) + I(litter/100) + I(forb/100) +
                      soil.nut.pcoa1 +
                    soil.nut.pcoa2,
                      data=gen_env)
summary(stem_global_lm_rescaled_litter)

stem_global_lm_rescaled_litter_grass <- lm(stem~
                     I(Sand/100) + I(litter/100) + I(grass/100) +
                      soil.nut.pcoa1 +
                    soil.nut.pcoa2,
                      data=gen_env)
summary(stem_global_lm_rescaled)

anova(stem_global_lmer_rescaled, stem_global_lm_rescaled)

```

```{r cooks_stem_lm}
cooksd <- cooks.distance(stem_global_lm_rescaled)
plot(cooksd)
abline(h = 4*mean(cooksd, na.rm=T), col="red")
text(x=1:length(cooksd)+1, y=cooksd,
     labels=ifelse(cooksd > 4*mean(cooksd,na.rm=T),
                   names(cooksd),""), col="red")  # add labels
influential <- as.numeric(names(cooksd)
                          [(cooksd > 4*mean(cooksd, na.rm=T) )] )

cbind(gen_env[influential,],
      soil.nut.pcoa1[influential],
      soil.nut.pcoa2[influential])

gen_env_pruned <- gen_env[-influential,]
soil.nut.pcoa1_pruned<-res$vectors[-influential,"Axis.1"]
soil.nut.pcoa2_pruned<-res$vectors[-influential,"Axis.2"]

```

Removed overly influential subplots - try again to fit a model. 

```{r}
stem_global_lmer_rescaled_pruned <-lmer(stem ~ 
           I(Sand/100) + I(grass/100) +I(forb/100)+
             soil.nut.pcoa1_pruned +
             soil.nut.pcoa2_pruned +                          
           (1|gen_env_pruned$Site),
           data=gen_env_pruned, 
           na.action = "na.fail")
summary(stem_global_lmer_rescaled_pruned)

stem_global_lm_rescaled_pruned <- lm(stem~
                     I(Sand/100) + I(forb/100) +I(grass/100)+
                    soil.nut.pcoa1_pruned +
                    soil.nut.pcoa2_pruned,
                      data=gen_env_pruned)
summary(stem_global_lm_rescaled_pruned)

stem_global_lm_rescaled_pruned <- lm(stem~
                     I(Sand/100) + I(forb/100) +I(grass/100),
                      data=gen_env_pruned)
summary(stem_global_lm_rescaled_pruned)

stem_global_lm_rescaled_pruned <- lm(stem~
                     I(Sand/100) + I(forb/100),
                      data=gen_env_pruned)

anova(stem_global_lmer_rescaled_pruned, stem_global_lm_rescaled_pruned)
```



```{r}

stem_redux1_lm_rescaled_pruned <- lm(stem ~
                     I(Sand/100) + I(forb/100)+
                    soil.nut.pcoa1_pruned +
                    soil.nut.pcoa2_pruned,
                      data=gen_env_pruned)
summary(stem_global_lm_rescaled_pruned)

anova(stem_global_lm_rescaled_pruned, stem_redux1_lm_rescaled_pruned) # nope

stem_redux2_lm_rescaled_pruned <- lm(stem ~
                     I(Sand/100) + I(forb/100)+
                    soil.nut.pcoa1_pruned, 
                      data=gen_env_pruned)
summary(stem_redux2_lm_rescaled_pruned)

anova(stem_global_lm_rescaled_pruned, stem_redux2_lm_rescaled_pruned) # nope 


stem_redux3_lm_rescaled_pruned <- lm(stem ~
                     I(Sand/100) + I(forb/100),
                      data=gen_env_pruned)
summary(stem_redux3_lm_rescaled_pruned)


anova(stem_global_lm_rescaled_pruned, stem_redux3_lm_rescaled_pruned) # nope 
```

```{r}
stem_nutrs_lm <- lm(stem ~
              I(Sand/100) + I(grass/100) +I(forb/100)+   
              I(K/100)+ OM + Fe + Zn + S + Mn,
              na.action = "na.fail",
             data=gen_env_pruned)
summary(stem_nutrs_lm)

dd<-dredge(stem_nutrs_lm)
subset(dd,delta<=2)
importance(dd)#)
importance(subset(dd, delta<=2))
```

```{r}
stem_redux_nutrs_lm <- lm(stem ~
              I(Sand/100) + I(forb/100) +
               Fe, 
              na.action = "na.fail",
             data=gen_env_pruned)
summary(stem_redux_nutrs_lm)

stem_redux_nutrs_lm <- lm(stem ~
              I(Sand/100),
              na.action = "na.fail",
             data=gen_env_pruned)
summary(stem_redux_nutrs_lm)
```
It's basically just sand. 

```{r}
ggplot(gen_env_pruned, 
       aes(x= Sand, y = stem)) +
  geom_smooth(method='lm', formula= y~x) +
  geom_point(aes(shape = as.factor(Clone), color = as.factor(Site))) + 
  theme_bw()
```
Not very convincing. 

Stacked barplot of clonality v nonclonality along Sand/Grass/OM gradient

```{r}
ggplot(data= gen_env) +
  geom_histogram(aes(x= Sand, fill = as.factor(Clone)), alpha = .5)

ggplot(data= filter(gen_env,Clone==0)) +
  geom_histogram(aes(x= Sand))
ggplot(data= filter(gen_env,Clone==1)) +
  geom_histogram(aes(x= Sand))

ggplot(data=gen_env,aes(x=Sand,fill=Clone)) + 
  geom_bar(data=subset(gen_env,Clone==1)) + 
  geom_bar(data=subset(gen_env,Clone==0), aes(y=..count..*(-1))) + 
  # scale_y_continuous(breaks=seq(-40,40,10),labels=abs(seq(-40,40,10))) + 
  coord_flip()

ggplot(data=gen_env,aes(x=grass,fill=Clone)) + 
  geom_bar(data=subset(gen_env,Clone==1)) + 
  geom_bar(data=subset(gen_env,Clone==0), aes(y=..count..*(-1))) + 
  # scale_y_continuous(breaks=seq(-40,40,10),labels=abs(seq(-40,40,10))) + 
  coord_flip()

ggplot(data=gen_env,aes(x=forb,fill=Clone)) + 
  geom_bar(data=subset(gen_env,Clone==1)) + 
  geom_bar(data=subset(gen_env,Clone==0), aes(y=..count..*(-1))) + 
  # scale_y_continuous(breaks=seq(-40,40,10),labels=abs(seq(-40,40,10))) + 
  coord_flip()
```


```{r}
stem_global_lm_rescaled_litter <- lm(stem~
                     I(Sand/100) + I(grass/100) +I(litter/100)+
                      soil.nut.pcoa1 +
                    soil.nut.pcoa2,
                      data=gen_env)
summary(stem_global_lm_rescaled_litter)
```



```{r}
stem_clone<- select(gen_env, c(stem, Clone))
gen_env_Clone <- filter(stem_clone, Clone==1)
gen_env_noClone <- filter(stem_clone, Clone==0)

gen_env$Clone <- as.factor(gen_env$Clone)

ggplot(stem_clone, 
       aes(x= Clone, y = stem)) +
  geom_violin() +
  geom_point()

ggstatsplot::ggbetweenstats(
  data = gen_env,
  x = Clone,
  y = stem,
  outlier.tagging = TRUE,
  outlier.label = site.plot.subplot,
  type = "p"
)

ggstatsplot::ggbetweenstats(
  data = gen_env,
  x = Clone,
  y = forb,
  outlier.tagging = TRUE,
  outlier.label = site.plot.subplot,
  type = "p"
)

```

paring down the soil data
have to NAomit as missing NH4_N values for rows 1,18,and 32

```{r}
soil<-na.omit(gen_env[,c("Site","pH","OM","Nitrate","K","S","Zn","Fe","Mn","Mg","Na","CEC","P")])
irisHmat <- ldaHmat(soil[,2:dim(soil)[2]],soil$Site)
eleaps(irisHmat$mat,kmin=2)#,H=irisHmat$H,r=irisHmat$r,crit="ccr12")
```


```{r}
fit <- lda(Site ~ K + Mg + Na, data=soil, na.action=na.exclude,
           CV=TRUE)
fit # show results
```


# Canonical Analysis of Principal Coordinates 
As in Andreson & Willis 2003, Biodiversity R package
In constrained ordination we do not want to display all or even most ofthe compositional variation, but only the variation that can be explained by the used environmental variables, or constraints.

```{r}
gen_env$factClone<-as.factor(gen_env$Clone)

Ordination.model1 <- CAPdiscrim(soilz~factClone,
                                data=gen_env,
                                dist="gower", 
                                axes=3, m=0, add=FALSE)
Ordination.model1

# data(env_fact)
# Ordination.model1 <- CAPdiscrim(env_fact~Site,
#                                 data=gen_env,
#                                 dist="gower",
#                                 axes=2, m=0,
#                                 add=FALSE,
#                                 permutations = 100)
# Ordination.model1

plot1 <- ordiplot(Ordination.model1)
ordisymbol(plot1, gen_env, "Clone", legend=TRUE)

sitz<-envfit(Ordination.model1, 
             env_fact[,c("grass","OM","S","Sand","Fe","Zn")], 
             choices = c(1,2))
sitz.text<-envfit(Ordination.model1,gen_env[,c("bare","grass","Mg","Na","K")])
ordisymbol(plot1, gen_env, "Site", legend=TRUE)
plot(sitz)
plot(sitz.text)
plot2 <- ordiplot(Ordination.model1, type="none",choices = c(1,2))
ordisymbol(plot2, gen_env,"Site", legend = T)
plot(sitz)

```



```{r}
# plot change in classification success against m (#classification dimensions for LDA)
plot(seq(1:14), rep(-1000, 14), xlim=c(1, 14), ylim=c(0, 100), xlab="m",
     ylab="classification success (percent)", type="n")

for (mseq in 1:14) {
  CAPdiscrim.result <- CAPdiscrim(soilz~Site, data=gen_env, 
                                  dist="gower", axes=2, m=mseq)
  points(mseq, CAPdiscrim.result$percent)
}

```

```{r}
stMod.1<-glm(Clone~grass+bare+Zn+Fe+OM+Mn,data=gen_env[gen_env$Site==1,],family="binomial",na.action = "na.fail")
summary(stMod.1)
stepAIC(stMod.1,direction = "both")
```


```{r}
gen_env$factClone<-as.factor(gen_env$Clone)

env.mds2

#### use vegetation matrix instead
Ordination.model1 <- CAPdiscrim(soilz~factClone,
                                data=gen_env,
                                dist="gower", 
                                axes=3, m=0, add=FALSE)
Ordination.model1

```

```{r}
plot1 <- ordiplot(Ordination.model1, type="none")
# ordisymbol(plot1, gen_env, "Clone", legend=TRUE)
ordisymbol(plot1, gen_env, "Site", legend=TRUE)
clonz<-envfit(Ordination.model1,soilz)
plot(clonz)
```

Plot change in classification success against m (#classification dimensions for LDA)
```{r}
plot(seq(1:14), rep(-1000, 14), xlim=c(1, 14), ylim=c(0, 100), xlab="m", 
     ylab="classification success (percent)", type="n")
for (mseq in 1:14) {
  CAPdiscrim.result <- CAPdiscrim(soilz~Site, data=gen_env, 
                                  dist="gower", axes=2, m=mseq)
  points(mseq, CAPdiscrim.result$percent)
}


summary(CAPdiscrim(soilz~Site, data=gen_env, 
                                  dist="gower", axes=2))
```


```{r}
# #####Diversity and Evenness (as calculated in Gaskin 2006)
# bySite<-read.csv("G_N_bysite.csv")
# byPlot<-read.csv("G_N_bysiteplot.csv")
# GID_S<-read.csv("G_ID_Site.csv")
# GID_P<-read.csv("G_ID_Plot.csv")
# 
# GID_P$Site.Plot<-paste(GID_P$Site,GID_P$Plot,sep = ".")
# byPlot$Div<-0
# byPlot$Evn<-0
# 
# Di<-function(ram, N) { sum(ram*(ram-1)) / (N*(N-1))  }
# 
# 
# for(i in seq_along(byPlot$site.plot)) byPlot[i,"Div"]<- 1 - Di(GID_P[GID_P$Site.Plot==byPlot$site.plot[i],"N_G_ID"],10)
# 
# Dmin<-function(G,N) { ((G-1)*(2*N-G))/(N*(N-1)) }
# Dmax<-function(G,N) { (N*(G-1))/(G*(N-1)) }
# Ev<-function(D,Dmi,Dma) { (D - Dmi)/(Dma - Dmi)}
# 
# byPlot$Evn<-round(Ev(byPlot$Div,Dmi = Dmin(G=byPlot$plot.G,10),Dma = Dmax(byPlot$plot.G,10)),2)
#               
# plot(byPlot$Div,byPlot$Evn)  
# plot(byPlot$plot.freq,byPlot$Evn)
# plot(byPlot$av.stm.dens,byPlot$Evn)

```


# CART
Do the same variables that divide sites also classify clonality?
```{r}
fitSite <-rpart(Site ~ pH+OM+Nitrate+K+S+Zn+Fe+Mn+Mg+Na+CEC+P, method = "class", data = gen_env)
fitClone <-rpart(Clone ~ pH+OM+Nitrate+K+S+Zn+Fe+Mn+Mg+Na+CEC+P, method = "class", data = gen_env)
```

```{r}
printcp(fitSite)
plot(fitSite)
text(fitSite)
# plotcp(fitSite)
summary(fitSite)
```


```{r}
printcp(fitClone)
plotcp(fitClone)
summary(fitClone)
plot(fitClone)
text(fitClone)
```


```{r}
pfit<- prune(fitSite, cp=fitSite$cptable[which.min(fitSite$cptable[,"xerror"]),"CP"])
printcp(pfit)

plot(pfit, uniform=TRUE,
     main="Pruned Classification Tree for Site")
text(pfit, use.n=TRUE, all=TRUE, cex=.8)
```


```{r}
pfitClone<- prune(fitClone, cp=fitClone$cptable[which.min(fitClone$cptable[,"xerror"]),"CP"])
printcp(pfitClone)

plot(pfitClone, uniform=TRUE,
     main="Pruned Classification Tree for Clones")
text(pfitClone, use.n=TRUE, all=TRUE, cex=.8)

```

### CI tree
```{r}
fit <- ctree(Site ~ pH+OM+Nitrate+K+S+Zn+Fe+Mn+Mg+Na+CEC+P,
             data=gen_env)
plot(fit, main="Conditional Inference Tree for Site")
```


```{r}
######NMDS extras
# nut.labs<-c("K","Clay","Na","S","Mg","BareG","P")
# 
# 
# md.soilz<-envfit(soilz.mds,gen_env[,c("K","S","Mg","Na","P","Sand","bare")])
# # md.soilz<-envfit(soilz.mds,gen_env[,names(soilz)])
# plot(md.soilz,lwd=2,col="black")#,labels =" ")
# # 
# # nut.vars<-locator(7)
# # soilz.mds$points[,1:2]
# #nut.vars<-locator(7)
# nut.labs<-c("K","Clay","Na","S","Mg","BareG","P")
# text(nut.vars,nut.labs,cex=2)
# clonz<-read.csv("G_N_bysite.csv")
# clonz.loc<-locator(6)
# text(clonz.loc,1:6)

#library(stringi)
#byPlot$Site<-substr(byPlot$site.plot,1,1)
#byPlot$Plot<-substr(byPlot$site.plot,3,3)

#boxplot(byPlot$Evn~byPlot$Site)
#boxplot(byPlot$Div~byPlot$Site)

#bySite$Div<-0
#byPlot$Evn<-0

#for(i in seq_along(bySite$site)) bySite[i,"Div"]<- 1 - Di(GID_S[GID_S$Site==bySite$site[i],"N_G_ID"],30)
#bySite$Evn<-round(Ev(bySite$Div,Dmi = Dmin(G=bySite$site.G,30),Dma = Dmax(bySite$site.G,30)),2)
#plot(bySite$Div,bySite$Evn)


####Principal Components Analysis -- making a soil nutrient variable
#gen_env<-gen_env[-which(gen_env$site.plot.subplot=="4.2.6"),]

#soilvar<-princomp(~pH+Salts+OM+Nitrate+K+S+Zn+Fe+Mn+Cu+Mg+Na+CEC+P, 
#                  data=gen_env, cor=FALSE, scores=TRUE)

#soilvar<-princomp(~K+S+Mg+Na+P, 
#                  data=gen_env, cor=FALSE, scores=TRUE)

#summary(soilvar)
#screeplot(soilvar)

#loadings(soilvar)
#gen_env$soil.nut<-soilvar$scores[,1]
```