Supplemental R code 2: R code adapted from Shade & Stopnisek (2019) to determine core ASVs.

# Save file as .R file and open in R or Rstudio
# Required data can be found at https://figshare.com/articles/dataset/ta-object_leaf_side/21524538


# R code used for determining core ASVs, adapted from Shade, Ashley, and Nejc Stopnisek. "Abundance-occupancy distributions to prioritize plant core microbiome membership." Current opinion in microbiology 49 (2019): 50-58.

library(reshape2)
library(tidyamplicons)
library(tidyverse)
theme_set(theme_light())

setwd("H:/Postdoc/Research/Publications/pH project")
set.seed(334)
#-----------------------------------------------------------------------------------------

load("runclean.Rdata")
nReads=4000                                                            # input dataset needs to be rarified and the rarifaction depth included 
runf <- run %>%
  filter_abundances(abundance > 2)%>%
  add_lib_size()%>%
  filter_samples(lib_size > (nReads-1))%>%
  rarefy(nReads)%>%
  add_total_rel_abundance()%>%
  add_rel_occurrence()

otu <- t(as_abundances_matrix(runf$abundances))
map <- runf$samples
#otu <- readRDS('switchgrassOTUtable.rds')
#map <- readRDS('switchgrassMAPtable.rds')

library(vegan)
otu_PA <- 1*((otu>0)==1)                                               # presence-absence data
otu_occ <- rowSums(otu_PA)/ncol(otu_PA)                                # occupancy calculation
otu_rel <- apply(decostand(otu, method="total", MARGIN=2),1, mean)     # mean relative abundance
occ_abun <- add_rownames(as.data.frame(cbind(otu_occ, otu_rel)),'otu') # combining occupancy and abundance data frame

PresenceSum <- data.frame(otu = as.factor(row.names(otu)), otu) %>%
  gather(sample_id, abun, -otu) %>%
  left_join(map, by = 'sample_id') %>%
  group_by(otu, Plant_sample) %>%
  summarise(site_freq=sum(abun>0)/length(abun),            # frequency of detection 
            coreSite=ifelse(site_freq == 1, 1, 0)) %>%     # 1 only if occupancy 1 with specific time, 0 if not
  group_by(otu) %>%
  summarise(sumF=sum(site_freq),
            sumG=sum(coreSite),
            nS=length(Plant_sample)*2,           
            Index=(sumF+sumG)/nS)


otu_ranked <- occ_abun %>%
  left_join(PresenceSum, by='otu') %>%
  transmute(otu=otu,
            rank=Index) %>%
  arrange(desc(rank))


# Calculating the contribution of ranked OTUs to the BC similarity
BCaddition <- NULL

# calculating BC dissimilarity based on the 1st ranked OTU
otu_start=otu_ranked$otu[1]                   
start_matrix <- as.matrix(otu[otu_start,])
start_matrix <- t(start_matrix)
x <- apply(combn(ncol(start_matrix), 2), 2, function(x) sum(abs(start_matrix[,x[1]]- start_matrix[,x[2]]))/(2*nReads))
x_names <- apply(combn(ncol(start_matrix), 2), 2, function(x) paste(colnames(start_matrix)[x], collapse=' - '))
df_s <- data.frame(x_names,x)
names(df_s)[2] <- 1 
BCaddition <- rbind(BCaddition,df_s)
# calculating BC dissimilarity based on additon of ranked OTUs from 2nd to 500th. Can be set to the entire length of OTUs in the dataset, however it might take some time if more than 5000 OTUs are included.
for(i in 2:500){                              
  otu_add=otu_ranked$otu[i]                       
  add_matrix <- as.matrix(otu[otu_add,])
  add_matrix <- t(add_matrix)
  start_matrix <- rbind(start_matrix, add_matrix)
  x <- apply(combn(ncol(start_matrix), 2), 2, function(x) sum(abs(start_matrix[,x[1]]-start_matrix[,x[2]]))/(2*nReads))
  x_names <- apply(combn(ncol(start_matrix), 2), 2, function(x) paste(colnames(start_matrix)[x], collapse=' - '))
  df_a <- data.frame(x_names,x)
  names(df_a)[2] <- i 
  BCaddition <- left_join(BCaddition, df_a, by=c('x_names'))
}
# calculating the BC dissimilarity of the whole dataset (not needed if the second loop is already including all OTUs) 
x <-  apply(combn(ncol(otu), 2), 2, function(x) sum(abs(otu[,x[1]]-otu[,x[2]]))/(2*nReads))   
x_names <- apply(combn(ncol(otu), 2), 2, function(x) paste(colnames(otu)[x], collapse=' - '))
df_full <- data.frame(x_names,x)
names(df_full)[2] <- length(rownames(otu))
BCfull <- left_join(BCaddition,df_full, by='x_names')

rownames(BCfull) <- BCfull$x_names
temp_BC <- BCfull
temp_BC$x_names <- NULL
temp_BC_matrix <- as.matrix(temp_BC)

BC_ranked <- data.frame(rank = as.factor(row.names(t(temp_BC_matrix))),t(temp_BC_matrix)) %>% 
  gather(comparison, BC, -rank) %>%
  group_by(rank) %>%
  summarise(MeanBC=mean(BC)) %>%            # mean Bray-Curtis dissimilarity
  arrange(desc(-MeanBC)) %>%
  mutate(proportionBC=MeanBC/max(MeanBC))   # proportion of the dissimilarity explained by the n number of ranked OTUs
Increase=BC_ranked$MeanBC[-1]/BC_ranked$MeanBC[-length(BC_ranked$MeanBC)]
increaseDF <- data.frame(IncreaseBC=c(0,(Increase)), rank=factor(c(1:(length(Increase)+1))))
BC_ranked <- left_join(BC_ranked, increaseDF)
BC_ranked <- BC_ranked[-nrow(BC_ranked),]

#Creating thresholds for core inclusion 

#Method: 
#A) Elbow method (first order difference) (script modified from https://pommevilla.github.io/random/elbows.html)
fo_difference <- function(pos){
  left <- (BC_ranked[pos, 2] - BC_ranked[1, 2]) / pos
  right <- (BC_ranked[nrow(BC_ranked), 2] - BC_ranked[pos, 2]) / (nrow(BC_ranked) - pos)
  return(left - right)
}
BC_ranked$fo_diffs <- sapply(1:nrow(BC_ranked), fo_difference)

elbow <- which.max(BC_ranked$fo_diffs)

#A2) Visual elbow method

elbowvis1<-15
elbowvis2<-64

#B) Final increase in BC similarity of equal or greater then 2% 
lastCall <- last(as.numeric(BC_ranked$rank[(BC_ranked$IncreaseBC>=1.02)]))

#Creating plot of Bray-Curtis similarity
ggplot(BC_ranked[1:100,], aes(x=factor(BC_ranked$rank[1:100], levels=BC_ranked$rank[1:100]))) +
  geom_point(aes(y=proportionBC)) +
  theme_classic() + theme(strip.background = element_blank(),axis.text.x = element_text(size=7, angle=45)) +
  geom_vline(xintercept=elbow, lty=3, col='red', cex=.5) +
  geom_vline(xintercept=elbowvis1, lty=3, col='darkgreen', cex=.5) +
  geom_vline(xintercept=elbowvis2, lty=3, col='darkolivegreen 3', cex=.5) +
  geom_vline(xintercept=last(as.numeric(BC_ranked$rank[(BC_ranked$IncreaseBC>=1.02)])), lty=3, col='blue', cex=.5) +
  labs(x='ranked OTUs',y='Bray-Curtis similarity') +
  annotate(geom="text", x=elbow+9, y=.07, label=paste("Elbow method"," (",elbow,")", sep=''), color="red")+
  annotate(geom="text", x=elbowvis1+9, y=.12, label=paste("Visual elbow 1"," (",elbowvis1,")", sep=''), color="darkgreen")+
  annotate(geom="text", x=elbowvis2+9, y=.12, label=paste("Visual elbow 2"," (",elbowvis2,")", sep=''), color="darkolivegreen3")+
  annotate(geom="text", x=last(as.numeric(BC_ranked$rank[(BC_ranked$IncreaseBC>=1.02)]))+3, y=.5, label=paste("Last 2% increase (",last(as.numeric(BC_ranked$rank[(BC_ranked$IncreaseBC>=1.02)])),")",sep=''), color="blue")

#Creating occupancy abundance plot
occ_abun$fill <- 'no'
occ_abun$fill[occ_abun$otu %in% otu_ranked$otu[1:last(as.numeric(BC_ranked$rank[(BC_ranked$IncreaseBC>=1.02)]))]] <- 'core'
#occ_abun$fill[occ_abun$otu %in% otu_ranked$otu[1:elbowvis1]] <- 'core'

#Fitting neutral model (Burns et al., 2016 (ISME J) - functions are in the sncm.fit.R)


#-----------------------------------

#Adam Burns - 2/10/2015
#From Burns et al. Contribution of neutral processes to the assembly of the gut microbial communities changes over host development
#Fits the neutral model from Sloan et al. 2006 to an OTU table and returns several fitting statistics. Alternatively, will return predicted occurrence frequencies for each OTU based on their abundance in the metacommunity when stats=FALSE.
#spp: A community table for communities of interest with local communities/samples as rows and taxa as columns. All samples must be rarefied to the same depth.
#pool: A community table for defining source community (optional; Default=NULL).
#taxon: A table listing the taxonomic calls for each otu, with OTU ids as row names and taxonomic classifications as columns.
#If stats=TRUE the function will return fitting statistics.
#If stats=FALSE the function will return a table of observed and predicted values for each otu.

sncm.fit <- function(spp, pool=NULL, stats=TRUE, taxon=NULL){
  require(minpack.lm)
  require(Hmisc)
  require(stats4)
  
  options(warn=-1)
  
  #Calculate the number of individuals per community
  N <- mean(apply(spp, 1, sum))
  
  #Calculate the average relative abundance of each taxa across communities
  if(is.null(pool)){
    p.m <- apply(spp, 2, mean)
    p.m <- p.m[p.m != 0]
    p <- p.m/N
  } else {
    p.m <- apply(pool, 2, mean)
    p.m <- p.m[p.m != 0]
    p <- p.m/N
  }
  
  #Calculate the occurrence frequency of each taxa across communities
  spp.bi <- 1*(spp>0)
  freq <- apply(spp.bi, 2, mean)
  freq <- freq[freq != 0]
  
  #Combine
  C <- merge(p, freq, by=0)
  C <- C[order(C[,2]),]
  C <- as.data.frame(C)
  C.0 <- C[!(apply(C, 1, function(y) any(y == 0))),] #Removes rows with any zero (absent in either source pool or local communities)
  p <- C.0[,2]
  freq <- C.0[,3]
  names(p) <- C.0[,1]
  names(freq) <- C.0[,1]
  
  #Calculate the limit of detection
  d = 1/N
  
  ##Fit model parameter m (or Nm) using Non-linear least squares (NLS)
  m.fit <- nlsLM(freq ~ pbeta(d, N*m*p, N*m*(1-p), lower.tail=FALSE), start=list(m=0.1))
  m.ci <- confint(m.fit, 'm', level=0.95)
  
  ##Fit neutral model parameter m (or Nm) using Maximum likelihood estimation (MLE)
  sncm.LL <- function(m, sigma){
    R = freq - pbeta(d, N*m*p, N*m*(1-p), lower.tail=FALSE)
    R = dnorm(R, 0, sigma)
    -sum(log(R))
  }
  m.mle <- mle(sncm.LL, start=list(m=0.1, sigma=0.1), nobs=length(p))
  
  ##Calculate Akaike's Information Criterion (AIC)
  aic.fit <- AIC(m.mle, k=2)
  bic.fit <- BIC(m.mle)
  
  ##Calculate goodness-of-fit (R-squared and Root Mean Squared Error)
  freq.pred <- pbeta(d, N*coef(m.fit)*p, N*coef(m.fit)*(1-p), lower.tail=FALSE)
  Rsqr <- 1 - (sum((freq - freq.pred)^2))/(sum((freq - mean(freq))^2))
  RMSE <- sqrt(sum((freq-freq.pred)^2)/(length(freq)-1))
  
  pred.ci <- binconf(freq.pred*nrow(spp), nrow(spp), alpha=0.05, method="wilson", return.df=TRUE)
  
  ##Calculate AIC for binomial model
  bino.LL <- function(mu, sigma){
    R = freq - pbinom(d, N, p, lower.tail=FALSE)
    R = dnorm(R, mu, sigma)
    -sum(log(R))
  }
  bino.mle <- mle(bino.LL, start=list(mu=0, sigma=0.1), nobs=length(p))
  
  aic.bino <- AIC(bino.mle, k=2)
  bic.bino <- BIC(bino.mle)
  
  ##Goodness of fit for binomial model
  bino.pred <- pbinom(d, N, p, lower.tail=FALSE)
  Rsqr.bino <- 1 - (sum((freq - bino.pred)^2))/(sum((freq - mean(freq))^2))
  RMSE.bino <- sqrt(sum((freq - bino.pred)^2)/(length(freq) - 1))
  
  bino.pred.ci <- binconf(bino.pred*nrow(spp), nrow(spp), alpha=0.05, method="wilson", return.df=TRUE)
  
  ##Calculate AIC for Poisson model
  pois.LL <- function(mu, sigma){
    R = freq - ppois(d, N*p, lower.tail=FALSE)
    R = dnorm(R, mu, sigma)
    -sum(log(R))
  }
  pois.mle <- mle(pois.LL, start=list(mu=0, sigma=0.1), nobs=length(p))
  
  aic.pois <- AIC(pois.mle, k=2)
  bic.pois <- BIC(pois.mle)
  
  ##Goodness of fit for Poisson model
  pois.pred <- ppois(d, N*p, lower.tail=FALSE)
  Rsqr.pois <- 1 - (sum((freq - pois.pred)^2))/(sum((freq - mean(freq))^2))
  RMSE.pois <- sqrt(sum((freq - pois.pred)^2)/(length(freq) - 1))
  
  pois.pred.ci <- binconf(pois.pred*nrow(spp), nrow(spp), alpha=0.05, method="wilson", return.df=TRUE)
  
  ##Results
  if(stats==TRUE){
    fitstats <- data.frame(m=numeric(), m.ci=numeric(), m.mle=numeric(), maxLL=numeric(), binoLL=numeric(), poisLL=numeric(), Rsqr=numeric(), Rsqr.bino=numeric(), Rsqr.pois=numeric(), RMSE=numeric(), RMSE.bino=numeric(), RMSE.pois=numeric(), AIC=numeric(), BIC=numeric(), AIC.bino=numeric(), BIC.bino=numeric(), AIC.pois=numeric(), BIC.pois=numeric(), N=numeric(), Samples=numeric(), Richness=numeric(), Detect=numeric())
    fitstats[1,] <- c(coef(m.fit), coef(m.fit)-m.ci[1], m.mle@coef['m'], m.mle@details$value, bino.mle@details$value, pois.mle@details$value, Rsqr, Rsqr.bino, Rsqr.pois, RMSE, RMSE.bino, RMSE.pois, aic.fit, bic.fit, aic.bino, bic.bino, aic.pois, bic.pois, N, nrow(spp), length(p), d)
    return(fitstats)
  } else {
    A <- cbind(p, freq, freq.pred, pred.ci[,2:3], bino.pred, bino.pred.ci[,2:3])
    A <- as.data.frame(A)
    colnames(A) <- c('p', 'freq', 'freq.pred', 'pred.lwr', 'pred.upr', 'bino.pred', 'bino.lwr', 'bino.upr')
    if(is.null(taxon)){
      B <- A[order(A[,1]),]
    } else {
      B <- merge(A, taxon, by=0, all=TRUE)
      row.names(B) <- B[,1]
      B <- B[,-1]
      B <- B[order(B[,1]),]
    }
    return(B)
  }
}
#-----------------------------------


spp=t(otu)
taxon=as.vector(rownames(otu))

library(stats4)

#Models for the whole community
obs.np=sncm.fit(spp, taxon, stats=FALSE, pool=NULL)
sta.np=sncm.fit(spp, taxon, stats=TRUE, pool=NULL)
sta.np$m.mle
sta.np$Rsqr

above.pred=sum(obs.np$freq > (obs.np$pred.upr), na.rm=TRUE)/sta.np$Richness
below.pred=sum(obs.np$freq < (obs.np$pred.lwr), na.rm=TRUE)/sta.np$Richness

ap = obs.np$freq > (obs.np$pred.upr)
bp = obs.np$freq < (obs.np$pred.lwr)

ggplot() +
  geom_point(data=occ_abun[occ_abun$fill=='no',], aes(x=log10(otu_rel), y=otu_occ), pch=21, fill='white', alpha=.2)+
  geom_point(data=occ_abun[occ_abun$fill!='no',], aes(x=log10(otu_rel), y=otu_occ), pch=21, fill='blue', size=1.8) +
  #geom_point(data=occ_abun, aes(x=log10(otu_rel), y=otu_occ), pch=21, fill='white', alpha=.2)+
  geom_line(color='black', data=obs.np, size=1, aes(y=obs.np$freq.pred, x=log10(obs.np$p)), alpha=.25) +
  geom_line(color='black', lty='twodash', size=1, data=obs.np, aes(y=obs.np$pred.upr, x=log10(obs.np$p)), alpha=.25)+
  geom_line(color='black', lty='twodash', size=1, data=obs.np, aes(y=obs.np$pred.lwr, x=log10(obs.np$p)), alpha=.25)+
  labs(x="log10(mean relative abundance)", y="Occupancy")

#Creating a plot of core taxa occupancy by time point
core <- occ_abun$otu[occ_abun$fill == 'core']
coretaxa <- as.tibble(core)%>%
  rename(taxon_id=value)%>%
  left_join(runf$taxa)%>%
  mutate(core="core")
  
otu_relabun <- decostand(otu, method="total", MARGIN=2)

plotDF <- data.frame(otu = as.factor(row.names(otu_relabun)), otu_relabun) %>% 
  gather(sample_id, relabun, -otu) %>%
  left_join(map, by = 'sample_id') %>%
  left_join(otu_ranked, bu='otu') %>%
  filter(otu %in% core) %>% 
  group_by(otu, Plant_sample) %>%
  summarise(site_freq=sum(relabun>0)/length(relabun),        
            coreSite=ifelse(site_freq == 1, 1, 0),      
            detect=ifelse(site_freq > 0, 1, 0))

plotDF$otu <- factor(plotDF$otu, levels=otu_ranked$otu[1:34])

ggplot(plotDF,aes(x=otu, site_freq,fill=factor(Plant_sample))) +    
  geom_bar(stat = 'identity', position = 'dodge') +
  coord_flip() +
  scale_x_discrete(limits = rev(levels(plotDF$otu))) +
  theme(axis.text = element_text(size=6)) +
  labs(x='Ranked OTUs', y='Occupancy by site')

tax<-left_join(runf$taxa,coretaxa)%>%
  select(family, taxon_name, ASV_id,total_rel_abundance,rel_occurrence,core)%>%
  arrange(desc(total_rel_abundance))%>%
  arrange(core)
taxc<-tax%>%
  filter(core=="core")
write.csv(taxc,file="coreASV.txt",sep="\t")


#############
#----------------------------------
# For top and bottom separately:

runb <- runf %>%
  filter_samples(Side=="Bottom")
runt <- runf %>%
  filter_samples(Side=="Top")

# Top

otu <- t(as_abundances_matrix(runt$abundances))
map <- runt$samples
library(vegan)
otu_PA <- 1*((otu>0)==1)                                               # presence-absence data
otu_occt <- rowSums(otu_PA)/ncol(otu_PA)                                # occupancy calculation
otu_relt <- apply(decostand(otu, method="total", MARGIN=2),1, mean)     # mean relative abundance
occ_abunt <- add_rownames(as.data.frame(cbind(otu_occt, otu_relt)),'otu')
otulist<-runt$taxa%>%
  select(otu=taxon_id,taxon_name)%>%
  left_join(tax)%>%
  select(otu,taxon_name,fill=core)%>%
  replace_na(list(fill="no"))
occ_abunt<-left_join(occ_abunt,otulist,by="otu")
spp=t(otu)
taxon=as.vector(rownames(otu))

library(stats4)

#Models for the whole community
obs.npt=sncm.fit(spp, taxon, stats=FALSE, pool=NULL)
sta.npt=sncm.fit(spp, taxon, stats=TRUE, pool=NULL)
sta.npt$m.mle
sta.npt$Rsqr

above.predt=sum(obs.npt$freq > (obs.npt$pred.upr), na.rm=TRUE)/sta.npt$Richness
below.predt=sum(obs.npt$freq < (obs.npt$pred.lwr), na.rm=TRUE)/sta.npt$Richness

ap = obs.npt$freq > (obs.npt$pred.upr)
bp = obs.npt$freq < (obs.npt$pred.lwr)
above.predt
below.predt

ggplot() +
  geom_point(data=occ_abunt[occ_abunt$fill=='no',], aes(x=log10(otu_relt), y=otu_occt), pch=21, fill='white', alpha=.2,size=1.2)+
  geom_point(data=occ_abunt[occ_abunt$fill!='no',], aes(x=log10(otu_relt), y=otu_occt), pch=21, fill='blue', size=1) +
  #geom_point(data=occ_abunt, aes(x=log10(otu_relt), y=otu_occt), pch=21, fill='white', alpha=.2)+
  geom_line(color='darkred', data=obs.npt, size=1, aes(y=obs.npt$freq.pred, x=log10(obs.npt$p)), alpha=.75) +
  geom_line(color='darkred', lty='twodash', size=1, data=obs.npt, aes(y=obs.npt$pred.upr, x=log10(obs.npt$p)), alpha=.75)+
  geom_line(color='darkred', lty='twodash', size=1, data=obs.npt, aes(y=obs.npt$pred.lwr, x=log10(obs.npt$p)), alpha=.75)+
  labs(x="log10(mean relative abundance)", y="Occupancy")


# Bottom

otu <- t(as_abundances_matrix(runb$abundances))
map <- runb$samples
otu_PA <- 1*((otu>0)==1)                                               # presence-absence data
otu_occb <- rowSums(otu_PA)/ncol(otu_PA)                                # occupancy calculation
otu_relb <- apply(decostand(otu, method="total", MARGIN=2),1, mean)     # mean relative abundance
occ_abunb <- add_rownames(as.data.frame(cbind(otu_occb, otu_relb)),'otu')
otulist<-runb$taxa%>%
  select(otu=taxon_id,taxon_name)%>%
  left_join(tax)%>%
  select(otu,taxon_name,fill=core)%>%
  replace_na(list(fill="no"))
occ_abunb<-left_join(occ_abunb,otulist,by="otu")
spp=t(otu)
taxon=as.vector(rownames(otu))

obs.npb=sncm.fit(spp, taxon, stats=FALSE, pool=NULL)
sta.npb=sncm.fit(spp, taxon, stats=TRUE, pool=NULL)
sta.npb$m.mle
sta.npb$Rsqr

above.predb=sum(obs.npb$freq > (obs.npb$pred.upr), na.rm=TRUE)/sta.npb$Richness
below.predb=sum(obs.npb$freq < (obs.npb$pred.lwr), na.rm=TRUE)/sta.npb$Richness

ap = obs.npb$freq > (obs.npb$pred.upr)
bp = obs.npb$freq < (obs.npb$pred.lwr)
above.predb
below.predb

ggplot() +
  geom_point(data=occ_abunb[occ_abunb$fill=='no',], aes(x=log10(otu_relb), y=otu_occb), pch=21, fill='white', alpha=.2,size=1.2)+
  geom_point(data=occ_abunb[occ_abunb$fill!='no',], aes(x=log10(otu_relb), y=otu_occb), pch=21, fill='blue', size=1) +
  #geom_point(data=occ_abunb, aes(x=log10(otu_relb), y=otu_occb), pch=21, fill='white', alpha=.2)+
  geom_line(color='#003300', data=obs.npb, size=1, aes(y=obs.npb$freq.pred, x=log10(obs.npb$p)), alpha=.75) +
  geom_line(color='#003300', lty='twodash', size=1, data=obs.npb, aes(y=obs.npb$pred.upr, x=log10(obs.npb$p)), alpha=.75)+
  geom_line(color='#003300', lty='twodash', size=1, data=obs.npb, aes(y=obs.npb$pred.lwr, x=log10(obs.npb$p)), alpha=.75)+
  labs(x="log10(mean relative abundance)", y="Occupancy")


ggplot() +
  #geom_point(data=occ_abun, aes(x=log10(otu_rel), y=otu_occ), pch=21, fill='white', alpha=.2)+
  #geom_line(color='black', data=obs.np, size=1, aes(y=obs.np$freq.pred, x=log10(obs.np$p)), alpha=.75) +
  #geom_line(color='black', lty='twodash', size=1, data=obs.np, aes(y=obs.np$pred.upr, x=log10(obs.np$p)), alpha=.75)+
  #geom_line(color='black', lty='twodash', size=1, data=obs.np, aes(y=obs.np$pred.lwr, x=log10(obs.np$p)), alpha=.75)+
  geom_line(color='#003300', data=obs.npb, size=0.8, aes(y=obs.npb$freq.pred, x=log10(obs.npb$p)), alpha=.75) +
  geom_line(color='#003300', lty='twodash', size=0.8, data=obs.npb, aes(y=obs.npb$pred.upr, x=log10(obs.npb$p)), alpha=.75)+
  geom_line(color='#003300', lty='twodash', size=0.8, data=obs.npb, aes(y=obs.npb$pred.lwr, x=log10(obs.npb$p)), alpha=.75)+
  geom_line(color='darkred', data=obs.npt, size=0.8, aes(y=obs.npt$freq.pred, x=log10(obs.npt$p)), alpha=.75) +
  geom_line(color='darkred', lty='twodash', size=0.8, data=obs.npt, aes(y=obs.npt$pred.upr, x=log10(obs.npt$p)), alpha=.75)+
  geom_line(color='darkred', lty='twodash', size=0.8, data=obs.npt, aes(y=obs.npt$pred.lwr, x=log10(obs.npt$p)), alpha=.75)+
  labs(x="log10(mean relative abundance)", y="Occupancy")