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Null_model_distribution.R
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### Author: Samuel Ayebare
## Null_model_elev.diet.strata.r
## Code : Generate a null distribution niche overlap (Pianka) for a community of birds (63) along three niche axis
## i) Elevation gradient
## ii) Diet
## iii) Forest strata
#------------------------------------------------------------------------------------------------##
#------------------------------------------------------------------------------------------------##
#----------------#
#-Load libraries-#
#----------------#
library(dplyr)
library(tidyr)
library(jagsUI)
library(tidyverse)
library(ggplot2)
library(ggthemes)
library(grid)
library(gridExtra)
library(extrafont)
library(spaa)
library(data.table)
loadfonts(device = "win")
#-----------------------#
#-Set working directory-#
#-----------------------#
setwd("./Data")
#---------------------#
#-Load Files and data-#
#---------------------#
#---------------------------------------------------------------#
## Data: For estimating a Null model distribution -elevation #
#---------------------------------------------------------------#
load("../Data/HCDSM63spp.RData")
## Model output
HCDSM_Virunga_63spp
# Importing elevation as a covariate
svy_pts <- read.csv("Virunga_covariates.csv", header=TRUE)
svy_pts <- tibble::as_tibble(svy_pts)
head(svy_pts)
# scaled Elevation
elev <- (svy_pts$elev - mean(svy_pts$elev))/sd(svy_pts$elev)
### - Diet
#--------------#
#---------------------------------------------------------------#
## Data: For estimating a Null model distribution - Diet #
#---------------------------------------------------------------#
## Import diet data
diet.63sp <- read.csv("Diet_categories_63species.csv",header = T)
head(diet.63sp)
#---------------------------------------------------------#
## Preparing data for Pianka niche overlap analysis - Diet
#---------------------------------------------------------#
diet.63sp.1 <- diet.63sp [,-1]
### - Forest strata
#---------------------#
#-------------------------------------------------------------------#
## Data: For estimating a Null model distribution - Forest strata #
#------------------------------------------------------------------#
## Import Forest strata
strata.63sp <- read.csv("Strata_categories_63species.csv",header = T)
head(strata.63sp)
#------------------------------------------------------------------#
## Preparing data for Pianka niche overlap analysis - Forest strata
#-----------------------------------------------------------------#
strata.63sp.1 <- strata.63sp [,-1]
## Elevation
##### Estimate Species-specific expected abundance along an elevation gradient
#--------------------------------------------------------------------------------#
Spp1 <- exp(HCDSM_Virunga_63spp$mean$beta0[1] + HCDSM_Virunga_63spp$mean$beta1[1] * elev + HCDSM_Virunga_63spp$mean$beta2[1] * elev^2)
Spp2 <- exp(HCDSM_Virunga_63spp$mean$beta0[2] + HCDSM_Virunga_63spp$mean$beta1[2] * elev + HCDSM_Virunga_63spp$mean$beta2[2] * elev^2)
Spp3 <- exp(HCDSM_Virunga_63spp$mean$beta0[3] + HCDSM_Virunga_63spp$mean$beta1[3] * elev + HCDSM_Virunga_63spp$mean$beta2[3] * elev^2)
Spp4 <- exp(HCDSM_Virunga_63spp$mean$beta0[4] + HCDSM_Virunga_63spp$mean$beta1[4] * elev + HCDSM_Virunga_63spp$mean$beta2[4] * elev^2)
Spp5 <- exp(HCDSM_Virunga_63spp$mean$beta0[5] + HCDSM_Virunga_63spp$mean$beta1[5] * elev + HCDSM_Virunga_63spp$mean$beta2[5] * elev^2)
Spp6 <- exp(HCDSM_Virunga_63spp$mean$beta0[6] + HCDSM_Virunga_63spp$mean$beta1[6] * elev + HCDSM_Virunga_63spp$mean$beta2[6] * elev^2)
Spp7 <- exp(HCDSM_Virunga_63spp$mean$beta0[7] + HCDSM_Virunga_63spp$mean$beta1[7] * elev + HCDSM_Virunga_63spp$mean$beta2[7] * elev^2)
Spp8 <- exp(HCDSM_Virunga_63spp$mean$beta0[8] + HCDSM_Virunga_63spp$mean$beta1[8] * elev + HCDSM_Virunga_63spp$mean$beta2[8] * elev^2)
Spp9 <- exp(HCDSM_Virunga_63spp$mean$beta0[9] + HCDSM_Virunga_63spp$mean$beta1[9] * elev + HCDSM_Virunga_63spp$mean$beta2[9] * elev^2)
Spp10 <- exp(HCDSM_Virunga_63spp$mean$beta0[10] + HCDSM_Virunga_63spp$mean$beta1[10] * elev + HCDSM_Virunga_63spp$mean$beta2[10] * elev^2)
Spp11 <- exp(HCDSM_Virunga_63spp$mean$beta0[11] + HCDSM_Virunga_63spp$mean$beta1[11] * elev + HCDSM_Virunga_63spp$mean$beta2[11] * elev^2)
Spp12 <- exp(HCDSM_Virunga_63spp$mean$beta0[12] + HCDSM_Virunga_63spp$mean$beta1[12] * elev + HCDSM_Virunga_63spp$mean$beta2[12] * elev^2)
Spp13 <- exp(HCDSM_Virunga_63spp$mean$beta0[13] + HCDSM_Virunga_63spp$mean$beta1[13] * elev + HCDSM_Virunga_63spp$mean$beta2[13] * elev^2)
Spp14 <- exp(HCDSM_Virunga_63spp$mean$beta0[14] + HCDSM_Virunga_63spp$mean$beta1[14] * elev + HCDSM_Virunga_63spp$mean$beta2[14] * elev^2)
Spp15 <- exp(HCDSM_Virunga_63spp$mean$beta0[15] + HCDSM_Virunga_63spp$mean$beta1[15] * elev + HCDSM_Virunga_63spp$mean$beta2[15] * elev^2)
Spp16 <- exp(HCDSM_Virunga_63spp$mean$beta0[16] + HCDSM_Virunga_63spp$mean$beta1[16] * elev + HCDSM_Virunga_63spp$mean$beta2[16] * elev^2)
Spp17 <- exp(HCDSM_Virunga_63spp$mean$beta0[17] + HCDSM_Virunga_63spp$mean$beta1[17] * elev + HCDSM_Virunga_63spp$mean$beta2[17] * elev^2)
Spp18 <- exp(HCDSM_Virunga_63spp$mean$beta0[18] + HCDSM_Virunga_63spp$mean$beta1[18] * elev + HCDSM_Virunga_63spp$mean$beta2[18] * elev^2)
Spp19 <- exp(HCDSM_Virunga_63spp$mean$beta0[19] + HCDSM_Virunga_63spp$mean$beta1[19] * elev + HCDSM_Virunga_63spp$mean$beta2[19] * elev^2)
Spp20 <- exp(HCDSM_Virunga_63spp$mean$beta0[20] + HCDSM_Virunga_63spp$mean$beta1[20] * elev + HCDSM_Virunga_63spp$mean$beta2[20] * elev^2)
Spp21 <- exp(HCDSM_Virunga_63spp$mean$beta0[21] + HCDSM_Virunga_63spp$mean$beta1[21] * elev + HCDSM_Virunga_63spp$mean$beta2[21] * elev^2)
Spp22 <- exp(HCDSM_Virunga_63spp$mean$beta0[22] + HCDSM_Virunga_63spp$mean$beta1[22] * elev + HCDSM_Virunga_63spp$mean$beta2[22] * elev^2)
Spp23 <- exp(HCDSM_Virunga_63spp$mean$beta0[23] + HCDSM_Virunga_63spp$mean$beta1[23] * elev + HCDSM_Virunga_63spp$mean$beta2[23] * elev^2)
Spp24 <- exp(HCDSM_Virunga_63spp$mean$beta0[24] + HCDSM_Virunga_63spp$mean$beta1[24] * elev + HCDSM_Virunga_63spp$mean$beta2[24] * elev^2)
Spp25 <- exp(HCDSM_Virunga_63spp$mean$beta0[25] + HCDSM_Virunga_63spp$mean$beta1[25] * elev + HCDSM_Virunga_63spp$mean$beta2[25] * elev^2)
Spp26 <- exp(HCDSM_Virunga_63spp$mean$beta0[26] + HCDSM_Virunga_63spp$mean$beta1[26] * elev + HCDSM_Virunga_63spp$mean$beta2[26] * elev^2)
Spp27 <- exp(HCDSM_Virunga_63spp$mean$beta0[27] + HCDSM_Virunga_63spp$mean$beta1[27] * elev + HCDSM_Virunga_63spp$mean$beta2[27] * elev^2)
Spp28 <- exp(HCDSM_Virunga_63spp$mean$beta0[28] + HCDSM_Virunga_63spp$mean$beta1[28] * elev + HCDSM_Virunga_63spp$mean$beta2[28] * elev^2)
Spp29 <- exp(HCDSM_Virunga_63spp$mean$beta0[29] + HCDSM_Virunga_63spp$mean$beta1[29] * elev + HCDSM_Virunga_63spp$mean$beta2[29] * elev^2)
Spp30 <- exp(HCDSM_Virunga_63spp$mean$beta0[30] + HCDSM_Virunga_63spp$mean$beta1[30] * elev + HCDSM_Virunga_63spp$mean$beta2[30] * elev^2)
Spp31 <- exp(HCDSM_Virunga_63spp$mean$beta0[31] + HCDSM_Virunga_63spp$mean$beta1[31] * elev + HCDSM_Virunga_63spp$mean$beta2[31] * elev^2)
Spp32 <- exp(HCDSM_Virunga_63spp$mean$beta0[32] + HCDSM_Virunga_63spp$mean$beta1[32] * elev + HCDSM_Virunga_63spp$mean$beta2[32] * elev^2)
Spp33 <- exp(HCDSM_Virunga_63spp$mean$beta0[33] + HCDSM_Virunga_63spp$mean$beta1[33] * elev + HCDSM_Virunga_63spp$mean$beta2[33] * elev^2)
Spp34 <- exp(HCDSM_Virunga_63spp$mean$beta0[34] + HCDSM_Virunga_63spp$mean$beta1[34] * elev + HCDSM_Virunga_63spp$mean$beta2[34] * elev^2)
Spp35 <- exp(HCDSM_Virunga_63spp$mean$beta0[35] + HCDSM_Virunga_63spp$mean$beta1[35] * elev + HCDSM_Virunga_63spp$mean$beta2[35] * elev^2)
Spp36 <- exp(HCDSM_Virunga_63spp$mean$beta0[36] + HCDSM_Virunga_63spp$mean$beta1[36] * elev + HCDSM_Virunga_63spp$mean$beta2[36] * elev^2)
Spp37 <- exp(HCDSM_Virunga_63spp$mean$beta0[37] + HCDSM_Virunga_63spp$mean$beta1[37] * elev + HCDSM_Virunga_63spp$mean$beta2[37] * elev^2)
Spp38 <- exp(HCDSM_Virunga_63spp$mean$beta0[38] + HCDSM_Virunga_63spp$mean$beta1[38] * elev + HCDSM_Virunga_63spp$mean$beta2[38] * elev^2)
Spp39 <- exp(HCDSM_Virunga_63spp$mean$beta0[39] + HCDSM_Virunga_63spp$mean$beta1[39] * elev + HCDSM_Virunga_63spp$mean$beta2[39] * elev^2)
Spp40 <- exp(HCDSM_Virunga_63spp$mean$beta0[40] + HCDSM_Virunga_63spp$mean$beta1[40] * elev + HCDSM_Virunga_63spp$mean$beta2[40] * elev^2)
Spp41 <- exp(HCDSM_Virunga_63spp$mean$beta0[41] + HCDSM_Virunga_63spp$mean$beta1[41] * elev + HCDSM_Virunga_63spp$mean$beta2[41] * elev^2)
Spp42 <- exp(HCDSM_Virunga_63spp$mean$beta0[42] + HCDSM_Virunga_63spp$mean$beta1[42] * elev + HCDSM_Virunga_63spp$mean$beta2[42] * elev^2)
Spp43 <- exp(HCDSM_Virunga_63spp$mean$beta0[43] + HCDSM_Virunga_63spp$mean$beta1[43] * elev + HCDSM_Virunga_63spp$mean$beta2[43] * elev^2)
Spp44 <- exp(HCDSM_Virunga_63spp$mean$beta0[44] + HCDSM_Virunga_63spp$mean$beta1[44] * elev + HCDSM_Virunga_63spp$mean$beta2[44] * elev^2)
Spp45 <- exp(HCDSM_Virunga_63spp$mean$beta0[45] + HCDSM_Virunga_63spp$mean$beta1[45] * elev + HCDSM_Virunga_63spp$mean$beta2[45] * elev^2)
Spp46 <- exp(HCDSM_Virunga_63spp$mean$beta0[46] + HCDSM_Virunga_63spp$mean$beta1[46] * elev + HCDSM_Virunga_63spp$mean$beta2[46] * elev^2)
Spp47 <- exp(HCDSM_Virunga_63spp$mean$beta0[47] + HCDSM_Virunga_63spp$mean$beta1[47] * elev + HCDSM_Virunga_63spp$mean$beta2[47] * elev^2)
Spp48 <- exp(HCDSM_Virunga_63spp$mean$beta0[48] + HCDSM_Virunga_63spp$mean$beta1[48] * elev + HCDSM_Virunga_63spp$mean$beta2[48] * elev^2)
Spp49 <- exp(HCDSM_Virunga_63spp$mean$beta0[49] + HCDSM_Virunga_63spp$mean$beta1[49] * elev + HCDSM_Virunga_63spp$mean$beta2[49] * elev^2)
Spp50 <- exp(HCDSM_Virunga_63spp$mean$beta0[50] + HCDSM_Virunga_63spp$mean$beta1[50] * elev + HCDSM_Virunga_63spp$mean$beta2[50] * elev^2)
Spp51 <- exp(HCDSM_Virunga_63spp$mean$beta0[51] + HCDSM_Virunga_63spp$mean$beta1[51] * elev + HCDSM_Virunga_63spp$mean$beta2[51] * elev^2)
Spp52 <- exp(HCDSM_Virunga_63spp$mean$beta0[52] + HCDSM_Virunga_63spp$mean$beta1[52] * elev + HCDSM_Virunga_63spp$mean$beta2[52] * elev^2)
Spp53 <- exp(HCDSM_Virunga_63spp$mean$beta0[53] + HCDSM_Virunga_63spp$mean$beta1[53] * elev + HCDSM_Virunga_63spp$mean$beta2[53] * elev^2)
Spp54 <- exp(HCDSM_Virunga_63spp$mean$beta0[54] + HCDSM_Virunga_63spp$mean$beta1[54] * elev + HCDSM_Virunga_63spp$mean$beta2[54] * elev^2)
Spp55 <- exp(HCDSM_Virunga_63spp$mean$beta0[55] + HCDSM_Virunga_63spp$mean$beta1[55] * elev + HCDSM_Virunga_63spp$mean$beta2[55] * elev^2)
Spp56 <- exp(HCDSM_Virunga_63spp$mean$beta0[56] + HCDSM_Virunga_63spp$mean$beta1[56] * elev + HCDSM_Virunga_63spp$mean$beta2[56] * elev^2)
Spp57 <- exp(HCDSM_Virunga_63spp$mean$beta0[57] + HCDSM_Virunga_63spp$mean$beta1[57] * elev + HCDSM_Virunga_63spp$mean$beta2[57] * elev^2)
Spp58 <- exp(HCDSM_Virunga_63spp$mean$beta0[58] + HCDSM_Virunga_63spp$mean$beta1[58] * elev + HCDSM_Virunga_63spp$mean$beta2[58] * elev^2)
Spp59 <- exp(HCDSM_Virunga_63spp$mean$beta0[59] + HCDSM_Virunga_63spp$mean$beta1[59] * elev + HCDSM_Virunga_63spp$mean$beta2[59] * elev^2)
Spp60 <- exp(HCDSM_Virunga_63spp$mean$beta0[60] + HCDSM_Virunga_63spp$mean$beta1[60] * elev + HCDSM_Virunga_63spp$mean$beta2[60] * elev^2)
Spp61 <- exp(HCDSM_Virunga_63spp$mean$beta0[61] + HCDSM_Virunga_63spp$mean$beta1[61] * elev + HCDSM_Virunga_63spp$mean$beta2[61] * elev^2)
Spp62 <- exp(HCDSM_Virunga_63spp$mean$beta0[62] + HCDSM_Virunga_63spp$mean$beta1[62] * elev + HCDSM_Virunga_63spp$mean$beta2[62] * elev^2)
Spp63 <- exp(HCDSM_Virunga_63spp$mean$beta0[63] + HCDSM_Virunga_63spp$mean$beta1[63] * elev + HCDSM_Virunga_63spp$mean$beta2[63] * elev^2)
##### Species species data.frame for expected abundance
Community.63sp <- data.frame(Spp1,Spp2,Spp3,Spp4,Spp5,Spp6,Spp7,Spp8,Spp9,Spp10,Spp11,Spp12,Spp13,Spp14,Spp15,Spp16,Spp17,Spp18,Spp19,
Spp20,Spp21,Spp22,Spp23,Spp24,Spp25,Spp26,Spp27,Spp28,Spp29,Spp30,Spp31,Spp32,Spp33,Spp34,Spp35,Spp36,Spp37,Spp38,Spp39,Spp40,
Spp41,Spp42,Spp43,Spp44,Spp45,Spp46,Spp47,Spp48,Spp49,Spp50,Spp51,Spp52,Spp53,Spp54,Spp55,Spp56,Spp57,Spp58,Spp59,Spp60,Spp61,
Spp62,Spp63 )
head(Community.63sp )
## Number of samples (each sample = 60 species pairs) selected to generate a null model expectation
n.samples <- 1000
## Vector for storing niche overlap indices for 46 species (i.e) 60 species pairs
niche_ov <- rep(NA, 60)
## Vector for storing proportion of species pairs with strong overlap.
prop.strong.overlap.samples <- rep(NA, n.samples)
## Vector for storing proportion of species pairs with weak overlap.
prop.weak.overlap.samples <- rep(NA, n.samples)
## Computing null distribution for Pianka's niche overlap: elevation
for (i in 1:n.samples) {
for (s in 1:60) {
# 1. Choose a random species pair from the total 63 species
# 2. Calculate the overlap metric for that pair and store in a vector.
niche_ov [s] <- niche.overlap(sample(Community.63sp, 2,F) , method = "pianka")
} # j
prop.weak.overlap.samples [i] <- (sum(niche_ov < 0.5)/60)*100 # 3. Calculate the proportion of pairs with weak overlap. Save in the prop.weak.overlap.samples vector
prop.strong.overlap.samples [i] <- (sum(niche_ov >= 0.5)/60)*100 # 4. Calculate the proportion of pairs with strong overlap. Save in the prop.strong.overlap.samples vector
} # i
### Write output to a csv file
write.csv (prop.weak.overlap.samples,"prop.weak.overlap.samples.elev.csv")
write.csv (prop.strong.overlap.samples,"prop.strong.overlap.samples.ele.csv")
# Diet
#-----------------------------------------------------------------#
## Computing null distribution for Pianka's niche overlap: Diet
#-----------------------------------------------------------------#
#### Number of samples (each sample = 60 species pairs) selected to generate a null model expectation
n.samples <- 1000
## Vector for storing niche overlap indices for 46 species (i.e) 60 species pairs
niche_ov.d <- rep(NA, 60)
## Vector for storing proportion of species pairs with strong overlap.
prop.strong.overlap.samples.d <- rep(NA, n.samples)
## Vector for storing proportion of species pairs with weak overlap.
prop.weak.overlap.samples.d <- rep(NA, n.samples)
## Computing null distribution for Pianka's niche overlap: diet
for (i in 1:n.samples) {
for (s in 1:60) {
# 1. Choose a random species pair from the total 63 species
# 2. Calculate the overlap metric for that pair and store in a vector.
niche_ov.d [s] <- niche.overlap(sample(diet.63sp.1, 2,F) , method = "pianka")
} # j
prop.weak.overlap.samples.d [i] <- (sum(niche_ov.d <= 0.6)/60)*100 # 3. Calculate the proportion of pairs with weak overlap. Save in the prop.weak.overlap.samples.d vector
prop.strong.overlap.samples.d [i] <- (sum(niche_ov.d > 0.6)/60)*100# 4. Calculate the proportion of pairs with strong overlap. Save in the prop.strong.overlap.samples.d vector
} # i
### Write output to a csv file
write.csv (prop.weak.overlap.samples.d,"prop.weak.overlap.samples.d.csv")
write.csv (prop.strong.overlap.samples.d,"prop.strong.overlap.samples.d.csv")
# Forest strata
#----------------------------------------------------------------------#
## Computing null distribution for Pianka's niche overlap: Forest strata
#----------------------------------------------------------------------#
#### Number of samples (each sample = 60 species pairs) selected to generate a null model expectation
n.samples <- 1000
## Vector for storing niche overlap indices for 46 species (i.e) 60 species pairs
niche_ov.s <- rep(NA, 60)
## Vector for storing proportion of species pairs with strong overlap.
prop.strong.overlap.samples.s <- rep(NA, n.samples)
## Vector for storing proportion of species pairs with weak overlap.
prop.weak.overlap.samples.s <- rep(NA, n.samples)
## Computing null distribution for Pianka's niche overlap: Forest strata
for (i in 1:n.samples) {
for (s in 1:60) {
# 1. Choose a random species pair from the total 63 species
# 2. Calculate the overlap metric for that pair and store in a vector.
niche_ov.s [s] <- niche.overlap(sample(strata.63sp.1, 2,F) , method = "pianka")
} # j
prop.weak.overlap.samples.s [i] <- (sum(niche_ov.s <= 0.6)/60)*100 # 5. Calculate the proportion of pairs with weak overlap. Save in the prop.weak.overlap.samples.s vector
prop.strong.overlap.samples.s [i] <- (sum(niche_ov.s > 0.6)/60)*100 # 4. Calculate the proportion of pairs with strong overlap. Save in the prop.strong.overlap.samples.s vector
} # i
### Write output to a csv file
write.csv (prop.weak.overlap.samples.s,"prop.weak.overlap.samples.s.csv")
write.csv (prop.strong.overlap.samples.s,"prop.strong.overlap.samples.s.csv")