Diversity index

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Question

How to calculate diversity indices?

Answer

Use the function diversity to calculate the most common indices. These parameters are used:

• amount: the number (or proportion) of individuals of a species in a transect.
• species: an identifier for a species
• transect: an identifier for a transect
• q: exponent for the diversity calculation

Amount, species, and transect are vectors (i.e. ordered sets of values). The parameters can be given to the function in several different ways. This is hopefully practical for the user.

• Amount, species, and transect must be of same length.
• If parameter names are not used (e.g. diversity(param1, param2, param3)), it is assumed that they are given in this order: amount, species, transect, q.
• If individual data is given using species identifiers, it the parameter name must be given: diversity(species = param1).
• The following default values are used for parameters:
  • Amount: 1 for each species, i.e. each species is equally abundant.
  • Species: 1, 2, 3, ... n, where n = number of rows in data, i.e. each row is a different species.
  • Transect: 1, i.e. there is only one transect.
  • q: q.wiki. You MUST define an object q.wiki before using diversity, otherwise alpha diversities will be calculated wrong. q.wiki can be a single number or a vector of numbers.

There are several ways to upload your data so that you can use the diversity function.

• Upload your data to Opasnet Base and call for the data using op_baseGetData function.
• Upload a CSV file to Opasnet using Special:Upload and call for the data using opasnet.data function.
• Use Example 1 code below to enter your data. The data must be in format c(4,6,2,5,7,4,3,9) where the values are either
  • identifiers of the species 1,2,3... in which the individuals belong (one entry per individual), or
  • abundancies of species, i.e. proportions or amounts of individuals belonging to each species among the whole population (one entry per species).

Rationale

Actual function diversity

Initiate functions

+ Show code- Hide code library(OpasnetUtils) ####NOTE! q.wiki MUST BE DEFINED OR ALPHA DIVERSITIES WILL BE CALCULATED WRONG ####### qD calculates true i.e. gamma diversity for abundance pi with exponent q. qD <- function(pi, q = q.wiki){ # q.wiki is the q given by the user. pi <- pi/sum(pi) out <- rep(NA, length(q)) for(i in 1:length(q)){ if(q[i] == 1) {out[i] <- exp(-sum(pi * log(pi)))} else if( q[i] == 999){ out[i] <- 1/max(pi)} else {out[i] <- (sum(pi^q[i]))^(1 / (1 - q[i])) } } q[q == 999] <- "∞" names(out) <- q return(out) } ###### qDa calculates alpha diversity using gamma diversities of each transect. qDa <- function(divj, wj = 1, q = q.wiki){ q. <- rep(q, times = length(wj)) wj <- rep(wj, each = length(q)) minqDj <- tapply(divj, q., min) # Should this be the inverse? out <- ifelse(q. == 1, wj * log(divj), wj * divj^(1-q.)) out <- tapply(out, q., sum) out <- ifelse(q == 1, exp(out), out^(1 / (1 - q))) out[q == 999] <- minqDj[q == 999] q[q == 999] <- "∞" names(out) <- q return(out) } ####### diversity is the function for the user. It calculates several diversity ####### indices. Parameters: ## amount: the number of individuals of a species in a transect. ## species: an identifier for a species ## transect: an identifier for a transect ## q: exponent for the diversity calculation diversity <- function(amount = rep(1,length(species)), species = 1:length(amount), transect = 1, q = q.wiki){ pij <- as.data.frame(as.table(tapply(amount, data.frame(Transect = transect, Species = species), sum))) colnames(pij)[3] <- "pij" pij <- dropall(pij[!is.na(pij$pij) & pij$pij != 0, ]) pij$pij <- pij$pij/sum(pij$pij) wj <- as.data.frame(as.table(tapply(pij$pij, pij$Transect, sum))) pi <- as.data.frame(as.table(tapply(pij$pij, pij$Species, sum)))[, 2] colnames(wj) <- c("Transect", "wj") out <- merge(pij, wj) out <- tapply(out$pij, out$Transect, qD) qDj <- NULL for(i in 1:nrow(wj)){ qDj <- c(qDj, out[[i]]) } gamma <- qD(pi, q) alpha <- qDa(qDj, wj$wj, q) dim(qDj) <- c(length(q), length(qDj)/length(q)) q[q == 999] <- "∞" dimnames(qDj) <- list(q, levels(as.factor(pij$Transect))) return(list(gamma = gamma, alpha = alpha, tr.gammas = t(qDj))) } ########## diversity.table makes a data table out of the results. diversity.table <- function(amount = rep(1,length(species)), species = 1:length(amount), transect = 1, q = q.wiki){ temp <- diversity(amount, species, transect, q) gamma <- temp[["gamma"]] alpha <- temp[["alpha"]] beta. <- gamma / alpha beta.A <- gamma - alpha beta.W <- gamma / alpha - 1 beta.P <- 1 - alpha / gamma qt <- gsub("999", "∞", q) outlabel <- c( paste("Gamma diversity with q=", qt, sep=""), paste("Alpha diversity with q=", qt, sep=""), paste("Beta diversity (strict) with q=", qt, sep=""), paste("Beta diversity (absolute turnover) with q=", qt, sep=""), paste("Beta diversity (Whittaker's turnover) with q=", qt, sep=""), paste("Beta diversity (proportional turnover) with q=", qt, sep="")) outsymbol <- c( paste(qt, "D", sep=""), paste(qt, "Da", sep=""), paste(qt, "Beta.", sep=""), paste(qt, "Beta.A", sep=""), paste(qt, "Beta.W", sep=""), paste(qt, "Beta.P", sep="")) out <- data.frame(Name = c(outlabel, "Richness", "Shannon index", "Simpson index", "Inverse Simpson index", "Gini-Simpson index", "Berger-Parker index"), Symbol = c(outsymbol, "S", "H' or log(1D)", "λ or 1/(2D)", "1/λ or 2D", "1-λ or 1-1/(2D)", "1/(∞D)"), Value = c(gamma, alpha, beta., beta.A, beta.W, beta.P, length(pi), log(qD(pi,1)), 1/qD(pi,2), qD(pi,2), 1-1/qD(pi,2), 1/qD(pi,999))) return(out) } ##################### Data management function longfo <- function( spraw, # Species data.frame in wide format trapraw, # Trap data.frame id.vars = character() # Column names used as identifiers (not species mearurements) ) { a <- merge(trapraw, spraw) # Assumed that the only common column is the Trap identifier. a$StartDay <- as.POSIXct(paste(a$StartYear, a$StartMonth, a$StartDay, sep = "-"), tz = "UTC") a$EndDay <- as.POSIXct(paste(a$EndYear, a$EndMonth, a$EndDay, sep = "-"), tz = "UTC") a$NumDays <- as.numeric(a$EndDay - a$StartDay) a <- a[ , !colnames(a) %in% c("StartYear", "StartMonth", "EndYear", "EndMonth")] id.vars <- colnames(a)[colnames(a) %in% union(id.vars, c("Trap", "StartDay", "EndDay", "NumDays", "TrapID", "SeqInTrap", "SampleCode", "SoilType", "Region", "Latitude"))] # The typical id.vars used. a <- melt(a, id.vars = id.vars, variable.name = "Species", value.name = "Individuals" ) return(a) } ########## THIS FUNCTION CREATES A SAMPLE OF INDIVIDUAL SAMPLING PERIODS ########## AND THEN AGGREGATES ACROSS THE GROUPS. prepare <- function( dat, # data.frame with the data samp = TRUE, # do we sample or take rows in order? lens = c(0, 1, 2, 3, 5, 7, 10, 14, 20, 30, 50, 70, 100, 99999999), # Numbers of lengths in samples reps = 2, # how many repetitions? cols = c("TrapID", "Species"), # Column names used for grouping verbose = FALSE # Verbose returns a list with out as well as a. ) { cols <- colnames(dat)[colnames(dat) %in% cols] groups <- aggregate(dat$Individuals, by = dat[cols], FUN = length) # This code makes a list of lengths that is used for index j to avoid overwhelmingly many samples for large groups. # First, possible lengths of a sample are determined by len. Second, the number of observations in each group # determine how far you go in the list. lengths <- list() for(i in 1:length(groups$x)) lengths[[i]] <- c(lens[1:(findInterval(groups$x[[i]], lens) - 1)], groups$x[[i]])[-1] if(!samp) reps <- 1 a <- data.frame() # Sampled data.frame going to aggregation for(i in 1:nrow(groups)) { for(j in lengths[[i]]) { for(k in 1:reps) { if(samp) ro <- sample(groups$x[i], j, replace = FALSE) else ro <- 1:j if(j != 0) {a <- rbind(a, data.frame( Len = j, Reps = k, merge(dat, groups[i , colnames(groups) != "x"])[ro , ] ))} } } } if(verbose) { print(head(a)) print(nrow(a)) } ##### Create new variable Spec which is the first occurrence of a species in a group. cols <- union(cols, c("Len", "Reps")) a <- a[order(a$StartDay) , ] # Order by start day. a$Spec <- 0 rownames(a) <- 1:nrow(a) a$Spec[as.numeric(rownames(unique(subset(a, Individuals > 0, cols))))] <- 1 ##### AGGREGATION FROM THE SAMPLED PERIODS out <- aggregate(a[colnames(a) %in% c("Individuals", "Spec", "NumDays")], by = a[cols], FUN = sum) temp <- aggregate(a[colnames(a) %in% c("Region")], by = a[cols], FUN = function(x) x[1]) out <- cbind(out, temp[!colnames(temp) %in% cols]) # Remove redundant columns before cbind. temp <- aggregate(a[colnames(a) %in% c("SoilType", "TrapID")], by = a[cols], FUN = function(x) paste(x, collapse = " ")) out <- cbind(out, temp[!colnames(temp) %in% cols]) temp <- aggregate(a[colnames(a) %in% c("StartDay")], by = a[cols], FUN = min) out <- cbind(out, temp[!colnames(temp) %in% cols]) temp <- aggregate(a[colnames(a) %in% c("EndDay", "Len", "Reps")], by = a[cols], FUN = max) out <- cbind(out, temp[!colnames(temp) %in% cols]) out$SamplingGap <- as.numeric(out$EndDay - out$StartDay - out$NumDays) if(verbose) return(list(out, a)) else return(out) } objects.store(qD, qDa, diversity, diversity.table, longfo, prepare) cat("Functions qD, qDa, diversity, and diversity.table, longfo, prepare stored.\n")

The function diversity produces a list where the first, second, and third element are the gamma, the alpha, and transect-specific gamma diversities, respectively.

Function diversity.table produces a data.frame of several diversity indices.

Examples

Example 1 to use function

Give your data in R format or leave empty for example data: Is your data individual data or group abundancies?: Individual Group + Show code- Hide code library(xtable) q.wiki = 0 if(is.null(data)) {data <- c(1,4,6,9,3,4,5,6,5,4,3,3,5,5,7,5,5,4,3,4,5,6,8,9,5,4,5,4,3,3,4,9,6,6,4,5,3,2,1,1,2,3,4,3,2,3,4,5,6,7,7)} data diversity(data) if(individual==TRUE) out <- diversity(species = data, q = q.wiki) else out <- diversity(amount = data, q = q.wiki) print(xtable(out), type = 'html')

Example 2

Select your data: Tigre Which q values you want to calculate.: 0 0.5 1 2 3 6 ∞ + Show code- Hide code library(OpasnetBaseUtils) library(xtable) data <- opasnet.csv(wikidata, wiki = "opasnet_en", sep = ",") data <- data[data$Species != 1, ] species <- data$Species amount <- data$Individuals transect <- data$Transect diversity(amount, species, transect, q.wiki) print(xtable(diversity(amount, species, transect, q.wiki)[[3]]), type = 'html') print(xtable(diversity.table(amount, species, transect, q.wiki)), type = 'html')

The data should be given in R format as a list of values in parenthesis, beginning with c:

c(3,5,3,5,2,1,3,3,4,2) or equivalently c(0.1,0.2,0.4,0.1,0.2)

where the values are either

• identifiers of the species 1,2,3... in which the individuals belong (one entry per individual), or
• abundancies of species, i.e. proportions of individuals belonging to each species among the whole population (one entry per species).

Calculations

Show details

library(reshape2) library(ggplot2) library(OpasnetUtils) library(vegan) # Sp accumulation ichno simple # version 2014-11-09 by Hanna Tuomisto # PART 1 # open a data tables with data of species per trap sample, environmental data and literature data # combine samples from the same trap, by soil type and by region # combine data within traps by sampling season # export the resulting data tables to text files # PART 2 # open data saved in PART 1 # calculate number of species and its chao and ACE estimates, number of individuals, diversity # save resulting table to a new file # PART 3 # open data saved in PART 2 and construct and save species-accumulation graphs # PART 4 # run NMDS with trapwise data and save the graphs ########## PART 1: Open data files and combine data ########## #### check default directory getwd() setwd("/Users/hantuo/Documents/j1 Anun koinobiontit") # for iMac setwd("/Users/hantuo/Documents/j1 Isrraelin iknot") # for iMac setwd("/Users/hannatuomisto/Documents/j1 Isrraelin iknot") # for Air setwd("/Users/hannatuomisto/Documents/Dokumentit/j1 Anun koinobiontit") # for Pro setwd("/Users/hannatuomisto/Documents/Dokumentit/j1 Isrraelin iknot") # for Pro ###### open raw data files ###### # open sites by species data file for the own field data # columns should be as follows: "TrapID","SeqInTrap","SampleCode","StartYear","StartMonth","StartDay", # "EndYear","EndMonth","EndDay", further columns each corresponding to one species path <- file.choose() spraw <- read.csv(path, header=TRUE, stringsAsFactors = FALSE) spname <- gsub(".csv", "", basename(path), ignore.case=TRUE) # open file with trap locality info # columns should be as follows: "TrapID","SoilType","Region","Latitude" path <- file.choose() trapraw <- read.csv(path, header=TRUE, stringsAsFactors = FALSE) trapname <- gsub(".csv", "", basename(path), ignore.case=TRUE) ###### ALLA OLEVA HOITUISI MERGELLÄ. JOS HALUTAAN, VOI LISÄTÄ SKIRPTIN JOKA KERTOO MITÄ TIPUTETTIIN. a <- merge(spraw, trapraw, by = "TrapID") # eliminate traps that are only found in one of the data files sptable <- spraw[spraw$TrapID %in% trapraw$TrapID,] traptable <- trapraw[trapraw$TrapID %in% spraw$TrapID,] if((el=nrow(spraw) - nrow(sptable)) != 0) { print(paste(el, "species data rows will be omitted from analyses because trap info is not available for:", paste0(spraw[!spraw$TrapID %in% trapraw$TrapID,"TrapID"], collapse=", "))) } if((el=nrow(trapraw) - nrow(traptable)) != 0) { print(paste(el, "traps had no species data:", paste0(trapraw[!trapraw$TrapID %in% spraw$TrapID,"TrapID"], collapse=", "))) } # open file with literature data # columns should contain: "MTM", "Species", "Individuals", "Latitude", "Longitude", Elev.min", "Elev.max" # coordinates can also be: "Lat.deg", "Lat.min" path <- file.choose() litraw <- read.csv(path, header=TRUE) litname <- gsub(".csv", "", basename(path), ignore.case=TRUE) if(FALSE) { # if needed, convert latitudes to decimal degrees by running the next line: litraw[,ncol(litraw+1)] <- litraw$Lat.deg + litraw$Lat.min/60 } ###### choose options and prepare the data ###### #### choose what combinations of sampling periods to use comb <- c("TrapID", "SoilType", "Region") comb <- c("TrapID", "Region") comb <- c("TrapID") comb <- c("Region") comb <- c("SoilType") #### set name for file with species accumulation data # info on combination will be added automatically # !!! any file with the same name in the working directory will be overwritten without warning !!! filename <- paste(spname,"sp-accum", sep="_") #### Calculate catch for different sampling periods and traps #### ALLA OLEVAN VOISI KORVATA POSIXct:llä # convert start and end date to sequential day days <- cbind(1:12, c(31,28,31,30,31,30,31,31,30,31,30,31), c(rep(0,12))) colnames(days) <- c("month", "monthlength", "cumdays") for(i in 2:nrow(days)) days[i,3] <- days[i-1,2]+days[i-1,3] StartDay <- (sptable$StartYear-min(sptable$StartYear))*365+sptable$StartDay+days[sptable$StartMonth,3] EndDay <- (sptable$EndYear-min(sptable$StartYear))*365+sptable$EndDay+days[sptable$EndMonth,3] NumDays <- EndDay-StartDay SamplingGap <- 0 # create a new data matrix with sequential days data <- cbind(TrapID=sptable$TrapID, StartDay, EndDay, NumDays, SamplingGap, sptable[,10:ncol(sptable)]) data <- na.omit(data) # eliminate rows with missing dates # aggregate data by trap data_tr <- aggregate(data[,-1], by=list(data$TrapID), FUN=sum, simplify=TRUE) colnames(data_tr)[1] <- colnames(data)[1] # add SoilType and Region (but not Latitude) data_sub <- merge(traptable[,-4], data) data_tr <- merge(traptable[,-4], data_tr) # fix start and end days data_tr$StartDay <- aggregate(data$StartDay, by=data["TrapID"], FUN=min, simplify=TRUE)[,2] data_tr$EndDay <- aggregate(data$EndDay, by=list(data$TrapID), FUN=max, simplify=TRUE)[,2] data_tr$SamplingGap <- data_tr$EndDay - data_tr$StartDay - data_tr$NumDays #### Code below can be used after data is managed with functions longfo and prepare. temp <- aggregate(a$Indiv_cum, INDEX = a[c("Time_cum", "Trap")], FUN = sum) temp2 <- aggregate(a$Spec_cum, INDEX = a[c("Time_cum", "Trap")], FUN = sum) ggplot(subset(temp, Trap == "a"), aes(x = Time_cum, y = Freq, colour = Trap))+geom_step() ggplot(a,aes(x=Cum,color=Trap, group = Trap)) + stat_bin(data=a, aes(y=cumsum(..count..)),geom="step")+ stat_bin(data=subset(a,Trap=="b"),aes(y=cumsum(..count..)),geom="step") ggplot(a, aes(x=Cum, y = cumsum(Individuals))) + geom_line() # run data aggregation within and across traps for(m in seq(length(comb))) { # loop through the aggregation criteria if(comb[m]=="TrapID") { data_m <- data_sub } else { # use data aggregated by trap data_m <- data_tr if(comb[m]=="SoilType") data_m <- data_m[data_m$SoilType != "",] # exclude traps with no SoilType } # create matrix to compile data on sampling times and numbers of species sp_time <- data_m for(n in seq(unique(data_m$Region))) { # repeat for each region separately comb_n <- data_m[data_m$Region==unique(data_m$Region)[n],] for(p in if(comb[m]=="TrapID") 1 else 1:10) { for(i in seq(unique(comb_n[,comb[m]]))) { # loop through the unique values of the m:th aggregation criterion comb_i <- comb_n[comb_n[,comb[m]]==unique(comb_n[,comb[m]])[i],] if(nrow(comb_i) > 1) { if(comb[m]=="TrapID") { comb_i <- comb_i[order(comb_i$StartDay, comb_i$EndDay),] # sort rows by date } else { comb_i <- comb_i[sample(nrow(comb_i), nrow(comb_i)),] # randomize row order } first <- comb_i[1,] for(k in 2:(nrow(comb_i))) { second <- comb_i[k,] new <- nrow(sp_time)+1 sp_time[new,"Region"] <- first$Region # this creates a new row sp_time[new,"SoilType"] <- if(first$SoilType==second$SoilType) {first$SoilType} else {paste(first$SoilType,second$SoilType,sep=" ")} sp_time[new,"TrapID"] <- if(first$TrapID==second$TrapID) {first$TrapID} else {paste(first$TrapID,second$TrapID,sep=" ")} sp_time[new,"StartDay"] <- min(first$StartDay,second$StartDay) sp_time[new,"EndDay"] <- max(first$EndDay,second$EndDay) sp_time[new,"NumDays"] <- sum(first$NumDays,second$NumDays) if(comb[m]=="TrapID") { sp_time[new,"SamplingGap"] <- max(first$StartDay,second$StartDay)-min(first$EndDay,second$EndDay)+first$SamplingGap+second$SamplingGap } else {sp_time[new,"SamplingGap"] <- NA} sp_time[new,8:ncol(sp_time)] <- first[,8:ncol(first)]+second[,8:ncol(second)] # redefine first to be the combination of first and second first <- sp_time[new,] } } } } } write.csv(sp_time, file=paste(filename, "_", comb[m], ".csv", sep="")) } ########## PART 2: Calculate number of individuals and species, estimates of S and diversity ########## library(vegan) #### open the file with aggregated sampling periods to be used in calculations path <- file.choose() to_est <- read.csv(path, row.names=1, stringsAsFactors = FALSE) to_estname <- gsub(".csv", "", basename(path), ignore.case=TRUE) #### calculate individuals, species, estimates and diversity and save as table estS <- t(estimateR(to_est[,8:ncol(to_est)])) estSadd <- cbind("ChaoAddRel"=100*(estS[,"S.chao1"]/estS[,"S.obs"]-1), "ChaoAddAbs"=estS[,"S.chao1"]-estS[,"S.obs"]) renyiD <- renyi(to_est[,8:ncol(to_est)], scales=c(0,1,2), hill=TRUE) colnames(renyiD) <- paste("Div.q", colnames(renyiD), sep="") estSdiv <- cbind( Region = to_est$Region, MTM = to_est$NumDays/30, StartDay = to_est$StartDay, Individuals = rowSums(to_est[,8:ncol(to_est)]), estS[,-(4:5)], estSadd, renyiD, TrapID = to_est$TrapID, SoilType = to_est$SoilType ) colnames(estSdiv)[which(colnames(estSdiv)=="S.obs")] <- "Species" write.csv(estSdiv, file=paste(to_estname, "_S_est_D.csv", sep="")) ########## PART 3: Make species accumulation graphs ########## #### open the result file for plotting, name ends in "_S_est_D.csv" #### path <- file.choose() toplot <- read.csv(path, row.names=1, stringsAsFactors = FALSE) toplotname <- gsub(".csv", "", basename(path), ignore.case=TRUE) if(any("Species" %in% colnames(toplot))) {"OK"} else {"The opened file has no Species column!"} #### choose if source file name is used as title for the plot #### title <- toplotname # title <- "" # choose this for publication quality #### choose the color scheme #### col_choice <- 1 # 6 colors by soil type; optimised for Clay, Floodplain, Loam, Sand, Secondary, Terrace # col_choice <- 5 # as 1, but add abbreviation of Region to legend # col_choice <- 2 # 2 colours by Region # col_choice <- 6 # all symbols black # col_choice <- 3 # 4 colours by SoilType (Loreto) NOT FUNCTIONAL YET # col_choice <- 4 # 1 colour (all sites the same) NOT FUNCTIONAL YET # the colors are automatically defined here on the basis of the above choice if((col_choice==1) | (col_choice==5)) { col_lut <- cbind("SoilType"=c(sort(unique(toplot$SoilType))), "Color"=c("darkgoldenrod","blue","brown4","red","darkgreen","darkblue") , "Rank"=c(1,5,2,3,4,6)) col_lut <- col_lut[order(col_lut[,"Rank"]),] col_source <- "SoilType" if(col_choice==5) { col_lut <- cbind(col_lut, "Reg.abbr"=col_lut[,"SoilType"]) for (i in seq(nrow(col_lut))) { col_lut[i,"Reg.abbr"] <- gsub("[:a-z: :blank:]","",toplot$Region[which(toplot$SoilType==col_lut[i,1])[1]]) } } } if(col_choice==2) { col_lut <- cbind(c(sort(unique(toplot$Region))), c("black", "blue")) col_source <- "Region" } if(col_choice==3) { # this will only work for Anu's data toplot <- toplot[which(toplot$Region %in% c("NRAM", "ACC")),] col_lut <- cbind(c(sort(unique(toplot$SoilType))), c("darkblue", "blue", "red", "darkgoldenrod")) col_source <- "SoilType" } if(col_choice==4) { # this will only work for Anu's data toplot <- toplot[which(toplot$Region %in% c("OnkoneGare", "Tiputini")),] col_lut <- cbind(c(sort(unique(toplot$Region))), c("black")) col_source <- "Region" } # legend specifications for figures col_legend <- ifelse(rbind(col_lut[,1])!="", rbind(col_lut[,1]), "Unspecified") if(col_choice == 5) { col_legend <- paste(col_lut[,"Reg.abbr", drop=FALSE], col_legend) } if((col_choice==1) | (col_choice==5)) {col_lit <- "black"} else {col_lit <- "red"} # check on screen that the colours are as they should print(col_lut) #### Choose one of the plot types: #### figure <- "Traplines" # FIG 1: trap-wise species accumulation lines figure <- "Estimates" # FIG 2: plot with estimated number and percentage of unseen species figure <- "Effort" # FIG 3: Plot with individuals and spp vs MTM figure <- "Diversity" # FIG 4: Plot with richness and diversity vs individuals figure <- "Latitude" # FIG 5: Plot with richness against latitude #### these plot options are set automatically on the basis of choices made above #### # FIG 1: Trap-wise species accumulation lines if(figure=="Traplines") { mfrow <- c(1,3) # defines the number of panels hw <- 2.7 # defines the dimensions of each panel x_own <- cbind(toplot$MTM, toplot$MTM, toplot$Individuals) xlab <- c("Trap months", "Trap months", "Individuals") y_own <- cbind(toplot$Individuals, toplot$Species, toplot$Species) ylab <- c("Individuals", "Species", "Species") lit <- FALSE cex_lat <- FALSE log <- "" col_pos <- "topleft" col_panel <- 1 panel_pos <- "bottomright" } # FIG 2: Plot with estimated number and percentage of unseen species if(figure=="Estimates") { mfrow <- c(1,2) # defines the number of panels hw <- 4.2 # defines the dimensions of each panel x_own <- cbind(toplot$Individuals, toplot$Individuals) xlab <- c("Individuals", "Individuals") y_own <- cbind(toplot$ChaoAddAbs, toplot$ChaoAddRel) ylab <- c("Estimated increase in richness (species)", "Estimated increase in richness (%)") # remove infinite values of ChaoAddRel elim <- which(is.na(y_own[,2])) if(length(elim > 0)) { y_own <- y_own[-elim,] x_own <- x_own[-elim,] if(cex_lat==TRUE) { cex1 <- cex1[-elim,] } col <- col[-elim] } lit <- FALSE cex_lat <- FALSE log <- "xy" col_pos <- "bottomleft" col_panel <- 2 panel_pos <- "topright" } # FIG 3: Plot with individuals and spp vs MTM if(figure=="Effort") { mfrow <- c(1,2) # defines the number of panels hw <- 4.2 # defines the dimensions of each panel x_own <- cbind(toplot$MTM, toplot$MTM) xlab <- c("Trap months", "Trap months") y_own <- cbind(toplot$Individuals, toplot$Species) ylab <- c("Individuals", "Species") lit <- TRUE x_lit <- cbind(litraw$MTM, litraw$MTM) y_lit <- cbind(litraw$Individuals, litraw$Species) cex_lat <- TRUE log <- "xy" col_pos <- "bottomright" col_panel <- 1 panel_pos <- "topleft" } # FIG 4: Plot with richness and diversity vs individuals if(figure=="Diversity") { mfrow <- c(1,3) # defines the number of panels hw <- 2.9 # defines the dimensions of each panel x_own <- cbind(toplot$Individuals, toplot$Individuals, toplot$Individuals) xlab <- c("Individuals", "Individuals", "Individuals") y_own <- cbind(toplot$Div.q0, toplot$Div.q1, toplot$Div.q2) ylab <- c("Richness", "Diversity q=1", "Diversity q=2") lit <- TRUE x_lit <- cbind(litraw$Individuals) y_lit <- cbind(litraw$Species) cex_lat <- TRUE log <- "xy" col_pos <- "bottomright" col_panel <- 2 panel_pos <- "topleft" } # colour vector for plotting if(col_choice == 6) {col <- "black"} else { col <- c(rep("", nrow(toplot))) for(a in seq(length(col))) col[a] <- col_lut[which(col_lut[,1]==toplot[a,col_source]),2] } # symbol size set to either constant or scaled by latitude if(cex_lat == FALSE) { cex1 <- cex2 <- 1 } else { cex1 <- c(rep(0, dim(toplot)[1])) for(a in seq(length(cex1))) cex1[a] <- traptable$Latitude[toplot$Region[a]==traptable$Region][1] cex1 <- 2.5*sqrt(cex1/max(abs(litraw$Latitude))) } # if data are log-transformed, zeroes are removed from the data if(charmatch("x", log, nomatch=-1)>=0) { col <- col[x_own[,2]>0] if(cex_lat==TRUE) { cex1 <- cex1[x_own[,2]>0] } y_own <- y_own[x_own[,2]>0,] x_own <- x_own[x_own[,2]>0,] } if(grep("y", log)>0) { col <- col[y_own[,2]>0] if(cex_lat==TRUE) { cex1 <- cex1[y_own[,2]>0] } x_own <- x_own[y_own[,2]>0,] y_own <- y_own[y_own[,2]>0,] } # axis limits x_lower <- apply(x_own,2,min) x_upper <- apply(x_own,2,max) if(figure=="Diversity") { y_lower <- rep(min(y_own), dim(y_own)[2]) y_upper <- rep(max(y_own), dim(y_own)[2]) } else { y_lower <- apply(y_own,2,min) y_upper <- apply(y_own,2,max) } # parameters for literature data ################# HUOM! make those sites gray that do not have Rhyssinae data!! #################### if(lit) { x_upper <- apply(rbind(apply(x_lit,2,max, na.rm=TRUE), x_upper), 2, max) y_upper <- apply(rbind(apply(y_lit,2,max, na.rm=TRUE), y_upper), 2, max) if(cex_lat) { cex2 <- 2.5*sqrt(abs(litraw$Latitude)/max(abs(litraw$Latitude))) } else { cex2 <- 1 } pch2 <- ifelse(litraw$Elev.max<1000, 1, 19) } # lettering for the panels panel <- LETTERS[1:(dim(x_own)[2]*dim(y_own)[2])] # name for the output file if(log != "") logged <- paste("-log",log,sep="") else logged <- "" filename <- paste(toplotname,"-", figure, "-lit", lit, logged, "-lat", cex_lat, "-col",col_source, sep="") #### end of automatic plot options #### #### Draw the graphs pdf(file=paste(toplotname, "-", figure, ".pdf", sep=""), height=hw*mfrow[1], width=hw*mfrow[2]) par(mfrow=mfrow, mar=c(4,4,1,1), oma=c(1,1,1,1)) for(i in seq(dim(x_own)[2])) { # loop through x variables plot(x_own[,i], y_own[,i], type="n", log=log, xlim=c(if(figure!="Effort") {x_lower[i]} else {x_lower[i]/2}, x_upper[i]), ylim=c(y_lower[i], y_upper[i]), xlab=xlab[i], ylab=ylab[i], cex=cex1, col=col) title(main=title, cex=0.5, outer=T) legend(panel_pos, panel[i], bty="n", cex=1.5) if(i==col_panel) { if(lit) { legend(col_pos, c(col_legend, "Literature"), text.col=c(col_lut[,2], col_lit), bty="n", cex=1) } else { legend(col_pos, col_legend, text.col=col_lut[,2], bty="n", cex=1) } } if(figure=="Traplines") { for(j in seq(unique(toplot$TrapID))) { sel_j <- which(toplot$TrapID==unique(toplot$TrapID)[j]) min_j <- min(toplot[sel_j,"StartDay"]) sel_j <- intersect(sel_j, which(toplot$StartDay==min(toplot[sel_j,"StartDay"]))) col1 <- col[sel_j] points(x_own[sel_j,i], y_own[sel_j,i], type="l", col=col1) } } if(figure=="Estimates") { points(x_own[,i], y_own[,i], type="p", col=col) } if(figure=="Effort" ) { points(x_own[,i], y_own[,i], type="p", col=col) if(lit) { points(x_lit[,i], y_lit[,i], type="p", col=col_lit, cex=cex2, pch=pch2) }} if(figure=="Diversity") { points(x_own[,i], y_own[,i], type="p", col=col) if(lit & i==1) { points(x_lit[,i], y_lit[,i], type="p", col=col_lit, cex=cex2, pch=pch2) }} if(figure=="Latitude") { points(x_own[,i], y_own[,i], type="p", col=col) if(lit & i==1) { points(x_lit[,i], y_lit[,i], type="p", col=col_lit, cex=cex2, pch=pch2) }} } dev.off() ##################################### hätäratkaisu # plot the figure=="Latitude" graph lat <- 0 for (i in seq(nrow(toplot))) { lat <- c(lat, trapraw[which(toplot$Region[i] == trapraw$Region)[1],"Latitude"])} lat <- as.numeric(lat[-1]) toplot2 <- as.data.frame(cbind("Latitude"=lat, "Species"=toplot$Species, "MTM"=toplot$MTM)) pdf(file=paste(toplotname, "-", figure, ".pdf", sep=""), height=4, width=4.8) par(mfrow=c(1,1), mar=c(4,4,1,1), oma=c(1,1,1,1)) plot(toplot2$Latitude, toplot2$Species, type="n", xlab="Latitude", ylab="Species", xlim=c(min(litraw$Latitude), max(litraw$Latitude)), ylim=c(0,max(toplot2$Species)+5)) for(i in seq(unique(toplot2$Latitude))) { dots <- toplot2[toplot2$Latitude==unique(toplot2$Latitude)[i],] dots2 <- dots[dots$Species<=max(dots$Species)/2,] dots2 <- dots2[sample(seq(nrow(dots2)), 10, replace = FALSE, prob = NULL),] points(dots2$Latitude, dots2$Species, cex=3*(dots2$MTM/max(litraw$MTM))^(1/3)) dots2 <- dots[dots$Species>max(dots$Species)/2,] dots2 <- dots[sample(seq(nrow(dots2)), 10, replace = FALSE, prob = NULL),] points(dots2$Latitude, dots2$Species, cex=3*(dots2$MTM/max(litraw$MTM))^(1/3)) dots2 <- (dots[dots$Species==max(dots$Species),][1,]) points(dots2$Latitude, dots2$Species, cex=3*(dots2$MTM/max(litraw$MTM))^(1/3)) } points(litraw$Latitude, litraw$Species, pch=pch2, cex=3*(litraw$MTM/max(litraw$MTM))^(1/3)) dev.off() ################# ########## PART 4: Run and plot NMDS with trapwise data ########## library(vegan) library(MASS) #### aggregate species data by trap trapdata <- aggregate(sptable[,-(1:11)], by=list(sptable$TrapID), FUN=sum, simplify=TRUE) colnames(trapdata)[1] <- "TrapID" trapdata <- trapdata[match(traptable$TrapID, trapdata$TrapID),] rownames(trapdata) <- trapdata$TrapID trapdata <- trapdata[,-1] #### run NMDS using both presence-absence data (Soerensen index) and abundance data (Bray-Curtis relative) sp.sor <- vegdist(trapdata, method="bray", binary=TRUE) # change here for other dissimilarity fileout <- paste(spname, "Soerensendist.txt", sep="_") write.table(as.matrix(sp.sor), file=fileout, sep="\t") ord_pa <- metaMDS(sp.sor) sp.bc <- vegdist(decostand(trapdata,"total"), method="bray", binary=FALSE) # change here for other dissimilarity fileout <- paste(spname, "BrayCurtdist.txt", sep="_") write.table(as.matrix(sp.bc), file=fileout, sep="\t") ord_ab <- metaMDS(sp.bc) #### define colors for the plots col_source <- traptable$SoilType if(length(unique(col_source))==5) { col_lut <- cbind(c(sort(unique(col_source))), c("black", "darkblue", "blue", "red", "darkgoldenrod")) } else { col_lut <- cbind(c(sort(unique(col_source))), c("darkblue", "blue", "red", "darkgoldenrod")) } # check that the colors are as they should print(col_lut) col <- c(rep("",length(col_source))) for(a in seq(length(col))) col[a] <- col_lut[which(col_lut[,1]==col_source[a]),2] # set symbols by Region pch_source <- traptable$Region pch_lut <- as.data.frame(cbind(c(sort(unique(pch_source))), c(1, 0, 2, 6)), stringsAsFactors = FALSE) # check that the symbols are as they should print(pch_lut) pch <- c(rep(0,length(pch_source))) for(a in seq(length(pch))) pch[a] <- as.numeric(pch_lut[which(pch_lut[,1]==pch_source[a]),2]) # plot the ordination result and save it as a pdf file pdf(file=paste(spname,"NMDS.pdf", sep="_"), height=4, width=8) par(mfrow=c(1,2), mar=c(4,4,1,1), oma=c(1,1,1,1)) # presence-absence ordination plot(ord_pa, display="sites", type="n", ylim=c(-0.4,0.4), xlim=c(-0.6, 0.6), xlab="Axis 1", ylab="Axis 2") points(ord_pa, col=col, pch=pch) legend("topleft", ifelse(rbind(col_lut[,1])!="", rbind(col_lut[,1]),"unspecified"), text.col=col_lut[,2], bty="n", cex=0.7) title(main="Presence-absence") # abundance ordination plot(ord_ab, display="sites", type="n", ylim=c(-0.4,0.4), xlim=c(-0.6, 0.6), xlab="Axis 1", ylab="Axis 2") points(ord_ab, col=col, pch=pch) legend("topleft", legend=pch_lut[,1], bty="n", cex=0.7, pch=as.numeric(pch_lut[,2])) title(main="Relative abundance") dev.off() ########## PART 5: Run and plot NMDS with seasonal data ########## TARKISTETTAVA library(vegan) library(MASS) #### aggregate species data by season within trap sp_data <- sptable[,-5] sp_data <- na.omit(sp_data) months <- list(c(12,1,2), c(3:5), c(6:8), c(9:11)) months.names <- c("Dec-Feb", "Mar-May", "Jun-Aug", "Sep-Nov") for(i in 1:4) { sp_season <- sp_data[which(sp_data$StartMonth %in% months[[i]]),] sp_season <- aggregate(sp_season[,-(1:10)], by=list(sp_season$TrapID), FUN=sum, simplify=TRUE) colnames(sp_season)[1] <- "TrapID" if(i==1) { trapdata <- sp_season season <- rep(months.names[i], nrow(sp_season)) soil <- rep("", nrow(sp_season)) for(k in seq(length(soil))) soil[k] <- traptable[which(trapdata$TrapID[k]==traptable$TrapID),2] } else { trapdata <- rbind(trapdata, sp_season) season <- c(season, rep(months.names[i], nrow(sp_season))) soil.t <- rep("", nrow(sp_season)) for(k in seq(length(soil.t))) soil.t[k] <- traptable[which(trapdata$TrapID[k]==traptable$TrapID),2] soil <- c(soil, soil.t) } } trap <- trapdata$TrapID rownames(trapdata) <- paste(season, trapdata$TrapID, sep=".") trapdata <- trapdata[,-1] min.ind <- 5 season <- season[which(rowSums(trapdata)>=min.ind)] soil <- soil[which(rowSums(trapdata)>=min.ind)] trapdata <- trapdata[which(rowSums(trapdata)>=min.ind),] file <- paste(spname, "_SeasonInd", min.ind, sep="") #### run NMDS using both presence-absence data (Soerensen index) and abundance data (Bray-Curtis relative) sp.sor <- vegdist(trapdata, method="bray", binary=TRUE) # change here for other dissimilarity fileout <- paste(file, "Soerensendist.txt", sep="_") write.table(as.matrix(sp.sor), file=fileout, sep="\t") ord_pa <- metaMDS(sp.sor) sp.bc <- vegdist(decostand(trapdata,"total"), method="bray", binary=FALSE) # change here for other dissimilarity fileout <- paste(file, "BrayCurtdist.txt", sep="_") write.table(as.matrix(sp.bc), file=fileout, sep="\t") ord_ab <- metaMDS(sp.bc) #### define colors for the plots col_source <- list(soil, season) col_lut <- list() if(length(unique(col_source[[1]]))==5) { col_lut[[1]] <- cbind(c(sort(unique(col_source[[1]]))), c("black", "darkblue", "blue", "red", "darkgoldenrod")) } else { col_lut[[1]] <- cbind(c(sort(unique(col_source[[1]]))), c("darkblue", "blue", "red", "darkgoldenrod")) } col_lut[[2]] <- cbind(c(unique(col_source[[2]])), c("black", "green", "blue", "brown")) # check that the colors are as they should print(col_lut) col <- cbind(rep("",length(col_source[[1]])), rep("",length(col_source[[2]]))) for(a in seq(nrow(col))) { col[a,1] <- col_lut[[1]][which(col_lut[[1]][,1]==col_source[[1]][a]),2] col[a,2] <- col_lut[[2]][which(col_lut[[2]][,1]==col_source[[2]][a]),2] } col_lut[[1]][1,1] <- "undefined" # set symbols by Region pch_source <- traptable$Region pch_lut <- as.data.frame(cbind(c(sort(unique(pch_source))), c(1, 0, 2, 6)), stringsAsFactors = FALSE) # check that the symbols are as they should print(pch_lut) pch <- c(rep(0,length(pch_source))) for(a in seq(length(pch))) pch[a] <- as.numeric(pch_lut[which(pch_lut[,1]==pch_source[a]),2]) ############ KESKEN ##################### # plot the ordination result and save it as a pdf file pdf(file=paste(file, "NMDS.pdf", sep="_"), height=7, width=7) par(mfrow=c(ncol(col),2), mar=c(4,4,1,1), oma=c(1,1,1,1)) for(j in seq(ncol(col))) { # presence-absence ordination plot(ord_pa, display="sites", type="n", xlab="Axis 1", ylab="Axis 2") points(ord_pa, col=col[,j], pch=pch) legend("topleft", rbind(col_lut[[j]][,1]), text.col=col_lut[[j]][,2], bty="n", cex=0.7) title(main="Presence-absence") # abundance ordination plot(ord_ab, display="sites", type="n", xlab="Axis 1", ylab="Axis 2") points(ord_ab, col=col[,j], pch=pch) legend("topleft", legend=pch_lut[,1], bty="n", cex=0.7, pch=as.numeric(pch_lut[,2])) title(main="Relative abundance") } dev.off()

Diversity indices are thoroughly described in Wikipedia.

Rcode about plotting diversity index results

library(reshape2) library(ggplot2) div <- read.csv("//cesium/jtue$/_Downloads/diversiteetit.csv") div <- melt(div, id.vars = "q", variable.name = "TrCode") levels(div$TrCode) <- gsub("^X", "", levels(div$TrCode)) # Remove X in front of TrCodes starting with a number. levels(div$TrCode) <- gsub("\\.", " ", levels(div$TrCode)) # Replace "." with " " in TrCode. levels(div$TrCode) <- gsub("Pin 1", "Pin", levels(div$TrCode)) # Replace "." with " " in TrCode. levels(div$TrCode) <- gsub("Caj 1", "Caj", levels(div$TrCode)) # Replace "." with " " in TrCode. div <- merge(div, div[div$q == 0 , c("TrCode", "value")], by = "TrCode") div$unevenness <- div$value.y / div$value.x # Unevenness div <- div[colnames(div) != "value.y"] colnames(div)[colnames(div) == "value.x"] <- "diversity" div <- melt(div, id.var = c("TrCode", "q"), variable.name = "parameter") envi <- read.csv("//cesium/jtue$/_Downloads/envitable.csv") envi <- envi[c("TrCode", "CatSum", "Reg", "RegNum")] levels(envi$TrCode) <- gsub("-", " ", levels(envi$TrCode)) # Replace "-" with " " envi$Cat <- cut(envi$CatSum, quantile(envi$CatSum, (0:5)/5), include_lowest = TRUE) out <- merge(div, envi, all.x = TRUE) p <- ggplot(out, aes(x = q, y = value, fill = TrCode)) + geom_line(aes(colour = Cat)) + scale_x_log10() + facet_grid(parameter ~ Reg, scales = "free_y") + theme_bw() # theme(panel.background = element_rect(colour = "white")) p

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