Diversity index

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Question

How to calculate diversity indices?

Answer

Upload your data to Opasnet Base. Use the function diversity to calculate the most common indices.

Actual function diversity

+ Show code- Hide code ####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])) } } names(qD) <- 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(qDa) <- 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)) dimnames(qDj) <- list(q, levels(as.factor(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) } cat("Functions loaded.\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 = 1 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 cat("Different diversities with the following q values \n") q.wiki 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).

Rationale

Diversity indices are thoroughly described in Wikipedia.

Related files

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