For the beginner or first-time user, you will need to familiarize yourself with the following functions and help pages: `niche.plot()`

, `niche.size()`

, `overlap()`

, and `overlap.plot()`

.

The first step is to format the data so that it can be properly read into functions. This should be in a data.frame set up, with niche variables (e.g., stable isotope, habitat or contaminant variables - stable isotope in this case) along the columns and observations along the rows. This vignette will use the example dataset `fish`

in the **nicheROVER** package, which contains the stable isotope values of $\delta^{15}\textrm{N}$, $\delta^{13}\textrm{C}$, and $\delta^{34}\textrm{S}$ from muscle tissue for 278 individual fish belonging to four arctic fish species (see `?fish`

for more information on the sample dataset).

We import the data using the `data()`

function. We then calculate the means for each isotope and species using the `aggregate()`

function:

# analysis for fish data library(nicheROVER) data(fish) # 4 fish, 3 isotopes aggregate(fish[2:4], fish[1], mean) # isotope means calculated for each species

This step is not absolutely necessary in generating the niche region and overlap plots, but can be useful during exploratory data analyses.

# fish data data(fish) # generate parameter draws from the "default" posteriors of each fish nsamples <- 1e3 system.time({ fish.par <- tapply(1:nrow(fish), fish$species, function(ii) niw.post(nsamples = nsamples, X = fish[ii,2:4])) }) # various parameter plots clrs <- c("black", "red", "blue", "orange") # colors for each species # mu1 (del15N), mu2 (del13C), and Sigma12 par(mar = c(4, 4, .5, .1)+.1, mfrow = c(1,3)) niche.par.plot(fish.par, col = clrs, plot.index = 1) niche.par.plot(fish.par, col = clrs, plot.index = 2) niche.par.plot(fish.par, col = clrs, plot.index = 1:2) legend("topleft", legend = names(fish.par), fill = clrs) # all mu (del15N, del13C, del34S) niche.par.plot(fish.par, col = clrs, plot.mu = TRUE, plot.Sigma = FALSE) legend("topleft", legend = names(fish.par), fill = clrs)

# all mu and Sigma par(mar = c(4.2, 4.2, 2, 1)+.1) niche.par.plot(fish.par, col = clrs, plot.mu = TRUE, plot.Sigma = TRUE) legend("topright", legend = names(fish.par), fill = clrs)

See `?niche.plot`

for more details on parameter values.

Here, we have chosen to display 10 random niche regions generated by the Bayesian analysis. The parameter list `fish.par`

is generated using the `niw.post()`

function provided by **nicheROVER**.

The resulting figure generates niche plots, density distributions, and raw data for each pairwise combination of isotope data for all four fish species (i.e., bivariate projections of 3-dimensional isotope data).

# 2-d projections of 10 niche regions clrs <- c("black", "red", "blue", "orange") # colors for each species nsamples <- 10 fish.par <- tapply(1:nrow(fish), fish$species, function(ii) niw.post(nsamples = nsamples, X = fish[ii,2:4])) # format data for plotting function fish.data <- tapply(1:nrow(fish), fish$species, function(ii) X = fish[ii,2:4]) niche.plot(niche.par = fish.par, niche.data = fish.data, pfrac = .05, iso.names = expression(delta^{15}*N, delta^{13}*C, delta^{34}*S), col = clrs, xlab = expression("Isotope Ratio (per mil)"))

We use the function `overlap()`

to calculate overlap metric estimates from a specified number of Monte Carlo draws (`nsamples`

) from the `fish.par`

parameter list. It is necessary to specify the $\alpha$-level. In this case, we have decided to calculate the overlap metric at two niche regions sizes for comparison: `alpha=0.95`

and `alpha=0.99`

, or 95% and 99%.

Then, we calculate the mean overlap metric between each species. Remember that the overlap metric is directional, such that it represents the probability that an individual from Species $A$ will be found in the niche of Species $B$.

# niche overlap plots for 95% niche region sizes nsamples <- 1000 fish.par <- tapply(1:nrow(fish), fish$species, function(ii) niw.post(nsamples = nsamples, X = fish[ii,2:4])) # Overlap calculation. use nsamples = nprob = 10000 (1e4) for higher accuracy. # the variable over.stat can be supplied directly to the overlap.plot function over.stat <- overlap(fish.par, nreps = nsamples, nprob = 1e3, alpha = c(.95, 0.99)) #The mean overlap metrics calculated across iteratations for both niche #region sizes (alpha = .95 and alpha = .99) can be calculated and displayed in an array. over.mean <- apply(over.stat, c(1:2,4), mean)*100 round(over.mean, 2) over.cred <- apply(over.stat*100, c(1:2, 4), quantile, prob = c(.025, .975), na.rm = TRUE) round(over.cred[,,,1]) # display alpha = .95 niche region

In the returned plot, Species $A$ is along the rows and Species $B$ is along columns. The plots represent the posterior probability that an individual from the species indicated by the row will be found within the niche of the species indicated by the column header. Before you plot, you must decide upon your $\alpha$-level, and make sure the variable `over.stat`

reflects this choice of $\alpha$.

# Overlap plot.Before you run this, make sure that you have chosen your #alpha level. clrs <- c("black", "red", "blue", "orange") # colors for each species over.stat <- overlap(fish.par, nreps = nsamples, nprob = 1e3, alpha = .95) overlap.plot(over.stat, col = clrs, mean.cred.col = "turquoise", equal.axis = TRUE, xlab = "Overlap Probability (%) -- Niche Region Size: 95%")

See `?niche.size`

for exactly how niche size is defined as a function of the parameters $\mu$ and $\Sigma$. In a Bayesian context, we calculate the posterior distribution of niche size by species. This done by calculating the niche size for every posterior sample of $\mu$ and $\Sigma$.

# posterior distribution of (mu, Sigma) for each species nsamples <- 1000 fish.par <- tapply(1:nrow(fish), fish$species, function(ii) niw.post(nsamples = nsamples, X = fish[ii,2:4])) # posterior distribution of niche size by species fish.size <- sapply(fish.par, function(spec) { apply(spec$Sigma, 3, niche.size, alpha = .95) }) # point estimate and standard error rbind(est = colMeans(fish.size), se = apply(fish.size, 2, sd)) # boxplots clrs <- c("black", "red", "blue", "orange") # colors for each species boxplot(fish.size, col = clrs, pch = 16, cex = .5, ylab = "Niche Size", xlab = "Species")

**Any scripts or data that you put into this service are public.**

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.