# Multiplicative partitioning of Hill numbers (Jost 2006, 2007)
?d
# Mean alpha species richness
d(spe, lev = "alpha", q = 0)
# Mean alpha Shannon diversity
d(spe, lev = "alpha", q = 1)
# Mean alpha Simpson diversity
d(spe, lev = "alpha", q = 2, boot = TRUE)
# Multiplicative beta species richness
d(spe, lev = "beta", q = 0)
# Multiplicative beta Shannon diversity
d(spe, lev = "beta", q = 1)
# Multiplicative beta Simpson diversity
d(spe, lev = "beta", q = 2, boot = TRUE)
# Gamma species richness
d(spe, lev = "gamma", q = 0)
# Gamma Shannon diversity
d(spe, lev = "gamma", q = 1)
# Gamma Simpson diversity
d(spe, lev = "gamma", q = 2, boot = TRUE)
# Plot multiplicative beta diversity vs order
mbeta <- data.frame(order = 0:20, beta = NA, se = NA)
for (i in 1:nrow(mbeta)) {
out <- d(spe, lev = "beta", q = mbeta$order[i], boot = TRUE)
mbeta$beta[i] <- out$D.Value
mbeta$se[i] <- out$StdErr
}
mbeta
ggplot(mbeta, aes(order, beta)) +
geom_point() +
geom_line() +
geom_errorbar(aes(order, beta, ymin = beta - se,
ymax = beta + se), width = 0.2) +
labs(y = "Multiplicative beta diversity",
x = "Order of the diversity measure")
Hint Note the non-conventional syntax of function ggplot() of the package
ggplot2 for the line plot of Fig. 8.3.
It turns out that multiplicative beta diversity increases from about 2 to 7 when
increasing the order, i.e. when giving more and more importance to the evenness
component against the richness component of species diversity (Fig. 8.3).
Another useful function to achieve additive partitioning of taxonomic, but also
functional and phylogenetic diversities in a unified framework is Rao(); it is not
8.4 Beta Diversity
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