library(vegan)
library(fossil)
data(dune)
### alpha indexes of site1
richness    <- vegan::specnumber(dune)
shannon     <- vegan::diversity(dune, index = "shannon")
simpson     <- vegan::diversity(dune, index = "simpson")
inv_simpson <- vegan::diversity(dune, index = "invsimpson")
pielou      <- shannon / log(richness)
chao        <- round(fossil::chao1(dune), 0)
abundance   <- sum(dune)
margalef    <- (richness - 1) / log(abundance)
berger      <- max(dune) / sum(dune)

library(vegan)
library(car)
library(FSA)
data("dune")
data("dune.env")
# compute Shannon for each site (each row)
shannon <- diversity(dune, index = "shannon")
# combine into one dataframe
alpha <- data.frame(
  Site       = rownames(dune),
  Management = dune.env$Management,
  Shannon    = round(shannon, 4)
)
# assumption checks
fit <- aov(alpha$Shannon ~ alpha$Management)
sw  <- shapiro.test(residuals(fit))
lev <- car::leveneTest(alpha$Shannon ~ alpha$Management)
# omnibus test + post-hoc
if (sw$p.value > 0.05 & lev$`Pr(>F)`[1] > 0.05) {
  summary(fit)
  pairwise.t.test(alpha$Shannon, alpha$Management,
                  p.adjust.method = "BH", pool.sd = TRUE)
} else {
  kruskal.test(alpha$Shannon ~ alpha$Management)
  FSA::dunnTest(alpha$Shannon ~ alpha$Management, method = "bh")
}

library(vegan)
data("dune")
data("dune.env")
# step 1: Bray-Curtis distance matrix
dist_bc <- vegdist(dune, method = "bray")
# step 2: PERMANOVA (Bray-Curtis)
set.seed(1234)
perm_bc <- adonis2(dist_bc ~ Management,
                   data         = dune.env,
                   permutations = 9999)
perm_bc
# step 3: dispersion pre-check
bd_bc <- betadisper(dist_bc, dune.env$Management)
anova(bd_bc)
# step 4: PERMANOVA — Hellinger / Euclidean (sensitivity check)
dune_hel <- decostand(dune, method = "hellinger")
dist_hel <- dist(dune_hel, method = "euclidean")
set.seed(1234)
perm_hel <- adonis2(dist_hel ~ Management,
                    data         = dune.env,
                    permutations = 9999)
perm_hel

library(vegan)
data("dune")
data("dune.env")
dist_bc <- vegdist(dune, method = "bray")
set.seed(1234)
anosim_res <- anosim(dist_bc, dune.env$Management, permutations = 9999)
anosim_res