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rao_entropy(comm, dist_traits)

Rao's quadratic entropy Q: expected trait dissimilarity between two randomly selected individuals. Decomposes into alpha and beta components.

functional diversitystatistics

Args:comm — community matrixdist_traits — trait distance matrix

rao_entropy <- function(comm, dist_traits) {
  if (!requireNamespace("FD", quietly = TRUE)) install.packages("FD")
  
  sp <- intersect(colnames(comm), labels(dist_traits))
  comm <- comm[, sp]
  D    <- as.matrix(dist_traits)[sp, sp]
  
  # Row-normalise
  p <- sweep(comm, 1, rowSums(comm), "/")
  
  # Rao Q = sum_ij p_i * p_j * d_ij
  Q <- apply(p, 1, function(pi) as.numeric(pi %*% D %*% pi))
  data.frame(site = rownames(comm), Rao_Q = Q)
}
# ── Example ──────────────────────────────────────────────────────
set.seed(42)
n_sp   <- 20
traits <- matrix(rnorm(80), n_sp, 4)
rownames(traits) <- paste0("sp", 1:n_sp)
d_traits <- dist(traits)

comm <- matrix(rbinom(60, 1, 0.5), 3, n_sp,
               dimnames = list(c("A","B","C"), paste0("sp", 1:n_sp)))
rao_entropy(comm, d_traits)