#####################################
# Function sigpca2
# This code tests for the significance of loadings as described in these papers:
# (Jackson, Ecology 1993, 74: 2204-2214; Peres-Neto and al. 2003. Ecology 84:2347-2363)
# Becuase this has not been implemented into a package, we need to enter the
# function manually. Code written by the authors of the papers.
# Select (or copy/paste) all of this function and send it to R at once.
# After that, we can use the sigpca() function as any other function (see below)
#####################################

sigpca2<-function (x, permutations=1000, ...)
{
  pcnull <- princomp(x, ...)
  res <- pcnull$loadings
  out <- matrix(0, nrow=nrow(res), ncol=ncol(res))
  N <- nrow(x)
  for (i in 1:permutations) {
    pc <- princomp(x[sample(N, replace=TRUE), ], ...)
    pred <- predict(pc, newdata = x)
    r <-  cor(pcnull$scores, pred)
    k <- apply(abs(r), 2, which.max)
    reve <- sign(diag(r[k,]))
    sol <- pc$loadings[ ,k]
    sol <- sweep(sol, 2, reve, "*")
    out <- out + ifelse(res > 0, sol <=  0, sol >= 0)
  }
  out/permutations
}