# Perform graphical classification of response shape

unimod.test <- function(mnr, ubnd, lbnd) {

     # Find the maximum and minimum predicted mean probabilities
     lmax <- max(mnr)
     lmin <- min(mnr)

     # Find index locations for these probabilities
     imax <- match(lmax, mnr)
     imin <- match(lmin, mnr)

     x.out <- F
     y.out <- F

     # Compare mean predicted probability to the left of maximum point
     # with upper confidence bound. Store a T in x.out if
     # any point in the mean response deviates from the
     # upper confidence limit
     if (imax > 1) {
           x.out <- sum(lmax == pmax(lmax, ubnd[1:(imax-1)])) > 0
     }

     # Store a T in y.out if any point in the mean probability
     # to the right of the maximum point deviates from the upper
     # confidence limit
     if (imax < length(ubnd)) {
           y.out <- sum(lmax == pmax(lmax,
           ubnd[(imax+1):length(ubnd)])) > 0
     }

     # Perform same set of tests for lower confidence limit
     a.out <- F
     b.out <- F
     if (imin > 1) {
           a.out <- sum(lmin == pmin(lmin, lbnd[1:(imin-1)])) > 0
     }
     if (imin < length(lbnd)) {
           b.out <- sum(lmin == pmin(lmin,
           lbnd[(imin+1):length(lbnd)])) > 0
     }

     # The information on where the mean curve deviates from the
     # confidence limits tells us its curve shape...
     if (x.out & y.out) {
           return("Unimodal")
     }
     if (a.out & b.out) {
          return("Concave up")
     }
     if (x.out | b.out) {
          return("Increasing")
     }
     if (y.out | a.out) {
          return("Decreasing")
     }
     if (! (x.out | y.out | a.out | b.out)) {
          return(NA)
     }
}

tolcl <- rep("", times = length(taxa.names))
for (i in 1:length(taxa.names)) {
     predres <- predict(modlist.gam, type= "link", se.fit = T)

     # Compute upper and lower 90% confidence limits
     up.bound.link <- predres$fit + 1.65*predres$se.fit
     low.bound.link <- predres$fit - 1.65*predres$se.fit
     mean.resp.link <- predres$fit

     # Convert from logit transformed values to probability.
     up.bound <- exp(up.bound.link)/(1+exp(up.bound.link))
     low.bound <- exp(low.bound.link)/(1+exp(low.bound.link))
     mean.resp <- exp(mean.resp.link)/(1+exp(mean.resp.link))

     # unimod.test requires that the responses be sorted by
     # the value of the environmental variable.
     iord <- order(dfmerge$temp)

     tolcl[i] <- unimod.test(mean.resp[iord], up.bound[iord],
     low.bound[iord])
}

names(tolcl) <- taxa.names
print(tolcl)

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