Laughlin et al. Appendix S2. Climatic constraints on trait-based forest assembly.
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Appendix S2. R code for evaluating the fit of MaxEnt predictions when the constraints are
predicted from environmental conditions.
This function will soon be available in the ‘FD’ library of R (Laliberté and Shipley 2010). In
order for the example to work properly, you must install the FD package.
# example with tussock data from FD package
# let's assume that constraints are not observed but predicted
traits <- tussock$trait[, c(2:7, 11)] # use only continuous traits
traits <- na.omit(traits) # remove 2 species with NA's
abun <- tussock$abun[, rownames(traits)] # abundance matrix
abun <- t(apply(abun, 1, function(x) x / sum(x) )) # relative abundances
agg <- functcomp(traits, abun) # community-aggregated traits
traits <- t(traits) # transpose matrix
# pred are the predicted relative abundances from maxent model
pred <- maxent(agg, traits)$prob
# obs are observed relative abundances
obs <- abun
##### maxent.test.pred function
maxent.test.pred <- function(pred, obs, nperm = 999, stat = c("R2", "RMSE", "RMSEsqrt") ) {
# match arg for stat
stat <- match.arg(stat)
# get number of sites
if (is.vector(pred) ) pred <- matrix(pred, nrow = 1)
nsites <- nrow(pred)
# get observed statistic
if (stat == "R2") {
obs.stat <- (cor(as.numeric(pred), as.numeric(obs) ) )^2
names(obs.stat) <- "R2"
}
if (stat == "RMSE") {
obs.stat <- sqrt(mean((obs - pred)^2))
names(obs.stat) <- "RMSE"
}
if (stat == "RMSEsqrt") {
obs.stat <- sqrt(mean((sqrt(obs) - sqrt(pred))^2))
names(obs.stat) <- "RMSEsqrt"
}
# get vector to dump results
dump <- rep(NA, nperm)
# permute columns of obs independently for each row
# each time, compute observed stat
# use nested for loop to do this
# R2
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if (stat == "R2") {
for (i in 1:nperm) {
obs.perm <- obs
for (j in 1:nsites) {
obs.perm[j, ] <- sample(obs[j, ])
}
dump[i] <- (cor(as.numeric(pred), as.numeric(obs.perm) ) )^2
} # end of i for loop
}
# RMSE
if (stat == "RMSE") {
for (i in 1:nperm) {
obs.perm <- obs
for (j in 1:nsites) {
obs.perm[j, ] <- sample(obs[j, ])
}
dump[i] <- sqrt(mean((obs.perm - pred)^2))
} # end of i for loop
}
# RMSEsqrt
if (stat == "RMSEsqrt") {
for (i in 1:nperm) {
obs.perm <- obs
for (j in 1:nsites) {
obs.perm[j, ] <- sample(obs[j, ])
}
dump[i] <- sqrt(mean((sqrt(obs.perm) - sqrt(pred))^2))
} # end of i for loop
}
# get permutational p-value
# test for R2 -> one-tailed test, upper
# test is upper because P-value reflects how many times R2 is equal or greater
# than observed, if null hypothesis is true
if (stat == "R2") p.perm <- (length(dump[dump >= obs.stat]) + 1) / (length(dump) + 1)
# test for RMSE or RMSEsqrt -> one-tailed, lower
# test is upper because P-value reflects how many times RMSE or RMSEsqrt is equal or smaller
# than observed, if null hypothesis is true
else p.perm <- (length(dump[dump <= obs.stat]) + 1) / (length(dump) + 1)
names(p.perm) <- "P-value"
# return results
return(c(obs.stat, p.perm) )
} # end of function
#####
# examples
maxent.test.pred(pred, obs, nperm = 999)
maxent.test.pred(pred, obs, nperm = 999, stat = "RMSE")
maxent.test.pred(pred, obs, nperm = 999, stat = "RMSEsqrt")
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# test when obs shares no link with pred
# shuffle obs to yield obs.perm
obs.perm <- obs
for (j in 1:nrow(obs)) {
obs.perm[j, ] <- sample(obs[j, ])
}
maxent.test.pred(pred, obs.perm, nperm = 999, stat = "R2")
Reference for Appendix S2
Laliberté, E., & Shipley, B. (2010) FD: Measuring functional diversity from multiple traits, and
other tools for functional ecology. R package in The Comprehensive R Archive Network
(CRAN) URL http://cran.r-project.org/package=FD, Vienna, Austria.
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