While working with a multivariate dataset, I noticed that Hellinger transformation reveals relationships with the dataset I did not see otherwise. The fact that a transformation affects species abundance - environmental variable relationships is, of course, nothing new. However, I guess I am a bit skeptical about Hellinger transformation based relationships since I do not completely understand how the data are transformed. OK, the equation is simple enough (stated for example here), but the transformation itself is not as intuitive as for example logarithm transformation. Here is an example using a subset of my dataset in R (looking at the plot should be enough to answer this question, but I paste a reproducible example in case someone wants it):
Copy the dataset from here and assign to
x$sp1.hel <- x$sp1.raw x$sp2.hel <- x$sp2.raw x$sp1.log <- log(x$sp1.raw + 1) x$sp2.log <- log(x$sp2.raw + 1) library(vegan) x[c("sp1.hel", "sp2.hel")] <- vegan::decostand(x[c("sp1.hel", "sp2.hel")], method = "hellinger") library(reshape2) mx <- reshape2::melt(x, id = "envvar") mx$trans <- factor(sapply(strsplit(as.character(mx$variable), "\\."), "[", 2)) levels(mx$trans) <- c("Hellinger", "Log + 1", "None") mx$species <- factor(sapply(strsplit(as.character(mx$variable), "\\."), "[", 1)) library(ggplot2) ggplot(mx, aes(x = envvar, y = value, color = species)) + geom_point(size = 1, alpha = 0.2) + geom_smooth() + facet_grid(trans~species, scales = "free") + theme_bw()
As you can see, there is probably no relationship between sp1 abundance and envvar in non-transformed or log + 1 transformed data, but such relationship becomes apparent for Hellinger transformed data. Sp2 seems to somewhat positively correlate with envvar regardless the transformation (see
If I was to Hellinger transform my dataset for a constrained multivariate ordination (RDA / CCA), I would probably end up concluding that sp1 and envvar have a rather strong relationship, even though such relationship is not evident for non-transformed or log-transformed data.
Therefore I am wondering whether Hellinger transformation is a suitable method to examine species community - environmental variable relationships in constrained multivariate ordinations?