codep (version 1.2-4)

LGTransforms: Transformation for Species Abundance Data

Description

Calculates the transformed species abundances following Legendre and Gallagher.

Usage

LGTransforms(
  x,
  method = c("chord", "chisq", "profile", "Hellinger"),
  offset = 0,
  power = 1
)

Value

A matrix of the transformed species abundances.

Arguments

x

A species abundance matrix (rows: sites, columns: species).

method

The transformation method, one of "chord" (the default), "chisq", "profile", or "Hellinger" (see details).

offset

Offset value applied to all the columns of x prior to the other transformations (default: 0, see Details).

power

Exponent for the power transformation (Box-Cox) applied to all columns of x after the offset and before the transformation specified by argument method (default: 1, see Details).

Author

tools:::Rd_package_author("codep") Maintainer: tools:::Rd_package_maintainer("codep")

Details

These transformations of species abundances values are useful for multivariate least squares methods for ordination methods, such as the principal component analysis, or modelling methods, such as the multiscale codependence analysis (MCA), the canonical redundancy analysis (RDA). They allow one to use least squares methods, which operate on the basis of the Euclidean metric, on species abundance data, for which the Euclidean metric have generally inadequate properties (see Legendre & Gallagher 2001 and Legendre & Borcard 2018, in references below, for a thorough discussion on the topic).

The power (Box Cox) transformation involves the following equation:

y' = (y + offset)^power if power != 0

y' = log(y + offset) if power == 0

The default values for offset (0) and power (1) correspond to applying no transformation besides that specified by argument methods.

References

Legendre P. & Gallagher E. D. 2001. Ecologically meaningful transformations for ordination of species data. Oecologia 129: 271-280 doi: 10.1007/s004420100716

Box G. E. P. & Cox D. R. 1964. An analysis of transformations. Journal of the Royal Statistical Society Series B 26: 211-243

Legendre P. & Borcard D. 2018. Box-Cox-chord transformations for community composition data prior to beta diversity analysis. Ecography 41: 1820-1824. doi: 0.1111/ecog.03498

Legendre, P. & Legendre, L. 2012. Numerical Ecology, Third English Edition. Elsevier B. V. Amsterdam, The Netherlands.

Examples

data(Doubs)

## Removing any species that have not been not observed:
Doubs.fish -> x
x[rowSums(x)!=0,] -> x

## Transforming the abundances
LGTransforms(x,"chord") -> chord
LGTransforms(x,"chord",offset=1,power=0) -> log.chord
LGTransforms(x,"chord",power=0.25) -> pow.chord
LGTransforms(x,"chisq") -> chisq
LGTransforms(x,"profile") -> sp_pr
LGTransforms(x,"Hellinger") -> Helli

dist(chord)
dist(log.chord)
dist(pow.chord)
dist(chisq)
dist(sp_pr)
dist(Helli)

## Legendre & Gallagher synthetic examples:

data(LGDat)

## Diastemograms:

as.matrix(dist(LGDat[,1L])) -> geo
geo[upper.tri(geo)] -> geo

## Raw Euclidean distances
par(mfrow=c(1,1), mar=c(5,5,4,2))

as.matrix(dist(LGDat[,-1L])) -> eco
eco[upper.tri(eco)] -> eco

plot(eco~geo, data=data.frame(geo=geo, eco=eco),
     xaxp=c(1,18,17), las=1, ylim=c(0,max(eco)),
     xlab="True geographic distance",
     ylab="Euclidean distance")

## Euclidean distances on the transformed abundances:
par(mfrow=c(3,2), mar=c(3,5,4,2))

LGTransforms(LGDat[,-1L],"chord") -> chord
as.matrix(dist(chord)) -> eco
eco[upper.tri(eco)] -> eco
plot(eco~geo,data=data.frame(geo=geo,eco=eco),
     xaxp=c(1,18,17),las=1,xlab="",ylab="",
     main="Chord distance",ylim=c(0,max(eco)))

LGTransforms(LGDat[,-1L],"chord",offset=1,power=0) -> log.chord
as.matrix(dist(log.chord)) -> eco
eco[upper.tri(eco)] -> eco
plot(eco~geo,data=data.frame(geo=geo,eco=eco),
     xaxp=c(1,18,17),las=1,xlab="",ylab="",
     main="Chord distance (log(x+1))",ylim=c(0,max(eco)))

par(mar=c(4,5,3,2))

LGTransforms(LGDat[,-1L],"chord",power=0.25) -> pow.chord
as.matrix(dist(pow.chord)) -> eco
eco[upper.tri(eco)] -> eco
plot(eco~geo,data=data.frame(geo=geo,eco=eco),
     xaxp=c(1,18,17),las=1,xlab="",ylab="",
     main="Chord distance (power=0.25)",ylim=c(0,max(eco)))

LGTransforms(LGDat[,-1L],"chisq") -> chisq
as.matrix(dist(chisq)) -> eco
eco[upper.tri(eco)] -> eco
plot(eco~geo,data=data.frame(geo=geo,eco=eco),
     xaxp=c(1,18,17),las=1,xlab="",ylab="",
     main="Chi-square distance",ylim=c(0,max(eco)))

par(mar=c(5,5,2,2))

LGTransforms(LGDat[,-1L],"profile") -> sp_pr
as.matrix(dist(sp_pr)) -> eco
eco[upper.tri(eco)] -> eco
plot(eco~geo,data=data.frame(geo=geo,eco=eco),
     xaxp=c(1,18,17),las=1,xlab="",ylab="",
     main="Dist. between profiles",ylim=c(0,max(eco)))

LGTransforms(LGDat[,-1L],"Hellinger") -> Helli
as.matrix(dist(Helli)) -> eco
eco[upper.tri(eco)] -> eco
plot(eco~geo,data=data.frame(geo=geo,eco=eco),
     xaxp=c(1,18,17),las=1,xlab="",ylab="",
     main="Hellinger distance",ylim=c(0,max(eco)))

mtext(text="True geographic distance", side=1, line=-1.5, outer=TRUE)
mtext(text="Ecological distance", side=2, line=-1.5, outer=TRUE)

## Examples from Legendre & Legendre 2012, page 329 (Figure 7.8):

matrix(c(0,0,1,4,1,0,8,1,0),3L,3L) -> LL329

## D1:  Euclidean distance
dist(LL329)

## Chord transformation (D3: chord distance)
LGTransforms(LL329,"chord") -> tr       
tr
dist(tr)

## "Species profile" transformation (D18)
LGTransforms(LL329,"profile") -> tr       
tr
dist(tr)

## Hellinger transformation (D17: Hellinger distance)
LGTransforms(LL329,"Hellinger") -> tr       
tr
dist(tr)

## Chi-square transformation (D16: Chi-square distance)
LGTransforms(LL329,"chisq") -> tr       
tr
dist(tr)