Multivariate environmental similarity surface (MESS)

The multivariate environmental similarity surface (MESS) indicates the degree to which a set of "projection" environmental conditions fall inside or outside a set of "reference" conditions. Values of 1 indicate a location falls at the exact median of all variables. Values of 0 indicate that the location has at least one environmental covariate that is at the upper or lower end of the range of reference conditions, and values <1 indicate that at least one variable falls above or below the reference conditions. MESS can be used, for example, to indicate the degree to which a model constructed in one time period and/or location must extrapolate when projected to another time period and/or location.

Usage

# S4 method for class 'GRaster,GRaster'
multivarEnvSim(ref, proj)

# S4 method for class 'GRaster,missing'
multivarEnvSim(ref, proj)

# S4 method for class 'data.frame,GRaster'
multivarEnvSim(ref, proj, na.rm = FALSE)

# S4 method for class 'data.table,GRaster'
multivarEnvSim(ref, proj, na.rm = FALSE)

# S4 method for class 'matrix,GRaster'
multivarEnvSim(ref, proj, na.rm = FALSE)

Arguments

ref

A data.frame, data.table, a points GVector, or "stack" of GRasters: This represents the set of "reference" environmental conditions:

• data.frame or data.table: There must be one column per layer in proj, and the columns must have the same names as the layers in proj.

• GRaster with one or more layers: Must have the same names() as the GRasters in proj. Values are assumed to be continuous (not categorical/factors).

proj

A GRaster or missing. If a GRaster, it must have the same layers as can have with one or more layers as ref. Values are assumed to be continuous (not categorical/factors). If missing, then ref is used, in which case the output represents the relative difference of each cell from the overall layer median.

na.rm

Logical: If FALSE (default), and ref is a data.frame, data.table, or matrix, and has NAs in it, then the function will likely fail.

Value

A GRaster "stack". There will be one layer per layer in ref, indicating the MESS score for that variable. There will also be a layer named "MESS" which represents the MESS value across all variables (the minimum value of each of the individual MESS rasters). A final layer represents the layer which is most different (has the lowest MESS value).

References

Elith, J, Kearney, M, and Phillips, S. 2010. The art of modelling range-shifting species. Methods in Ecology and Evolution 1:330-342. doi:10.1111/j.2041-210X.2010.00036.x (see especially the Supplement)

Examples

if (grassStarted()) {

# Setup
library(terra)

# Climatic conditions with 4 variables
madChelsa <- fastData("madChelsa")
chelsa <- fast(madChelsa)

# Simulate new conditions by multiplying values by (1 + small number)
proj <- 1.05 * chelsa
names(proj) <- names(chelsa) # proj must have same names as ref

messes <- multivarEnvSim(ref = chelsa, proj = proj)
plot(messes)

# Where is at least one variable outside the reference range?
extrap <- messes[["MESS"]] < 0
levs <- data.frame(value = 0:1, labels = c('no extrapolation', 'extrapolation'))
levels(extrap) <- levs
plot(extrap)

# Using a data frame as "reference" conditions:
madDypsis <- fastData("madDypsis") # Dypsis occurrences
dypsis <- fast(madDypsis)

dypEnv <- extract(chelsa, dypsis)
dypMess <- multivarEnvSim(ref = dypEnv, proj = proj)
plot(dypMess)

}