This function determines the number of embedded absences in an interaction
matrix, and compares this value against null simulated matrices. Species
ranges should be coherent along the ordination axis, as this axis represents
a latent environmental gradient. A negative value of coherence (empirical
matrix has more embedded absences than null matrices) indicates a
'checkerboard' pattern (Leibold & Mikkelson 2002). Nonsignificance has been
historically interpreted as being indicative of a 'random' pattern, though
this may be seen as accepting the null hypothesis, as nonsignificance cannot
be used to infer a process.
logical argument indicating whether to ordinate the interaction
matrix or not. See details.
allowEmpty
logical argument indicating whether to allow null
matrices to have empty rows or columns
binary
logical argument indicating whether to ordinate the community
matrix based on abundance or binary (default) data.
verbose
Logical. Prints a graphical progress bar that tracks the
creation of null matrices. Useful for conservative null models on large
and/or sparse data.
Details
'method' is an argument handed to functions in the 'vegan' package. Leibold
& Mikkelson advocated the use of equiprobable rows and columns (provided
that rows and columns had at least one entry). This method is called 'r00'.
Methods maintaining row (site) frequencies include 'r0','r1' & 'r2'. The
default method argument is 'r1', which maintains the species richness of a
site (row totals) and fills species ranges (columns) based on their marginal
probabilities. Arguably the most conservative null algorithm is the fixed
row - fixed column total null, which is implemented as 'fixedfixed'. See the
help file for 'commsimulator' or Wright et al. 1998 for more information.
If 'order' is FALSE, the interaction matrix is not ordinated, allowing the
user to order the matrix based on site characteristics or other biologically
relevant characteristics.
This function can either be used as a standalone, or can be used through the
'metacommunity()' function, which determines all 3 elements of metacommunity
structure (coherence, boundary clumping, & turnover) (Leibold & Mikkelson
2002)
Value
A vector containing the number of embedded absences (embAbs), z-score (z), p-value (pval), mean (simulatedMean) and variance (simulatedVariance) of simulations, and null model randomization method (method).
Author(s)
Tad Dallas
References
Leibold, M.A. and G.M. Mikkelson. 2002. Coherence, species
turnover, and boundary clumping: elements of meta-community structure. Oikos
97: 237 - 250.
Wright, D.H., Patterson, B.D., Mikkelson, G.M., Cutler, A. & Atmar, W.
(1998). A comparative analysis of nested subset patterns of species
composition. Oecologia 113, 1-20.