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.
Coherence(comm, method = "r1", sims = 1000, scores = 1,
order = TRUE, orderNulls = FALSE, allowEmpty = FALSE,
binary = TRUE, verbose = FALSE, seed = 1)community data in the form of a presence absence matrix
null model randomization method used by 'nullmaker'. See details below (and the help file of fucntion 'nullmaker') for more information.
number of simulated null matrices to use in analysis
axis scores to ordinate matrix. 1: primary axis scores (default) 2: secondary axis scores
logical argument indicating whether to ordinate the interaction matrix or not. See details.
logical argument indicating whether to ordinate the null matrices. Default is FALSE.
logical argument indicating whether to allow null matrices to have empty rows or columns
logical argument indicating whether to ordinate the community matrix based on abundance or binary (default) data.
Logical. Prints a graphical progress bar that tracks the creation of null matrices. Useful for conservative null models on large and/or sparse data.
seed for simulating the null model. Null matrices should be repeatable.
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).
'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. The 'orderNulls' argument allows the user to ordinate the null matrices. While creating a more conservative test, this may negate the null model implemented (fixed row and column sums will not be maintained)
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)
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.
# NOT RUN {
#define an interaction matrix
data(TestMatrices)
intmat=TestMatrices[[7]]
#determine coherence of interaction matrix
coh.intmat <- Coherence(intmat, method='r1', sims=100,
scores=1, order=TRUE, binary=TRUE)
#return results
coh.intmat
# }
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