Null Model and Simulation
Description
The nullmodel
function creates an object,
which can serve as a basis for Null Model simulation
via the simulate
method.
The update
method updates the nullmodel
object without sampling (effective for sequential algorithms).
smbind
binds together multiple simmat
objects.
Usage
1 2 3 4 5 6 7 8 9 10 11  nullmodel(x, method)
## S3 method for class 'nullmodel'
print(x, ...)
## S3 method for class 'nullmodel'
simulate(object, nsim = 1, seed = NULL,
burnin = 0, thin = 1, ...)
## S3 method for class 'nullmodel'
update(object, nsim = 1, seed = NULL, ...)
## S3 method for class 'simmat'
print(x, ...)
smbind(object, ..., MARGIN, strict = TRUE)

Arguments
x 
A community matrix.
For the 
method 
Character, specifying one of the null model algorithms
listed on the help page of 
object 
An object of class 
nsim 
Positive integer, the number of simulated matrices to return.
For the 
seed 
An object specifying if and how the random number
generator should be initialized ("seeded").
Either 
burnin 
Nonnegative integer, specifying the number of steps discarded before starting simulation. Active only for sequential null model algorithms. Ignored for nonsequential null model algorithms. 
thin 
Positive integer, number of simulation steps made between each returned matrix. Active only for sequential null model algorithms. Ignored for nonsequential null model algorithms. 
MARGIN 
Integer, indicating the dimension over which multiple

strict 
Logical, if consistency of the time series attributes
( 
... 
Additional arguments supplied to algorithms.
In case of 
Details
The purpose of the nullmodel
function is to
create an object, where all necessary statistics of the
input matrix are calculated only once.
This information is reused, but not recalculated
in each step of the simulation process done by
the simulate
method.
The simulate
method carries out the simulation,
the simulated matrices are stored in an array.
For sequential algorithms, the method updates the state
of the input nullmodel
object.
Therefore, it is possible to do diagnostic
tests on the returned simmat
object,
and make further simulations, or use
increased thinning value if desired.
The update
method makes burnin steps in case
of sequential algorithms to update the status of the
input model without any attempt to return matrices.
For nonsequential algorithms the method does nothing.
update
is the preferred way of making burnin iterations
without sampling. Alternatively, burnin can be done
via the simulate
method. For convergence
diagnostics, it is recommended to use the
simulate
method without burnin.
The input nullmodel object is updated, so further
samples can be simulated if desired without having
to start the process all over again. See Examples.
The smbind
function can be used to combine multiple
simmat
objects. This comes handy when null model
simulations are stratified by sites (MARGIN = 1
)
or by species (MARGIN = 2
), or in the case when
multiple objects are returned by identical/consistent settings
e.g. during parallel computations (MARGIN = 3
).
Sanity checks are made to ensure that combining multiple
objects is sensible, but it is the user's responsibility
to check independence of the simulated matrices
and the null distribution has converged
in case of sequential null model algorithms.
The strict = FALSE
setting can relax
checks regarding start, end, and thinning values
for sequential null models.
Value
The function nullmodel
returns an object of class nullmodel
.
It is a set of objects sharing the same environment:
data
: original matrix in integer mode.nrow
: number of rows.ncol
: number of columns.rowSums
: row sums.colSums
: column sums.rowFreq
: row frequencies (number of nonzero cells).colFreq
: column frequencies (number of nonzero cells).totalSum
: total sum.fill
: number of nonzero cells in the matrix.commsim
: thecommsim
object as a result of themethod
argument.state
: current state of the permutations, a matrix similar to the original. It isNULL
for nonsequential algorithms.iter
: current number of iterations for sequential algorithms. It isNULL
for nonsequential algorithms.
The simulate
method returns an object of class simmat
.
It is an array of simulated matrices (third dimension
corresponding to nsim
argument).
The update
method returns the current state (last updated matrix)
invisibly, and update the input object for sequential algorithms.
For non sequential algorithms, it returns NULL
.
The smbind
function returns an object of class simmat
.
Note
Care must be taken when the input matrix only contains a single
row or column. Such input is invalid for swapping and hypergeometric
distribution (calling r2dtable
) based algorithms.
This also applies to cases when the input is stratified into subsets.
Author(s)
Jari Oksanen and Peter Solymos
See Also
commsim
, make.commsim
,
permatfull
, permatswap
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70  data(mite)
x < as.matrix(mite)[1:12, 21:30]
## nonsequential nullmodel
(nm < nullmodel(x, "r00"))
(sm < simulate(nm, nsim=10))
## sequential nullmodel
(nm < nullmodel(x, "swap"))
(sm1 < simulate(nm, nsim=10, thin=5))
(sm2 < simulate(nm, nsim=10, thin=5))
## sequential nullmodel with burnin and extra updating
(nm < nullmodel(x, "swap"))
(sm1 < simulate(nm, burnin=10, nsim=10, thin=5))
(sm2 < simulate(nm, nsim=10, thin=5))
## sequential nullmodel with separate initial burnin
(nm < nullmodel(x, "swap"))
nm < update(nm, nsim=10)
(sm2 < simulate(nm, nsim=10, thin=5))
## combining multiple simmat objects
## stratification
nm1 < nullmodel(x[1:6,], "r00")
sm1 < simulate(nm1, nsim=10)
nm2 < nullmodel(x[7:12,], "r00")
sm2 < simulate(nm2, nsim=10)
smbind(sm1, sm2, MARGIN=1)
## binding subsequent samples from sequential algorithms
## start, end, thin retained
nm < nullmodel(x, "swap")
nm < update(nm, nsim=10)
sm1 < simulate(nm, nsim=10, thin=5)
sm2 < simulate(nm, nsim=20, thin=5)
sm3 < simulate(nm, nsim=10, thin=5)
smbind(sm3, sm2, sm1, MARGIN=3)
## 'replicate' based usage which is similar to the output
## of 'parLapply' or 'mclapply' in the 'parallel' package
## start, end, thin are set, also noting number of chains
smfun < function(x, burnin, nsim, thin) {
nm < nullmodel(x, "swap")
nm < update(nm, nsim=burnin)
simulate(nm, nsim=nsim, thin=thin)
}
smlist < replicate(3, smfun(x, burnin=50, nsim=10, thin=5), simplify=FALSE)
smbind(smlist, MARGIN=3) # Number of permuted matrices = 30
## Not run:
## parallel null model calculations
library(parallel)
if (.Platform$OS.type == "unix") {
## forking on Unix systems
smlist < mclapply(1:3, function(i) smfun(x, burnin=50, nsim=10, thin=5))
smbind(smlist, MARGIN=3)
}
## socket type cluster, works on all platforms
cl < makeCluster(3)
clusterEvalQ(cl, library(vegan))
clusterExport(cl, c("smfun", "x"))
smlist < parLapply(cl, 1:3, function(i) smfun(x, burnin=50, nsim=10, thin=5))
stopCluster(cl)
smbind(smlist, MARGIN=3)
## End(Not run)
