idar (version 1.5)

ipsim: Simulate Multivariate Point Patterns

Description

These functions simulate multivariate point patterns from a variety of null models, in the way required to test IDAR(r) functions.

Usage

ipsim(pp, mimark,sigma=0, lambda=NULL, namesmark=NULL)
  ipsimlist(pp, mimark, listsim)
  simulador2(mimark, milambda, nsim=99)
  multifocalsimulator(pp, mimark, simulate,nsim=99,nmin=NULL)

Value

ipsim produces a multivariate point pattern (with the ppp format of spatstat); ipsimlist and multifocalsimulator produce a list of multivariate point patterns; simulador2 produces a list of univariate marked patterns.

Arguments

pp

A multitype (a.k.a. multivariate) marked point pattern. An object with the ppp format of spatstat

mimark

Character. Name of the focal species in the multitype pp.

namesmark

Character. If the marks in pp are within a data.frame, the name of the column with the species names

sigma

Sigma for the Gaussian kernel to estimate the intensity of the point pattern to simulate

listsim

List with simulated point paterns from simulador2

lambda

intensity surface, e.g., an image from density.ppp or predict.ppm

milambda

intensity surface, e.g., an image from density.ppp or predict.ppm

nsim

number of simulations

nmin

expected minimum number of points in each simulated pattern

simulate

either a list of pre-computed univariate point patterns or an expression in the R language indicating how to simulate the patterns.

Author

Marcelino de la Cruz

Details

This functions produce simulated point patterns appropriate to to compute envelopes of IDAR(r) functions. The usual tests of IDAR(r) functions require that the multivariate (i.e. multispecies) pattern remains fixed, except for the focal species, that is simulated acording to, e.g., an (inhomogeneous) Poisson process.

ipsim returns the multivariate pp pattern with all species in the same locations except the "focal" one (i.e., the one indicated by the argument mimark) that is simulated using rpoispp. If an intensity surface (argument lambda) is provided, the focal species will be simulated from this surface. If no lambda is provided but the argument sigma is >0, an intensity surface will be estimated with a Gaussian kernel with the sigma provided (using density.ppp) and the simulation will be made form this surface. If no lambda is provided and sigma=0, a homogeneos Poisson process will be simulated.

simulador2 generates a list (length = nsim) of marked (with mark = mimark) univariate point patterns from an intensity surface using rpoispp.

ipsimlist uses the results of simulador2 and the multivariate pp pattern to generate a list of multivariate point patterns with all species in the same locations except the "focal" one (i.e., the one indicated by the argument mimark) that has the locations simulated with simulador2.

multifocalsimulator is more flexible and allows the simulation of whichever null model of the focal species that could be described by an R expression.

Examples

# Build a multivariate point pattern where maple is simulated according to a Poisson process
# and where all the other species are keep fixed in their original coordinates.
# (The warnings are because in the original lansing point pattern there is a dupplicated
#  point)

data(lansing) 
ipsim(pp=lansing, mimark="maple")

# Build a multivariate point pattern where maple is simulated according to an Inhomogeneous
# Poisson process from an intensity surface estimated "on the fly" with a Gaussian kernel with
# sd = "sigma", and where all the other species are keep fixed in their original coordinates.

ipsim(pp=lansing, mimark="maple", sigma=0.1)

# Build a multivariate point pattern where maple is simulated according to an Inhomogeneous
# Poisson process from a predefined  intensity surface "lambda" and where all the other
# species are keep fixed in their original coordinates. "Lambda" is an im object resulting
# from density.ppp(), from predict.ppm() or converted from any other rasterized image. 

maple.lambda<- density.ppp(lansing[lansing$marks=="maple"])
ipsim(pp=lansing, mimark="maple", lambda=maple.lambda)

# Build a list of 19 multivariate point pattern where maple is simulated according to an
# Inhomogeneous Poisson process from a predefined  intensity surface "lambda" and where all
# the other species are keep fixed in their original coordinates. "Lambda" is an im object
# resulting  from density.ppp(), # from predict.ppm() or converted from any other rasterized
# image. 

  # Estimate the intensity of maple
   maple.lambda<- density(unmark(lansing[lansing$marks=="maple"]))

  # first simulate the individual maple patterns
   maple.sim<- simulador2(mimark="maple", milambda=maple.lambda, nsim=19)

  # Then, mix the simulated maple patterns with the rest of the multivariate pattern
  # (which remains "fixed")
   multi.maple.sim<- ipsimlist(pp=lansing, mimark="maple", listsim=maple.sim)


## Use of multifocalsimulator() ##

# The same but in a single step with multifocalsimulator(): Build a list of 19 multivariate
# point pattern where maple is simulated according to an Inhomogeneous Poisson process
# from a predefined  intensity surface "lambda" and where all the other species are keep 
# fixed in their original coordinates. "Lambda" is an im object resulting from density.ppp(),
# from predict.ppm() or converted from any other rasterized image. 

   # Estimate the intensity of maple
   maple.lambda<- density(unmark(lansing[lansing$marks=="maple"]))

   # get 99 simulated multivariate point patterns where only maple varies,
   # according to an inhomogeneous Poisson process
   multi.maple.sim <- multifocalsimulator(lansing, "maple", nsim=99,
                                         simulate=expression(rpoispp(maple.lambda)))

if (FALSE) {
   # Use the simulated multivariate patterns to compute  envelopes for the ISAR against
   # a null model of IPP for maple 
   isar.maple.env<- envelope(lansing, fun=isar, mimark="maple", nsim=99, savefuns=TRUE,
                                         r=seq(0.01, 0.25, le=100), simulate=multi.maple.sim)
   plot( isar.maple.env)



# Use multifocalsimulator()  to compute  envelopes for the ISAR against a null model of
# Poisson cluster for maple.

   # First, adjust a Poisson Cluster process to maple
   require(ecespa)
   maple.pc<- ipc.estK(unmark(lansing[lansing$marks=="maple"]))

  # generate list of simulated multivariate partterns (all other species fixed and maple
  # simulated according to the adjusted PC process):
   maple.pc.sim<-multifocalsimulator(pp=lansing, mimark="maple", nsim=99,nmin=NULL,
                                                 simulate=expression(rIPCP(maple.pc)))

  # compute envelopes
   isar.maple.pc.env<- envelope(lansing, fun=isar, mimark="maple", nsim=99, savefuns=TRUE, 
                                            simulate=maple.pc.sim, r=seq(0.01, 0.25, le=100))
   plot( isar.maple.pc.env)


# Compute  envelopes for the IFDAR against a null model of Poisson cluster for sp_44 in
# San Francisco forest.
   data(SF)
   data(SFtraits)

   # first, get the original point pattern but with marks only for the species (i.e., dsicard 
   # the data.frame of marks and keep only the vector of species names)
   SFsp<- unmark(SF)
   marks(SFsp)<- SF$marks$species

   # second, adjust a PCP to sp_44
   sp_44.pc<- ipc.estK(unmark(SFsp[SFsp$marks=="sp_44"]))

  # third, generate multivariate simulated patterns with only sp_44 varying according
  # to the adjusted PCP
   sp_44.pc.sim<-multifocalsimulator(pp=SFsp, mimark="sp_44",nsim=99,nmin=NULL,
                                                 simulate=expression(rIPCP(sp_44.pc)))

   # finally, compute envelopes
   ifdar.sp_44.pc.env<- envelope(SFsp, fun=ifdar, mimark="sp_44", traits=SFtraits, r=1:30,
                        correct.trait.na=TRUE, nsim=99, simulate=sp_44.pc.sim,  savefuns=TRUE)

   plot( ifdar.sp_44.pc.env)

}