idar (version 1.5)

pisar: Phylogenetic Individual Species Area Relationship

Description

Compute Phylogenetic Individual Species Area Relationship function, i.e., PISAR(r) and its normalized version rISAR(r).

Usage

pisar(mippp, mippp.sp = NULL, mimark = NULL, namesmark = NULL, d = NULL, r = NULL,
         buffer = 0, bfw = NULL)
risar(mippp, mippp.sp = NULL, mimark = NULL, namesmark = NULL, d = NULL, d0 = NULL,
        r = NULL, buffer = 0, bfw = NULL)
controldis(d, m, mimark)

Value

pisar and risar return an object of class fv, see fv.object, which can be plotted directly using plot.fv.

Essentially a data frame containing a column named r with the vector of values of the argument r at which the PISAR(r) or rISAR(r) function had been estimated and another column, named "risar" or "pidar",which contains an estimate of the selected function.

controldis returns either the vector of distances between the focal and the rest of species or a vector of 1's if there is not phyloegenetic distance provided.

Arguments

mippp

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

mippp.sp

Univariate point pattern of the focal species. An object with the ppp format of spatstat.

mimark

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

namesmark

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

buffer

One of "adapt", i.e., compute an adaptive buffer, or a number indicating the width of a fixed buffer area around the plot border.

bfw

An owin object indicating the limits of the buffer area.

r

Vector of distances to compute PIDAR(r) functions.

d

A matrix expresing relationships (usually functional or phylogenetic) between species present in the multivariate point pattern.

d0

Another matrix expresing relationships (usually functional or phylogenetic) between species present in the multivariate point pattern.

m

A community (sites x species) data table.

Simulation envelopes

To compute simulation envelopes for pisar or risar functions, use envelope. See the examples in this help page and in multifocalsimulator to know how to compute simulation envelopes from appropriate null models.

Author

Marcelino de la Cruz

NOTE

When computing risar it is necessary to provide a phylogenetic or functional distance matrix to the argument d. By default, argument d0 will be set to a vector of 1's. It is however possible to provide a different matrix to d0 and compute instead, e.g., a ratio of phylogenetic to functional diversity.

Details

The original definition of ISAR(r) (Wiegand et al. 2007) was reformulated as:

$$ISAR_f (r) =\sum_{m=1}^{S} \delta_{fm} D_{fm} (r)$$ (Wiegand and Moloney 2014; Wang et al. 2016), where \(D_{fm}(r)\) describe the probabilities that the nearest species m neighbor of the typical individual of the focal species f is located within distance r, and \(\delta_{fm} \) yields a value of zero if f = m and a value of one otherwise (note that in their original proposal ISAR was formulated as if the value assigned to \(\delta_{fm} \) were 1 for all species pairs, including f = m). Based in this re-formulation, they defined the Phylogenetic Individual Species Area Relationship, i.e., PISAR(r), as:

$$PISAR_f (r) =\sum_{m=1}^{S} \delta_{fm}^{phy}D_{fm} (r)$$

where \(\delta_{fm}^{phy}\) is an index of phylogenetic (or functional) dissimilarity between species f and m. PISAR(r) quantifies the expected phylogenetic (or functional) diversity of species within the neighborhood with radius r around the typical individual of the focal species f.

They also defined rISAR(r) as a a function that is independent of local species richness within the neighborhood r; for this, they divided the PISAR function by the ISAR function:

$$rISAR_f (r) = \frac{\sum_{m=1}^{S} \delta_{fm}^{phy}D_{fm} (r)}{\sum_{m=1}^{S} \delta_{fm}D_{fm} (r)} $$

If the placement of the focal species f is unrelated with functional or phylogenetic relationships with their neighbors, the \(rISAR_f(r)\) will approximate the mean pairwise functional (or phylogenetic) dissimilarity \(\Delta_f^P = \sum_m \delta_{fm}^{phy}/(S-1)\) between an individual of the focal species f and all other species in the plot.

The function controldis controls that the order of species in the phylogenetic distance matrix matches the order of species amomng the levels of species marks in the point pattern, and extracts the vector of distances from all species to the focal one (mimark).

References

Wang, X., et al. (2016). Stochastic dilution effects weaken deterministic effects of niche-based processes in species rich forests. Ecology, in press

Wiegand,T., Gunatilleke, C.V.S., Gunatilleke, I.A.U.N. and Huth, A. (2007) How individual species structure diversity in tropical forests. PNAS 104, 19029-19033.

Wiegand, T., and K.A. Moloney. (2014). A handbook of spatial point pattern analysis in ecology. Chapman and Hall/CRC press, Boca Raton, FL

See Also

See also isar for other individual diversity area functions.

Examples

data(SF)
data(SFphylotree)

# Discard the size mark and keep the species mark in SF ppp:
sfsp<- ppp(SF$x, SF$y, window=SF$window, marks=SF$marks$species)

# compute phylogenetic distance among species
dphy <- cophenetic(SFphylotree)

# compute and plot PISAR function for sp_44
pisar_44 <- pisar(sfsp, mimark="sp_44", r=1:15,  d=dphy)
plot(pisar_44)

if (FALSE) {

# Compute rISAR and plot envelopes for an inhomogeneous Poisson model
#  of each species in San Francisco plot 
# BEWARE: THIS TAKES QUITE A FEW MINUTES !!!

# Split sfsp point pattern ppp by species
sfsp.sp<- split(sfsp)

#  Species with >= 10 individuals
sfsp10 <- sapply(sfsp.sp, function(x) x$n>=10)
#names of those species
nombressf<- names(sfsp10[sfsp10])

# parameters for the simulations, estimation of intensity, etc.
nsim<-199
nmin<-10
sigma <- 8
r<- seq(1,15, by=0.5)

# list to store results
risar.sf<- list()
# start computation
for( sp in nombressf){
   print(sp)
   # estimate intensity of the focal species
   lambda<- density(unmark(sfsp[sfsp$marks==sp]), sigma=sigma, positive=TRUE)      
   # obtain simulated patterns were all species ecept the focal remain fixed 
   #  and the focal varies according to an inhomomgeneous Poiisson process 
   simulados<- multifocalsimulator(sfsp, mimark=sp,
              simulate=expression(rpoispp(lambda)), nsim=nsim,nmin=nmin)
   # compute risar
   risar.sf[[sp]] <- envelope(sfsp, risar, mimark=sp, d=dphy, r=r,
        simulate=simulados,nsim=nsim, savefuns=T, buffer=0)
}

# plot the results
 dev.new(height=7, width=16)
 par(mfrow=c(3,9))
 for(i in 1:27) plot(risar.sf[[i]], legend=F, main=nombressf[i])

}