Parametric bootstrap test of a null model of i.i.d., but spatially
autocorrelated species against clustering of the species' population
patterns. Note that most relevant functionality of prabtest
(except of the use of the geco distance) is
also included in abundtest, so that abundtest can also
be used on binary presence-absence data.
In spite of the lots of
parameters, a standard execution (for the default test statistics, see
parameter teststat below) will be
prabmatrix <- prabinit(file="path/abundmatrixfile",
neighborhood="path/neighborhoodfile")
test <- abundtest(prabmatrix)
summary(test)
Note: Data formats are described
on the prabinit help page. You may also consider the example datasets
kykladspecreg.dat and nb.dat. Take care of the
parameter rows.are.species of prabinit.
abundtest(prabobj, teststat = "distratio", tuning = 0.25,
times = 1000, p.nb = NULL,
prange = c(0, 1), nperp = 4, step = 0.1, step2 = 0.01,
twostep = TRUE, species.fixed=TRUE, prab01=NULL,
groupvector=NULL,
sarestimate=prab.sarestimate(prabobj),
dist = prabobj$distance,
n.species = prabobj$n.species)an object of class prab (presence-absence data), as
generated by prabinit.
string, indicating the test statistics. "isovertice":
number of isolated vertices in the graph of tuning
smallest distances
between species. "lcomponent": size of largest connectivity
component in this graph. "distratio": ratio between tuning
smallest and largest distances. "nn": average distance of species to
tuningth nearest neighbor.
"inclusions": number of inclusions between areas of different
species (tests for nestedness structure, not for clustering, and
treats abundance matrices as presence-absence-data). "mean":
mean of the distances between species (this is a rough measure of
species co-occurrence).
"groups": this requires a specification of a vector defining
different groups of species via parameter groupvector. The
test statistic is then the mean of the distances between species of
the same group. This is computed over all species, but also for
every single group of species. It also includes the
"mean"-test, so that the number of tests carried out is
number of species groups with more than one element plus two.
integer or (if teststat="distratio") numerical
between 0 and 1. Tuning constant for test statistics, see
teststat.
integer. Number of simulation runs.
numerical between 0 and 1. The probability that a new
region is drawn from the non-neighborhood of the previous regions
belonging to a species under generation. If NULL (the
default), and prabobj$spatial,
prabtest estimates this by function
autoconst. Otherwise the next five parameters have no effect.
If NULL, and !prabobj$spatial,
spatial structure is ignored.
numerical range vector, lower value not smaller than 0, larger
value not larger than 1. Range where pd is to be found. Used
by function autoconst.
integer. Number of simulations per pd-value. Used
by function autoconst.
numerical between 0 and 1. Interval length between
subsequent choices of pd for the first simulation. Used
by function autoconst.
numerical between 0 and 1. Interval length between
subsequent choices of pd for the second simulation (see
parameter twostep). Used
by function autoconst.
logical. If TRUE, a first estimation step for
pd is
carried out in the whole prange, and then the final
estimation is determined between the preliminary estimator
-5*step2 and +5*step2. Else, the first simulation
determines the final estimator. Used
by function autoconst.
logical. Indicates if the range sizes of the species
are held fixed
in the test simulation (TRUE) or generated from their empirical
distribution in x (FALSE) for presence-absence data.
See function randpop.nb. Use always TRUE for abundance
data (not necessary if teststat="inclusions").
prabinit-object based on
presence-absence matrix of same dimensions than the
abundance matrix of prabobj. This specifies the presences and
absences on which the presence/absence step of abundance-based tests
is based (see details). If NULL (which is usually the only
reasonable choice), prab01 is computed in order to indicate
the nonzeroes of prabobj$prab.
integer vector. For every species, a number
indicating the species' group membership. Needed only if
teststat="groups".
Estimator of the parameters of a simultaneous
autoregression model corresponding to the null model for abundance
data from Hausdorf and Hennig (2007) as generated by
prab.sarestimate. This requires package spdep.
Note that by explicitly specifying sarestimate=NULL simulation
of 0-1 matrices can be enforced.
One of "jaccard", "kulczynski",
"qkulczynski" or "logkulczynski" specifying the distance
measure on which the test is based. By default, this is taken from
prabobj.
number of species. By default this is taken from
prabobj. This should normally not be changed.
An object of class prabtest, which is a list with components
vector of test statistic values for all simulated
populations. For teststat="groups" a list with components
overall (means of within group-distances), mean (means
of all distances), gr (matrix with a row for every group,
giving the groupwise within-group distance means).
p-value against an alternative that generates large
values of the test statistic (usually reasonable for
teststat="inclusions", "groups", "mean").
p-value against an alternative that generates small
values of the test statistic (usually reasonable for
"lcomponent", "nn", "distratio"; for
"isovertice", the two-sided p may make sense which is twice
the smaller one of p.above and p.below).
test statistic value for the original
data. (specgroups-output for teststat="groups").
see above.
dist above.
see above.
p.nb above.
TRUE if simultaneous autoregression has been used
(i.e., a sarestimate has been supplied or computed).
Estimator of the autocorrelation
parameter lambda (see errorsarlm)
defined so that the average weight of neighbors (see
nb2listw) is standardized to 1.
the output object of prab.sarestimate.
list containing information from
"groups" tests, with components lg (levels of
groupvector), ng (number of groups), nsg
(vector of group sizes), testm (value of "means" test
statistic for input prabobj), pa (group-wise
p.above), pb (group-wise
p.below), pma (p.above of "means" test),
pmb (p.below of "means" test).
For presence-absence data, the routine is described in
prabtest. For abundance data, the first step under the
null model is to
simulated presence-absence patterns as in prabtest. The second
step is to fit a simultaneous autoregression (SAR) model (Ripley 1981,
section 5.2) to the log-abundances, see
prab.sarestimate. The simulation from the null model is
implemented in regpop.sar.
For more details see Hennig
and Hausdorf (2004) for presence-absence data and Hausdorf and Hennig
(2007) for abundance data and the test statistics "mean" and
"groups", which can also be applied to binary data.
If p.nb=NA was
specified, a diagnostic plot
for the estimation of pd is plotted by autoconst.
For details see Hennig
and Hausdorf (2004) and the help pages of the cited functions.
Hausdorf, B. and Hennig, C. (2007) Null model tests of clustering of species, negative co-occurrence patterns and nestedness in meta-communities. Oikos 116, 818-828.
Hennig, C. and Hausdorf, B. (2004) Distance-based parametric bootstrap tests for clustering of species ranges. Computational Statistics and Data Analysis 45, 875-896. http://stat.ethz.ch/Research-Reports/110.html.
Ripley, B. D. (1981) Spatial Statistics. Wiley.
prabinit generates objects of class prab.
autoconst estimates pd from such objects.
prabtest (analogous function for presence-absence data).
regpop.sar generates populations from the null model.
prab.sarestimate (parameter estimators for simultaneous
autoregression model). This calls
errorsarlm (original estimation function from
package spdep).
Some more information on the test statistics is given in
homogen.test, lcomponent,
distratio, nn,
incmatrix.
Summary and print methods: summary.prabtest.
# NOT RUN {
# Note: NOT RUN.
# This needs package spdep and a bunch of packages that are
# called by spdep!
# data(siskiyou)
# set.seed(1234)
# x <- prabinit(prabmatrix=siskiyou, neighborhood=siskiyou.nb,
# distance="logkulczynski")
# a1 <- abundtest(x, times=5, p.nb=0.0465)
# a2 <- abundtest(x, times=5, p.nb=0.0465, teststat="groups",
# groupvector=siskiyou.groups)
# These settings are chosen to make the example execution
# faster; usually you will use abundtest(x).
# summary(a1)
# summary(a2)
# }
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