syrjala: Syrjala's test for the difference between the spatial...

In ecespa: Functions for Spatial Point Pattern Analysis

Syrjala's test for the difference between the spatial distributions of two populations

Description

Computes a two-sample Cramer-von Mises (and Kolmogorov-Smirnov) type test for a difference between the spatial distributions of two populations. It is designed to be sensitive to differences in the way the populations are distributed across the study area but insensitive to differences in abundance between the two populations.

Usage

syrjala0(coords, var1, var2, nsim, R=FALSE)
syrjala(coords = NULL, var1 = NULL, var2 = NULL, nperm = 999)
syrjala.test(ppp1, ppp2, nsim = 999)
## S3 method for class 'syrjala.test'
plot(x, coline=1, ...)
## S3 method for class 'ecespa.syrjala'
plot(x, ...)

Arguments

coords	A data.frame with '$x' and '$y' components.
var1	The first numeric variable
var2	The second numeric variable.
nperm	Number of permutations.
nsim	Number of permutations.
R	Logical. Should be computed using R approach?
ppp1	A marked point pattern, with the ppp format of spatstat, representing the values of some parameter measured on the corresponding sampling locations.
ppp2	A marked point pattern, with the ppp format of spatstat, representing the values of some other parameter measured on the same locations than ppp1.
x	An object of class 'syrjala.test' or 'ecespa.syrjala' resulting from syrjala or syrjala.test, respectively.
coline	color for drawing the statistic's line in the plot.
...	Graphical parameters passed to hist.

Details

The null hypothesis of Syrjala's test is that across the study area, the normalized distributions of the two populations are the same (Syrjala, 1996). Population density data are collected at K sampling locations on two populations. Let (xk, yk) denote the coordinates of the kth sampling location ( k= 1,...,K ); let d.i(xk, yk) denote the sample density at the Kth sampling location of the ith population. To construct a test that is independent of the population sizes, the observed density data is first normalized:

gamma.i(xk, yk) = di(xk, yk)/Di,

where Di is the sum of d.i(xk, yk) observations across the K sampling locations. The value of the cumulative distribution function at the location (xk, yk) for the ith population, denoted GAMMA.i(xk, yk), is the sum of all normalized density observations, gamma.i(xk, yk), whose location (x, y) is such that x <= xk and y <= yk. The statistic proposed by Syrjala to test the null hypothesis is the square of the difference between the cumulative distribution functions of the two populations, summed over all sampling locations, that is

psi = sum{GAMMA.1(xk, yk) - GAMMA.2(xk, yk)}^2.

As psi is not invariant with respect to the 'corner' of the rectangle enclosing the study area that is chosen as the origin of the coordinate sytem, psi is computed four times, one with each corner as the origin, and the average psi is employed as the test statistic. The level of significance of the observed psi is determined from its position in the ordered set of test statistic values from all 2^K pairwise permutations (that is approximated from a large number of randomly selected permutations).

Value

Functions syrjala or syrjala0 (with the argument R=FALSE) return an object of class 'syrjala.test'. Functions syrjala.test or syrjala0 (with the argument R=TRUE) return an object of class 'ecespa.syrjala'. In Both cases, the result is a list with the following elements:

cvm.obs	(class syrjala.test). The observed (averaged) psi statistic for the CvM test.
cvm.sim	(class syrjala.test). A numeric vector with the nperm+1 simulated psi's statistics (including cvm.obs).
ks.obs	(class syrjala.test). The observed (averaged) psi statistic for the K-S test.
ks.sim	(class syrjala.test). A numeric vector with the nperm+1 simulated psi's statistics (including ks.obs).
datanames	(class syrjala.test). A character vector with the names of the two patterns, the spatial congruence of which is been analyzed.
nperm	(class syrjala.test). The number of permutations employed in the test (not counting the original data).
psi.obs	(class ecespa.syrjala).The observed (averaged) psi statistic.
psi.sim	(class ecespa.syrjala). A vector with the nsim simulated psi's statistics.
datanames	(class ecespa.syrjala). A vector with the names of the two point patterns whose spatial congruence is been analyzed.
nsim	(class ecespa.syrjala). The number of permutations employed in the test.

Both S3 plot methods plot an histogram with the distribution of the simulated psi's statistics and draws the observed psi as a vertical line.

Warning

The test requires both populations being sampled in exactly the same sampling locations. Althoug this implementation employs ppp's as the supporting data format, this kind of data are not spatial point patterns. They cannot be analysed with the usual tools employed for marked point patterns.

Note

syrjala or syrjala0 (with the argument R=FALSE) implement a Fortran version of Syrjala's test. They run considerably faster than the "whole-R" implementation of syrjala.test or syrjala0 (with the argument R=TRUE). This last implementation is supplied for illustrative purposes and to maintain compability with previous versions of package ecespa. One can use function haz.ppp to easily build the ppp objects from a data.frame with only three columns (x-coordinate, y-coordinate and abundance).

This function has been employed to compute Syrjala's test in Rey-Benayas et al. (2008).

Author(s)

Jose M. Blanco-Moreno [e-mail] for the Fortran implementation of Syrjala's original QBasic function, Marcelino de la Cruz Rot for the R version, the wrapping functions and the documentation

References

Rey-Benayas, J.M., de la Montaña, E., Pérez-Camacho, L., de la Cruz, M., Moreno, D., Parejo, J.L. and Suárez-Seoane, S. 2010. Inter-annual dynamics and spatial congruence of a nocturnal bird assemblage inhabiting a Mediterranean agricultural mosaic. Ardeola,57(2): 303-320.

Syrjala, S. E. 1996. A statistical test for a difference between the spatial distributions of two populations. Ecology 77: 75-80. doi: 10.2307/2265656.

Examples

   
   data(syr1); data(syr2); data(syr3)
   
   coords <- data.frame(x=syr1$x, y=syr1$y); var1<- syr1$marks; var2<- syr2$marks
   
   (stest<-syrjala(coords, var1, var2, 9999))
   plot(stest)
   
   
   ## Not run: 
   
   plot(syrjala.test(syr1, syr2, nsim=999)) 
   
   plot(syrjala.test(syr1, syr3, nsim=999)) 
   
   syrjala0(coords, var1, var2, 9999)
   
   syrjala0(coords, var1, var2, 999, R=TRUE)
   
   
   coords <- expand.grid(x=1:10,y=1:10)
   var1 <- runif(100)
   var2 <- runif(100)
   syrjala(coords, var1, var2, 9999)
   
   

## End(Not run)

ecespa documentation built on Jan. 6, 2023, 1:21 a.m.