| Title: | Test Overlapping of Polygons Against Random Rotation |
|---|---|
| Description: | Tests the observed overlapping polygon area in a collection of polygons against a null model of random rotation, as explained in De la Cruz et al. (2017) <doi:10.13140/RG.2.2.12825.72801>. |
| Authors: | Marcelino de la Cruz Rot |
| Maintainer: | Marcelino de la Cruz <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.3 |
| Built: | 2024-10-31 06:52:27 UTC |
| Source: | CRAN |
Oulines of the individuals of Astragalus sempervirens and Sesleria albicans present in a 2 x 2 m plot in the Pyrenean montains.
data("Astragalus") data("Sesleria")data("Astragalus") data("Sesleria")
Each object is a multiple-polygon window with the format owin of spatstat.
data(Astragalus) Astragalus plot(Astragalus) # total area covered by Astragalus area.owin(Astragalus) # number of individual polygons length(Astragalus$bdry) # area of each individual sapply(Astragalus$bdry, function(x) area.owin(owin(poly=x)))data(Astragalus) Astragalus plot(Astragalus) # total area covered by Astragalus area.owin(Astragalus) # number of individual polygons length(Astragalus$bdry) # area of each individual sapply(Astragalus$bdry, function(x) area.owin(owin(poly=x)))
Computes the centroid and diameter of each individual polygon in a multi-polygon owin object.
centroidiam(ventana1)centroidiam(ventana1)
ventana1 |
A multiple-polygon window with the format |
Iteratively applies the functions centroid.owin and diameter of spatstat to each polygon in the multipolygon owin and computes its centroid and its diameter.
diams |
Vector of diameters |
centroids |
Matrix with the coordinates of the centroids |
Marcelino de la Cruz Rot
data(Astragalus) X<-centroidiam(Astragalus) X$centroids X$diamsdata(Astragalus) X<-centroidiam(Astragalus) X$centroids X$diams
Checks that the vertices of polygons in a multi-polygon owin object are listed anticlockwise and, if some are not, tries to correct them.
check.ventana(ventana)check.ventana(ventana)
ventana |
A multiple-polygon window with the format |
This functions should be employed after importing shapefiles into owin objetcs (see vignette). Vertices of the individual polygons in the multiple-polygon owin objects should be listed anticlockwise to avoid errors in the computations of area overlapp (clockwise listed polygons represent "holes" in spatstat). This functions checks this and, in case that the vertices of some polygons are listed clockwise, tries to revert their order.
A multiple-polygon window with the format owin of spatstat with the vertices of all polygons listed anticockwise. The order number of the corrected polygons are included in the attribute "malos1". If there has been any polygon whose vertices have not been corrected, their orden number are included in the attribute "malos2": these polygons should be corrected manually.
Marcelino de la Cruz Rot
data(Astragalus) # For illustrative purposes, make the vertices of some individual polygon to be listed clockwise Astragalus.malo<-Astragalus Astragalus.malo$bdry[[14]]<-lapply(Astragalus.malo$bdry[[14]], rev) # check and correct Astragalus.corrected<-(check.ventana(Astragalus.malo)) attributes(Astragalus.corrected)data(Astragalus) # For illustrative purposes, make the vertices of some individual polygon to be listed clockwise Astragalus.malo<-Astragalus Astragalus.malo$bdry[[14]]<-lapply(Astragalus.malo$bdry[[14]], rev) # check and correct Astragalus.corrected<-(check.ventana(Astragalus.malo)) attributes(Astragalus.corrected)
Computes the p-value and sign of deviation for the hypothesis that the first value in a vector is larger or smaller (i.e., a two-sided test) than the expected value represented by all the other values in the vector, or alternatively, computes a one-sided test.
pval(x, alternative=c("two.sided", "less", "greater"))pval(x, alternative=c("two.sided", "less", "greater"))
x |
A vector, usually with some observed statistic in the first position (the observed overlapp) followed by a sequence of the same statistic computed for several realizations of a null model against which we test our hypothesis (i.e., a sequence of simulated, i.e., rotated, overlapps). |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter. |
Vector of length one whose absolute value represents the p-value and whose sign indicates wether the first value in x is larger (positive) or smaller (negative) than the expected value.
Marcelino de la Cruz
pval(c(0,1:99)) pval(c(100,1:99)) pval(c(100,1:199)) pval(c(200,1:199)) pval(c(0,1:199))pval(c(0,1:99)) pval(c(100,1:99)) pval(c(100,1:199)) pval(c(200,1:199)) pval(c(0,1:199))
Randomly rotates individual polygons around their centroids.
rotawin(ventana)rotawin(ventana)
ventana |
A multiple-polygon window with the format |
rotawin applies an independent random rotation to each of the polygons in a multiple-polygon owin object.
rotawin returns the original owin object with the individual polygons randomly rotated.
Marcelino de la Cruz Rot
data(Astragalus) plot(Astragalus) plot(rotawin(Astragalus), add=TRUE, border=2)data(Astragalus) plot(Astragalus) plot(rotawin(Astragalus), add=TRUE, border=2)
These functions test the overlaping surface area of a colection of polygons against a a null model of random rotation. test.auto.intersection test for overlapping between polygons of the same type (i.e., the same species) whereas test.intersection test for overlapping between polygons of different types (i.e., between different species). test.auto.intersection.p and test.intersection.p functions are parallelized versions which might significantly reduce computing times.
test.auto.intersection(ventana1, nsim = 199, win = NULL, prop=1, centroides1= NULL, diametros1 =NULL) test.intersection(ventana1, ventana2, nsim, prop = 1, win = NULL, centroides1 = NULL, diametros1 = NULL, centroides2 = NULL, diametros2 = NULL) test.auto.intersection.p(ventana1, nsim = 199, win = NULL, prop=1, centroides1= NULL, diametros1 =NULL, ncl=2) test.intersection.p(ventana1, ventana2, nsim, prop = 1, win = NULL, centroides1 = NULL, diametros1 = NULL, centroides2 = NULL, diametros2 = NULL, ncl=2)test.auto.intersection(ventana1, nsim = 199, win = NULL, prop=1, centroides1= NULL, diametros1 =NULL) test.intersection(ventana1, ventana2, nsim, prop = 1, win = NULL, centroides1 = NULL, diametros1 = NULL, centroides2 = NULL, diametros2 = NULL) test.auto.intersection.p(ventana1, nsim = 199, win = NULL, prop=1, centroides1= NULL, diametros1 =NULL, ncl=2) test.intersection.p(ventana1, ventana2, nsim, prop = 1, win = NULL, centroides1 = NULL, diametros1 = NULL, centroides2 = NULL, diametros2 = NULL, ncl=2)
ventana1 |
A multiple-polygon window with the format |
ventana2 |
A multiple-polygon window with the format |
nsim |
Number of simulations for the Monte Carlo test. |
prop |
Proportion of the diameter of each polygon which will be employed to select potential close neighbours. See details. |
win |
Observation window, employed to control for edge effects. An objetct with the format |
centroides1 |
Matrix or |
diametros1 |
Vector with the diameters of the polygons of |
centroides2 |
Matrix or |
diametros2 |
Vector with the diameters of the polygons of |
ncl |
Number of clusters for the parallel implementation. |
The summary statistic employed in the test is the overall sum of the overlapping areas of intersecting polygons. To reduce the computing burden, area intersections are only computed for polygon pairs for which the distance between their centoids is smaller than the sum of their largest diameters (weighted by the argument prop). To avoid edge effects, the test only considers polygons whose centroids are separated from the border of the observation window by a distance larger than their largest diameter.
In the pairwise tests, the polygons of ventana1 are kept fixed in their original positions (i.e., the accessory species) and the polygons of ventana2 (i.e., the focal species) are rotated.
Both test.auto.intersection and test.intersection return a vector of length nsim+1, with the sum of observed overlaping areas in the first position and subsequently with the sum of overlapping areas in each the simulated (i.e., randomly rotated) realizations of the null model.
Marcelino de la Cruz Rot
data(Astragalus) data(Sesleria) # Test overlapping between Astragalus individuals # Ideally nsim should be at least 199 Astragalus.test<- test.auto.intersection(Astragalus, nsim=19) # Observed overlapping area Astragalus.test[1] # p-value (negative value indicates that the observed overlapping is smaller # than expected) pval(Astragalus.test) # Test overlapping between Astragalus and Sesleria individuals. # Here, Sesleria is the accesory species (its individuals are kept fixed during the # test) and Astragalus the focal one (its individuals are rotated) # Ideally nsim should be at least 199 Sesleria.Astragalus.test<- test.intersection(ventana1= Sesleria, ventana2= Astragalus, nsim=19) # Observed overlapping area Sesleria.Astragalus.test[1] # p-value (negative value indicates that the observed overlapping is smaller # than expected) pval(Sesleria.Astragalus.test) # Reducing computing burden when making repetitive testing # First, put all the polygonal regions in a list, i.e. owins<- list(Astragalus, Sesleria) # compute diameters and centroids of the individual polygons # in each polygonal region centroids<- list() diams<- list() for ( i in 1: length(owins)){ cd<- centroidiam(owins[[i]]) centroids[[i]] <- cd$centroids diams[[i]] <- cd$diams } # set the number of simulations for each test # Ideally nsim should be at least 199 online <- interactive() Nsim <- if(online) 19 else 3 # create an array to store the results result <- array(NA, dim=c(length(owins),length(owins),Nsim+1)) t0<-Sys.time() for ( i in 1: length(owins)){ for ( j in 1: length(owins)){ cat(i,j,"\n") if(j!=i) result[i,j,] <- test.intersection(owins[[i]], owins[[j]], nsim=Nsim, centroides1=centroids[[i]], diametros1=diams[[i]], centroides2=centroids[[j]], diametros2=diams[[j]]) else result[i,j,] <- test.auto.intersection(owins[[i]], nsim=Nsim, centroides1=centroids[[i]], diametros1=diams[[i]]) } } Sys.time()-t0 # observed values (focal species in columns) (observed<- t(result[,,1])) # p-values tabla.p<- apply(result,c(1,2),pval) (p_values <- t(tabla.p)) # Compare with parallelized versions: # create an array to store the result.ps result.p<- array(NA, dim=c(length(owins),length(owins),Nsim+1)) t0<-Sys.time() for ( i in 1: length(owins)){ for ( j in 1: length(owins)){ cat(i,j,"\n") if(j!=i) result.p[i,j,] <- test.intersection.p(owins[[i]], owins[[j]], nsim=Nsim, centroides1=centroids[[i]], diametros1=diams[[i]], centroides2=centroids[[j]], diametros2=diams[[j]]) else result.p[i,j,] <- test.auto.intersection.p(owins[[i]], nsim=Nsim, centroides1=centroids[[i]], diametros1=diams[[i]]) } } Sys.time()-t0 # observed values (focal species in columns) (observed.p<- t(result.p[,,1])) # p-values tabla.p.p<- apply(result.p,c(1,2),pval) (p_values.p <- t(tabla.p.p))data(Astragalus) data(Sesleria) # Test overlapping between Astragalus individuals # Ideally nsim should be at least 199 Astragalus.test<- test.auto.intersection(Astragalus, nsim=19) # Observed overlapping area Astragalus.test[1] # p-value (negative value indicates that the observed overlapping is smaller # than expected) pval(Astragalus.test) # Test overlapping between Astragalus and Sesleria individuals. # Here, Sesleria is the accesory species (its individuals are kept fixed during the # test) and Astragalus the focal one (its individuals are rotated) # Ideally nsim should be at least 199 Sesleria.Astragalus.test<- test.intersection(ventana1= Sesleria, ventana2= Astragalus, nsim=19) # Observed overlapping area Sesleria.Astragalus.test[1] # p-value (negative value indicates that the observed overlapping is smaller # than expected) pval(Sesleria.Astragalus.test) # Reducing computing burden when making repetitive testing # First, put all the polygonal regions in a list, i.e. owins<- list(Astragalus, Sesleria) # compute diameters and centroids of the individual polygons # in each polygonal region centroids<- list() diams<- list() for ( i in 1: length(owins)){ cd<- centroidiam(owins[[i]]) centroids[[i]] <- cd$centroids diams[[i]] <- cd$diams } # set the number of simulations for each test # Ideally nsim should be at least 199 online <- interactive() Nsim <- if(online) 19 else 3 # create an array to store the results result <- array(NA, dim=c(length(owins),length(owins),Nsim+1)) t0<-Sys.time() for ( i in 1: length(owins)){ for ( j in 1: length(owins)){ cat(i,j,"\n") if(j!=i) result[i,j,] <- test.intersection(owins[[i]], owins[[j]], nsim=Nsim, centroides1=centroids[[i]], diametros1=diams[[i]], centroides2=centroids[[j]], diametros2=diams[[j]]) else result[i,j,] <- test.auto.intersection(owins[[i]], nsim=Nsim, centroides1=centroids[[i]], diametros1=diams[[i]]) } } Sys.time()-t0 # observed values (focal species in columns) (observed<- t(result[,,1])) # p-values tabla.p<- apply(result,c(1,2),pval) (p_values <- t(tabla.p)) # Compare with parallelized versions: # create an array to store the result.ps result.p<- array(NA, dim=c(length(owins),length(owins),Nsim+1)) t0<-Sys.time() for ( i in 1: length(owins)){ for ( j in 1: length(owins)){ cat(i,j,"\n") if(j!=i) result.p[i,j,] <- test.intersection.p(owins[[i]], owins[[j]], nsim=Nsim, centroides1=centroids[[i]], diametros1=diams[[i]], centroides2=centroids[[j]], diametros2=diams[[j]]) else result.p[i,j,] <- test.auto.intersection.p(owins[[i]], nsim=Nsim, centroides1=centroids[[i]], diametros1=diams[[i]]) } } Sys.time()-t0 # observed values (focal species in columns) (observed.p<- t(result.p[,,1])) # p-values tabla.p.p<- apply(result.p,c(1,2),pval) (p_values.p <- t(tabla.p.p))