| ecespa {ecespa} | R Documentation |
Functions for spatial point pattern analysis in ecology
Description
This is a summary of the features of ecespa by way of examples of its main functions.
Author(s)
Marcelino de la Cruz Rot, with contributions of Philip M. Dixon and Jose M. Blanco-Moreno and heavily borrowing Baddeley's & Turner's spatstat code.
References
De la Cruz, M. 2006. Introducción al análisis de datos mapeados o algunas de las (muchas) cosas que puedo hacer si tengo coordenadas. Ecosistemas 15 (3): 19-39.
De la Cruz, M. 2008. Métodos para analizar datos puntuales. En: Introducción al Análisis Espacial de Datos en Ecología y Ciencias Ambientales: Métodos y Aplicaciones (eds. Maestre, F. T., Escudero, A. y Bonet, A.), pp 76-127. Asociación Española de Ecología Terrestre, Universidad Rey Juan Carlos y Caja de Ahorros del Mediterráneo, Madrid.
De la Cruz, M., Romao, R.L., Escudero, A. and Maestre, F.T. 2008. Where do seedlings go? A spatio-temporal analysis of early mortality in a semiarid specialist. Ecography, 31(6): 720-730. doi:10.1111/j.0906-7590.2008.05299.x.
Diggle, P. J. 2003. Statistical analysis of spatial point patterns. Arnold, London.
Dixon, P.M. 2002. Nearest-neighbor contingency table analysis of spatial segregation for several species. Ecoscience, 9 (2): 142-151. doi:10.1080/11956860.2002.11682700.
Dixon, P. M. 2002. Ripley's K function. In The encyclopedia of environmetrics (eds. El-Shaarawi, A.H. & Piergorsch, W.W.), pp. 1976-1803. John Wiley & Sons Ltd, NY.
Escudero, A., Romao, R.L., De la Cruz, M. & Maestre, F. 2005. Spatial pattern and neighbour effects on Helianthemum squamatum seedlings in a Mediterranean gypsum community. Journal of Vegetation Science, 16: 383-390. doi:10.1111/j.1654-1103.2005.tb02377.x.
Getis, A. and Franklin, J. 1987. Second-order neighbourhood analysis of mapped point patterns. Ecology 68: 473-477. doi:10.2307/1938452.
Loosmore, N.B. and Ford, E.D. (2006) Statistical inference using the G or K point pattern spatial statistics. Ecology 87, 1925-1931. doi:10.1890/0012-9658(2006)87[1925:SIUTGO]2.0.CO;2.
Lotwick,H.W. & Silverman, B. W. 1982. Methods for analysing spatial processes of several types of points. Journal of the Royal Statistical Society B, 44: 406-413. doi:10.1111/j.2517-6161.1982.tb01221.x.
Olano, J.M., Laskurain, N.A., Escudero, A. and De la Cruz, M. 2009. Why and where adult trees die in a secondary temperate forest? The role of neighbourhood. Annals of Forest Science, 66: 105. doi:10.1051/forest:2008074.
Penttinen, A. 2006. Statistics for Marked Point Patterns. In The Yearbook of the Finnish Statistical Society, pp. 70-91.
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.
Waagepetersen, R. P. 2007. An estimating function approach to inference for inhomogeneous Neymann-Scott processes. Biometrics 63: 252-258. doi:10.1111/j.1541-0420.2006.00667.x.
Examples
## Not run:
#############################################
### Transfom easily data from a data.frame into the ppp format
### of spatstat:
data(fig1)
plot(fig1) #typical xyplot
fig1.ppp <- haz.ppp (fig1)
fig1.ppp
plot(fig1.ppp) # point pattern plot of spatstat
#############################################
### Summarize the joint pattern of points and marks at different scales
### with the normalized mark-weighted K-function (Penttinen, 2006).
### Compare this function in two consecutive cohorts of Helianthemum
### squamatum seedlings:
## Figure 3.10 of De la Cruz (2008):
data(seedlings1)
data(seedlings2)
s1km <- Kmm(seedlings1, r=1:100)
s2km <- Kmm(seedlings2, r=1:100)
plot(s1km, ylime=c(0.6,1.2), lwd=2, maine="", xlabe="r(cm)")
plot(s2km, lwd=2, lty=2, add=T )
abline(h=1, lwd=2, lty=3)
legend(x=60, y=1.2, legend=c("Hs_C1", "Hs_C2", "H0"),
lty=c(1, 2, 3), lwd=c(3, 2, 2), bty="n")
## A pointwise test of normalized Kmm == 1 for seedlings1:
s1km.test <- Kmm(seedlings1, r=1:100, nsim=99)
plot(s1km.test, xlabe="r(cm)")
#############################################
### Explore the local relationships between marks and locations (e.g. size
### of one cohort of H. squamatum seedlings). Map the marked point pattern
### to a random field for visual inspection, with the normalized mark-sum
### measure (Penttinen, 2006).
data(seedlings1)
seed.m <- marksum(seedlings1, R=25)
plot(seed.m, what="marksum", sigma = 5) # raw mark-sum measure; sigma is bandwith for smoothing
plot(seed.m, what="pointsum", sigma = 5) # point sum measure
plot(seed.m, what="normalized", dimyx=200, contour=TRUE, sigma = 5) # normalized mark-sum measure
# the same with added grid
plot(seed.m, what="normalized", dimyx=200, contour=TRUE, sigma = 5, grid=TRUE)
#############################################
### Test against the null model of "independent labelling",
### i.e. test asociation/repulsion between a "fixed" pattern (e.g. adult
### H. squamatum plants) and a "variable" pattern (e.g. of surviving and
### dead seedlings), with 2.5% and 97.5% envelopes of 999 random
### labellings (De la Cruz & al. 2008).
data(Helianthemum)
cosa <- K012(Helianthemum, fijo="adultHS", i="deadpl", j="survpl",
r=seq(0,200,le=201), nsim=999, nrank=25, correction="isotropic")
plot(cosa$k01, sqrt(./pi)-r~r, col=c(3, 1, 3), lty=c(3, 1, 3), las=1,
ylab=expression(L[12]), xlim=c(0, 200),
main="adult HS vs. dead seedlings", legend=FALSE)
plot(cosa$k02, sqrt(./pi)-r~r, col=c(3, 1, 3), lty=c(3, 1, 3), las=1,
ylab=expression(L[12]), xlim=c(0, 200),
main="adult HS vs. surviving seedlings", legend=FALSE)
#############################################
### Test differences of agregation and segregation between two patterns,
### e.g. surviving and dying H. squamatum seedlings (De la Cruz & al. 2008).
data(Helianthemum)
cosa12 <- K1K2(Helianthemum, j="deadpl", i="survpl", r=seq(0,200,le=201),
nsim=999, nrank=1, correction="isotropic")
plot(cosa12$k1k2, lty=c(2, 1, 2), col=c(2, 1, 2), xlim=c(0, 200),
main= "survival- death",ylab=expression(K[1]-K[2]), legend=FALSE)
plot(cosa12$k1k12, lty=c(2, 1, 2), col=c(2, 1, 2), xlim=c(0, 200),
main="segregation of surviving seedlings",ylab=expression(K[1]-K[12]), legend=FALSE)
plot(cosa12$k2k12, lty=c(2, 1, 2), col=c(2, 1, 2), xlim=c(0, 200),
main= "segregation of dying seedlings",ylab=expression(K[2]-K[12]), legend=FALSE)
#############################################
### Test 'univariate' and 'bivariate' point patterns
### against non-Poisson (in-)homogeneous models
### (De la Cruz and Escudero, submited).
data(urkiola)
#####################
## univariate example
# get univariate pp
I.ppp <- split.ppp(urkiola)$birch
# estimate inhomogeneous intensity function
I.lam <- predict (ppm(I.ppp, ~polynom(x,y,2)), type="trend", ngrid=200)
# Compute and plot envelopes to Kinhom, simulating from an Inhomogeneous
# Poisson Process:
I2.env <- envelope( I.ppp,Kinhom, lambda=I.lam, correction="trans",
nsim=99, simulate=expression(rpoispp(I.lam)))
plot(I2.env, sqrt(./pi)-r~r, xlab="r (metres)", ylab= "L (r)", col=c(1,3,2,2),legend=FALSE)
# It seems that there is short scale clustering; let's fit an Inhomogeneous
# Poisson Cluster Process:
I.ki <- ipc.estK(mippp=I.ppp, lambda=I.lam, correction="trans")
# Compute and plot envelopes to Kinhom, simulating from the fitted IPCP:
Ipc.env <- Ki(I.ki, correction="trans", nsim=99, ngrid=200)
plot (Ipc.env, xlab="r (metres)", ylab= "L (r)")
#####################
## bivariate example: test independence between birch and quercus in Urkiola
J.ppp <- split.ppp(urkiola)$oak
# We want to simulate oak from a homogeneous Poisson model:
J.ppm <- ppm(J.ppp, trend=~1, interaction=Poisson() )
IJ.env <- Kci (mod1=I.ki, mod2=J.ppm, nsim=99)
plot(IJ.env, type=12)
plot(IJ.env, type=21)
#############################################
### Simulate envelopes from the fitted values of a logistic model,
### as in Olano et al. (2009)
data(quercusvm)
# read fitted values from logistic model:
probquercus <-c(0.99955463, 0.96563477, 0.97577094, 0.97327199, 0.92437309,
0.84023396, 0.94926682, 0.89687281, 0.99377915, 0.74157478, 0.95491518,
0.72366493, 0.66771787, 0.77330148, 0.67569082, 0.9874892, 0.7918891,
0.73246803, 0.81614635, 0.66446411, 0.80077908, 0.98290508, 0.54641754,
0.53546689, 0.73273626, 0.7347013, 0.65559655, 0.89481468, 0.63946334,
0.62101995, 0.78996371, 0.93179582, 0.80160346, 0.82204428, 0.90050059,
0.83810669, 0.92153079, 0.47872421, 0.24697004, 0.50680935, 0.6297911,
0.46374812, 0.65672284, 0.87951682, 0.35818237, 0.50932432, 0.92293014,
0.48580241, 0.49692053, 0.52290553, 0.7317549, 0.32445982, 0.30300865,
0.73599359, 0.6206056, 0.85777043, 0.65758613, 0.50100406, 0.31340849,
0.22289286, 0.40002879, 0.29567678, 0.56917817, 0.56866864, 0.27718552,
0.4910667, 0.47394411, 0.40543788, 0.29571349, 0.30436276, 0.47859015,
0.31754526, 0.42131675, 0.37468782, 0.73271225, 0.26786274, 0.59506388,
0.54801851, 0.38983575, 0.64896835, 0.37282031, 0.67624306, 0.29429766,
0.29197755, 0.2247629, 0.40697843, 0.17022391, 0.26528042, 0.24373722,
0.26936163, 0.13052254, 0.19958585, 0.18659692, 0.36686678, 0.47263005,
0.39557661, 0.68048997, 0.74878567, 0.88352322, 0.93851375)
################################
## Envelopes for an homogeneous point pattern:
cosap <- Kinhom.log(A=quercusvm, lifemark="0", nsim=99, prob=probquercus)
plot(cosap)
################################
## Envelopes for an inhomogeneous point pattern:
## First, fit an inhomogeneous Poisson model to alive trees :
quercusalive <- unmark(quercusvm[quercusvm$marks == 0])
mod2 <- ppm(quercusalive, ~polynom(x,y,2))
## Now use mod2 to estimate lambda for K.inhom:
cosapm <- Kinhom.log(A=quercusvm, lifemark="0", prob=probquercus,
nsim=99, mod=mod2)
plot(cosapm)
#############################################
### Test segregation based on the counts in the contingency table
### of nearest neighbors in a multitype point pattern (Dixon, 2002)
data(swamp)
dixon2002(swamp,nsim=99)
#############################################
### Fit the Poisson cluster point process to a point pattern with
### the method of minimum contrast (Diggle 2003).
data(gypsophylous)
# Estimate K function ("Kobs").
gyps.env <- envelope(gypsophylous, Kest, correction="iso", nsim=99)
plot(gyps.env, sqrt(./pi)-r~r, ylab="L(r)", legend=FALSE)
# Fit Poisson Cluster Process. The limits of integration
# rmin and rmax are setup to 0 and 60, respectively.
cosa.pc <- pc.estK(Kobs = gyps.env$obs[gyps.env$r<=60],
r = gyps.env$r[gyps.env$r<=60])
# Add fitted Kclust function to the plot.
lines(gyps.env$r,sqrt(Kclust(gyps.env$r, cosa.pc$sigma2,cosa.pc$rho)/pi)-gyps.env$r,
lty=2, lwd=3, col="purple")
# A kind of pointwise test of the gypsophylous pattern been a realisation
# of the fitted model, simulating with sim.poissonc and using function J (Jest).
gyps.env.sim <- envelope(gypsophylous, Jest, nsim=99,
simulate=expression(sim.poissonc(gypsophylous,
sigma=sqrt(cosa.pc$sigma2), rho=cosa.pc$rho)))
plot(gyps.env.sim, main="",legendpos="bottomleft")
#############################################
### Compute Syrjala's test for the difference between the spatial
### distributions of two populations, as in Rey-Benayas et al.
### (submited)
data(syr1); data(syr2); data(syr3)
plot(syrjala.test(syr1, syr2, nsim=999))
plot(syrjala.test(syr1, syr3, nsim=999))
## End(Not run)