Title: | Datasets for 'spatstat' Family |
---|---|
Description: | Contains all the datasets for the 'spatstat' family of packages. |
Authors: | Adrian Baddeley [aut, cre] |
Maintainer: | Adrian Baddeley <[email protected]> |
License: | GPL (>= 2) |
Version: | 3.1-2 |
Built: | 2024-08-13 13:00:40 UTC |
Source: | https://github.com/spatstat/spatstat.data |
The spatstat.data package contains the datasets for the spatstat family of packages.
The spatstat.data package contains the datasets for the spatstat family of packages.
These are spatial datasets; they are objects belonging to classes of spatial data defined in other sub-packages of the spatstat family. In order to handle these datasets correctly, we recommend loading the spatstat package.
This library and its documentation are usable under the terms of the “GNU General Public License”, a copy of which is distributed with R.
Adrian Baddeley [email protected], Rolf Turner [email protected] and Ege Rubak [email protected].
Austin Hughes' data: a point pattern of displaced amacrine cells in the retina of a rabbit. A marked point pattern.
data(amacrine)
data(amacrine)
An object of class "ppp"
representing the point pattern of cell locations.
Entries include
x |
Cartesian -coordinate of cell |
y |
Cartesian -coordinate of cell |
marks |
factor with levels off and on |
indicating ``off'' and ``on'' cells |
See ppp.object
for details of the format.
Austin Hughes' data: a point pattern of displaced amacrine cells in the retina of a rabbit. 152 “on” cells and 142 “off” cells in a rectangular sampling frame.
The true dimensions of the rectangle are 1060 by 662 microns.
The coordinates here are scaled to a rectangle of height 1 and width
so the unit of measurement is approximately 662 microns.
The data were analysed by Diggle (1986).
Peter Diggle, personal communication
Diggle, P. J. (1986). Displaced amacrine cells in the retina of a rabbit: analysis of a bivariate spatial point pattern. J. Neurosci. Meth. 18, 115–125.
if(require(spatstat.geom)) { amacrine (Ama <- rescale(amacrine)) }
if(require(spatstat.geom)) { amacrine (Ama <- rescale(amacrine)) }
These data give the spatial locations and diameters of sea anemones (beadlet anemone Actinia equina) in a sample plot on the north face of a boulder, well above low tide level, at Quiberon (Bretagne, France) in May 1976.
The data were originally described and discussed by Kooijman (1979a). Kooijman (1979b) shows a hand-drawn plot of the original data. The data are discussed by Upton and Fingleton (1985) as Example 1.8 on pages 64–67.
The anemones
dataset is taken directly from Table 1.11
of Upton and Fingleton (1985). The coordinates and
diameters are integer multiples of an idiosyncratic unit of length.
The boundary is a rectangle 280 by 180 units.
data(anemones)
data(anemones)
anemones
is an object of class "ppp"
representing the point pattern of anemone locations.
It is a marked point pattern with numeric marks representing
anemone diameter.
See ppp.object
for details of the format.
There is some confusion about the correct physical scale for these data. According to Upton and Fingleton (1985), one unit in the dataset is approximately 0.475 cm. According to Kooijman (1979a, 1979b) and also quoted by Upton and Fingleton (1985), the physical size of the sample plot was 14.5 by 9.75 decimetres (145 by 97.5 centimetres). However if the data are plotted at this scale, they are too small for a rectangle of this size, and the appearance of the plot does not match the original hand-drawn plot in Kooijman (1979b). To avoid confusion, we have not assigned a unit scale to this dataset.
Table 1.11 on pages 62–63 of Upton and Fingleton (1985), who acknowledge Kooijman (1979a) as the source.
Kooijman, S.A.L.M. (1979a) The description of point patterns. In Spatial and temporal analysis in ecology (ed. R.M. Cormack and J.K. Ord), International Cooperative Publishing House, Fairland, Maryland, USA. Pages 305–332.
Kooijman, S.A.L.M. (1979b) Inference about dispersal patterns. Acta Biotheoretica 28, 149–189.
Upton, G.J.G. and Fingleton, B. (1985) Spatial data analysis by example. Volume 1: Point pattern and quantitative data. John Wiley and Sons, Chichester.
data(anemones) if(require(spatstat.geom)) { # plot diameters on same scale as x, y plot(anemones, markscale=1) }
data(anemones) if(require(spatstat.geom)) { # plot diameters on same scale as x, y plot(anemones, markscale=1) }
These data give the spatial locations of nests of two species of ants, Messor wasmanni and Cataglyphis bicolor, recorded by Professor R.D. Harkness at a site in northern Greece, and described in Harkness & Isham (1983). The full dataset (supplied here) has an irregular polygonal boundary, while most analyses have been confined to two rectangular subsets of the pattern (also supplied here).
The harvester ant M. wasmanni collects seeds for food and builds a nest composed mainly of seed husks. C. bicolor is a heat-tolerant desert foraging ant which eats dead insects and other arthropods. Interest focuses on whether there is evidence in the data for intra-species competition between Messor nests (i.e. competition for resources) and for preferential placement of Cataglyphis nests in the vicinity of Messor nests.
The full dataset is displayed in Figure 1 of Harkness & Isham (1983). See Usage below to produce a comparable plot. It comprises 97 nests (68 Messor and 29 Cataglyphis) inside an irregular convex polygonal boundary, together with annotations showing a foot track through the region, the boundary between field and scrub areas inside the region, and indicating the two rectangular subregions A and B used in their analysis.
Rectangular subsets of the data were analysed by Harkness & Isham (1983), Isham (1984), Takacs & Fiksel (1986), S\"arkk\"a (1993, section 5.3), H\"ogmander and S\"arkk\"a (1999) and Baddeley & Turner (2000). The full dataset (inside its irregular boundary) was first analysed by Baddeley & Turner (2005b).
The dataset ants
is the full point pattern
enclosed by the irregular polygonal boundary.
The and
coordinates are eastings (E-W) and northings (N-S)
scaled so that 1 unit equals 0.5 feet.
This is a multitype point pattern object, each point carrying a mark
indicating the ant species (with levels
Cataglyphis
and Messor
).
The dataset ants.extra
is a list of auxiliary
information:
A
and B
The subsets of the pattern within the rectangles A and B demarcated in Figure 1 of Harkness & Isham (1983). These are multitype point pattern objects.
trackNE
and trackSW
coordinates of two straight lines bounding the foot track.
fieldscrub
The endpoints of a straight line separating the regions of ‘field’ and ‘scrub’: scrub to the North and field to the South.
side
A function(x,y)
that determines whether the location
(x,y)
is in the scrub or the field. The function can be applied
to numeric vectors x
and y
, and returns a factor
with levels "scrub"
and "field"
.
This function is useful as a spatial covariate.
plotit
A function which produces a plot of the full dataset.
data(ants)
data(ants)
ants
is an object of class "ppp"
representing the full point pattern of ants' nests.
See ppp.object
for details of the format.
The coordinates are scaled so that 1 unit equals 0.5 feet.
The points are marked by species (with levels Cataglyphis
and Messor
).
ants.extra
is a list with entries
point pattern of class "ppp"
point pattern of class "ppp"
data in format list(x=numeric(2),y=numeric(2))
giving the two endpoints of line markings
data in format list(x=numeric(2),y=numeric(2))
giving the two endpoints of line markings
data in format list(x=numeric(2),y=numeric(2))
giving the two endpoints of line markings
Function with arguments x,y
Function
Harkness and Isham (1983). Nest coordinates kindly provided by Prof Valerie Isham. Polygon coordinates digitised by Adrian Baddeley from a reprint of Harkness & Isham (1983).
Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.
Baddeley, A. and Turner, R. (2005a)
Spatstat: an R package for analyzing spatial point patterns.
Journal of Statistical Software 12:6, 1–42.
URL: www.jstatsoft.org
, ISSN: 1548-7660.
Baddeley, A. and Turner, R. (2005b) Modelling spatial point patterns in R. In: A. Baddeley, P. Gregori, J. Mateu, R. Stoica, and D. Stoyan, editors, Case Studies in Spatial Point Pattern Modelling, Lecture Notes in Statistics number 185. Pages 23–74. Springer-Verlag, New York, 2006. ISBN: 0-387-28311-0.
Harkness, R.D. and Isham, V. (1983) A bivariate spatial point pattern of ants' nests. Applied Statistics 32, 293–303.
Hogmander, H. and Sarkka, A. (1999) Multitype spatial point patterns with hierarchical interactions. Biometrics 55, 1051–1058.
Isham, V.S. (1984) Multitype Markov point processes: some approximations. Proceedings of the Royal Society of London, Series A, 391, 39–53.
Takacs, R. and Fiksel, T. (1986) Interaction pair-potentials for a system of ants' nests. Biometrical Journal 28, 1007–1013.
Sarkka, A. (1993) Pseudo-likelihood approach for pair potential estimation of Gibbs processes. Number 22 in Jyvaskyla Studies in Computer Science, Economics and Statistics. University of Jyvaskyla, Finland.
if(require(spatstat.geom)) { # Equivalent to Figure 1 of Harkness and Isham (1983) data(ants) ants.extra$plotit() # Data in subrectangle A, rotated # Approximate data used by Sarkka (1993) angle <- atan(diff(ants.extra$fieldscrub$y)/diff(ants.extra$fieldscrub$x)) plot(rotate(ants.extra$A, -angle)) # Approximate window used by Takacs and Fiksel (1986) tfwindow <- boundingbox(Window(ants)) antsTF <- ppp(ants$x, ants$y, window=tfwindow) plot(antsTF) }
if(require(spatstat.geom)) { # Equivalent to Figure 1 of Harkness and Isham (1983) data(ants) ants.extra$plotit() # Data in subrectangle A, rotated # Approximate data used by Sarkka (1993) angle <- atan(diff(ants.extra$fieldscrub$y)/diff(ants.extra$fieldscrub$x)) plot(rotate(ants.extra$A, -angle)) # Approximate window used by Takacs and Fiksel (1986) tfwindow <- boundingbox(Window(ants)) antsTF <- ppp(ants$x, ants$y, window=tfwindow) plot(antsTF) }
The states and large mainland territories of Australia are represented as polygonal regions forming a tessellation.
data(austates)
data(austates)
Object of class "tess"
.
Western Australia, South Australia, Queensland, New South Wales, Victoria and Tasmania (which are states of Australia) and the Northern Territory (which is a ‘territory’ of Australia) are represented as polygonal regions.
Offshore territories, and smaller mainland territories, are not shown.
The dataset austates
is a tessellation object (class "tess"
)
whose tiles are the states and territories.
The coordinates are latitude and longitude in degrees, so the space is effectively a Mercator projection of the earth.
Obtained from the oz package and reformatted.
data(austates) if(require(spatstat.geom)) { plot(austates) }
data(austates) if(require(spatstat.geom)) { plot(austates) }
A list of three point patterns, each giving the locations of electrical breakdown spots on a circular electrode in a microelectronic capacitor.
data(bdspots)
data(bdspots)
A list (of class "listof"
) of three spatial point patterns,
each representing the spatial locations of breakdown spots on an
electrode. The three electrodes are circular discs, of radii
169, 282 and 423 microns respectively. Spatial coordinates are
given in microns.
The application of successive voltage sweeps to the metal gate electrode of a microelectronic capacitor generates multiple breakdown spots on the electrode. The spatial distribution of these breakdown spots in MIM (metal-insulator-metal) and MIS (metal-insulator-semiconductor) structures was observed and analysed by Miranda et al (2010, 2013) and Saura et al (2013a, 2013b, 2014).
The data given here are the breakdown spot patterns for three circular electrodes of different radii, 169, 282 and 423 microns respectively, in MIM structures analysed in Saura et al (2013a).
Professor Enrique Miranda, Departament d'Enginyeria Electronica, Escola d'Enginyeria, Universitat Autonoma de Barcelona, Barcelona, Spain.
Miranda, E. and O'Connor, E. and Hurley, P.K. (2010) Simulation of the breakdown spots spatial distribution in high-K dielectrics and model validation using the spatstat package for R language. ECS Transactions 33 (3) 557–562.
Miranda, E., Jimenez, D., Sune, J., O'Connor, E., Monaghan, S., Povey, I., Cherkaoui, K. and Hurley, P. K. (2013) Nonhomogeneous spatial distribution of filamentary leakage current paths in circular area Pt/HfO2/Pt capacitors. J. Vac. Sci. Technol. B 31, 01A107.
Saura, X., Sune, J., Monaghan, S., Hurley, P.K. and Miranda, E. (2013a) Analysis of the breakdown spot spatial distribution in Pt/HfO2/Pt capacitors using nearest neighbor statistics. J. Appl. Phys. 114, 154112.
Saura, X., Moix, D., Sune, J., Hurley, P.K. and Miranda, E. (2013b) Direct observation of the generation of breakdown spots in MIM structures under constant voltage stress. Microelectronics Reliability 53, 1257–1260.
Saura, X., Monaghan, S., Hurley, P.K., Sune, J. and Miranda, E. (2014) Failure analysis of MIM and MIS structures using point-to-event distance and angular probability distributions. IEEE Transactions on Devices and Materials Reliability 14 (4) 1080–1090.
data(bdspots) if(require(spatstat.geom)) { plot(bdspots, equal.scales=TRUE) }
data(bdspots) if(require(spatstat.geom)) { plot(bdspots, equal.scales=TRUE) }
A point pattern giving the locations of 3605 trees in a tropical rain forest. Accompanied by covariate data giving the elevation (altitude) and slope of elevation in the study region.
data(bei)
data(bei)
bei
is an object of class "ppp"
representing the point pattern of tree locations.
See ppp.object
for details of the format.
bei.extra
is a list containing
two pixel images, elev
(elevation in metres) and
grad
(norm of elevation gradient). These pixel images are objects
of class "im"
, see im.object
.
The dataset bei
gives the positions of 3605 trees
of the species Beilschmiedia pendula (Lauraceae)
in a 1000 by 500 metre rectangular sampling region
in the tropical rainforest of Barro Colorado Island.
The accompanying dataset bei.extra
gives information
about the altitude (elevation) in the study region. It is a list
containing two pixel images, elev
(elevation in metres) and
grad
(norm of elevation gradient).
All spatial coordinates are given in metres.
These data are part of a much larger dataset containing the positions of hundreds of thousands of trees belong to thousands of species; see Hubbell and Foster (1983), Condit, Hubbell and Foster (1996) and Condit (1998).
The present data were analysed by Moller and Waagepetersen (2007).
Hubbell and Foster (1983), Condit, Hubbell and Foster (1996) and Condit (1998). Data files kindly supplied by Rasmus Waagepetersen. The data were collected in the forest dynamics plot of Barro Colorado Island. The study was made possible through the generous support of the U.S. National Science Foundation, the John D. and Catherine T. MacArthur Foundation, and the Smithsonian Tropical Research Institute.
Condit, R. (1998) Tropical Forest Census Plots. Springer-Verlag, Berlin and R.G. Landes Company, Georgetown, Texas.
Condit, R., Hubbell, S.P and Foster, R.B. (1996) Changes in tree species abundance in a neotropical forest: impact of climate change. Journal of Tropical Ecology 12, 231–256.
Hubbell, S.P and Foster, R.B. (1983) Diversity of canopy trees in a neotropical forest and implications for conservation. In: Tropical Rain Forest: Ecology and Management (eds. S.L. Sutton, T.C. Whitmore and A.C. Chadwick), Blackwell Scientific Publications, Oxford, 25–41.
Moller, J. and Waagepetersen, R.P. (2007) Modern spatial point process modelling and inference (with discussion). Scandinavian Journal of Statistics 34, 643–711.
Point pattern of cells in the retina, each cell classified as ‘on’ or ‘off’ and labelled with the cell profile area.
data(betacells)
data(betacells)
betacells
is an object of class "ppp"
representing the point pattern of cell locations.
Entries include
x |
Cartesian -coordinate of cell |
y |
Cartesian -coordinate of cell |
marks |
data frame of marks |
Cartesian coordinates are given in microns.
The data frame of marks has two columns:
type |
factor with levels off and on |
indicating ``off'' and ``on'' cells | |
area |
numeric vector giving the |
areas of cell profiles (in square microns) |
See ppp.object
for details of the format.
This is a new, corrected version of the old dataset
ganglia
. See below.
These data represent a pattern of beta-type ganglion cells in the retina of a cat recorded by W\"assle et al. (1981). Beta cells are associated with the resolution of fine detail in the cat's visual system. They can be classified anatomically as “on” or “off”.
Statistical independence of the arrangement of the “on”- and “off”-components would strengthen the evidence for Hering's (1878) ‘opponent theory’ that there are two separate channels for sensing “brightness” and “darkness”. See W\"assle et al (1981). There is considerable current interest in the arrangement of cell mosaics in the retina, see Rockhill et al (2000).
The dataset is a marked point pattern giving the locations,
types (“on” or “off”), and profile areas of beta cells observed
in a rectangle of dimensions microns.
Coordinates are given in microns (thousandths of a millimetre)
and areas are given in square microns.
The original source is Figure 6 of W\"assle et al (1981), which is a manual drawing of the beta mosaic observed in a microscope field-of-view of a whole mount of the retina. Thus, all beta cells in the retina were effectively projected onto the same two-dimensional plane.
The data were scanned in 2004 by Stephen Eglen from
Figure 6(a) of W\"assle et al (1981).
Image analysis software was used to identify the soma (cell
body). The location of each cell was taken to be the
centroid of the soma. The type of each cell (“on” or 'off”)
was identified by referring to Figures 6(b) and 6(d).
The area of each soma (in square microns) was also computed.
Note that this is a corrected version of
the ganglia
dataset provided in earlier versions of spatstat.
The earlier data ganglia
were not faithful to the scale
in the original paper and contain some scanning errors.
W\"assle et al (1981), Figure 6(a), scanned and processed by Stephen Eglen [email protected].
Hering, E. (1878) Zur Lehre von Lichtsinn. Vienna.
Van Lieshout, M.N.M. and Baddeley, A.J. (1999) Indices of dependence between types in multivariate point patterns. Scandinavian Journal of Statistics 26, 511–532.
Rockhill, R.L., Euler, T. and Masland, R.H. (2000) Spatial order within but not between types of retinal neurons. Proc. Nat. Acad. Sci. USA 97(5), 2303–2307.
W\"assle, H., Boycott, B. B. & Illing, R.-B. (1981). Morphology and mosaic of on- and off-beta cells in the cat retina and some functional considerations. Proc. Roy. Soc. London Ser. B 212, 177–195.
plot(betacells) if(require(spatstat.geom)) { area <- marks(betacells)$area plot(betacells %mark% sqrt(area/pi), markscale=1) }
plot(betacells) if(require(spatstat.geom)) { area <- marks(betacells)$area plot(betacells %mark% sqrt(area/pi), markscale=1) }
Data giving the locations and ages of bramble canes in a field. A marked point pattern.
data(bramblecanes)
data(bramblecanes)
An object of class "ppp"
representing the point pattern of plant locations.
Entries include
x |
Cartesian -coordinate of plant |
y |
Cartesian -coordinate of plant |
marks |
factor with levels 0,1, 2 indicating age |
See ppp.object
for details of the format.
These data record the locations and ages of bramble canes in a
field
metres square, rescaled to the unit square.
The canes were classified according to age as either newly emergent,
one or two years old. These are encoded as marks 0, 1 and 2 respectively
in the dataset.
The data were recorded and analysed by Hutchings (1979) and further analysed by Diggle (1981a, 1981b, 1983), Diggle and Milne (1983), and Van Lieshout and Baddeley (1999). All analyses found that the pattern of newly emergent canes exhibits clustering, which Hutchings attributes to “vigorous vegetative reproduction”.
Hutchings (1979), data published in Diggle (1983)
Diggle, P. J. (1981a) Some graphical methods in the analysis of spatial point patterns. In Interpreting multivariate data, V. Barnett (Ed.) John Wiley and Sons.
Diggle, P. J. (1981b). Statistical analysis of spatial point patterns. N.Z. Statist. 16, 22–41.
Diggle, P.J. (1983) Statistical analysis of spatial point patterns. Academic Press.
Diggle, P. J. and Milne, R. K. (1983) Bivariate Cox processes: some models for bivariate spatial point patterns. Journal of the Royal Statistical Soc. Series B 45, 11–21.
Hutchings, M. J. (1979) Standing crop and pattern in pure stands of Mercurialis perennis and Rubus fruticosus in mixed deciduous woodland. Oikos 31, 351–357.
Van Lieshout, M.N.M. and Baddeley, A.J. (1999) Indices of dependence between types in multivariate point patterns. Scandinavian Journal of Statistics 26, 511–532.
if(require(spatstat.geom)) { bramblecanes # convert coordinates to metres (Bram <- rescale(bramblecanes)) }
if(require(spatstat.geom)) { bramblecanes # convert coordinates to metres (Bram <- rescale(bramblecanes)) }
These data represent a spatially inhomogeneous pattern of circular section profiles of particles, observed in a longitudinal plane section through a gradient sinter filter made from bronze powder, prepared by Ricardo Bernhardt, Dresden.
The material was produced by sedimentation of bronze powder with varying grain diameter and subsequent sintering, as described in Bernhardt et al. (1997).
The data are supplied as a marked point pattern of circle centres marked by
circle radii.
The coordinates of the centres and the radii are recorded in mm.
The field of view is an mm rectangle.
The data were first analysed by Hahn et al. (1999).
data(bronzefilter)
data(bronzefilter)
An object of class "ppp"
representing the point pattern of cell locations.
Entries include
x |
Cartesian -coordinate of bronze grain profile centre |
y |
Cartesian -coordinate of bronze grain profile centre |
marks |
radius of bronze grain profile |
See ppp.object
for details of the format.
All coordinates are recorded in mm.
R.\ Bernhardt (section image), H.\ Wendrock (coordinate measurement). Adjusted, formatted and communicated by U.\ Hahn.
Bernhardt, R., Meyer-Olbersleben, F. and Kieback, B. (1997) Fundamental investigation on the preparation of gradient structures by sedimentation of different powder fractions under gravity. Proc. of the 4th Int. Conf. On Composite Engineering, July 6–12 1997, ICCE/4, Hawaii, Ed. David Hui, 147–148.
Hahn U., Micheletti, A., Pohlink, R., Stoyan D. and Wendrock, H.(1999) Stereological analysis and modelling of gradient structures. Journal of Microscopy, 195, 113–124.
data(bronzefilter) if(require(spatstat.geom)) { plot(bronzefilter, markscale=2) }
data(bronzefilter) if(require(spatstat.geom)) { plot(bronzefilter, markscale=2) }
Geospatial data of 873 farm locations with detected bovine tuberculosis in Cornwall, UK, over the years 1989-2002. This data-set was first analysed in Diggle, Zheng and Durr (2005).
data(btb)
data(btb)
Loading this dataset supplies the point pattern btb
and the additional object btb.extra
.
btb
is a marked point pattern
(see ppp.object
)
containing 873 points.
Its spatial coordinates are Eastings and Northings in kilometres
giving the farm locations. It has two columns of marks:
year |
Year of detection:
a factor with levels 1989 to 2002
|
spoligotype |
Spoligotype of tuberculosis:
a factor with four levels
“9”, “12”, “15”, “20” |
Loading the dataset btb
will also load the object
btb.extra
containing additional data. This is a list
(of class "solist"
) containing two elements,
standard |
The standard version of the BTB dataset
used in many publications. This is a marked point pattern,
identical to btb except that its window of observation
is a slightly larger and simpler polygon than the window of
btb .
|
full |
A more extensive dataset
compiled from files supplied by Professor Diggle.
This is a marked point pattern, identical to standard
except that it includes 46 additional farm locations where
bovine tuberculosis was detected, but where the spoligotype
was not one of the four common spoligotypes. There are 919 data
points altogether.
The attribute attr(full, "retained") is a logical vector
indicating which of the points in full was retained
or deleted to obtain standard .
|
Professor Peter Diggle.
Roger Sainsbury of the UK's State Veterinary Service helped to collect the data-set. Jackie Inwald and Si Palmer of the Department of Bacterial Diseases, Veterinary Laboratories Agency, Weybridge, UK carried out the spoligotyping.
Peter Diggle supplied the point coordinates, spoligotype data
and year data, and the coordinates of the window used in
btb.extra
.
Tilman Davies drew the finer window used in btb
.
Diggle, P.J., Zheng, P. and Durr, P. (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. Applied Statistics, 54, 645–658.
if(require(spatstat.geom)) { summary(btb) plot(subset(btb, select=spoligotype), cols=2:5) }
if(require(spatstat.geom)) { summary(btb) plot(subset(btb, select=spoligotype), cols=2:5) }
The data record the locations of the centres of 42 biological cells observed under optical microscopy in a histological section. The microscope field-of-view has been rescaled to the unit square.
The data were recorded by F.H.C. Crick and B.D. Ripley, and analysed in Ripley (1977, 1981) and Diggle (1983). They are often used as a canonical example of an ‘ordered’ point pattern.
data(cells)
data(cells)
An object of class "ppp"
representing the point pattern of cell centres.
See ppp.object
for details of the format.
Crick and Ripley, see Ripley (1977)
Diggle, P.J. (1983) Statistical analysis of spatial point patterns. Academic Press.
Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B 39, 172–212.
Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.
Nine (independent replicate) point patterns of whale and dolphin sightings obtained from aircraft flying along eight parallel transects in the region of Great Barrier Island, the Hauraki Gulf and the Coromandel Peninsula (New Zealand). Most of the transects are interrupted by portions of land mass. Observations were recorded within narrow rectangles of total width 840 metres (420 metres on each side of the transect).
data(cetaceans)
data(cetaceans)
The object cetaceans
is a hyperframe (see
hyperframe()
) with 9 rows and 4 columns.
Each row of this hyperframe represents a replicate survey.
The columns are whales
, dolphins
, fish
and plankton
.
Each entry in the hyperframe is a point pattern.
The dolphins
column consists of
marked patterns (with marks having levels dd
and tt
)
while the other columns contain unmarked point patterns.
The object cetaceans.extra
is a list containing auxiliary data.
It currently contains only one entry, patterns
, which
contains the same information as cetaceans
in another form.
This is a list, of class solist
(“spatial object list”; see solist()
,
as.solist()
).
It is a list of length 9, in which each entry is a marked point
pattern, representing the result of one survey.
Each pattern was obtained by superimposing the
whales
, dolphins
, fish
and plankton
patterns
from the corresponding row of cetaceans
.
The marks of these patterns have levels be
, dd
,
fi
, tt
and zo
.
The data were obtained from nine aerial surveys, conducted from 02/12/2013 to 22/04/2014. Each survey was conducted over the course of a single day. The gap between successive surveys ranged from two to six weeks (making it “not unreasonable” to treat the patterns obtained as being independent). The marks of the patterns referred to above may be interpreted as follows:
be
: whales — Bryde's whale (Balaenoptera edeni)
dd
: dolphins — Common dolphin (Delphinus delphis)
fi
: fish — Any species that forms schools
tt
: dolphins — Bottlenose dolphin (Tursiops truncatus)
zo
: plankton — Zooplankton
The window for the point patterns in these data sets is of type
polygonal
and consists of a number of thin rectangular
strips. These are arranged along eight parallel transects.
The units in which the patterns are presented are kilometres.
These data are rather “sparse”. For example there are a total of only eight whale observations in the entire data set (all nine surveys). Thus conclusions drawn from these data should be treated with even more than the usual amount of circumspection.
These data were kindly supplied by Lily Kozmian-Ledward, who studied them in the course of writing her Master's thesis at the University of Auckland, under the joint supervision of Dr. Rochelle Constantine, University of Auckland and Dr Leigh Torres, Oregon State University.
Kozmian-Ledward, L. (2014). Spatial ecology of cetaceans in the Hauraki Gulf, New Zealand. Unpublished MSc thesis, University of Auckland, New Zealand.
if(require(spatstat.model)) { cet <- cetaceans cet$dMplank <- with(cet, distfun(plankton, undef=20)) cet$dMfish <- with(cet, distfun(fish, undef=20)) fit.whales <- mppm(whales ~ dMplank + dMfish,data=cet) anova(fit.whales,test="Chi") # Note that inference is *conditional* on the fish and # plankton patterns. cetPats <- cetaceans.extra$patterns plot(Window(cetPats[[1]]),main="The window") plot(cetPats,nrows=3,main="All data") }
if(require(spatstat.model)) { cet <- cetaceans cet$dMplank <- with(cet, distfun(plankton, undef=20)) cet$dMfish <- with(cet, distfun(fish, undef=20)) fit.whales <- mppm(whales ~ dMplank + dMfish,data=cet) anova(fit.whales,test="Chi") # Note that inference is *conditional* on the fish and # plankton patterns. cetPats <- cetaceans.extra$patterns plot(Window(cetPats[[1]]),main="The window") plot(cetPats,nrows=3,main="All data") }
This dataset is a record of spatial locations of crimes reported in the period 25 April to 8 May 2002, in an area of Chicago (Illinois, USA) close to the University of Chicago. The original crime map was published in the Chicago Weekly News in 2002.
The data give the spatial location (street address) of each crime report, and the type of crime. The type labels are interpreted as follows:
assault |
battery/assault |
burglary |
burglary |
cartheft |
motor vehicle theft |
damage |
criminal damage |
robbery |
robbery |
theft |
theft |
trespass |
criminal trespass |
All crimes occurred on or near a street. The data give the coordinates of all streets in the survey area, and their connectivity.
Spatial coordinates are expressed in feet (one foot is 0.3048 metres).
The dataset chicago
is an object of class "lpp"
representing a point pattern on a linear network.
See lpp
for further information on the format.
These data were published and analysed in Ang, Baddeley and Nair (2012).
data(chicago)
data(chicago)
Object of class "lpp"
.
See lpp
.
Chicago Weekly News, 2002. Manually digitised by Adrian Baddeley [email protected].
Ang, Q.W. (2010) Statistical methodology for events on a network. Master's thesis, School of Mathematics and Statistics, University of Western Australia.
Ang, Q.W., Baddeley, A. and Nair, G. (2012) Geometrically corrected second-order analysis of events on a linear network, with applications to ecology and criminology. Scandinavian Journal of Statistics 39, 591–617.
Chicago Weekly News website: http://www.chicagoweeklynews.com
data(chicago) if(require(spatstat.linnet)) { plot(chicago) plot(as.linnet(chicago), main="Chicago Street Crimes",col="green") plot(as.ppp(chicago), add=TRUE, col="red", chars=c(16,2,22,17,24,15,6)) }
data(chicago) if(require(spatstat.linnet)) { plot(chicago) plot(as.linnet(chicago), main="Chicago Street Crimes",col="green") plot(as.ppp(chicago), add=TRUE, col="red", chars=c(16,2,22,17,24,15,6)) }
Spatial locations of cases of cancer of the larynx and cancer of the lung, and the location of a disused industrial incinerator. A marked point pattern.
data(chorley)
data(chorley)
The dataset chorley
is
an object of class "ppp"
representing a marked point pattern.
Entries include
x |
Cartesian -coordinate of home address |
y |
Cartesian -coordinate of home address |
marks |
factor with levels larynx and lung |
indicating whether this is a case of cancer of the larynx | |
or cancer of the lung. |
See ppp.object
for details of the format.
The dataset chorley.extra
is a list with two components.
The first component plotit
is a function which will
plot the data in a sensible fashion. The second
component incin
is a list with entries x
and y
giving the location of the industrial incinerator.
Coordinates are given in kilometres, and the resolution is 100 metres (0.1 km)
The data give the precise domicile addresses of new cases of cancer of the larynx (58 cases) and cancer of the lung (978 cases), recorded in the Chorley and South Ribble Health Authority of Lancashire (England) between 1974 and 1983. The supplementary data give the location of a disused industrial incinerator.
The data were first presented and analysed by Diggle (1990). They have subsequently been analysed by Diggle and Rowlingson (1994) and Baddeley et al. (2005).
The aim is to assess evidence for an increase in the incidence of cancer of the larynx in the vicinity of the now-disused industrial incinerator. The lung cancer cases serve as a surrogate for the spatially-varying density of the susceptible population.
The data are represented as a marked point pattern, with the points giving the spatial location of each individual's home address and the marks identifying whether each point is a case of laryngeal cancer or lung cancer.
Coordinates are in kilometres, and the resolution is 100 metres (0.1 km).
The dataset chorley
has a polygonal window with 132 edges
which closely approximates the boundary of the Chorley and South
Ribble Health Authority.
Note that, due to the rounding of spatial coordinates,
the data contain duplicated points (two points at the
same location). To determine which points are duplicates,
use duplicated.ppp
.
To remove the duplication, use unique.ppp
.
Coordinates of cases were provided by the Chorley and South Ribble Health Authority, and were kindly supplied by Professor Peter Diggle. Region boundary was digitised by Adrian Baddeley [email protected], 2005, from a photograph of an Ordnance Survey map.
Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005) Residual analysis for spatial point processes. Journal of the Royal Statistical Society, Series B 67, 617–666.
Diggle, P. (1990) A point process modelling approach to raised incidence of a rare phenomenon in the vicinity of a prespecified point. Journal of the Royal Statistical Soc. Series A 153, 349-362.
Diggle, P. and Rowlingson, B. (1994) A conditional approach to point process modelling of elevated risk. Journal of the Royal Statistical Soc. Series A 157, 433-440.
chorley if(require(spatstat.geom)) { summary(chorley) chorley.extra$plotit() }
chorley if(require(spatstat.geom)) { summary(chorley) chorley.extra$plotit() }
This dataset is a record of forest fires in the Castilla-La Mancha region of Spain between 1998 and 2007. This region is approximately 400 by 400 kilometres. The coordinates are recorded in kilometres.
The dataset clmfires
is a point pattern (object of class
"ppp"
) containing the spatial coordinates of each fire,
with marks containing information about each fire. There are 4
columns of marks:
cause |
cause of fire (see below) |
burnt.area |
total area burned, in hectares |
date |
the date of fire, as a value of class Date |
julian.date |
number of days elapsed since 1 January 1998 |
The cause
of the fire is a factor with the levels
lightning
, accident
(for accidents or negligence),
intentional
(for intentionally started fires) and
other
(for other causes including unknown cause).
The format of date
is “Year-month-day”, e.g.
“2005-07-14” means 14 July, 2005.
The accompanying dataset clmfires.extra
is a list
of two items clmcov100
and clmcov200
containing covariate
information for the entire Castilla-La Mancha region. Each
of these two elements is a list of four images (objects of
class "im"
) named elevation
, orientation
,
slope
and landuse
. The landuse
image is
factor-valued with the factor having levels urban
,
farm
(for farms or orchards), meadow
,
denseforest
(for dense forest), conifer
(for conifer
forest or plantation), mixedforest
, grassland
,
bush
, scrub
and artifgreen
for artificial
greens such as golf courses.
These images (effectively) provide values for the four
covariates at every location in the study area. The images in
clmcov100
are 100 by 100 pixels in size, while those in
clmcov200
are 200 by 200 pixels. For easy handling,
clmcov100
and clmcov200
also belong to the
class "listof"
so that they can be plotted and printed
immediately.
data(clmfires)
data(clmfires)
clmfires
is a marked point pattern (object of class "ppp"
).
See ppp.object
.
clmfires.extra
is a list with two components, named
clmcov100
and clmcov200
, which are lists of pixel images
(objects of class "im"
).
The precision with which the coordinates of the locations of the fires changed between 2003 and 2004. From 1998 to 2003 many of the locations were recorded as the centroid of the corresponding “district unit”; the rest were recorded as exact UTM coordinates of the centroids of the fires. In 2004 the system changed and the exact UTM coordinates of the centroids of the fires were used for all fires. There is thus a strongly apparent “gridlike” quality to the fire locations for the years 1998 to 2003.
There is however no actual duplication of points in the 1998 to 2003
patterns due to “jittering” having been applied in order to
avoid such duplication. It is not clear just how the fire
locations were jittered. It seems unlikely that the jittering was
done using the jitter()
function from R
or the
spatstat function rjitter
.
Of course there are many sets of points which are virtually identical, being separated by distances induced by the jittering. Typically these distances are of the order of 40 metres which is unlikely to be meaningful on the scale at which forest fires are observed.
Caution should therefore be exercised in any analyses of the patterns for the years 1998 to 2003.
Professor Jorge Mateu.
if(require(spatstat.geom)) { plot(clmfires, which.marks="cause", cols=2:5, cex=0.25) plot(clmfires.extra$clmcov100) # Split the clmfires pattern by year and plot the first and last years: yr <- factor(format(marks(clmfires)$date,format="%Y")) X <- split(clmfires,f=yr) fAl <- c("1998","2007") plot(X[fAl],use.marks=FALSE,main.panel=fAl,main="") }
if(require(spatstat.geom)) { plot(clmfires, which.marks="cause", cols=2:5, cex=0.25) plot(clmfires.extra$clmcov100) # Split the clmfires pattern by year and plot the first and last years: yr <- factor(format(marks(clmfires)$date,format="%Y")) X <- split(clmfires,f=yr) fAl <- c("1998","2007") plot(X[fAl],use.marks=FALSE,main.panel=fAl,main="") }
Prof. Shin-ichi Igarashi's data: a point pattern of the locations, in a cross-section of a concrete body, of the centroids of air bubbles in the cement paste matrix surrounding particles of aggregate.
data("concrete")
data("concrete")
An object of class "ppp"
representing the point pattern
of air bubble centroid locations. Spatial coordinates are expressed in microns.
The window of the point pattern is a binary mask
(window of type "mask"
; see owin
and as.mask
for more information
about this type of window).
This window in effect consists of the
cement paste matrix, or equivalently of the complement (in the
observed cross-section) of the aggregate.
Major scientific interest is focussed on analysing the distribution of the location of the air bubbles in the cement paste matrix. These bubbles are important in assuring frost resistance of the concrete. Each air bubble protects a region around it to a certain distance. To protect an entire concrete object against severe frost attack, it is necessary to cover the whole of the cement paste matrix with subsets of protected regions formed around the air bubbles. It is believed that the protected regions are related to the Dirichlet tessellation of the centroids of the bubbles, and the statistical properties of the protected regions can be determined from those of the Dirichlet tessellation. In this regard, the areas of the tiles are particularly important.
Prof. Shin-ichi Igarashi, of the School of Geoscience and Civil Engineering, Kanazawa University, personal communication.
Natesaiyer, K., Hover, K.C. and Snyder, K.A. (1992). Protected-paste volume of air-entrained cement paste: part 1. Journal of Materials in Civil Engineering 4 No.2, 166 – 184.
Murotani, T., Igarashi, S. and Koto, H. (2019). Distribution analysis and modeling of air voids in concrete as spatial point processes. Cement and Concrete Research 115 124 – 132.
if(require(spatstat.geom)) { plot(concrete,chars="+",cols="blue",col="yellow") # The aggregate is in yellow; the cement paste matrix is in white. # Unit of length: use \mu symbol for micron unitname(concrete) <- "\u00B5m" if(interactive()) { # Compute the Dirichlet tessellation dtc <- dirichlet(concrete) plot(dtc,ribbon=FALSE, col=sample(rainbow(dtc$n))) # Study Dirichlet tile areas areas <- tile.areas(dtc) aa <- areas/1000 # Divide by 1000 to avoid numerical instability # Fit a gamma distribution by the method of moments mm <- mean(aa) vv <- var(aa) shape <- mm^2/vv rate <- mm/vv rate <- rate/1000 # Adjust for rescaling hist(areas,probability=TRUE,ylim=c(0,7.5e-6), main="Histogram and density estimates for areas",ylab="",xlab="area") lines(density(areas),col="red") curve(dgamma(x,shape=shape,rate=rate),add=TRUE,col="blue") legend("topright",lty=1,col=c("red","blue"), legend=c("non-parametric","gamma fit"),bty="n") } }
if(require(spatstat.geom)) { plot(concrete,chars="+",cols="blue",col="yellow") # The aggregate is in yellow; the cement paste matrix is in white. # Unit of length: use \mu symbol for micron unitname(concrete) <- "\u00B5m" if(interactive()) { # Compute the Dirichlet tessellation dtc <- dirichlet(concrete) plot(dtc,ribbon=FALSE, col=sample(rainbow(dtc$n))) # Study Dirichlet tile areas areas <- tile.areas(dtc) aa <- areas/1000 # Divide by 1000 to avoid numerical instability # Fit a gamma distribution by the method of moments mm <- mean(aa) vv <- var(aa) shape <- mm^2/vv rate <- mm/vv rate <- rate/1000 # Adjust for rescaling hist(areas,probability=TRUE,ylim=c(0,7.5e-6), main="Histogram and density estimates for areas",ylab="",xlab="area") lines(density(areas),col="red") curve(dgamma(x,shape=shape,rate=rate),add=TRUE,col="blue") legend("topright",lty=1,col=c("red","blue"), legend=c("non-parametric","gamma fit"),bty="n") } }
These data come from an intensive geological survey of a 70 x 158 km region in central Queensland, Australia. They consist of 67 points representing copper ore deposits, and 146 line segments representing geological ‘lineaments’. Lineaments are linear features, visible on a satellite image, that are believed to consist largely of geological faults (Berman, 1986, p. 55). It would be of great interest to predict the occurrence of copper deposits from the lineament pattern, since the latter can easily be observed on satellite images.
These data were introduced and analysed by Berman (1986). They have also been studied by Berman and Diggle (1989), Berman and Turner (1992), Baddeley and Turner (2000, 2005), Foxall and Baddeley (2002) and Baddeley et al (2005).
Many analyses have been performed on the southern half of the data only. This subset is also provided.
data(copper)
data(copper)
copper
is a list with the following entries:
a point pattern (object of class "ppp"
)
representing the full point pattern of copper deposits.
See ppp.object
for details of the format.
a line segment pattern (object of class "psp"
)
representing the lineaments in the full dataset.
See psp.object
for details of the format.
the window delineating the southern half of
the study region. An object of class "owin"
.
the point pattern of copper deposits in the
southern half of the study region. An object of class
"ppp"
.
the line segment pattern of the lineaments in the
southern half of the study region. An object of class "psp"
.
All spatial coordinates are expressed in kilometres.
Dr Jonathan Huntington, CSIRO Earth Science and Resource Engineering, Sydney, Australia. Coordinates kindly provided by Dr. Mark Berman and Dr. Andy Green, CSIRO, Sydney, Australia.
Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.
Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005) Residual analysis for spatial point processes. Journal of the Royal Statistical Society, Series B 67, 617–666.
Baddeley, A. and Turner, R. (2005) Modelling spatial point patterns in R. In: A. Baddeley, P. Gregori, J. Mateu, R. Stoica, and D. Stoyan, editors, Case Studies in Spatial Point Pattern Modelling, Lecture Notes in Statistics number 185. Pages 23–74. Springer-Verlag, New York, 2006. ISBN: 0-387-28311-0.
Berman, M. (1986). Testing for spatial association between a point process and another stochastic process. Applied Statistics 35, 54–62.
Berman, M. and Diggle, P.J. (1989) Estimating Weighted Integrals of the Second-order Intensity of a Spatial Point Process. Journal of the Royal Statistical Society, series B 51, 81–92.
Berman, M. and Turner, T.R. (1992) Approximating point process likelihoods with GLIM. Applied Statistics 41, 31–38.
Foxall, R. and Baddeley, A. (2002) Nonparametric measures of association between a spatial point process and a random set, with geological applications. Applied Statistics 51, 165–182.
data(copper) if(require(spatstat.model)) { # Plot full dataset plot(copper$Points) plot(copper$Lines, add=TRUE) # Plot southern half of data plot(copper$SouthPoints) plot(copper$SouthLines, add=TRUE) if(interactive()) { Z <- distmap(copper$SouthLines) plot(Z) X <- copper$SouthPoints ppm(X, ~D, covariates=list(D=Z)) } }
data(copper) if(require(spatstat.model)) { # Plot full dataset plot(copper$Points) plot(copper$Lines, add=TRUE) # Plot southern half of data plot(copper$SouthPoints) plot(copper$SouthLines, add=TRUE) if(interactive()) { Z <- distmap(copper$SouthLines) plot(Z) X <- copper$SouthPoints ppm(X, ~D, covariates=list(D=Z)) } }
This command copies several data files to a folder (directory) chosen by the user, so that they can be used for a practice example.
copyExampleFiles(which, folder = getwd())
copyExampleFiles(which, folder = getwd())
which |
Character string name (partially matched)
of one of the datasets installed in |
folder |
Character string path name of a folder (directory) in which the files will be placed. Defaults to the current working directory. |
The original text files containing data for the selected dataset are copied to the chosen folder.
This is part of an exercise described in Chapter 3 of Baddeley, Rubak and Turner (2015).
Adrian Baddeley [email protected], Rolf Turner [email protected] and Ege Rubak [email protected].
Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press.
copyExampleFiles()
copyExampleFiles()
This is an artificially constructed example of a
hyperframe of spatial data. The data could have been obtained
from an experiment in which there are two groups of
experimental units, the response from each unit
is a point pattern Points
, and for each unit there is explanatory
data in the form of a pixel image Image
.
data(demohyper)
data(demohyper)
A hyperframe
with 3 rows and 3 columns:
List of spatial point patterns
(objects of class "ppp"
)
serving as the responses in an experiment.
List of images (objects of class "im"
)
serving as explanatory variables.
Factor with two levels a
and b
serving as an explanatory variable.
Artificially generated by Adrian Baddeley [email protected].
if(require(spatstat.model)) { plot(demohyper, quote({ plot(Image, main=""); plot(Points, add=TRUE) }), parargs=list(mar=rep(1,4))) mppm(Points ~ Group/Image, data=demohyper) }
if(require(spatstat.model)) { plot(demohyper, quote({ plot(Image, main=""); plot(Points, add=TRUE) }), parargs=list(mar=rep(1,4))) mppm(Points ~ Group/Image, data=demohyper) }
This is an artificial dataset, for use in testing and demonstrating the
capabilities of the spatstat
package.
It is a multitype point pattern in an irregular polygonal window. There are two types of points. The window contains a polygonal hole. Spatial coordinates are expressed in furlongs (one furlong equals 660 feet).
data(demopat)
data(demopat)
An object of class "ppp"
representing the point pattern.
See ppp.object
for details of the format of a
point pattern object.
Adrian Baddeley [email protected]
Dendrites are branching filaments which extend from the main body of a neuron (nerve cell) to propagate electrochemical signals. Spines are small protrusions on the dendrites.
This dataset gives the locations of 566 spines observed on one branch of the dendritic tree of a rat neuron. The spines are classified according to their shape into three types: mushroom, stubby or thin.
The data have been analysed in Jammalamadaka et al (2013) and Baddeley et al (2014). Please cite these papers and acknowledge the Kosik Lab, UC Santa Barbara, in any use of the data.
data("dendrite")
data("dendrite")
Object of class "lpp"
.
See lpp
.
Spatial coordinates are expressed in microns.
Kosik Lab, UC Santa Barbara (Dr Kenneth Kosik, Dr Sourav Banerjee).
Formatted for spatstat
by Dr Aruna Jammalamadaka.
Baddeley, A, Jammalamadaka, A. and Nair, G. (2014) Multitype point process analysis of spines on the dendrite network of a neuron. Applied Statistics (Journal of the Royal Statistical Society, Series C), 63, 673–694.
Jammalamadaka, A., Banerjee, S., Manjunath, B.S. and Kosik, K. (2013) Statistical Analysis of Dendritic Spine Distributions in Rat Hippocampal Cultures. BMC Bioinformatics 14, 287.
if(require(spatstat.linnet)) { plot(dendrite,leg.side="bottom", main="", cex=0.75, cols=2:4) }
if(require(spatstat.linnet)) { plot(dendrite,leg.side="bottom", main="", cex=0.75, cols=2:4) }
The data record the locations of 126 pine saplings in a Finnish forest, their heights and their diameters.
The dataset finpines
is a marked point pattern
containing the locations of the saplings marked by their heights
and their diameters.
Sapling locations are given in metres (to six significant digits); heights are in metres (rounded to the nearest 0.1 metre, except in one case to the nearest 0.05 metres); diameters are in centimetres (rounded to the nearest centimetre).
The data were recorded by Professor Seppo Kellomaki, Faculty of Forestry, University of Joensuu, Finland, and subsequently massaged by Professor Antti Penttinen, Department of Statistics, University of Jyv\"askyl\"a, Finland.
Originally the point locations were observed in polar coordinates with rather poor angular precision. Hence the coordinates are imprecise for large radius because of rounding errors: indeed the alignments can be observed by eye.
The data were manipulated by Prof Penttinen by making small angular perturbations at random. After this transformation, the original data (in a circular plot) were clipped to a square window, for convenience.
Professor Penttinen emphasises that the data were intended only for initial experimentation. They have some strange features. For example, if the height is less than 1.3 metres then the diameter can be uncertain. Also there are some very close pairs of points. Some pairs of trees (namely (58,59), (78,79), (96,97) and (102,103)) violate the requirement that the interpoint distance should be greater than half the sum of their diameters.
These data have subsequently been analysed by Van Lieshout (2004).
data(finpines)
data(finpines)
Object of class "ppp"
representing the point pattern of sapling locations marked by
their heights and diameters.
See ppp.object
for details of the format.
Prof Antti Penttinen
Van Lieshout, M.N.M. (2004) A J-function for marked point patterns. Research Report PNA-R0404, June 2004. Centrum voor Wiskunde en Informatica (CWI), Amsterdam, 2004.
data(finpines) if(require(spatstat.geom)) { plot(unmark(finpines), main="Finnish pines: locations") plot(finpines, which.marks="height", main="heights") plot(finpines, which.marks="diameter", main="diameters") plot(finpines, which.marks="diameter", main="diameters to scale", markscale=1/200) }
data(finpines) if(require(spatstat.geom)) { plot(unmark(finpines), main="Finnish pines: locations") plot(finpines, which.marks="height", main="heights") plot(finpines, which.marks="diameter", main="diameters") plot(finpines, which.marks="diameter", main="diameters to scale", markscale=1/200) }
Replicated spatial point patterns giving the locations of two different virus proteins on the membranes of cells infected with influenza virus.
data(flu)
data(flu)
A hyperframe
with 41 rows and four columns:
List of spatial point patterns
(objects of class "ppp"
)
with points of two types, identifying the locations of
two different proteins on a membrane sheet.
Coordinates are expressed in nanometres (nm) and the
window of observation is a square of side length 3331 nm.
Factor identifying whether the infecting virus was
the wild type (wt
) or mutant (mut1
).
Factor identifying whether the membrane sheet was stained
for the proteins M2 and M1
(stain="M2-M1"
)
or stained for the proteins M2 and HA
(stain="M2-HA"
).
Integer. Serial number of the microscope frame
in the original experiment. Frame identifier is not unique
across different values of virustype
and stain
.
The row names of the hyperframe can be used as succinct labels in plots.
The data consist of 41 spatial point patterns, each giving the locations of two different virus proteins on the membranes of cells infected with influenza virus.
Chen et al (2008) conducted the experiment and used spatial analysis to establish evidence for an interaction between the influenza virus proteins M1 and M2 that is important for the study of viral replication.
Canine kidney cells were infected with human influenza, Udorn strain, either the wild type or a mutant which encodes a defective M2 protein. At twelve hours post-infection, membrane sheets were prepared and stained for viral proteins, using two antibodies conjugated to gold particles of two sizes (6 nanometre and 12 nanometre diameter) enabling localisation of two different proteins on each sheet. The 6 nm particles were stained for M2 (ion channel protein), while the 12 nm particles were stained either for M1 (matrix protein) or for HA (hemagglutinin). Membrane sheets were visualised in electron microscopy.
Experimental technique and spatial analysis of the membranes stained for M2 and M1 is reported in Chen et al (2008). Analysis of the membranes stained for M2 and HA is reported in Rossman et al (2010). The M2-HA data shows a stronger association between the two proteins which has also been observed biochemically and functionally (Rossman et al, 2010).
The dataset flu
is a hyperframe
with one row for each membrane sheet. The column named pattern
contains the spatial point patterns of gold particle locations,
with two types of points (either M1
and M2
or
HA
and M2
). The column named virustype
is a factor identifying the virus: either wild type wt
or mutant mut1
. The column named stain
is a factor
identifying whether the membrane was stained for
M1 and M2 (stain="M2-M1"
) or stained for HA and M2
(stain="M2-HA"
).
The row names of the hyperframe are a succinct summary of
the experimental conditions and can be used as labels
in plots. See the Examples.
Data generously provided by Dr G.P. Leser and Dr R.A. Lamb. Please cite Chen et al (2008) in any use of these data.
Chen, B.J., Leser, G.P., Jackson, D. and Lamb, R.A. (2008) The influenza virus M2 protein cytoplasmic tail interacts with the M1 protein and influences virus assembly at the site of virus budding. Journal of Virology 82, 10059–10070.
Rossman, J.S., Jing, X.H., Leser, G.P. and Lamb, R.A. (2010) Influenza virus M2 protein mediates ESCRT-independent membrane scission Cell 142, 902–913.
if(require(spatstat.geom)) { flu Y <- flu$pattern[10] Y <- flu[10, 1, drop=TRUE] wildM1 <- with(flu, virustype == "wt" & stain == "M2-M1") plot(flu[wildM1, 1, drop=TRUE], main=c("flu data", "wild type virus, M2-M1 stain"), pch=c(3,16), cex=0.4, cols=2:3) }
if(require(spatstat.geom)) { flu Y <- flu$pattern[10] Y <- flu[10, 1, drop=TRUE] wildM1 <- with(flu, virustype == "wt" & stain == "M2-M1") plot(flu[wildM1, 1, drop=TRUE], main=c("flu data", "wild type virus, M2-M1 stain"), pch=c(3,16), cex=0.4, cols=2:3) }
Point pattern of retinal ganglion cells identified as ‘on’ or ‘off’. A marked point pattern.
data(ganglia)
data(ganglia)
An object of class "ppp"
representing the point pattern of cell locations.
Entries include
x |
Cartesian -coordinate of cell |
y |
Cartesian -coordinate of cell |
marks |
factor with levels off and on |
indicating ``off'' and ``on'' cells |
See ppp.object
for details of the format.
Important: these data are INCORRECT. See below.
The data represent a pattern of beta-type ganglion cells in the retina of a cat recorded in Figure 6(a) of W\"assle et al. (1981).
The pattern was first analysed by W\"assle et al (1981) using nearest neighbour distances. The data used in their analysis are not available.
The present dataset ganglia
was
scanned from Figure 6(a) of W\"assle et al (1981)
in the early 1990's, but we have no further information.
This dataset is the one analysed by Van Lieshout and Baddeley (1999)
using multitype J functions, and by Stoyan (1995) using second
order methods (pair correlation and mark correlation).
It has now been discovered that these data are incorrect. They are not faithful to the scale in Figure 6 of W\"assle et al (1981), and they contain some scanning errors. Hence they should not be used to address the original scientific question. They have been retained only for comparison with other analyses in the statistical literature.
A new, corrected dataset, scanned from the original microscope image,
has been provided under the name betacells
. Use that
dataset for any further study.
These data are incorrect.
Use the new corrected dataset betacells
.
W\"assle et al (1981), data supplied by Marie-Colette van Lieshout and attributed to Peter Diggle
Stoyan, D. (1995) Personal communication.
Van Lieshout, M.N.M. and Baddeley, A.J. (1999) Indices of dependence between types in multivariate point patterns. Scandinavian Journal of Statistics 26, 511–532.
W\"assle, H., Boycott, B. B. & Illing, R.-B. (1981). Morphology and mosaic of on- and off-beta cells in the cat retina and some functional considerations. Proc. Roy. Soc. London Ser. B 212, 177–195.
This dataset records the location of people sitting on a grass patch in Gordon Square, London, at 3pm on a sunny afternoon.
The dataset gordon
is a point pattern
(object of class "ppp"
) containing the spatial coordinates
of each person.
The grass patch is an irregular polygon with two holes.
Coordinates are given in metres.
data(gordon)
data(gordon)
Andrew Bevan, University College London.
Baddeley, A., Turner, R., Mateu, J. and Bevan, A. (2013)
Hybrids of Gibbs point process models and their implementation.
Journal of Statistical Software 55:11, 1–43.
DOI: 10.18637/jss.v055.i11
data(gordon) if(require(spatstat.geom)) { plot(gordon) }
data(gordon) if(require(spatstat.geom)) { plot(gordon) }
Locations of nesting sites of gorillas, and associated covariates, in a National Park in Cameroon.
data(gorillas)
data(gorillas)
gorillas
is a marked point pattern (object
of class "ppp"
) representing nest site locations.
gorillas.extra
is a named list of 7 pixel images (objects of
class "im"
) containing spatial covariates.
It also belongs to the class "listof"
.
All spatial coordinates are in metres.
The coordinate reference system is WGS_84_UTM_Zone_32N
.
These data come from a study of gorillas in the Kagwene Gorilla Sanctuary, Cameroon, by the Wildlife Conservation Society Takamanda-Mone Landscape Project (WCS-TMLP). A detailed description and analysis of the data is reported in Funwi-Gabga and Mateu (2012).
The dataset gorillas
is a marked point pattern
(object of class "ppp"
)
giving the spatial locations of 647 nesting sites of gorilla groups
observed in the sanctuary over time.
Locations are given as UTM (Zone 32N) coordinates in metres.
The observation window is the boundary of the sanctuary, represented
as a polygon. Marks attached to the points are:
Identifier of the gorilla group
that constructed the nest site:
a categorical variable with values major
or minor
.
Season in which data were collected:
categorical, either rainy
or dry
.
Day of observation. A value of class "Date"
.
Note that the data contain duplicated points (two points at the
same location). To determine which points are duplicates,
use duplicated.ppp
.
To remove the duplication, use unique.ppp
.
The accompanying dataset gorillas.extra
contains
spatial covariate information. It is a named list containing
seven pixel images (objects of class "im"
) giving the values of
seven covariates over the study region. It also belongs
to the class "listof"
so that it can be plotted.
The component images are:
Compass direction of the terrain slope.
Categorical, with levels
N
,
NE
,
E
,
SE
,
S
,
SW
,
W
and
NW
.
Digital elevation of terrain, in metres.
Heat Load Index at each point on the surface (Beer's aspect),
discretised. Categorical with values Warmest
(Beer's aspect between 0 and 0.999),
Moderate
(Beer's aspect between 1 and 1.999),
Coolest
(Beer's aspect equals 2).
Terrain slope, in degrees.
Type of slope.
Categorical, with values
Valley
, Toe
(toe slope), Flat
,
Midslope
, Upper
and Ridge
.
Vegetation or cover type.
Categorical, with values
Disturbed
(highly disturbed forest), Colonising
(colonising forest), Grassland
(savannah),
Primary
(primary forest), Secondary
(secondary forest), and
Transition
(transitional vegetation).
Euclidean distance from nearest water body, in metres.
For further information see Funwi-Gabga and Mateu (2012).
For demonstration and training purposes,
the raw data file for the vegetation
covariate is
also provided in the spatstat.data package installation,
as the file vegetation.asc
in the folder rawdata/gorillas
.
Use system.file
to obtain the file path:
system.file("rawdata/gorillas/vegetation.asc", package="spatstat.data")
.
This is a text file in the simple ASCII file format of the geospatial
library GDAL
. The file can be read by the function
readGDAL
in the rgdal package, or alternatively
read directly using scan
.
Field data collector: Wildlife Conservation Society Takamanda-Mone Landscape Project (WCS-TMLP). Please acknowledge WCS-TMLP in any use of these data.
Data kindly provided by Funwi-Gabga Neba, Data Coordinator of A.P.E.S. Database Project, Department of Primatology, Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany.
The collaboration of Prof Jorge Mateu, Universitat Jaume I, Castellon, Spain is gratefully acknowledged.
Funwi-Gabga, N. (2008) A pastoralist survey and fire impact assessment in the Kagwene Gorilla Sanctuary, Cameroon. M.Sc. thesis, Geology and Environmental Science, University of Buea, Cameroon.
Funwi-Gabga, N. and Mateu, J. (2012) Understanding the nesting spatial behaviour of gorillas in the Kagwene Sanctuary, Cameroon. Stochastic Environmental Research and Risk Assessment 26 (6), 793–811.
if(require(spatstat.geom)) { summary(gorillas) plot(gorillas) plot(gorillas.extra) }
if(require(spatstat.geom)) { summary(gorillas) plot(gorillas) plot(gorillas.extra) }
Point pattern of cell nuclei in hamster kidney, each nucleus classified as either ‘dividing’ or ‘pyknotic’. A multitype point pattern.
data(hamster)
data(hamster)
An object of class "ppp"
representing the point pattern of cell locations.
Entries include
x |
Cartesian -coordinate of cell |
y |
Cartesian -coordinate of cell |
marks |
factor with levels "dividing"
and "pyknotic" .
|
See ppp.object
for details of the format.
These data were presented and analysed by Diggle (1983, section 7.3).
The data give the positions of the centres of the nuclei of certain cells in a histological section of tissue from a laboratory-induced metastasising lymphoma in the kidney of a hamster.
The nuclei are classified as either "pyknotic" (corresponding to dying cells) or "dividing" (corresponding to cells arrested in metaphase, i.e. in the act of dividing). The background void is occupied by unrecorded, interphase cells in relatively large numbers.
The sampling window is a square, originally about 0.25 mm square in real units, which has been rescaled to the unit square.
Dr W. A. Aherne, Department of Pathology, University of Newcastle-upon-Tyne, UK. Data supplied by Prof. Peter Diggle
Diggle, P.J. (1983) Statistical analysis of spatial point patterns. Academic Press.
if(require(spatstat.geom)) { hamster ## rescale to microns (Ham <- rescale(hamster)) }
if(require(spatstat.geom)) { hamster ## rescale to microns (Ham <- rescale(hamster)) }
The spatial mosaic of vegetation of the heather plant (Calluna vulgaris) recorded in a 10 by 20 metre sampling plot in Sweden.
data(heather)
data(heather)
A list with three entries, representing the same data at different spatial resolutions:
coarse |
original heather data, 100 by 200 pixels |
medium |
current heather data, 256 by 512 pixels |
fine |
finest resolution data, 778 by 1570 pixels |
Each of these entries is an object of class "owin"
containing a binary pixel mask. All spatial coordinates are
given in metres.
These data record the spatial mosaic of vegetation of the heather plant (Calluna vulgaris) in a 10 by 20 metre sampling plot near Jadraas, Sweden. They were recorded and first analysed by Diggle(1981).
The dataset heather
contains three different versions of the data
that have been analysed by different writers over the decades.
Data as originally digitised by Diggle in 1983 at 100 by 200 pixels resolution (i.e. 10 pixels = 1 metre).
These data were entered by hand in the form of a run-length encoding (original file no longer available) and translated by a program into a 100 by 200 pixel binary image.
There are known to be some errors in the image which arise from errors in counting the run-length so that occasionally there will be an unexpected 'spike' on one single column.
A fine scale digitisation of the original map, prepared by CWI (Centre for Computer Science, Amsterdam, Netherlands) in 1994.
The original hand-drawn map was scanned by Adrian Baddeley [email protected], and processed by Chris Jonker, Henk Heijmans and Adrian Baddeley [email protected] to yield a clean binary image of 778 by 1570 pixels resolution.
The version of the heather data currently supplied on Professor Diggle's website. This is a 256 by 512 pixel image. The method used to create this image is not stated.
The data were recorded, presented and analysed by Diggle (1983). He proposed a Boolean model consisting of discs of random size with centres generated by of a Poisson point process.
Renshaw and Ford (1983) reported that spectral analysis of the data suggested the presence of strong row and column effects. However, this may have been attributable to errors in the run-length encoding of the original data.
Hall (1985) and Hall (1988, pp 301-318) took a bootstrap approach.
Ripley (1988, pp. 121-122, 131-135] used opening and closing functions to argue that a Boolean model of discs is inappropriate.
Cressie (1991, pp. 763-770) tried a more general Boolean model.
Peter Diggle
Cressie, N.A.C. (1991) Statistics for Spatial Data. John Wiley and Sons, New York.
Diggle, P.J. (1981) Binary mosaics and the spatial pattern of heather. Biometrics 37, 531-539.
Hall, P. (1985) Resampling a coverage pattern. Stochastic Processes and their Applications 20 231-246.
Hall, P. (1988) An introduction to the theory of coverage processes. John Wiley and Sons, New York.
Renshaw, E. and Ford, E.D. (1983) The interpretation of process from pattern using two-dimensional spectral analysis: Methods and problems of interpretation. Applied Statistics 32 51-63.
Ripley, B.D. (1988) Statistical Inference for Spatial Processes. Cambridge University Press.
Spatial locations of cases of childhood leukaemia and lymphoma, and randomly-selected controls, in North Humberside. A marked point pattern.
data(humberside)
data(humberside)
The dataset humberside
is
an object of class "ppp"
representing a marked point pattern.
Entries include
x |
Cartesian -coordinate of home address |
y |
Cartesian -coordinate of home address |
marks |
factor with levels case and control |
indicating whether this is a disease case | |
or a control. |
See ppp.object
for details of the format.
Spatial coordinates are expressed as multiples of 100 metres.
The dataset humberside.convex
is an object of the
same format, representing the same point pattern data,
but contained in a larger, 5-sided convex polygon.
Cuzick and Edwards (1990) first presented and analysed these data.
The data record 62 cases of childhood leukaemia and lymphoma diagnosed in the North Humberside region of England between 1974 and 1986, together with 141 controls selected at random from the birth register for the same period.
The data are represented as a marked point pattern, with the points giving the spatial location of each individual's home address (actually, the centroid for the postal code) and the marks identifying cases and controls.
Coordinates are expressed in units of 100 metres, and the resolution is
100 metres. At this resolution, there are some duplicated points.
To determine which points are duplicates,
use duplicated.ppp
.
To remove the duplication, use unique.ppp
.
Two versions of the dataset are supplied, both containing the
same point coordinates, but using different windows.
The dataset humberside
has a polygonal window with 102 edges
which closely approximates the Humberside region,
while humberside.convex
has a convex 5-sided polygonal window
originally used by Diggle and Chetwynd (1991) and shown in
Figure 1 of that paper. (This pentagon has been modified slightly
from the original data, by shifting two vertices horizontally by 1 unit,
so that the pentagon contains all the data points.)
Dr Ray Cartwright and Dr Freda Alexander. Published and analysed in Cuzick and Edwards (1990), see Table 1. Pentagonal boundary from Diggle and Chetwynd (1991), Figure 1. Point coordinates and pentagonal boundary supplied by Andrew Lawson. Detailed region boundary was digitised by Adrian Baddeley [email protected], 2005, from a reprint of Cuzick and Edwards (1990).
J. Cuzick and R. Edwards (1990) Spatial clustering for inhomogeneous populations. Journal of the Royal Statistical Society, series B, 52 (1990) 73-104.
P.J. Diggle and A.G. Chetwynd (1991) Second-order analysis of spatial clustering for inhomogeneous populations. Biometrics 47 (1991) 1155-1163.
if(require(spatstat.geom)) { humberside summary(humberside) plot(humberside) plot(Window(humberside.convex), add=TRUE, lty=2) ## convert to metres (Hum <- rescale(humberside)) ## convert to kilometres (HumK <- rescale(humberside, 10, "km")) }
if(require(spatstat.geom)) { humberside summary(humberside) plot(humberside) plot(Window(humberside.convex), add=TRUE, lty=2) ## convert to metres (Hum <- rescale(humberside)) ## convert to kilometres (HumK <- rescale(humberside, 10, "km")) }
This dataset is a spatial point pattern of trees recorded at Hyytiala, Finland. The majority of the trees are Scots pines. See Kokkila et al (2002).
The dataset hyytiala
is a point pattern
(object of class "ppp"
) containing the spatial coordinates
of each tree, marked by species (a factor with levels aspen
,
birch
, pine
and rowan
).
The survey region is a 20 by 20 metre square.
Coordinates are given in metres.
data(hyytiala)
data(hyytiala)
Nicolas Picard
Kokkila, T., Makela, A. and Nikinmaa E. (2002) A method for generating stand structures using Gibbs marked point process. Silva Fennica 36 265–277.
Picard, N, Bar-Hen, A., Mortier, F. and Chadoeuf, J. (2009) The multi-scale marked area-interaction point process: a model for the spatial pattern of trees. Scandinavian Journal of Statistics 36 23–41
data(hyytiala) if(require(spatstat.geom)) { plot(hyytiala, cols=2:5) }
data(hyytiala) if(require(spatstat.geom)) { plot(hyytiala, cols=2:5) }
The data give the locations of saplings of Japanese black pine (Pinus thunbergii) in a square sampling region in a natural forest. The observations were originally collected by Numata (1961).
These data are used as a standard example in the textbook of Diggle (2003); see pages 1, 14, 19, 22, 24, 56–57 and 61.
data(japanesepines)
data(japanesepines)
An object of class "ppp"
representing the point pattern of 65 tree sapling locations
in a 5.7 x 5.7 metre square, rescaled to the unit square
and rounded to two decimal places.
See ppp.object
for details of the format of a
point pattern object.
Diggle (2003), obtained from Numata (1961)
Diggle, P.J. (2003) Statistical Analysis of Spatial Point Patterns. Arnold Publishers.
Numata, M. (1961) Forest vegetation in the vicinity of Choshi. Coastal flora and vegetation at Choshi, Chiba Prefecture. IV. Bulletin of Choshi Marine Laboratory, Chiba University 3, 28–48 (in Japanese).
if(require(spatstat.geom)) { japanesepines summary(japanesepines) ## rescale to metres (Jpines <- rescale(japanesepines)) }
if(require(spatstat.geom)) { japanesepines summary(japanesepines) ## rescale to metres (Jpines <- rescale(japanesepines)) }
A collection of 41 different sequences of colours, each sequence having a uniform perceptual contrast over its whole range. These sequences make very good colour maps which avoid introducing artefacts when displaying image data.
data(Kovesi)
data(Kovesi)
A hyperframe
with the following columns:
linear |
Logical: whether the sequence is linear. |
diverging |
Logical: whether the sequence is diverging. |
rainbow |
Logical: whether the sequence is a rainbow. |
cyclic |
Logical: whether the sequence is cyclic. |
isoluminant |
Logical: whether the sequence is isoluminant. |
ternary |
Logical: whether the sequence is ternary. |
colsig |
Character: colour signature (see Details) |
l1 , l2 |
Numeric: lightness parameters |
chro |
Numeric: average chroma (percent) |
n |
Numeric: length of colour sequence |
cycsh |
Numeric: cyclic shift (percent) |
values |
: Character: the colour values. |
Kovesi (2014, 2015) presented a collection of colour sequences that have uniform perceptual contrast over their whole range.
The dataset Kovesi
provides these data. It is a
hyperframe
with 41 rows, in which each row provides information
about one colour sequence.
Additional information in each row specifies whether the colour sequence is ‘linear’, ‘diverging’, ‘rainbow’, ‘cyclic’, ‘isoluminant’ and/or ‘ternary’ as defined by Kovesi (2014, 2015).
The ‘colour signature’ is a string composed of letters representing the successive hues, using the following code:
r | red |
g | green |
b | blue |
c | cyan |
m | magenta |
y | yellow |
o | orange |
v | violet |
k | black |
w | white |
j | grey (j rhymes with grey) |
For example kryw
is the sequence from black to red to yellow to
white.
The column values
contains the colour data themselves.
The i
th colour sequence is Kovesi$values[[i]]
,
a character vector of length 256.
Dr Peter Kovesi, Centre for Exploration Targeting, University of Western Australia.
Kovesi, P. (2014) Website CET Uniform Perceptual Contrast Colour Maps https://www.peterkovesi.com/projects/colourmaps/
Kovesi, P. (2015)
Good Colour Maps: How to Design Them.
arXiv:1509.03700 [cs.GR]
Kovesi LinearBMW <- Kovesi$values[[28]] if(require(spatstat.geom)) { plot(colourmap(LinearBMW, range=c(0,1))) ## The following would be suitable for spatstat.options(image.colfun) BMWfun <- function(n) { interp.colours(LinearBMW, n) } }
Kovesi LinearBMW <- Kovesi$values[[28]] if(require(spatstat.geom)) { plot(colourmap(LinearBMW, range=c(0,1))) ## The following would be suitable for spatstat.options(image.colfun) BMWfun <- function(n) { interp.colours(LinearBMW, n) } }
Locations and botanical classification of trees in Lansing Woods.
The data come from an investigation of a 924 ft x 924 ft (19.6 acre) plot in Lansing Woods, Clinton County, Michigan USA by D.J. Gerrard. The data give the locations of 2251 trees and their botanical classification (into hickories, maples, red oaks, white oaks, black oaks and miscellaneous trees). The original plot size (924 x 924 feet) has been rescaled to the unit square.
Note that the data contain duplicated points (two points at the
same location). To determine which points are duplicates,
use duplicated.ppp
.
To remove the duplication, use unique.ppp
.
data(lansing)
data(lansing)
An object of class "ppp"
representing the point pattern of tree locations.
Entries include
x |
Cartesian -coordinate of tree |
y |
Cartesian -coordinate of tree |
marks |
factor with levels indicating species of each tree |
The levels of marks
are
blackoak
,
hickory
,
maple
,
misc
,
redoak
and
whiteoak
.
See ppp.object
for details of the format of a
point pattern object.
Besag, J. (1978) Some methods of statistical analysis for spatial data. Bull. Internat. Statist. Inst. 44, 77–92.
Cox, T.F. (1976) The robust estimation of the density of a forest stand using a new conditioned distance method. Biometrika 63, 493–500.
Cox, T.F. (1979) A method for mapping the dense and sparse regions of a forest stand. Applied Statistics 28, 14–19.
Cox, T.F. and Lewis, T. (1976) A conditioned distance ratio method for analysing spatial patterns. Biometrika 63, 483–492.
Diggle, P.J. (1979a) The detection of random heterogeneity in plant populations. Biometrics 33, 390–394.
Diggle, P.J. (1979b) Statistical methods for spatial point patterns in ecology. Spatial and temporal analysis in ecology. R.M. Cormack and J.K. Ord (eds.) Fairland: International Co-operative Publishing House. pages 95–150.
Diggle, P.J. (1981) Some graphical methods in the analysis of spatial point patterns. In Interpreting Multivariate Data. V. Barnett (eds.) John Wiley and Sons. Pages 55–73.
Diggle, P.J. (1983) Statistical analysis of spatial point patterns. Academic Press.
Gerrard, D.J. (1969) Competition quotient: a new measure of the competition affecting individual forest trees. Research Bulletin 20, Agricultural Experiment Station, Michigan State University.
Lotwick, H.W. (1981) Spatial stochastic point processes. PhD thesis, University of Bath, UK.
Ord, J.K. (1978) How many trees in a forest? Mathematical Scientist 3, 23–33.
data(lansing) if(require(spatstat.geom)) { plot(lansing) summary(lansing) plot(split(lansing)) plot(split(lansing)$maple) ## rescale to feet (Lan <- rescale(lansing)) }
data(lansing) if(require(spatstat.geom)) { plot(lansing) summary(lansing) plot(split(lansing)) plot(split(lansing)$maple) ## rescale to feet (Lan <- rescale(lansing)) }
A window in the shape of the capital letter R, for use in demonstrations.
data(letterR)
data(letterR)
An object of class "owin"
representing the capital letter R,
in the same font as the R package logo.
See owin.object
for details of the format.
Adrian Baddeley [email protected]
Locations and sizes of Longleaf pine trees. A marked point pattern.
The data record the locations and diameters of 584 Longleaf pine (Pinus palustris) trees in a 200 x 200 metre region in southern Georgia (USA). They were collected and analysed by Platt, Evans and Rathbun (1988).
This is a marked point pattern; the mark associated with a tree is its
diameter at breast height (dbh
), a convenient measure of its size.
Several analyses have considered only the “adult” trees which
are conventionally defined as those trees with dbh
greater than or equal to 30 cm.
The pattern is regarded as spatially inhomogeneous.
data(longleaf)
data(longleaf)
An object of class "ppp"
representing the point pattern of tree locations.
Entries include
x |
Cartesian -coordinate of tree in metres |
y |
Cartesian -coordinate of tree in metres |
marks |
diameter at breast height, in centimetres. |
See ppp.object
for details of the format of a
point pattern object.
Platt, Evans and Rathbun (1988)
Platt, W. J., Evans, G. W. and Rathbun, S. L. (1988) The population dynamics of a long-lived Conifer (Pinus palustris). The American Naturalist 131, 491–525.
Rathbun, S. L. and Cressie, N. (1994) A space-time survival point process for a longleaf pine forest in southern Georgia. Journal of the American Statistical Association 89, 1164–1173.
data(longleaf) if(require(spatstat.geom)) { plot(longleaf) plot(cut(longleaf, breaks=c(0,30,Inf), labels=c("Sapling","Adult"))) }
data(longleaf) if(require(spatstat.geom)) { plot(longleaf) plot(cut(longleaf, breaks=c(0,30,Inf), labels=c("Sapling","Adult"))) }
A bivariate inhomogeneous point pattern, giving the locations of the centres of two types of cells in a cross-section of the gastric mucosa of a rat.
data(mucosa)
data(mucosa)
An object of class "ppp"
, see ppp.object
.
This is a multitype point pattern with two types of points,
ECL
and other
.
This point pattern dataset gives the locations of cell centres in a cross-section of the gastric mucosa (mucous membrane of the stomach) of a rat. The rectangular observation window has been scaled to unit width. The lower edge of the window is closest to the outside of the stomach.
The cells are classified into two types: ECL cells (enterochromaffin-like cells) and other cells. There are 86 ECL cells and 807 other cells in the dataset. ECL cells are a type of neuroendocrine cell which synthesize and secrete histamine. One hypothesis of interest is whether the spatially-varying intensities of ECL cells and other cells are proportional.
The data were originally collected by Dr Thomas Berntsen. The data were discussed and analysed in Moller and Waagepetersen (2004, pp. 2, 169).
The associated object mucosa.subwin
is the smaller window
to which the data were restricted for analysis by Moller and
Waagepetersen.
The scale of spatial coordinates is unknown (R. Waagepetersen, personal communication).
Dr Thomas Berntsen and Prof Rasmus Waagepetersen.
Moller, J. and Waagepetersen, R. (2004). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC.
if(require(spatstat.geom)) { plot(mucosa, chars=c(1,3), cols=c("red", "green")) plot(mucosa.subwin, add=TRUE, lty=3) }
if(require(spatstat.geom)) { plot(mucosa, chars=c(1,3), cols=c("red", "green")) plot(mucosa.subwin, add=TRUE, lty=3) }
Data recording the spatial locations of gold deposits and associated geological features in the Murchison area of Western Australia. Extracted from a large scale (1:500,000) study of the Murchison area by the Geological Survey of Western Australia (Watkins and Hickman, 1990). The features recorded are
the locations of gold deposits;
the locations of geological faults;
the region that contains greenstone bedrock.
The study region is contained in a kilometre
rectangle. At this scale, gold deposits are points, i.e. their spatial
extent is negligible.
Gold deposits in this region occur only in greenstone bedrock.
Geological faults can be observed reliably only within the same
region. However, some faults have been extrapolated
(by geological “interpretation”) outside the greenstone boundary
from information observed in the greenstone region.
Deposit locations were extracted from the Minedex database (Geological Survey of Western Australia, n.d.) and include deposits of all sizes. The fault geometry and greenstone boundaries were mapped and collated by Watkins and Hickman (1990).
These data were analysed by Foxall and Baddeley (2002) and Brown et al (2002); see also Groves et al (2000), Knox-Robinson and Groves (1997), Baddeley, Rubak and Turner (2015) and Baddeley (2019). The main aim is to predict the intensity of the point pattern of gold deposits from the more easily observable fault pattern.
data(murchison)
data(murchison)
murchison
is a list with the following entries:
a point pattern (object of class "ppp"
)
representing the point pattern of gold deposits.
See ppp.object
for details of the format.
a line segment pattern (object of class "psp"
)
representing the geological faults.
See psp.object
for details of the format.
the greenstone bedrock region.
An object of class "owin"
. Consists of multiple
irregular polygons with holes.
All coordinates are given in metres.
Data were kindly provided by Dr Carl Knox-Robinson of the Department of Geology and Geophysics, University of Western Australia. Permission to use the data is granted by Dr Tim Griffin, Geological Survey of Western Australia and by Dr Knox-Robinson. Please make appropriate acknowledgement to Watkins and Hickman (1990) and the Geological Survey of Western Australia.
Baddeley, A. (2018) A statistical commentary on mineral prospectivity analysis. In Daya Sagar, B.S., Cheng, Q. and Agterberg, F.P. (eds.) Handbook of Mathematical Geosciences: Fifty Years of IAMG. International Association for Mathematical Geosciences. Chapter 2, pages 25–65.
Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press.
Brown, W.M., Gedeon, T.D., Baddeley, A.J. and Groves, D.I. (2002) Bivariate J-function and other graphical statistical methods help select the best predictor variables as inputs for a neural network method of mineral prospectivity mapping. In U. Bayer, H. Burger and W. Skala (eds.) IAMG 2002: 8th Annual Conference of the International Association for Mathematical Geology, Volume 1, 2002. International Association of Mathematical Geology. Pages 257–268.
Foxall, R. and Baddeley, A. (2002) Nonparametric measures of association between a spatial point process and a random set, with geological applications. Applied Statistics 51, 165–182.
Geological Survey of Western Australia (n.d.) MINEDEX database of Mines and Mineral Deposits. https://www.dmp.wa.gov.au/Mines-and-mineral-deposits-1502.aspx.
Groves, D.I., Goldfarb, R.J., Knox-Robinson, C.M., Ojala, J., Gardoll, S, Yun, G.Y. and Holyland, P. (2000) Late-kinematic timing of orogenic gold deposits and significance for computer-based exploration techniques with emphasis on the Yilgarn Block, Western Australia. Ore Geology Reviews, 17, 1–38.
Knox-Robinson, C.M. and Groves, D.I. (1997) Gold prospectivity mapping using a geographic information system (GIS), with examples from the Yilgarn Block of Western Australia. Chronique de la Recherche Miniere 529, 127–138.
Watkins, K.P. and Hickman, A.H. (1990)
Geological evolution and mineralization of the Murchison Province,
Western Australia.
Bulletin 137, Geological Survey of Western Australia. 267 pages.
Published by Department of Mines, Western Australia, 1990.
Available online from Department of Industry and Resources,
State Government of Western Australia, www.doir.wa.gov.au
if(require(spatstat.geom)) { if(interactive()) { data(murchison) plot(murchison$greenstone, main="Murchison data", col="lightgreen") plot(murchison$gold, add=TRUE, pch="+",col="blue") plot(murchison$faults, add=TRUE, col="red") } ## rescale to kilometres Mur <- solapply(murchison, rescale, s=1000, unitname="km") }
if(require(spatstat.geom)) { if(interactive()) { data(murchison) plot(murchison$greenstone, main="Murchison data", col="lightgreen") plot(murchison$gold, add=TRUE, pch="+",col="blue") plot(murchison$faults, add=TRUE, col="red") } ## rescale to kilometres Mur <- solapply(murchison, rescale, s=1000, unitname="km") }
Point patterns created from yearly records, provided by the New Brunswick Department of Natural Resources, of all fires falling under their jurisdiction for the years 1987 to 2003 inclusive (with the year 1988 omitted until further notice).
data(nbfires)
data(nbfires)
Executing data(nbfires)
gives access to four objects:
nbfires
, nbw.rect
, nbw.seg
and nbfires.extra
.
The object nbfires
is a marked point pattern (an object of
class "ppp"
) consisting of all of the fires in the years
1987 to 2003 inclusive, with the omission of 1988. The marks
consist of a data frame of auxiliary information about the fires;
see Details. Patterns for individual years can be extracted
using the function split.ppp()
. (See Examples.)
The object nbw.rect
is a rectangular window which covers
central New Brunswick. It is provided for use in illustrative and
‘practice’ calculations inasmuch as the use of a rectangular
window simplifies some computations considerably.
The object nbw.seg
is a line segment pattern (object of class
"psp"
) consisting of all the boundary segments of the polygonal window
of New Brunswick. The segments are classified into different types of
boundary by marks(nbw.seg)
.
This is a data frame with three columns:
The column type
describes the
physical type of the border. It is a factor with levels
"land"
(land border),
"river"
(river border),
"coast"
(coast of the mainland)
and "island"
(coast of the 5 islands).
To plot this classification, type plot(nbw.seg)
.
The column share
specifies the territory which
shares the border with New Brunswick. It is a factor with
levels "Quebec"
, "NovaScotia"
, "USA"
and "water"
.
To plot this classification, type plot(nbw.seg,which.marks="share")
.
The column full
specifies both the physical type of border
and the adjacent territory. It is a factor with levels
"coast"
,
"island"
,
"landNovaScotia"
,
"landQuebec"
,
"riverQuebec"
,
"landUSA"
,
"riverUSAnorth"
,
"riverUSAsouth"
.
To plot this classification, type plot(nbw.seg,which.marks="full")
.
For conformity with other datasets, nbfires.extra
is a list
containing all the supplementary data. It contains copies of
nbw.rect
and nbw.seg
.
The coordinates of the fire locations were provided in terms of
latitude and longitude, to the nearest minute of arc. These were
converted to New Brunswick stereographic projection coordinates
(Thomson, Mephan and Steeves, 1977) which was the coordinate
system in which the map of New Brunswick — which constitutes the
observation window for the pattern — was obtained. The conversion
was done using a C
program kindly provided by Jonathan
Beaudoin of the Department of Geodesy and Geomatics, University of
New Brunswick.
Finally the data and window were rescaled since the use of the New Brunswick stereographic projection coordinate system resulted in having to deal with coordinates which are expressed as very large integers with a bewildering number of digits. Amongst other things, these huge numbers tended to create very untidy axis labels on graphs. The width of the bounding box of the window was made equal to 1000 units. In addition the lower left hand corner of this bounding box was shifted to the origin. The height of the bounding box was changed proportionately, resulting in a value of approximately 959.
In the final dataset nbfires
, one coordinate unit is equivalent to
0.403716 kilometres. To convert the data to kilometres,
use rescale(nbfires)
.
The window for the fire patterns comprises 6 polygonal components, consisting of mainland New Brunswick and the 5 largest islands. Some lakes which should form holes in the mainland component are currently missing; this problem may be remedied in future releases. The window was formed by ‘simplifying’ the map that was originally obtained. The simplification consisted in reducing (using an interactive visual technique) the number of polygon edges in each component. For instance the number of edges in the mainland component was reduced from over 138,000 to 500.
For some purposes it is probably better to use a discretized (mask type) window. See Examples.
Because of the coarseness of the coordinates of the original data (1 minute of longitude is approximately 1 kilometer at the latitude of New Brunswick), data entry errors, and the simplification of the observation window, many of the original fire locations appeared to be outside of the window. This problem was addressed by shifting the location of the ‘outsider’ points slightly, or deleting them, as seemed appropriate.
Note that the data contain duplicated points (two points at the
same location). To determine which points are duplicates,
use duplicated.ppp
.
To remove the duplication, use unique.ppp
.
The columns of the data frame comprising the marks of
nbfires
are:
This a factor with levels 1987, 1989, ..., 2002, 2003. Note that 1988 is not present in the levels.
A factor with levels forest
,
grass
, dump
, and other
.
The discovery date of the fire, which is the
nearest possible surrogate for the starting time
of the fire. This is an object of class POSIXct
and gives the starting discovery time of the fire to
the nearest minute.
The discovery date and time of the fire, expressed in ‘Julian days’, i.e. as a decimal fraction representing the number of days since the beginning of the year (midnight 31 December).
The date on which the fire was judged to be
‘out’. This is an object of class POSIXct
and gives the
‘out’ time of the fire to the nearest minute.
The date and time at which the fire was judged to be ‘out’, expressed in Julian days.
General cause of the fire. This is a factor with
levels unknown
, rrds
(railroads), misc
(miscellaneous), ltning
(lightning), for.ind
(forest industry), incend
(incendiary), rec
(recreation), resid
(resident), and oth.ind
(other industry). Causes unknown
, ltning
, and
incend
are supposedly designated as ‘final’ by the New Brunswick
Department of Natural Resources, meaning (it seems) “that's
all there is to it”. Other causes are apparently intended
to be refined by being combined with “source of ignition”.
However cross-tabulating cause
with ign.src
—
see below — reveals that very often these three ‘causes’
are associated with an “ignition source” as well.
Source of ignition, a factor with levels
cigs
(cigarette/match/pipe/ashes), burn.no.perm
(burning without a permit), burn.w.perm
(burning with a
permit), presc.burn
(prescribed burn), wood.spark
(wood spark), mach.spark
(machine spark), campfire
,
chainsaw
, machinery
, veh.acc
(vehicle
accident), rail.acc
(railroad accident), wheelbox
(wheelbox on railcars), hot.flakes
(hot flakes off
railcar wheels), dump.fire
(fire escaping from a dump),
ashes
(ashes, briquettes, burning garbage, etc.)
The final size of the fire (area burned) in hectares, to the nearest 10th hectare.
Note that due to data entry errors some of the “out dates” and
“out times” in the original data sets were actually earlier
than the corresponding “discovery dates” and “discover times”.
In such cases all corresponding entries of the marks data frame
(i.e. dis.date
, dis.julian
, out.date
, and
out.julian
) were set equal to NA
. Also, some of the
dates and times were missing (equal to NA
) in the original
data sets.
The ‘ignition source’ data were given as integer codes
in the original data sets. The code book that I obtained
gave interpretations for codes 1, 2, ..., 15. However
the actually also contained codes of 0, 16, 17, 18, and in
one instance 44. These may simply be data entry errors.
These uninterpretable values were assigned the level
unknown
. Many of the years had most, or sometimes
all, of the ignition source codes equal to 0 (hence turning
out as unknown
, and many of the years had many
missing values as well. These were also assigned the
level unknown
. Of the 7108 fires in nbfires
,
4354 had an unknown
ignition source. This variable
is hence unlikely to be very useful.
There are also anomalies between cause
and ign.src
,
e.g. cause
being unknown
but ign.src
being cigs
, burn.no.perm
, mach.spark
,
hot.flakes
, dump.fire
or ashes
. Particularly
worrisome is the fact that the cause ltning
(!!!) is
associate with sources of ignition cigs
, burn.w.perm
,
presc.burn
, and wood.spark
.
The data were kindly provided by the New Brunswick Department of Natural Resources. Special thanks are due to Jefferey Betts for a great deal of assistance.
Turner, Rolf.
Point patterns of forest fire locations.
Environmental and Ecological Statistics
16 (2009) 197 – 223, DOI:10.1007/s10651-007-0085-1
.
Thomson, D. B., Mephan, M. P., and Steeves, R. R. (1977)
The stereographic double projection.
Technical Report 46, University of New Brunswick,
Fredericton, N. B., Canada
URL: gge.unb.ca/Pubs/Pubs.html
.
if(interactive()) { if(require(spatstat.geom)) { # Get the year 2000 data. X <- split(nbfires,"year") Y.00 <- X[["2000"]] # Plot all of the year 2000 data, marked by fire type. plot(Y.00,which.marks="fire.type") # Cut back to forest and grass fires. Y.00 <- Y.00[marks(Y.00)$fire.type %in% c("forest","grass")] # Plot the year 2000 forest and grass fires marked by fire duration time. stt <- marks(Y.00)$dis.julian fin <- marks(Y.00)$out.julian marks(Y.00) <- cbind(marks(Y.00),dur=fin-stt) plot(Y.00,which.marks="dur") # Look at just the rectangular subwindow (superimposed on the entire window). nbw.mask <- as.mask(Window(nbfires), dimyx=500) plot(nbw.mask, col=c("green", "white")) plot(Window(nbfires), border="red", add=TRUE) plot(Y.00[nbw.rect],use.marks=FALSE,add=TRUE) plot(nbw.rect,add=TRUE,border="blue") if(require(spatstat.explore)) { # Look at the K function for the year 2000 forest and grass fires. K.00 <- Kest(Y.00) plot(K.00) } # Rescale to kilometres NBF <- rescale(nbfires) } }
if(interactive()) { if(require(spatstat.geom)) { # Get the year 2000 data. X <- split(nbfires,"year") Y.00 <- X[["2000"]] # Plot all of the year 2000 data, marked by fire type. plot(Y.00,which.marks="fire.type") # Cut back to forest and grass fires. Y.00 <- Y.00[marks(Y.00)$fire.type %in% c("forest","grass")] # Plot the year 2000 forest and grass fires marked by fire duration time. stt <- marks(Y.00)$dis.julian fin <- marks(Y.00)$out.julian marks(Y.00) <- cbind(marks(Y.00),dur=fin-stt) plot(Y.00,which.marks="dur") # Look at just the rectangular subwindow (superimposed on the entire window). nbw.mask <- as.mask(Window(nbfires), dimyx=500) plot(nbw.mask, col=c("green", "white")) plot(Window(nbfires), border="red", add=TRUE) plot(Y.00[nbw.rect],use.marks=FALSE,add=TRUE) plot(nbw.rect,add=TRUE,border="blue") if(require(spatstat.explore)) { # Look at the K function for the year 2000 forest and grass fires. K.00 <- Kest(Y.00) plot(K.00) } # Rescale to kilometres NBF <- rescale(nbfires) } }
The data give the locations of trees in a forest plot.
They were collected by Mark and Esler (1970) and were extracted and analysed by Ripley (1981, pp. 169-175). They represent the positions of 86 trees in a forest plot approximately 140 by 85 feet.
Ripley discarded from his analysis the eight trees at the right-hand edge of the plot (which appear to be part of a planted border) and trimmed the window by a 5-foot margin accordingly.
data(nztrees)
data(nztrees)
An object of class "ppp"
representing the point pattern of tree locations.
The Cartesian coordinates are in feet.
See ppp.object
for details of the format of a
point pattern object.
To trim a 5-foot margin off the window, type
nzsub <- nztrees[owin(c(0,148),c(0,95)) ]
Mark and Esler (1970), Ripley (1981).
Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.
Mark, A.F. and Esler, A.E. (1970) An assessment of the point-centred quarter method of plotless sampling in some New Zealand forests. Proceedings of the New Zealand Ecological Society 17, 106–110.
These data give the three-dimensional locations of osteocyte lacunae observed in rectangular volumes of solid bone using a confocal microscope.
There were four samples of bone, and ten regions were mapped in each bone, yielding 40 spatial point patterns. The data can be regarded as replicated observations of a three-dimensional point process, nested within bone samples.
data(osteo)
data(osteo)
A hyperframe
with the following columns:
id |
character string identifier of bone sample |
shortid |
last numeral in id |
brick |
serial number (1 to 10) of sampling volume within this bone sample |
pts |
three dimensional point pattern (class pp3 ) |
depth |
the depth of the brick in microns |
These data are three-dimensional point patterns representing the positions of osteocyte lacunae, holes in bone which were occupied by osteocytes (bone-building cells) during life.
Observations were made on four different skulls of Macaque monkeys iusing a three-dimensional microscope. From each skull, observations were collected in 10 separate sampling volumes. In all, there are 40 three-dimensional point patterns in the dataset.
The data were collected in 1984 by A. Baddeley, A. Boyde, C.V. Howard and S. Reid (see references) using the tandem-scanning reflected light microscope (TSRLM) at University College London. This was one of the first optical confocal microscopes available.
Each point pattern dataset gives the coordinates
(in microns) of all points visible in a
three-dimensional rectangular box (“brick”) of dimensions
microns,
where
varies.
The
coordinate is depth into the bone
(depth of the focal plane of the confocal microscope); the
plane is parallel to the exterior surface of the bone;
the relative orientation of the
and
axes is not important.
The bone samples were three intact skulls and one skull cap, all originally identified as belonging to the macaque monkey Macaca fascicularis, from the collection of the Department of Anatomy, University of London. Later analysis (Baddeley et al, 1993) suggested that the skull cap, given here as the first animal, was a different subspecies, and this was confirmed by anatomical inspection.
The following extract from Baddeley et al (1987) describes the sampling procedure.
The parietal bones of three fully articulated adult Macaque monkey
(Macaca fascicularis) skulls from the collection of
University College London were used. The right parietal bone was
examined, in each case, approximately 1 cm lateral to the sagittal
suture and 2 cm posterior to the coronal suture. The skulls were
mounted on plasticine on a moving stage placed beneath the TSRLM.
Immersion oil was applied and a , NA 1.0 oil immersion
objective lens (Lomo) was focussed at 10 microns below the cranial
surface. The TV image was produced by a Panasonic WB 1850/B camera
on a Sony PVM 90CE TV monitor.
A graduated rectangular counting frame
mm (representing
microns in real units)
was marked on a Perspex overlay
and fixed to the screen. The area of tissue seen within the frame defined
a subfield: a guard area of 10 mm width was visible on all sides of the
frame. Ten subfields were examined, arranged approximately in
a rectangular grid pattern, with at least one field width separating
each pair of fields. The initial field position was determined randomly
by applying a randomly-generated coordinate shift to the moving stage.
Subsequent fields were attained
using the coarse controls of the microscope stage, in accordance with
the rectangular grid pattern.
For each subfield, the focal plane was racked down from its initial
10 micron depth until all visible osteocyte lacunae had been examined.
This depth was recorded. The 3-dimensional sampling volume was
therefore a rectangular box of dimensions
microns,
called a “brick”.
For each visible lacuna, the fine focus racking control was adjusted until
maximum brightness was obtained. The depth of the focal plane was then
recorded as the $z$ coordinate of the “centre point” of the
lacuna. Without moving the focal plane, the
and
coordinates of
the centre of the lacunar image were read off the graduated counting frame.
This required a subjective judgement of the position of the centre of the
2-dimensional image. Profiles were approximately elliptical and the centre
was considered to be well-defined. Accuracy of
the recording procedure was tested by independent repetition (by the
same operator and by different operators) and found to be reproducible
to plus or minus 2 mm on the screen.
A lacuna was counted only if its coordinates lay inside
the
mm counting frame.
Data were collected by Adrian Baddeley [email protected].
Baddeley, A.J., Howard, C.V, Boyde, A. and Reid, S.A. (1987) Three dimensional analysis of the spatial distribution of particles using the tandem-scanning reflected light microscope. Acta Stereologica 6 (supplement II) 87–100.
Baddeley, A.J., Moyeed, R.A., Howard, C.V. and Boyde, A. (1993) Analysis of a three-dimensional point pattern with replication. Applied Statistics 42 (1993) 641–668.
Howard, C.V. and Reid, S. and Baddeley, A.J. and Boyde, A. (1985) Unbiased estimation of particle density in the tandem-scanning reflected light microscope. Journal of Microscopy 138 203–212.
data(osteo) if(require(spatstat.geom)) { osteo if(interactive()) { plot(osteo$pts[[1]], main="animal 1, brick 1") ape1 <- osteo[osteo$shortid==4, ] plot(ape1, tick.marks=FALSE) with(osteo, intensity(pts)) plot(with(ape1, K3est(pts))) } }
data(osteo) if(require(spatstat.geom)) { osteo if(interactive()) { plot(osteo$pts[[1]], main="animal 1, brick 1") ape1 <- osteo[osteo$shortid==4, ] plot(ape1, tick.marks=FALSE) with(osteo, intensity(pts)) plot(with(ape1, K3est(pts))) } }
This dataset is a point pattern of adult and juvenile Kimboto trees (Pradosia cochlearia or P. ptychandra) recorded at Paracou in French Guiana. See Flores (2005).
The dataset paracou
is a point pattern
(object of class "ppp"
) containing the spatial coordinates
of each tree, marked by age (a factor with levels adult
and
juvenile
. The survey region is a rectangle
approximately 400 by 525 metres. Coordinates are given in metres.
Note that the data contain duplicated points (two points at the
same location). To determine which points are duplicates,
use duplicated.ppp
.
To remove the duplication, use unique.ppp
.
data(paracou)
data(paracou)
Data kindly contributed by Olivier Flores. All data belong to CIRAD https://www.cirad.fr and UMR EcoFoG http://www.ecofog.gf and are included in spatstat with permission. Original data sources: juvenile and some adult trees collected by Flores (2005); adult tree data sourced from CIRAD Paracou experimental plots dataset (2003 campaign).
Flores, O. (2005) Determinisme de la regeneration chez quinze especes d'arbres tropicaux en foret guyanaise: les effets de l'environnement et de la limitation par la dispersion. PhD Thesis, University of Montpellier 2, Montpellier, France.
Picard, N, Bar-Hen, A., Mortier, F. and Chadoeuf, J. (2009) The multi-scale marked area-interaction point process: a model for the spatial pattern of trees. Scandinavian Journal of Statistics 36 23–41
if(require(spatstat.geom)) { plot(paracou, cols=2:3, chars=c(16,3)) }
if(require(spatstat.geom)) { plot(paracou, cols=2:3, chars=c(16,3)) }
The data record the locations of 108 Ponderosa Pine (Pinus ponderosa) trees in a 120 metre square region in the Klamath National Forest in northern California, published as Figure 2 of Getis and Franklin (1987).
Franklin et al. (1985) determined the locations of approximately 5000
trees from United States Forest Service aerial photographs and
digitised them for analysis. Getis and Franklin (1987) selected a 120
metre square subregion that appeared to exhibit clustering. This subregion
is the ponderosa
dataset.
In principle these data are equivalent to Figure 2 of Getis and Franklin (1987) but they are not exactly identical; some of the spatial locations appear to be slightly perturbed.
The data points identified as A, B, C on Figure 2 of Getis and Franklin (1987) correspond to points numbered 42, 7 and 77 in the dataset respectively.
data(ponderosa)
data(ponderosa)
Typing data(ponderosa)
gives access to two objects,
ponderosa
and ponderosa.extra
.
The dataset ponderosa
is a spatial point pattern
(object of class "ppp"
)
representing the point pattern of tree positions.
See ppp.object
for details of the format.
Spatial coordinates are given in metres.
The dataset ponderosa.extra
is a list containing supplementary
data. The entry id
contains the index numbers of the
three special points A, B, C in the point pattern. The entry
plotit
is a function that can be called to produce a nice plot
of the point pattern.
Prof. Janet Franklin, University of California, Santa Barbara
Franklin, J., Michaelsen, J. and Strahler, A.H. (1985) Spatial analysis of density dependent pattern in coniferous forest stands. Vegetatio 64, 29–36.
Getis, A. and Franklin, J. (1987) Second-order neighbourhood analysis of mapped point patterns. Ecology 68, 473–477.
data(ponderosa) if(require(spatstat.geom)) { ponderosa.extra$plotit() }
data(ponderosa) if(require(spatstat.geom)) { ponderosa.extra$plotit() }
Point patterns giving the locations of pyramidal neurons in micrographs from area 24, layer 2 of the cingulate cortex in the human brain. There is one point pattern from each of 31 human subjects. The subjects are divided into three groups: controls (12 subjects), schizoaffective (9 subjects) and schizophrenic (10 subjects).
Each point pattern is recorded in a unit square region; the unit of measurement is unknown.
These data were introduced and analysed by Diggle, Lange and Benes (1991).
data(pyramidal)
data(pyramidal)
pyramidal
is a hyperframe with 31 rows, one row for each
subject. It has a column named
Neurons
containing the point patterns of neuron locations,
and a column named group
which is a factor with levels
"control", "schizoaffective", "schizophrenic"
identifying the grouping of subjects.
Peter Diggle's website.
Diggle, P.J., Lange, N. and Benes, F.M. (1991). Analysis of variance for replicated spatial point patterns in clinical neuroanatomy. Journal of the American Statistical Association 86, 618–625.
if(require(spatstat.geom)) { pyr <- pyramidal pyr$grp <- abbreviate(pyramidal$group, minlength=7) plot(pyr, quote(plot(Neurons, pch=16, main=grp)), main="Pyramidal Neurons") }
if(require(spatstat.geom)) { pyr <- pyramidal pyr$grp <- abbreviate(pyramidal$group, minlength=7) plot(pyr, quote(plot(Neurons, pch=16, main=grp)), main="Pyramidal Neurons") }
The data represent the locations of 62 seedlings and saplings of California Giant Redwood (Sequoiadendron giganteum) recorded in a square sampling region. They originate from Strauss (1975); the present data are a subset extracted by Ripley (1977) in a subregion that has been rescaled to a unit square. (The original physical size of the unit is approximately 63.1 feet).
Two versions of this dataset are provided: redwood
and redwood3
.
The dataset redwood
was obtained from the spatial package.
In this version the coordinates are given to 2 decimal places
(multiples of 0.01 units) except for one point which has an coordinate
of 0.999, presumably to ensure that it is properly inside the window.
The dataset redwood3
was obtained from Peter Diggle's webpage.
In this version the coordinates are given to 3 decimal places
(multiples of 0.001 units). The ordering of the points is not the same
in the two datasets.
There are many further analyses of this dataset. It is often used as a canonical example of a clustered point pattern (see e.g. Diggle, 1983).
The original, full redwood dataset is supplied in the spatstat.data
package as redwoodfull
.
data(redwood)
data(redwood)
An object of class "ppp"
representing the point pattern of tree locations.
The window has been rescaled to the unit square.
See ppp.object
for details of the format of a
point pattern object.
Original data of Strauss (1975), subset extracted by Ripley (1977). Data obtained from Ripley's package spatial and from Peter Diggle's website.
Diggle, P.J. (1983) Statistical analysis of spatial point patterns. Academic Press.
Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B 39, 172–212.
Strauss, D.J. (1975) A model for clustering. Biometrika 62, 467–475.
These data represent the locations of 195 seedlings and saplings of California Giant Redwood (Sequoiadendron giganteum) in a square sampling region.
They were described and analysed by Strauss (1975).
This is the “full” dataset; most writers have
analysed a subset extracted by Ripley (1977)
which is available as redwood
.
Strauss (1975) divided the sampling region into two subregions I and II demarcated by a diagonal line. The spatial pattern appears to be slightly regular in region I and strongly clustered in region II.
Strauss (1975) writes: “It was felt that the seedlings would be scattered fairly randomly, except that a number of tight clusters would form around some of the redwood tree stumps present in the plot. A discontinuity in the soil, very roughly demarked by the diagonal line in the figure, was expected to cause a difference in clustering behaviour between regions I and II. Moreover, almost all the redwood stumps were situated in region II.”
The dataset redwoodfull
contains the full point pattern
of 195 trees.
The window has been rescaled to the unit square.
Its physical size is approximately 130 feet across.
The auxiliary information about the subregions is contained in
redwoodfull.extra
, which is a list with entries
rdiag
|
The coordinates of the diagonal boundary |
between regions I and II | |
regionI |
Region I as a window object |
regionII |
Region II as a window object |
regionR |
Ripley's subrectangle (approximate) |
plotit |
Function to plot the full data and auxiliary markings |
Ripley (1977) extracted a subset of these data, containing 62 points,
lying within a square subregion which overlaps regions I and II.
He rescaled that subset to the unit square.
This subset has been re-analysed many times,
and is the dataset usually known as
“the redwood data” in the spatial statistics literature.
The exact dataset used by Ripley is supplied in the spatstat
library as redwood
.
The approximate position of the square chosen by Ripley
within the redwoodfull
pattern
is indicated by the window redwoodfull.extra$regionR
.
There are some minor inconsistencies with
redwood
since it originates from a different digitisation.
data(redwoodfull)
data(redwoodfull)
The dataset redwoodfull
is an object of class "ppp"
representing the point pattern of tree locations.
See ppp.object
for details of the format of a
point pattern object.
The window has been rescaled to the unit square.
Its physical size is approximately 128 feet across.
The dataset redwoodfull.extra
is a list with entries
rdiag
|
coordinates of endpoints of a line, |
in format list(x=numeric(2),y=numeric(2)) |
|
regionI |
a window object |
regionII |
a window object |
regionR |
a window object |
plotit |
Function with no arguments |
Strauss (1975). The plot of the data published by Strauss (1975) was scanned and digitised by Sandra Pereira, University of Western Australia, 2002.
Diggle, P.J. (1983) Statistical analysis of spatial point patterns. Academic Press.
Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B 39, 172–212.
Strauss, D.J. (1975) A model for clustering. Biometrika 62, 467–475.
data(redwoodfull) if(require(spatstat.geom)) { plot(redwoodfull) redwoodfull.extra$plotit() # extract the pattern in region II redwoodII <- redwoodfull[, redwoodfull.extra$regionII] }
data(redwoodfull) if(require(spatstat.geom)) { plot(redwoodfull) redwoodfull.extra$plotit() # extract the pattern in region II redwoodII <- redwoodfull[, redwoodfull.extra$regionII] }
This dataset contains the point patterns
used as examples in the paper of Baddeley et al (2005).
[Figure 2 is already available in spatstat.data
as the copper
dataset.]
R code is also provided to reproduce all
the Figures displayed in Baddeley et al (2005).
The component plotfig
is a function, which can be called
with a numeric or character argument specifying the Figure or Figures
that should be plotted. See the Examples.
data(residualspaper)
data(residualspaper)
residualspaper
is a list with the following components:
The locations of Japanese pine seedlings and saplings
from Figure 1 of the paper.
A point pattern (object of class "ppp"
).
The Chorley-Ribble data from Figure 3 of the paper.
A list with three components, lung
, larynx
and incin
. Each is a matrix with 2 columns
giving the coordinates of the lung cancer cases,
larynx cancer cases, and the incinerator, respectively.
Coordinates are Eastings and Northings in km.
The synthetic dataset in Figure 4 (a) of the paper.
The synthetic dataset in Figure 4 (b) of the paper.
The synthetic dataset in Figure 4 (c) of the paper.
The covariate displayed in Figure 11. A pixel image (object of
class "im"
) whose pixel values are distances to the
nearest line segment in the copper
data.
A function which will compute and plot
any of the Figures from the paper. The argument of
plotfig
is either a numeric vector or a character vector,
specifying the Figure or Figures to be plotted. See the Examples.
Figure 1: Prof M. Numata. Data kindly supplied by Professor Y. Ogata with kind permission of Prof M. Tanemura.
Figure 3: Professor P.J. Diggle (rescaled by Adrian Baddeley [email protected])
Figure 4 (a,b,c): Adrian Baddeley [email protected]
Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005) Residual analysis for spatial point processes. Journal of the Royal Statistical Society, Series B 67, 617–666.
if(FALSE) { data(residualspaper) if(require(spatstat.model)) { X <- residualspaper$Fig4a summary(X) plot(X) # reproduce all Figures residualspaper$plotfig() # reproduce Figures 1 to 10 residualspaper$plotfig(1:10) # reproduce Figure 7 (a) residualspaper$plotfig("7a") } }
if(FALSE) { data(residualspaper) if(require(spatstat.model)) { X <- residualspaper$Fig4a summary(X) plot(X) # reproduce all Figures residualspaper$plotfig() # reproduce Figures 1 to 10 residualspaper$plotfig(1:10) # reproduce Figure 7 (a) residualspaper$plotfig("7a") } }
A point pattern recording the sky positions of 4215 galaxies in the Shapley Supercluster.
data(shapley)
data(shapley)
shapley
is an object of class "ppp"
representing the point pattern of galaxy locations
(see ppp.object
).
shapley.extra
is a list containing additional data
described under Notes.
This dataset comes from a survey by Drinkwater et al (2004) of the Shapley Supercluster, one of the most massive concentrations of galaxies in the local universe. The data give the sky positions of 4215 galaxies observed using the FLAIR-II spectrograph on the UK Schmidt Telescope (UKST). They were kindly provided by Dr Michael Drinkwater through the Centre for Astrostatistics at Penn State University.
Sky positions are given using the coordinates Right Ascension (degrees from 0 to 360) and Declination (degrees from -90 to 90).
The point pattern has three mark variables:
Galaxy magnitude (a negative logarithmic measure of visible brightness).
Recession velocity (km/sec) inferred from redshift, with corrections applied.
Estimated standard error for V
.
The region covered by the survey was approximately the UKST's standard quadrilateral survey fields 382 to 384 and 443 to 446. However, a few of the galaxy positions lie outside these fields.
The point pattern dataset shapley
consists of all 4215 galaxy
locations. The observation window for this pattern is a
dilated copy of the convex hull of the galaxy positions,
constructed so that all galaxies lie within the window.
Note that the data contain duplicated points (two points at the
same location). To determine which points are duplicates,
use duplicated.ppp
.
To remove the duplication, use unique.ppp
.
The auxiliary dataset shapley.extra
contains
the following components:
UKSTfields
a list of seven windows
(objects of class "owin"
) giving the UKST standard survey
fields.
UKSTdomain
the union of these seven fields,
an object of class "owin"
.
plotit
a function (called without arguments) that will plot the data and the survey fields in the conventional astronomical presentation, in which Right Ascension is converted to hours and minutes (1 hour equals 15 degrees) and Right Ascension decreases as we move to the right of the plot.
M.J. Drinkwater, Department of Physics, University of Queensland
Drinkwater, M.J., Parker, Q.A., Proust, D., Slezak, E.
and Quintana, H. (2004)
The large scale distribution of galaxies in the Shapley
Supercluster.
Publications of the Astronomical Society of Australia
21, 89-96. DOI 10.1071/AS03057
data(shapley) if(require(spatstat.geom)) { shapley.extra$plotit(main="Shapley Supercluster") }
data(shapley) if(require(spatstat.geom)) { shapley.extra$plotit(main="Shapley Supercluster") }
The simba
dataset contains simulated data from an
experiment with a ‘control’ group and a ‘treatment’ group, each
group containing 5 experimental units.
The responses in the experiment are point patterns.
The responses in the control group are independent realisations of a Poisson point process with intensity 80.
The responses in the treatment group are independent realisations of
a Strauss process with activity parameter ,
interaction parameter
and
interaction radius
in the unit square.
data(simba)
data(simba)
simba
is a hyperframe with 10 rows, and columns named:
Points
containing the point patterns
group
factor identifying the experimental group,
with levels control
and treatment
).
Simulated data, generated by Adrian Baddeley [email protected].
This point pattern data set was simulated (using the Metropolis-Hastings algorithm) from a model fitted to the Numata Japanese black pine data set referred to in Baddeley and Turner (2000).
data(simdat)
data(simdat)
An object of class "ppp"
in a square window of size 10 by 10 units.
See ppp.object
for details of the format of a
point pattern object.
Rolf Turner [email protected]
Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.
A simple, artificially created, example of a linear network.
data(simplenet)
data(simplenet)
simplenet
is an object of class "linnet"
.
Created by Adrian Baddeley [email protected].
Data recording the locations of small spider webs on the network of mortar lines of a brick wall.
data("spiders")
data("spiders")
Object of class "lpp"
representing a pattern of points
on a linear network. Spatial coordinates are expressed in millimetres.
The data give the positions of 48 webs of the urban wall spider Oecobius navus on the mortar lines of a brick wall, recorded by Voss (1999) and manually digitised by Mark Handcock. The mortar spaces provide the only opportunity for constructing webs (Voss 1999; Voss et al 2007) so this is a pattern of points on a network of lines.
The habitat preferences of this species were studied in detail by Voss et al (2007). Questions of interest include evidence for non-uniform density of webs and for interaction between nearby individuals.
Observations were made inside a square quadrat of side length 1.125 metres.
The original hand-drawn map was digitised manually by Mark
S. Handcock, and reformatted as a spatstat
object by
Ang Qi Wei.
The dataset spiders
is an object of class "lpp"
(point pattern on a linear network). Coordinates are given in millimetres.
The linear network has 156 vertices and a total length of 20.22 metres.
Please cite Voss et al (2007) with any use of these data.
Dr Sasha Voss. Coordinates manually recorded by M.S. Handcock and formatted by Q.W. Ang.
Please cite Voss et al (2007) with any use of these data.
Ang, Q.W. (2010) Statistical methodology for events on a network. Master's thesis, School of Mathematics and Statistics, University of Western Australia.
Voss, S. (1999) Habitat preferences and spatial dynamics of the urban wall spider: Oecobius annulipes Lucas. Honours Thesis, Department of Zoology, University of Western Australia.
Voss, S., Main, B.Y. and Dadour, I.R. (2007) Habitat preferences of the urban wall spider Oecobius navus (Araneae, Oecobiidae). Australian Journal of Entomology 46, 261–268.
if(require(spatstat.linnet)) { plot(spiders, show.window=FALSE, pch=16) }
if(require(spatstat.linnet)) { plot(spiders, show.window=FALSE, pch=16) }
Spatial pattern of sporophores of three species of fungi around a tree.
data(sporophores)
data(sporophores)
A multitype spatial point pattern (an object of class "ppp"
with factor-valued marks indicating the species).
Spatial coordinates are given in centimetres.
Levels of the species variable are
"L laccata"
, "L pubescens"
and "Hebloma spp"
.
Ford, Mason and Pelham (1980) studied the spatial locations of sporophores of three species of mycorrhizal fungi distributed around a young birch tree in agricultural soil. The dataset given here is the spatial pattern in the fifth year after the tree was planted. The species are Laccaria laccata, Lactarius pubescens and Hebloma spp.
Data generously provided by Dr E.D. Ford. Please cite Ford et al (1980) in any use of these data.
Ford, E.D., Mason, P.A. and Pelham, J. (1980) Spatial patterns of sporophore distribution around a young birch tree in three successive years. Transactions of the British Mycological Society 75, 287–296.
if(require(spatstat.geom)) { ## reproduce Fig 1 in Ford et al (1980) plot(sporophores, chars=c(16,1,2), cex=0.6, leg.args=list(cex=1.1)) points(0,0,pch=16, cex=2) text(15,8,"Tree", cex=0.75) }
if(require(spatstat.geom)) { ## reproduce Fig 1 in Ford et al (1980) plot(sporophores, chars=c(16,1,2), cex=0.6, leg.args=list(cex=1.1)) points(0,0,pch=16, cex=2) text(15,8,"Tree", cex=0.75) }
The data give the locations of Norwegian spruce trees in a natural forest stand in Saxonia, Germany. Each tree is marked with its diameter at breast height.
data(spruces)
data(spruces)
An object of class "ppp"
representing the point pattern of tree locations
in a 56 x 38 metre sampling region. Each tree is marked
with its diameter at breast height. All values are given in metres.
See ppp.object
for details of the format of a
point pattern object. The marks are numeric.
These data have been analysed by Fiksel (1984, 1988), Stoyan et al (1987), Penttinen et al (1992) and Goulard et al (1996).
Stoyan et al (1987). Original source unknown.
Fiksel, T. (1984) Estimation of parameterized pair potentials of marked and nonmarked Gibbsian point processes. Elektron. Informationsverarb. u. Kybernet. 20, 270–278.
Fiksel, T. (1988) Estimation of interaction potentials of Gibbsian point processes. Statistics 19, 77-86
Goulard, M., S\"arkk\"a, A. and Grabarnik, P. (1996) Parameter estimation for marked Gibbs point processes through the maximum pseudolikelihood method. Scandinavian Journal of Statistics 23, 365–379.
Penttinen, A., Stoyan, D. and Henttonen, H. (1992) Marked point processes in forest statistics. Forest Science 38, 806–824.
Stoyan, D., Kendall, W.S. and Mecke, J. (1987) Stochastic Geometry and its Applications. Wiley.
if(require(spatstat.geom)) { plot(spruces) # To reproduce Goulard et al. Figure 3 # (Goulard et al: "influence zone radius equals 5 * stem diameter") # (help(plot.ppp) says: "size of symbol = diameter") plot(spruces, maxsize=10*max(spruces$marks)) plot(unmark(spruces), add=TRUE) }
if(require(spatstat.geom)) { plot(spruces) # To reproduce Goulard et al. Figure 3 # (Goulard et al: "influence zone radius equals 5 * stem diameter") # (help(plot.ppp) says: "size of symbol = diameter") plot(spruces, maxsize=10*max(spruces$marks)) plot(unmark(spruces), add=TRUE) }
This dataset is a spatial point pattern giving the locations of palaeolithic stone tools (‘lithic’ specimens) and animal bone fragments (‘bone’), accurately surveyed in a layer of soil at David's Site, Olduvai Gorge, Tanzania. The surveyed layer is about 20 cm thick and approximately 1.85 million years old.
Details of the study, and data analysis, are reported by Diez-Martin et al. (2021). Please cite this article in any use of the data.
The data are presented as a two-dimensional point pattern
with two columns of marks: the vertical position Z
(numeric)
and the type of artefact TYPE
(factor with levels
BONE
and LITHIC
). The window of observation is an
irregular polygon, approximately 40 by 30 metres across.
Spatial coordinates and vertical coordinate are expressed in metres.
There are 3563 bone fragments and 1182 lithic
specimens making a total of 4745 points.
data("stonetools")
data("stonetools")
Marked spatial point pattern (object of class "ppp"
, see
ppp.object
) with two columns of marks,
Z
(numeric) and TYPE
(factor with levels
BONE
and LITHIC
). The window of observation is
an irregular polygon. Spatial coordinate unit is metres.
Dr. L. Cobo and Prof. F. Diez-Martin. Please cite Diez-Martin et al (2021) in any use of these data.
Diez-Martin, F., Cobo-Sanchez, L., Baddeley, A., Uribelarrea, D.,
Mabulla, A., Baquedano, E. and Dominguez-Rodrigo, M. (2021)
Tracing the spatial imprint of Oldowan technological behaviors: A view
from DS (Bed I, Olduvai Gorge, Tanzania).
PLOS ONE, Public Library of Science, 16, 1–47.
DOI: 10.1371/journal.pone.0254603
if(require(spatstat.geom)) { plot(subset(stonetools, select=TYPE), cex=0.5, cols=2:3) }
if(require(spatstat.geom)) { plot(subset(stonetools, select=TYPE), cex=0.5, cols=2:3) }
The data give the locations of pine saplings in a Swedish forest.
data(swedishpines)
data(swedishpines)
An object of class "ppp"
representing the point pattern of tree locations
in a rectangular plot 9.6 by 10 metres.
Cartesian coordinates are given in decimetres (multiples of 0.1 metre)
rounded to the nearest decimetre.
Type rescale(swedishpines)
to get an equivalent dataset
where the coordinates are expressed in metres.
See ppp.object
for details of the format of a
point pattern object.
For previous analyses see Ripley (1981, pp. 172-175), Venables and Ripley (1997, p. 483), Baddeley and Turner (2000).
Strand (1972), Ripley (1981)
Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.
Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.
Strand, L. (1972). A model for stand growth. IUFRO Third Conference Advisory Group of Forest Statisticians, INRA, Institut National de la Recherche Agronomique, Paris. Pages 207–216.
Venables, W.N. and Ripley, B.D. (1997) Modern applied statistics with S-PLUS. Second edition. Springer Verlag.
if(require(spatstat.geom)) { swedishpines ## rescale to metres rescale(swedishpines) }
if(require(spatstat.geom)) { swedishpines ## rescale to metres rescale(swedishpines) }
Locations of birch (Betula celtiberica) and oak (Quercus robur) trees in a secondary wood in Urkiola Natural Park (Basque country, northern Spain). They are part of a more extensive dataset collected and analysed by Laskurain (2008). The coordinates of the trees are given in meters.
data(urkiola)
data(urkiola)
An object of class "ppp"
representing the point pattern of
tree locations. Entries include
Cartesian x-coordinate of tree in metres
Cartesian y-coordinate of tree in metres
factor indicating species of each tree
The levels of marks
are birch
and oak
.
See ppp.object
for details of the format of a ppp object.
N.A. Laskurain. Kindly formatted and communicated by M. de la Cruz Rot
Laskurain, N. A. (2008) Dinámica espacio-temporal de un bosque secundario en el Parque Natural de Urkiola (Bizkaia). Tesis Doctoral. Universidad del País Vasco /Euskal Herriko Unibertsitatea.
Point pattern of synaptic vesicles observed in rat brain tissue.
data(vesicles)
data(vesicles)
The dataset vesicles
is a point pattern
(object of class "ppp"
) representing the location
of the synaptic vesicles. The window of the point pattern
represents the region of presynapse where synaptic vesicles were
observed in this study.
There is a hole in the window, representing the region occupied by
mitochondria, where synaptic vesicles do not occur.
The dataset vesicles.extra
is a list with entries
presynapse
|
outer polygonal boundary of presynapse |
mitochondria |
polygonal boundary of mitochondria |
mask |
binary mask representation of vesicles window |
activezone |
line segment pattern representing |
the active zone. |
All coordinates are in nanometres (nm).
As part of a study on the effects of stress on brain function, Khanmohammadi et al (2014) analysed the spatial pattern of synaptic vesicles in 45-nanometre-thick sections of rat brain tissue visualised in transmission electron microscopy.
To investigate the influence of stress, Khanmohammadi et al (2014) study the distribution of the synaptic vesicles in the pre-synaptic neuron in relation to the active zone of the presynaptic membrane. They hypothesize that the synaptic vesicle density is a decreasing function of distance to the active zone.
The boundaries for the active zone, mitochondria, pre- and post synaptic terminals, and the centre of the synaptic vesicles were annotated by hand on the image.
For demonstration and training purposes, the raw data files for this dataset are also provided in the spatstat.data package installation:
vesicles.txt
|
spatial locations of vesicles |
presynapse.txt
|
vertices of presynapse |
mitochondria.txt |
vertices of mitochondria |
vesiclesimage.tif |
greyscale microscope image |
vesiclesmask.tif |
binary image of mask |
activezone.txt |
coordinates of activezone
|
The files are in the folder rawdata/vesicles
in the
spatstat.data installation directory. The precise location of the
files can be obtained using system.file
, as shown
in the examples.
Nicoletta Nava, Mahdieh Khanmohammadi and Jens Randel Nyengaard. Experiment performed by Nicoletta Nava at the Stereology and Electron Microscopy Laboratory, Aarhus University, Denmark. Images were annotated by Mahdieh Khanmohammadi at the Department of Computer Science, University of Copenhagen. Jens Randel Nyengaard provided supervision and guidance, and curated the data.
Khanmohammadi, M., Waagepetersen, R., Nava, N., Nyengaard, J.R. and Sporring, J. (2014) Analysing the distribution of synaptic vesicles using a spatial point process model. 5th ACM Conference on Bioinformatics, Computational Biology and Health Informatics, Newport Beach, CA, USA, September 2014.
if(require(spatstat.geom)) { plot(vesicles) with(vesicles.extra, plot(activezone, add=TRUE, col="red")) } ## read coordinates of vesicles from raw data, for training purposes vf <- system.file("rawdata", "vesicles", "vesicles.txt", package="spatstat.data") if(!any(nzchar(vf))) stop("Could not find raw data file vesicles.txt") vdf <- read.table(vf, header=TRUE)
if(require(spatstat.geom)) { plot(vesicles) with(vesicles.extra, plot(activezone, add=TRUE, col="red")) } ## read coordinates of vesicles from raw data, for training purposes vf <- system.file("rawdata", "vesicles", "vesicles.txt", package="spatstat.data") if(!any(nzchar(vf))) stop("Could not find raw data file vesicles.txt") vdf <- read.table(vf, header=TRUE)
This dataset is a spatial point pattern of trees recorded at Waka National Park, Gabon. See Balinga et al (2006).
The dataset waka
is a point pattern
(object of class "ppp"
) containing the spatial coordinates
of each tree, marked by the tree diameter at breast height
dbh
.
The survey region is a 100 by 100 metre squawre.
Coordinates are given in metres, while the dbh
is in centimetres.
data(waka)
data(waka)
Nicolas Picard
Balinga, M., Sunderland, T., Walters, G., Issembe', Y., Asaha, S. and Fombod, E. (2006) A vegetation assessment of the Waka national park, Gabon. Herbier National du Gabon, LBG, MBG, WCS, FRP and Simthsonian Institution, Libreville, Gabon. CARPE Report, 154 pp. http://carpe.umd.edu/
Picard, N., Bar-Hen, A., Mortier, F. and Chadoeuf, J. (2009) The multi-scale marked area-interaction point process: a model for the spatial pattern of trees. Scandinavian Journal of Statistics 36 23–41
data(waka) if(require(spatstat.geom)) { plot(waka, markscale=0.01) title(sub="Tree diameters to scale") plot(waka, markscale=0.04) title(sub="Tree diameters 4x scale") }
data(waka) if(require(spatstat.geom)) { plot(waka, markscale=0.01) title(sub="Tree diameters to scale") plot(waka, markscale=0.04) title(sub="Tree diameters 4x scale") }
The territorial behaviour of an insect group called waterstriders was studied in a series of laboratory experiments by Dr Matti Nummelin (University of Helskini). The data were analysed in the pioneering PhD thesis of Antti Penttinen (1984).
The dataset waterstriders
is
a list of three point patterns. Each point pattern gives
the locations of larvae of the waterstrider
Limnoporus (Gerris) rufoscutellatus (larval stage V)
in a homogeneous area about 48 cm square. The point
patterns can be assumed to be independent.
It is known that this species of waterstriders exhibits territorialism at older larvae stages and at the adult stage. Therefore, if any deviation from Complete Spatial Randomness exists in these three point patterns, it is expected to be towards inhibition.
The data were obtained from photographs which were scanned manually. The waterstriders are in a pool which is larger than the picture. A guard area (width about 2.5 cm) has been deleted because it is a source of inhomogeneity to interactions.
Penttinen (1984, chapter 5) fitted a pairwise interaction model with
a Strauss/hardcore interaction (see StraussHard
)
with hard core radius 1.5 cm and interaction radius 4.5 cm.
data(waterstriders)
data(waterstriders)
waterstriders
is a list of three point patterns
(objects of class "ppp"
). It also has class "listof"
so that it can be plotted and printed directly. The point pattern
coordinates are in centimetres.
Data were collected by Dr. Matti Nummelin (University of Helsinki, Finland). Data kindly provided by Prof. Antti Penttinen, University of Jyv\"askyl\"a, Finland.
Penttinen, A. (1984) Modelling interaction in spatial point patterns: parameter estimation by the maximum likelihood method. Jyv\"askyl\"a Studies in Computer Science, Economics and Statistics 7, University of Jyv\"askyl\"a, Finland.