# knitr::opts_chunk$set(fig.width = 7, fig.height = 6) options(digits = 4)
This document describes the geoGraph package for the R software. geoGraph aims at implementing graph approaches for geographic data. In geoGraph, a given geographic area is modelled by a fine regular grid, where each vertice has a set of spatial coordinates and a set of attributes, which can be for instance habitat descriptors, or the presence/abundance of a given species. 'Travelling' within the geographic area can then be easily modelled as moving between connected vertices. The cost of moving from one vertex to another can be defined according to attribute values, which allows for instance to define friction routes based on habitat.
geoGraph harnesses the full power of graph algorithms implemented in R by the graph and RBGL (R Boost Graph Library) packages. In particular, RBGL is an interface between R and the comprehensive Boost Graph Library in C++, which provides fast and efficient implementations of a wide range of graph algorithms. Once we have defined frictions for an entire geographic area, we can easily, for instance, find the least costs path from one location to another, or find the most parsimonious way of connecting a set of locations.
Interfacing spatial data and graphs can be a complicated task.
The purpose of geoGraph is to provide tools to achieve and simplify this 'preliminary' step.
This is achieved by defining new classes of objects which are essentially geo-referenced graphs
with node attributes (gGraph
objects), and interfaced spatial data (gData
objects).
In this vignette, we show how to install geoGraph, construct and handle
gGraph
/gData
objects, and illustrate some basic features of graph algorithms.
All the following instructions should be entered from a new R session to avoid errors due to installing attached packages.
devtools is also needed to install geoGraph:
install.packages("devtools")
Then, to install geoGraph, simply type:
library(devtools) install_github("thibautjombart/geoGraph")
Once installed, the package can be loaded using:
library("geoGraph")
If you have an error regarding missing packages, you may need to install manually the packages graph and RBGL from Bioconductor:
install.packages("BiocManager") BiocManager::install(c("graph", "RBGL"))
And then attempt to reinstall geoGraph from GitHub.
Data representation refers to the way a given type of data is handled by a
computer program. Two types of objects are used in geoGraph: gGraph
, and
gData
objects. Both objects are defined as formal (S4) classes and often have
methods for similar generic function (e.g. getNodes
is defined for both
objects). Essentially, gGraph
objects contain underlying layers of
informations, including a spatial grid and possibly node attributes, and
covering the area of interest. gData
are sets of locations (like sampled
sites, for instance) which have been interfaced to a gGraph
object, to allow
further manipulations such as finding paths on the grid between pairs of
locations.
The definition of the formal class gGraph
can be obtained using:
getClass("gGraph")
and a new empty object can be obtained using the constructor:
new("gGraph")
The documentation ?gGraph
explains the basics about the object's content. In
a nutshell, these objects are spatial grids with nodes and segments connecting
neighbouring nodes, and additional informations on the nodes or on the graph
itself. coords
is a matrix of longitudes and latitudes of the nodes.
nodes.attr
is a data.frame storing attributes of the nodes, such as habitat
descriptors; each row corresponds to a node of the grid, while each column
corresponds to a variable. meta
is a list containing miscellanous
informations about the graph itself. There is no contraint applying to the
components of the list, but some typical components such as $costs
or
$colors
will be recognised by certain functions. For instance, you can
specify plotting rules for representing a given node attribute by a given color
by defining a component $colors
. Similarly, you can associate costs to a
given node attribute by defining a component $costs
. An example of this can
be found in already existing gGraph
objects. For instance, worldgraph.10k
is a graph of the world with approximately 10,000 nodes, and only on-land
connectivity (\textit{i.e.no travelling on the seas). ```r worldgraph.10k
worldgraph.10k@meta ``` Lastly, the
graphcomponent is a
graphNEL` object,
which is the standard class for graphs in the graph and RBGL packages. This
object contains all information on the connections between nodes, and the
weights (costs) of these connections.
Four main gGraph
are provided with geoGraph: rawgraph.10k
, rawgraph.40k
,
worldgraph.10k
, and worldgraph.40k
. These datasets are available using the
command data
. The grid used in these datasets are the best geometric
approximation of a regular grid for the surface of a sphere. One advantage of
working with these grids is that we do not have to use a projection for
geographic coordinates, which is a usual issue in regular GIS.
The difference between rawgraphs and worldgraphs is that the first are entirely
connected, while in the second connections occur only on land. Numbers 10k'
and
40k' indicate that the grids consist of roughly 10,000 and 40,000 nodes.
For illustrative purposes, we will often use the 10k grids, since they are less
heavy to handle. For most large-scale applications, the 40k versions should
provide sufficient resolution. New gGraph
can be constructed using the
constructor (new(...)
), but this topic is not documented in this vignette.
gData
are essentially sets of locations that are interfaced with a gGraph
object.
During this operation, each location is assigned to the closest node on the grid of the
gGraph
, then allowing for travelling between locations using the grid.
Then, it is for instance possible to find the shortest path between two locations through various
types of habitats.
Like for gGraph
, the content of the formal class gData
can be obtained using:
getClass("gData")
and a new empty object can be obtained using the constructor:
new("gData")
As before, the description of the content of these objects can be found in the
documentation (?gData
). coords
is a matrix of xy (longitude/latitude)
coordinates in which each row is a location. nodes.id
is vector of characters
giving the name of the vertices matching the locations; this is defined
automatically when creating a new gData
, or using the function closestNode
.
data
is a slot storing data associated to the locations; it can be any type of
object, but a data.frame should cover most requirements for storing data. Note
that this object should be subsettable (i.e. the [
operator should be
defined), so that data can be subsetted when subsetting the gData
object.
Lastly, the slot gGraph.name
contains the name of the gGraph
object to which
the gData
has been interfaced.
Contrary to gGraph
objects, gData
objects will frequently be constructed by
the user. In the next sections, we illustrate how we can build and use gData
objects from a set of locations.
An overview of the material implemented in the package is summarized the package's manpage, accessible via:
?geoGraph
The html version of this manpage may be preferred to browse more easily the content of geoGraph; it is accessible by typing:
help("geoGraph", package = "geoGraph", html = TRUE)
To revert help back to text mode, simply type:
options(htmlhelp = FALSE)
In the following, we go through various tasks that can be achieve using geoGraph.
GeoGraphic data consist of a set of locations, possibly accompanied by
additional information. For instance, one may want to study the migrations
amongst a set of biological populations with known geographic coordinates. In
geoGraph, geographic data are stored in gData
objects. These objects match
locations to the closest nodes on a grid (a gGraph
object), and store
additional data if needed.
As a toy example, let us consider four locations: Bordeaux (France), London (UK), Malaga (Spain), and Zagreb (Croatia). Since we will be working with a crude grid (10,000 nodes), locations need not be exact. We enter the longitudes and latitudes (in this order, that is, xy coordinates) of these cities in decimal degrees, as well as approximate population sizes:
Bordeaux <- c(-1, 45) London <- c(0, 51) Malaga <- c(-4, 37) Zagreb <- c(16, 46) cities.dat <- rbind.data.frame(Bordeaux, London, Malaga, Zagreb) colnames(cities.dat) <- c("lon", "lat") cities.dat$pop <- c(1e6, 13e6, 5e5, 1.2e6) row.names(cities.dat) <- c("Bordeaux", "London", "Malaga", "Zagreb") cities.dat
We load a gGraph
object which contains the grid that will support the data:
worldgraph.10k
plot(worldgraph.10k)
(we could use worldgraph.40k
for a better resolution). In this figure, each
node is represented with a color depending on the habitat type, either 'sea'
(blue) or 'land' (green). We are going to interface the cities data with this
grid; to do so, we create a gData
object using new
(see ?gData
object):
cities <- new("gData", coords = cities.dat[, 1:2], data = cities.dat[, 3, drop = FALSE], gGraph.name = "worldgraph.10k") cities plot(cities, type = "both", reset = TRUE) plotEdges(worldgraph.10k)
This figure illustrates the matching of original locations (black crosses) to nodes of the grid
(red circles).
As we can see, an issue occured for Bordeaux, which has been assigned to a node in the sea (in blue).
Locations can be re-assigned to nodes with restrictions for some node attribute values using
closestNode
; for instance, here we constrain matching nodes to have an habitat
value
(defined as node attribute in worldgraph.10k
) equalling land
(green points):
cities <- closestNode(cities, attr.name = "habitat", attr.value = "land") plot(cities, type = "both", reset = TRUE) plotEdges(worldgraph.10k)
Now, all cities have been assigned to a land' node of the grid (again, better accuracy will be
gained on 40k or finer grids - we use 10k for illustrative purposes only).
Content of
citiescan be accessed via various accessors (see
?gData`).
For instance, we can retrieve original locations, assigned nodes, and stored data using:
getCoords(cities) getNodes(cities) getData(cities)
We can also get the coordinates of the matching nodes (\textit{i.e.}, red circle on previous figure) using:
getCoords(cities, original = FALSE)
More interestingly, we can now retrieve all the geographic information contained in the underlying
grid (\textit{i.e.}, gGraph
object) as node attributes:
getNodesAttr(cities)
In this example, the information stored in worldgraph.10k
is rather crude: habitat
only
distinguishes the land from the sea.
However, more complex habitat information could be incorporated, for instance from GIS shapefiles
(see dedicated section below).
An essential aspect of spatial analysis lies in visualizing the data.
In geoGraph, the spatial grids (gGraph
) and spatial data (gData
) can be plotted
and browsed using a variety of functions.
gGraph
objectsDisplaying a gGraph
object is done through plot
and points
functions.
The first opens a new plotting region, while the second draws in the current plotting region;
functions have otherwise similar arguments (see ?plot.gGraph
).
By default, plotting a gGraph
displays the grid of nodes overlaying a shapefile (by default,
the landmasses).
Edges can be plotted at the same time (argument edges
), or added afterwards using plotEdges
.
If the gGraph
object possesses an adequately formed meta$colors
component, the
colors of the nodes are chosen according to the node attributes and the color scheme specified in meta$colors
.
Alternatively, the color of the nodes can be specified via the col
argument in plot
/points
.
Here is an example using worldgraph.10k
:
worldgraph.10k@meta$colors head(getNodesAttr(worldgraph.10k)) table(getNodesAttr(worldgraph.10k)) plot(worldgraph.10k, reset = TRUE) title("Default plotting of worldgraph.10k")
It may be worth noting that plotting gGraph
objects involves plotting a fairly
large number of points and edges.
On some graphical devices, the resulting plotting can be slow.
For instance, one may want to disable cairo
under linux: this graphical device yields better
graphics than Xlib
, but at the expense of increase computational time.
To switch to Xlib
, type:
X11.options(type = "Xlib")
and to revert to cairo
, type:
X11.options(type = "cairo")
In practice, it is often useful to be able to peer at specific regions, and more generally to
navigate inside the graphical representation of the data.
For this, we can use the interactive functions geo.zoomin
, geo.zoomout
, geo.slide
,
geo.back
, geo.bookmark
, and geo.goto
.
The zoom and slide functions require to left-click on the graphics to zoom in, zoom out, or slide to
adjacent areas; in all cases, a right click ends the function.
Also note that geo.zoomin
can accept an argument specifying a rectangular region, which will
be adapted by the function to fit best a square area with similar position and centre, and zoom to
this area (see ?geo.zoomin
).
geo.bookmark
and geo.goto
respectively set and go to a bookmark, i.e. a tagged area.
This is most useful when one has to switch between distant areas repeatedly.
Here are some examples based on the previous plotting of worldgraph.10k
:
Zooming in:
geo.zoomin()
geo.zoomin(c(-19.25, 44.77, 15.09, 66.19))
Zooming out:
geo.zoomout()
geo.zoomin(c(-51.26, 76.78, -23.38, 90.00))
Sliding to the east:
geo.slide()
geo.zoomin(c(41.76, 169.80, -28.28, 99.76))
One important thing which makes plotting gGraph
objects different from most other plotting in
R is that geoGraph
keeps the changes made to the plotting area in memory.
This allows to undo one or several moves using geo.back
.
Moreover, even if the graphical device is killed, plotting again a gGraph
will use the old
parameters by default.
To disable this behavior, set the argument reset=TRUE
when calling upon plot
.
Technically, this 'plotting memory' is implemented by storing plotting information in an environment
defined as the hidden environment geoGraph:::.geoGraphEnv
:
ls(env = geoGraph:::.geoGraphEnv)
You can inspect individual variables within this environment:
get("last.plot.param", envir = geoGraph:::.geoGraphEnv)
However, it is recommended not to modify these objects directly, unless you really know what you are doing.
In any case, plotting a gGraph
object with argument reset=TRUE
will remove previous
plotting history and undo possible wrong manipulations.
gData
objectsgData
objects are by default plotted overlaying the corresponding gGraph
.
For instance, using the cities
example from above:
plot(cities, reset = TRUE) text(getCoords(cities), rownames(getData(cities)))
Note the argument reset=TRUE
, which tells the plotting function to adapt the
plotting area to the geographic extent of the dataset.
To plot additional information, it can be useful to extract the spatial coordinates from the data.
This is achieved by getCoords
.
This method takes an extra argument original
, which is TRUE if original spatial coordinates
are seeked, or FALSE for coordinates of the nodes on the grid.
We can use this to represent, for instance, the population sizes for the different cities:
transp <- function(col, alpha = .5) { res <- apply(col2rgb(col), 2, function(c) rgb(c[1] / 255, c[2] / 255, c[3] / 255, alpha)) return(res) } plot(cities, reset = TRUE) par(xpd = TRUE) text(getCoords(cities) + -.5, rownames(getData(cities))) symbols(getCoords(cities)[, 1], getCoords(cities)[, 2], circ = sqrt(unlist(getData(cities))), inch = .2, bg = transp("red"), add = TRUE)
gGraphs
Editing graphs is an essential task in geoGraph.
While available gGraph
objects provide a basis to work with (see ?worldgraph.10k
),
one may want to adapt a graph to a specific case.
For instance, connectivity should be defined according to biological knowledge of the organism under study.
gGraph
can be modified in different ways: by changing the connectivity, the costs of
edges, or the attribute values.
gGraph
There are two main ways of changing the connectivity of a gGraph
, which match two different objectives.
The first approach is to perform global and systematic changes of the connectivity of the graph.
Typically, one will want to remove all connections over a given type of landscape, which is
uncrossable by the organism under study.
Let's assume we are interested in saltwater fishes.
To model fish dispersal, we have to define a graph which connects only nodes overlaying the sea.
We load the gGraph
object rawgraph.10k
, and zoom in to a smaller area (Madagascar) to illustrate
changes in connectivity:
geo.zoomin(c(35, 54, -26, -10)) plotEdges(rawgraph.10k)
We shall set a bookmark for this area, in case we would want to get back to this place later on:
geo.bookmark("madagascar")
What we now want to do is remove all but sea-sea connections. To do so, the easiest approach is to i) define costs for the edges based on habitat, with land being given large costs and ii) remove all edges with large costs.
Costs of a given node attribute (here, habitat') are indicated in the
meta$costs` slot:
rawgraph.10k@meta$costs newGraph <- rawgraph.10k newGraph@meta$costs[2:6, 2] <- 100 newGraph@meta$costs[1, 2] <- 1 newGraph@meta$costs
We have just changed the costs associated to habitat type, but this change is not yet effective on
edges between nodes.
We use setCosts
to set the cost of an edge to the average of the costs of its nodes:
newGraph <- setCosts(newGraph, attr.name = "habitat") plot(newGraph, edge = TRUE)
On this new graph, we represent the edges with a width inversely proportional to the associated
cost; that is, bold lines for easy travelling and light edges/dotted lines for more costly mouvement.
This is not enough yet, since travelling on land is still possible.
However, we can tell geoGraph to remove all edges associated to too strong a cost, as defined
by a given threshold (using dropDeadEdges
).
Here, only sea-sea connections shall be retained, that is, edges with cost 1.
newGraph <- dropDeadEdges(newGraph, thres = 1.1) plot(newGraph, edge = TRUE)
Here we are: newGraph
only contains connections in the sea.
Note that, although we restrained the plotting area to Madagascar, this change is effective everywhere.
For instance, travelling to the nort-west Australian coasts:
geo.zoomin(c(110, 130, -27, -12)) geo.bookmark("australia")
gGraph
A second approach to changing a gGraph
is to refine the graph by hand, adding or removing
locally some connections, or altering the attributes of some nodes.
This can be necessary to connect components such as islands to the main landmasses, or to correct
erroneous data.
Adding and removing edges from the grid of a gGraph
can be achieved by geo.add.edges
and geo.remove.edges
, respectively.
These functions are interactive, and require the user to select individual nodes or a rectangular
area in which edges are added or removed.
See ?geo.add.edges
for more information on these functions.
For instance, we can remove a few odd connections in the previous graph, near the Australian coasts
(note that we have to save the changes using <-
):
geo.goto("australia") newGraph <- geo.remove.edges(newGraph)
newGraph <- readRDS("Robjects/newGraph.RDS") #load("Robjects/newGraph.RData")
When adding connections within an area or in an entire graph, node addition is based on
another gGraph
,i.e. only connections existing in another gGraph
serving as
reference can be added to the current gGraph
.
For graphs based on 10k or 40k grids, the raw graphs provided in geoGraph
should be used,
(rawgraph.10k
, rawgraph.40k
), since they are fully connected.
In addition to changing grid connectivity, we may also want to modify the attributes of specific nodes.
This is again done interactively, using the function geo.change.attr
.
For instance, here, we define a new value shalowwater
(plotted in light blue) for the attribute habitat
,
selecting affected nodes using the 'area' mode first, and refining the changes using the 'point' mode:
plot(newGraph, edge = TRUE) temp <- geo.change.attr(newGraph, mode = "area", attr.name = "habitat", attr.value = "shallowwater", newCol = "deepskyblue") temp <- geo.change.attr(temp, attr.name = "habitat", attr.value = "shallowwater", newCol = "deepskyblue") newGraph <- temp
newGraph <- readRDS("Robjects/newGraph2.RDS") #load("Robjects/newGraph2.RData")
newGraph@meta$colors plot(newGraph, edge = TRUE)
Again, note that the changes made to the graph have to be save in an object (using <-
) to be
effective.
An important feature of geoGraph is serving as an interface between geographic information
system (GIS) layers and geographic data.
As currently implemented, geoGraph can extract information from shapefiles with the Arc GIS
(http://www.esri.com/software/arcgis/index.html) format, using the function extractFromLayer
.
Here, we illustrate this procedure using the shapefile world-countries.shp
provided with the
package. geoGraph still relies on SpatialPolygonDataFrame
objects from the sp
package.
A move to sf
objects is planned, but for the moment we have to use sf::st_read()
to read
a GIS shapefile into an sf
object, and then cast it to a SpatialPolygonDataFrame
with
sf::as_Spatial()
:
library(sf) world.countries <- sf::st_read(system.file("files/shapefiles/world-countries.shp", package = "geoGraph")) world.countries <- sf::as_Spatial(world.countries) class(world.countries) summary(world.countries)
The summary of world.countries
shows the data (attributes) stored in the layer.
Let us assume that we are interested in retrieving continent and country information for the
worldgraph.10k
object.
Note that extractFromLayer
can extract information to other types of objects than gGraph
(see ?extractFromLayer
)
summary(getNodesAttr(worldgraph.10k)) newGraph <- extractFromLayer(worldgraph.10k, layer = world.countries, attr = c("CONTINENT", "NAME")) summary(getNodesAttr(newGraph))
The new object newGraph
is a gGraph
which now includes, for each node of the grid, the
corresponding continent and country retrieved from the GIS layer.
We can use the newly acquired information for plotting newGraph
, by defining new color rules:
temp <- unique(getNodesAttr(newGraph)$"NAME") col <- c("transparent", rainbow(length(temp) - 1)) colMat <- data.frame(NAME = temp, color = col) head(colMat) tail(colMat) plot(newGraph, col.rules = colMat, reset = TRUE)
This information could in turn be used to define costs for travelling on the grid. For instance, one could import habitat descriptors from a GIS, use these values to formulate a habitat model, and derive costs for dispersal on the grid.
As soon as a GIS layer has been extracted to a gGraph
, this information becomes also available for
any gData
interfaced with this object.
For instance, we can re-use the cities
example defined in a previous section, and interface it
with newGraph
to retrieve continent and country information for the cities of the dataset:
cities.dat cities <- new("gData", coords = cities.dat[, 1:2], data = cities.dat[, 3, drop = FALSE], gGraph.name = "newGraph") cities <- closestNode(cities, attr.name = "habitat", attr.value = "land") getData(cities) getNodesAttr(cities)
One of the most useful applications of geoGraph is the research of least-cost paths between
couples of locations.
This can be achieved using the functions dijkstraFrom
and dijkstraBetween
on a
gData
object which contains all the locations of interest.
These functions return least-cost paths with the format gPath
.
dijkstraFrom
compute the paths from a given node of the grid to all locations of the
gData
, while dijkstraBetween
computes the paths between pairs of locations of the
gData
.
Below, we detail the example of the documentation of these functions, which uses the famous dataset of native
Human populations, HGDP:
hgdp plot(hgdp, reset = TRUE)
Populations of the dataset are shown by red circles, while the underlying grid
(worldgraph.40k
) is represented with colors depending on habitat (blue: sea; green: land;
pink: coasts).
Population genetics predicts that genetic diversity within populations should decay as populations are
located further away from the geographic origin of the species.
Here, we verify this relationship for a theoretical origin in Addis abeba, Ethiopia.
We shall seek all paths through landmasses to the HGDP populations.
First, we check that all populations are connected on the grid using isConnected
:
isConnected(hgdp)
Note that in practice, we may often want to assess graphically the connectivity of the underlying grid, especially
if not all locations of the gData
are connected.
This can be done using connectivityPlot
, which has methods for both gGraph
and
gData
, and represents different connected components using different colors.
For instance, for worldgraph.10k
:
connectivityPlot(worldgraph.10k, edges = TRUE, seed = 1)
geo.zoomin(c(90, 150, 18, -25)) title("Different connected components\n in worldgraph.10k")
Since all locations in hgdp
are connected, we can proceed further.
We have to set the costs of edges in the gGraph
grid.
To do so, we can choose between i) strictly uniform costs (using dropCosts
) ii)
distance-based costs -- roughly uniform -- (using setDistCosts
) or iii) attribute-driven
costs (using setCosts
).
We shall first illustrate the strictly uniform costs.
After setting a gGraph
with uniform costs, we use dijkstraFrom
to find the shortest
paths between Addis abeba and the populations of hgdp
:
myGraph <- dropCosts(worldgraph.40k) hgdp@gGraph.name <- "myGraph" addis <- cbind(38, 9) ori <- closestNode(myGraph, addis) paths <- dijkstraFrom(hgdp, ori)
The object paths
contains the identified paths, which are stored as a list with class gPath
(see ?gPath
).
Paths can be plotted easily:
addis <- as.vector(addis) plot(myGraph, col = NA, reset = TRUE) plot(paths) points(addis[1], addis[2], pch = "x", cex = 2) text(addis[1] + 35, addis[2], "Addis abeba", cex = .8, font = 2) points(hgdp, col.node = "black")
In this graph, each path is plotted with a different color, but several paths overlap in several places.
We can extract the distances from the origin' using
gPath2dist, and then examine the
relationship between genetic diversity within populations (stored in
hgdp`) and the distance from the origin:
div <- getData(hgdp)$"Genetic.Div" dgeo.unif <- gPath2dist(paths, res.type = "vector") plot(div ~ dgeo.unif, xlab = "GeoGraphic distance (arbitrary units)", ylab = "Genetic diversity") lm.unif <- lm(div ~ dgeo.unif) abline(lm.unif, col = "red") summary(lm.unif) title("Genetic diversity vs geographic distance \n uniform costs ")
Alternatively, we can use costs based on habitat. As a toy example, we will consider that coasts are four times more favourable for dispersal than the rest of the landmasses. We define these new costs, and then compute and plot the corresponding shortest paths:
myGraph@meta$costs[7, ] <- c("coast", 0.25) myGraph@meta$costs myGraph <- setCosts(myGraph, attr.name = "habitat") paths.2 <- dijkstraFrom(hgdp, ori)
plot(newGraph, col = NA, reset = TRUE) plot(paths.2) points(addis[1], addis[2], pch = "x", cex = 2) text(addis[1] + 35, addis[2], "Addis abeba", cex = .8, font = 2) points(hgdp, col.node = "black")
The new paths are slightly different from the previous ones. We can examine the new relationship with genetic distance:
dgeo.hab <- gPath2dist(paths.2, res.type = "vector") plot(div ~ dgeo.hab, xlab = "GeoGraphic distance (arbitrary units)", ylab = "Genetic diversity") lm.hab <- lm(div ~ dgeo.hab) abline(lm.hab, col = "red") summary(lm.hab) title("Genetic diversity vs geographic distance \n habitat costs ")
Of course, the distinction between coasts and inner landmasses is a somewhat poor description of habitat. In practice, complex habitat models can be used as simply.
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