Note

Go to the end to download the full example code. or to run this example in your browser via JupyterLite or Binder

Kernel Density Estimate of Species Distributions#

This shows an example of a neighbors-based query (in particular a kernel density estimate) on geospatial data, using a Ball Tree built upon the Haversine distance metric – i.e. distances over points in latitude/longitude. The dataset is provided by Phillips et. al. (2006). If available, the example uses basemap to plot the coast lines and national boundaries of South America.

This example does not perform any learning over the data (see Species distribution modeling for an example of classification based on the attributes in this dataset). It simply shows the kernel density estimate of observed data points in geospatial coordinates.

The two species are:

"Bradypus variegatus" , the Brown-throated Sloth.
"Microryzomys minutus" , also known as the Forest Small Rice Rat, a rodent that lives in Peru, Colombia, Ecuador, Peru, and Venezuela.

References#

"Maximum entropy modeling of species geographic distributions" S. J. Phillips, R. P. Anderson, R. E. Schapire - Ecological Modelling, 190:231-259, 2006.

Bradypus Variegatus, Microryzomys Minutus

- computing KDE in spherical coordinates
- plot coastlines from coverage
- computing KDE in spherical coordinates
- plot coastlines from coverage

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
importmatplotlib.pyplotasplt
importnumpyasnp
fromsklearn.datasetsimport fetch_species_distributions
fromsklearn.neighborsimport KernelDensity
# if basemap is available, we'll use it.
# otherwise, we'll improvise later...
try:
 frommpl_toolkits.basemapimport Basemap
 basemap = True
except ImportError:
 basemap = False
defconstruct_grids(batch):
"""Construct the map grid from the batch object
 Parameters
 ----------
 batch : Batch object
 The object returned by :func:`fetch_species_distributions`
 Returns
 -------
 (xgrid, ygrid) : 1-D arrays
 The grid corresponding to the values in batch.coverages
 """
 # x,y coordinates for corner cells
 xmin = batch.x_left_lower_corner + batch.grid_size
 xmax = xmin + (batch.Nx * batch.grid_size)
 ymin = batch.y_left_lower_corner + batch.grid_size
 ymax = ymin + (batch.Ny * batch.grid_size)
 # x coordinates of the grid cells
 xgrid = np.arange (xmin, xmax, batch.grid_size)
 # y coordinates of the grid cells
 ygrid = np.arange (ymin, ymax, batch.grid_size)
 return (xgrid, ygrid)
# Get matrices/arrays of species IDs and locations
data = fetch_species_distributions ()
species_names = ["Bradypus Variegatus", "Microryzomys Minutus"]
Xtrain = np.vstack ([data["train"]["dd lat"], data["train"]["dd long"]]).T
ytrain = np.array (
 [d.decode("ascii").startswith("micro") for d in data["train"]["species"]],
 dtype="int",
)
Xtrain *= np.pi / 180.0 # Convert lat/long to radians
# Set up the data grid for the contour plot
xgrid, ygrid = construct_grids(data)
X, Y = np.meshgrid (xgrid[::5], ygrid[::5][::-1])
land_reference = data.coverages[6][::5, ::5]
land_mask = (land_reference > -9999).ravel()
xy = np.vstack ([Y.ravel(), X.ravel()]).T
xy = xy[land_mask]
xy *= np.pi / 180.0
# Plot map of South America with distributions of each species
fig = plt.figure ()
fig.subplots_adjust(left=0.05, right=0.95, wspace=0.05)
for i in range(2):
 plt.subplot (1, 2, i + 1)
 # construct a kernel density estimate of the distribution
 print(" - computing KDE in spherical coordinates")
 kde = KernelDensity (
 bandwidth=0.04, metric="haversine", kernel="gaussian", algorithm="ball_tree"
 )
 kde.fit(Xtrain[ytrain == i])
 # evaluate only on the land: -9999 indicates ocean
 Z = np.full (land_mask.shape[0], -9999, dtype="int")
 Z[land_mask] = np.exp (kde.score_samples(xy))
 Z = Z.reshape(X.shape)
 # plot contours of the density
 levels = np.linspace (0, Z.max(), 25)
 plt.contourf (X, Y, Z, levels=levels, cmap=plt.cm.Reds)
 if basemap:
 print(" - plot coastlines using basemap")
 m = Basemap(
 projection="cyl",
 llcrnrlat=Y.min(),
 urcrnrlat=Y.max(),
 llcrnrlon=X.min(),
 urcrnrlon=X.max(),
 resolution="c",
 )
 m.drawcoastlines()
 m.drawcountries()
 else:
 print(" - plot coastlines from coverage")
 plt.contour (
 X, Y, land_reference, levels=[-9998], colors="k", linestyles="solid"
 )
 plt.xticks ([])
 plt.yticks ([])
 plt.title (species_names[i])
plt.show ()