Mapping Monarch Butterfly migration¶

We will be getting data from a source called GBIF (Global Biodiversity Information Facility). We need a package called pygbif to access the data, which is not included in your environment. Install it by running the cell below:

In [1]:
%%bash
pip install pygbif

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In [2]:
import calendar
import os
import pathlib
import requests
import time
import zipfile
from getpass import getpass

import cartopy.crs as ccrs
import panel as pn
import pygbif.occurrences as occ
from glob import glob

import pandas as pd
import geopandas as gpd
import hvplot.pandas
import pygbif.species as species

INFO:NumExpr defaulting to 2 threads.

Create a folder for your data¶

For this challenge, you will need to save some data to your computer. We suggest saving to somewhere in your home folder (e.g. /home/username), rather than to your GitHub repository, since data files can easily become too large for GitHub.

Warning

The home directory is different for every user! Your home directory probably won’t exist on someone else’s computer. Make sure to use code like pathlib.Path.home() to compute the home directory on the computer the code is running on. This is key to writing reproducible and interoperable code.

Your Task: Create a project folder

The code below will help you get started with making a project directory

  1. Replace 'your-project-directory-name-here' and 'your-gbif-data-directory-name-here' with descriptive names
  2. Run the cell
  3. (OPTIONAL) Check in the terminal that you created the directory using the command ls ~/earth-analytics/data
In [3]:
# Create data directory in the home folder
data_dir = os.path.join(
    # Home directory
    pathlib.Path.home(),
    # Earth analytics data directory
    'earth-analytics',
    'data',
    # Project directory
    'species-distribution-ESIIL',
)
os.makedirs(data_dir, exist_ok=True)

# Define the directory name for GBIF data
gbif_dir = os.path.join(data_dir, 'monarch-data')

Define your study area – the ecoregions of North America¶

Track observations of Taciyagnunpa across the different ecoregions of North America! You should be able to see changes in the number of observations in each ecoregion throughout the year.

Download and save ecoregion boundaries¶

Your Task

  1. Find the URL for for the level III ecoregion boundaries. You can get ecoregion boundaries from the Environmental Protection Agency (EPA)..
  2. Replace your/url/here with the URL you found, making sure to format it so it is easily readable.
  3. Change all the variable names to descriptive variable names
  4. Run the cell to download and save the data.
In [4]:
# Set up the ecoregions level III boundary URL
ecoregion_url = ("https://gaftp.epa.gov/EPADataCommons/ORD/Ecoregions/"
                  "cec_na/NA_CEC_Eco_Level3.zip")
# Set up a path to save the dataon your machine
ecoregionpath = os.path.join(data_dir, 'NA_CEC_Eco_Level3.zip')

# Don't download twice
if not os.path.exists(ecoregionpath):
    # Download, and don't check the certificate for the EPA
    ecoregions_response = requests.get(ecoregion_url, verify=False)
    # Save the binary data to a file
    with open(ecoregionpath, 'wb') as ecoregions_file:
        ecoregions_file.write(ecoregions_response.content)

Load the ecoregions into Python¶

Your task

Download and save ecoregion boundaries from the EPA:

  1. Replace a_path with the path your created for your ecoregions file.
  2. (optional) Consider renaming and selecting columns to make your GeoDataFrame easier to work with.
  3. Make a quick plot with .plot() to make sure the download worked.
  4. Run the cell to load the data into Python
In [5]:
# Open up the ecoregions boundaries
ecoregions_gdf = (gpd.read_file(ecoregionpath)
.rename(columns={
        'NA_L3NAME': 'name',
        'Shape_Area': 'area'})
    [['name', 'area', 'geometry']]
)
# Name the index so it will match the other data later on
ecoregions_gdf.index.name = 'ecoregion'

# Plot the ecoregions to check download
ecoregions_gdf.plot()
Out[5]:
<Axes: >
No description has been provided for this image

Create a simplified GeoDataFrame for plotting¶

Plotting larger files can be time consuming. The code below will streamline plotting with hvplot by simplifying the geometry, projecting it to a Mercator projection that is compatible with geoviews, and cropping off areas in the Arctic.

Your task

Download and save ecoregion boundaries from the EPA:

  1. Make a copy of your ecoregions GeoDataFrame with the .copy() method, and save it to another variable name. Make sure to do everything else in this cell with your new copy!
  2. Simplify the ecoregions with .simplify(1000), and save it back to the geometry column.
  3. Change the Coordinate Reference System (CRS) to Mercator with .to_crs(ccrs.Mercator())
  4. Use the plotting code in the cell to check that the plotting runs quickly and looks the way you want, making sure to change gdf to YOUR GeoDataFrame name.
In [6]:
# Make a copy of the ecoregions
ecoregion_plot = ecoregions_gdf.copy()

# Simplify the geometry to speed up processing
ecoregion_plot.geometry = ecoregion_plot.simplify(1000)

# Change the CRS to Mercator for mapping
ecoregion_plot = ecoregion_plot.to_crs(ccrs.Mercator())

# Check that the plot runs
ecoregion_plot.hvplot(geo=True, crs=ccrs.Mercator())
Out[6]:

Access locations and times of Monarch Butterfly encounters¶

For this challenge, you will use a database called the Global Biodiversity Information Facility (GBIF). GBIF is compiled from species observation data all over the world, and includes everything from museum specimens to photos taken by citizen scientists in their backyards.

Your task: Explore GBIF

Before your get started, go to the GBIF occurrences search page and explore the data.

Contribute to open data

You can get your own observations added to GBIF using iNaturalist!

Register and log in to GBIF¶

You will need a GBIF account to complete this challenge. You can use your GitHub account to authenticate with GBIF. Then, run the following code to save your credentials on your computer.

Tip

If you accidentally enter your credentials wrong, you can set reset_credentials=True instead of reset_credentials=False

In [7]:
reset_credentials = False
# GBIF needs a username, password, and email
credentials = dict(
    GBIF_USER=(input, 'GBIF username:'),
    GBIF_PWD=(getpass, 'GBIF password'),
    GBIF_EMAIL=(input, 'GBIF email'),
)
for env_variable, (prompt_func, prompt_text) in credentials.items():
    # Delete credential from environment if requested
    if reset_credentials and (env_variable in os.environ):
        os.environ.pop(env_variable)
    # Ask for credential and save to environment
    if not env_variable in os.environ:
        os.environ[env_variable] = prompt_func(prompt_text)

Get the species key¶

Your task

  1. Replace the species_name with the name of the species you want to look up
  2. Run the code to get the species key
In [8]:
# Query species
species_info = species.name_lookup('danaus plexippus', rank='SPECIES')

# Get the first result
first_result = species_info['results'][0]

# Get the species key (nubKey)
species_key = first_result['nubKey']

# Check the result
first_result['species'], species_key
Out[8]:
('Danaus plexippus', 5133088)

Download data from GBIF¶

Your task

  1. Replace csv_file_pattern with a string that will match any .csv file when used in the glob function. HINT: the character * represents any number of any values except the file separator (e.g. /)

  2. Add parameters to the GBIF download function, occ.download() to limit your query to:

    • Danaus plexippus observations
    • in north america (NORTH_AMERICA)
    • from 2023
    • with spatial coordinates.

  3. Then, run the download. This can take a few minutes.

In [9]:
# Only download once
gbif_pattern = os.path.join(gbif_dir, '*.csv')
if not glob(gbif_pattern):
    # Submit query to GBIF
    gbif_query = occ.download([
        "continent = NORTH_AMERICA",
        "speciesKey = 5133088",
        "year = 2023",
        "hasCoordinate = TRUE",
    ])
    download_key = gbif_query[0]

    #wait for download to build
    if not 'GBIF_DOWNLOAD_KEY' in os.environ:
        os.environ['GBIF_DOWNLOAD_KEY'] = gbif_query[0]

        # Wait for the download to build
        wait = occ.download_meta(download_key)['status']
        while not wait=='SUCCEEDED':
            wait = occ.download_meta(download_key)['status']
            time.sleep(5)

    # Download GBIF data
    download_info = occ.download_get(
        os.environ['GBIF_DOWNLOAD_KEY'], 
        path=data_dir)

    # Unzip GBIF data
    with zipfile.ZipFile(download_info['path']) as download_zip:
        download_zip.extractall(path=gbif_dir)

# Find the extracted .csv file path
gbif_path = glob(gbif_pattern)[0]

Load the GBIF data into Python¶

Your task

  1. Look at the beginning of the file you downloaded using the code below. What do you think the delimiter is?
  2. Run the following code cell. What happens?
  3. Uncomment and modify the parameters of pd.read_csv() below until your data loads successfully and you have only the columns you want.

You can use the following code to look at the beginning of your file:

In [10]:
!head $gbif_path

gbifID	datasetKey	occurrenceID	kingdom	phylum	class	order	family	genus	species	infraspecificEpithet	taxonRank	scientificName	verbatimScientificName	verbatimScientificNameAuthorship	countryCode	locality	stateProvince	occurrenceStatus	individualCount	publishingOrgKey	decimalLatitude	decimalLongitude	coordinateUncertaintyInMeters	coordinatePrecision	elevation	elevationAccuracy	depth	depthAccuracy	eventDate	day	month	year	taxonKey	speciesKey	basisOfRecord	institutionCode	collectionCode	catalogNumber	recordNumber	identifiedBy	dateIdentified	license	rightsHolder	recordedBy	typeStatus	establishmentMeans	lastInterpreted	mediaType	issue
4868184771	50c9509d-22c7-4a22-a47d-8c48425ef4a7	https://www.inaturalist.org/observations/217003637	Animalia	Arthropoda	Insecta	Lepidoptera	Nymphalidae	Danaus	Danaus plexippus		SPECIES	Danaus plexippus (Linnaeus, 1758)	Danaus plexippus		CA		Ontario	PRESENT		28eb1a3f-1c15-4a95-931a-4af90ecb574d	43.27179	-79.903956	800.0						2023-08-14T08:52	14	8	2023	5133088	5133088	HUMAN_OBSERVATION	iNaturalist	Observations	217003637		leewarren	2024-05-20T07:33:39	CC_BY_NC_4_0	leewarren	leewarren			2024-05-28T03:40:01.071Z	StillImage	COORDINATE_ROUNDED;CONTINENT_DERIVED_FROM_COORDINATES;TAXON_MATCH_TAXON_ID_IGNORED
4868152100	50c9509d-22c7-4a22-a47d-8c48425ef4a7	https://www.inaturalist.org/observations/153340665	Animalia	Arthropoda	Insecta	Lepidoptera	Nymphalidae	Danaus	Danaus plexippus		SPECIES	Danaus plexippus (Linnaeus, 1758)	Danaus plexippus		US		Georgia	PRESENT		28eb1a3f-1c15-4a95-931a-4af90ecb574d	31.620569	-81.265035	5.0						2023-03-27T16:14:37	27	3	2023	5133088	5133088	HUMAN_OBSERVATION	iNaturalist	Observations	153340665		Christa F. Hayes	2023-04-03T16:49:40	CC_BY_NC_4_0	Christa F. Hayes	Christa F. Hayes			2024-05-28T03:32:03.160Z	StillImage	COORDINATE_ROUNDED;CONTINENT_DERIVED_FROM_COORDINATES;TAXON_MATCH_TAXON_ID_IGNORED
4868139350	50c9509d-22c7-4a22-a47d-8c48425ef4a7	https://www.inaturalist.org/observations/216122131	Animalia	Arthropoda	Insecta	Lepidoptera	Nymphalidae	Danaus	Danaus plexippus		SPECIES	Danaus plexippus (Linnaeus, 1758)	Danaus plexippus		US		Ohio	PRESENT		28eb1a3f-1c15-4a95-931a-4af90ecb574d	40.044079	-83.065383	3.0						2023-09-14T09:29:28	14	9	2023	5133088	5133088	HUMAN_OBSERVATION	iNaturalist	Observations	216122131		Craig	2024-05-16T15:15:27	CC_BY_NC_4_0	Craig	Craig			2024-05-28T03:43:39.432Z	StillImage	COORDINATE_ROUNDED;CONTINENT_DERIVED_FROM_COORDINATES;TAXON_MATCH_TAXON_ID_IGNORED
4868122462	50c9509d-22c7-4a22-a47d-8c48425ef4a7	https://www.inaturalist.org/observations/215824428	Animalia	Arthropoda	Insecta	Lepidoptera	Nymphalidae	Danaus	Danaus plexippus		SPECIES	Danaus plexippus (Linnaeus, 1758)	Danaus plexippus		US		Wisconsin	PRESENT		28eb1a3f-1c15-4a95-931a-4af90ecb574d	43.08413	-89.375661	50.0						2023-09-23T17:06:53	23	9	2023	5133088	5133088	HUMAN_OBSERVATION	iNaturalist	Observations	215824428		gmzelle	2024-05-15T01:16:46	CC_BY_NC_4_0	gmzelle	gmzelle			2024-05-28T04:07:43.933Z	StillImage	COORDINATE_ROUNDED;CONTINENT_DERIVED_FROM_COORDINATES;TAXON_MATCH_TAXON_ID_IGNORED
4868121692	50c9509d-22c7-4a22-a47d-8c48425ef4a7	https://www.inaturalist.org/observations/215795948	Animalia	Arthropoda	Insecta	Lepidoptera	Nymphalidae	Danaus	Danaus plexippus		SPECIES	Danaus plexippus (Linnaeus, 1758)	Danaus plexippus		US		Texas	PRESENT		28eb1a3f-1c15-4a95-931a-4af90ecb574d	32.624855	-97.559147	29066.0						2023-08-22T10:00	22	8	2023	5133088	5133088	HUMAN_OBSERVATION	iNaturalist	Observations	215795948		angel00	2024-05-14T22:11:25	CC_BY_NC_4_0	angel00	angel00			2024-05-28T03:39:58.290Z	StillImage	COORDINATE_ROUNDED;CONTINENT_DERIVED_FROM_COORDINATES;TAXON_MATCH_TAXON_ID_IGNORED
4868115887	50c9509d-22c7-4a22-a47d-8c48425ef4a7	https://www.inaturalist.org/observations/182977421	Animalia	Arthropoda	Insecta	Lepidoptera	Nymphalidae	Danaus	Danaus plexippus		SPECIES	Danaus plexippus (Linnaeus, 1758)	Danaus plexippus		US		Maryland	PRESENT		28eb1a3f-1c15-4a95-931a-4af90ecb574d	39.049817	-76.512772	10.0						2023-09-12T14:11:45	12	9	2023	5133088	5133088	HUMAN_OBSERVATION	iNaturalist	Observations	182977421		Cassidy Martin	2023-09-12T18:30:58	CC_BY_4_0	Cassidy Martin	Cassidy Martin			2024-05-28T04:03:36.876Z		COORDINATE_ROUNDED;CONTINENT_DERIVED_FROM_COORDINATES;TAXON_MATCH_TAXON_ID_IGNORED
4868110167	50c9509d-22c7-4a22-a47d-8c48425ef4a7	https://www.inaturalist.org/observations/217163459	Animalia	Arthropoda	Insecta	Lepidoptera	Nymphalidae	Danaus	Danaus plexippus		SPECIES	Danaus plexippus (Linnaeus, 1758)	Danaus plexippus		US		California	PRESENT		28eb1a3f-1c15-4a95-931a-4af90ecb574d	38.685764	-119.813653	17.0						2023-09-27T11:30	27	9	2023	5133088	5133088	HUMAN_OBSERVATION	iNaturalist	Observations	217163459		Alpine Watershed Group	2024-05-20T21:57:51	CC_BY_NC_4_0	Alpine Watershed Group	Alpine Watershed Group			2024-05-28T03:40:27.629Z	StillImage	COORDINATE_ROUNDED;CONTINENT_DERIVED_FROM_COORDINATES;TAXON_MATCH_TAXON_ID_IGNORED
4868082186	50c9509d-22c7-4a22-a47d-8c48425ef4a7	https://www.inaturalist.org/observations/215922552	Animalia	Arthropoda	Insecta	Lepidoptera	Nymphalidae	Danaus	Danaus plexippus		SPECIES	Danaus plexippus (Linnaeus, 1758)	Danaus plexippus		US		Texas	PRESENT		28eb1a3f-1c15-4a95-931a-4af90ecb574d	32.899845	-96.78312	12.0						2023-10-10T10:26:45	10	10	2023	5133088	5133088	HUMAN_OBSERVATION	iNaturalist	Observations	215922552		pacogomez	2024-05-15T15:20:08	CC_BY_NC_4_0	pacogomez	pacogomez			2024-05-28T04:07:57.848Z	StillImage	CONTINENT_DERIVED_FROM_COORDINATES;TAXON_MATCH_TAXON_ID_IGNORED
4868068554	50c9509d-22c7-4a22-a47d-8c48425ef4a7	https://www.inaturalist.org/observations/181231441	Animalia	Arthropoda	Insecta	Lepidoptera	Nymphalidae	Danaus	Danaus plexippus		SPECIES	Danaus plexippus (Linnaeus, 1758)	Danaus plexippus		CA		Ontario	PRESENT		28eb1a3f-1c15-4a95-931a-4af90ecb574d	43.125176	-81.268889	1871.0						2023-09-01T12:45:13	1	9	2023	5133088	5133088	HUMAN_OBSERVATION	iNaturalist	Observations	181231441		paul_dennehy	2024-05-16T02:04:36	CC_BY_NC_4_0	barnesmike41	barnesmike41			2024-05-28T04:09:20.647Z	StillImage	COORDINATE_ROUNDED;CONTINENT_DERIVED_FROM_COORDINATES;TAXON_MATCH_TAXON_ID_IGNORED
In [11]:
# Load the GBIF data
gbif_df = pd.read_csv(
    gbif_path, 
    delimiter='\t',
    index_col='gbifID',
    usecols=['gbifID', 'decimalLatitude', 'decimalLongitude', 'month']
)
gbif_df.head()
Out[11]:
decimalLatitude decimalLongitude month
gbifID
4868184771 43.271790 -79.903956 8
4868152100 31.620569 -81.265035 3
4868139350 40.044079 -83.065383 9
4868122462 43.084130 -89.375661 9
4868121692 32.624855 -97.559147 8

Convert the GBIF data to a GeoDataFrame¶

To plot the GBIF data, we need to convert it to a GeoDataFrame first.

Your task

  1. Replace your_dataframe with the name of the DataFrame you just got from GBIF
  2. Replace longitude_column_name and latitude_column_name with column names from your `DataFrame
  3. Run the code to get a GeoDataFrame of the GBIF data.
In [12]:
gbif_gdf = (
    gpd.GeoDataFrame(
        gbif_df, 
        geometry=gpd.points_from_xy(
            gbif_df.decimalLongitude, 
            gbif_df.decimalLatitude), 
        crs="EPSG:4326")
    # Select the desired columns
    [['month', 'geometry']]
)
gbif_gdf
Out[12]:
month geometry
gbifID
4868184771 8 POINT (-79.90396 43.27179)
4868152100 3 POINT (-81.26503 31.62057)
4868139350 9 POINT (-83.06538 40.04408)
4868122462 9 POINT (-89.37566 43.08413)
4868121692 8 POINT (-97.55915 32.62485)
... ... ...
4011504290 1 POINT (-95.49225 30.16971)
4011503220 1 POINT (-122.06137 37.58708)
4011499223 1 POINT (-122.03414 37.51129)
4011493281 1 POINT (-97.40997 25.82311)
4011490187 1 POINT (-122.01204 37.45983)

35944 rows × 2 columns

Count the number of observations in each ecosystem, during each month of 2023¶

Identify the ecoregion for each observation¶

You can combine the ecoregions and the observations spatially using a method called .sjoin(), which stands for spatial join.

Further reading

Check out the geopandas documentation on spatial joins to help you figure this one out. You can also ask your favorite LLM (Large-Language Model, like ChatGPT)

Your task

  1. Identify the correct values for the how= and predicate= parameters of the spatial join.
  2. Select only the columns you will need for your plot.
  3. Run the code.
In [13]:
gbif_ecoregion_gdf = (
    ecoregions_gdf
    # Match the CRS of the GBIF data and the ecoregions
    .to_crs(gbif_gdf.crs)
    # Find ecoregion for each observation
    .sjoin(
        gbif_gdf,
        how='inner', 
        predicate='contains')
    # Select the required columns
    [['month', 'name']]
)
gbif_ecoregion_gdf
Out[13]:
month name
ecoregion
57 7 Thompson-Okanogan Plateau
57 6 Thompson-Okanogan Plateau
57 7 Thompson-Okanogan Plateau
57 6 Thompson-Okanogan Plateau
57 8 Thompson-Okanogan Plateau
... ... ...
2545 6 Eastern Cascades Slopes and Foothills
2545 7 Eastern Cascades Slopes and Foothills
2545 6 Eastern Cascades Slopes and Foothills
2545 9 Eastern Cascades Slopes and Foothills
2545 9 Eastern Cascades Slopes and Foothills

35423 rows × 2 columns

Count the observations in each ecoregion each month¶

Your task:

  1. Replace columns_to_group_by with a list of columns. Keep in mind that you will end up with one row for each group – you want to count the observations in each ecoregion by month.
  2. Select only month/ecosystem combinations that have more than one occurrence recorded, since a single occurrence could be an error.
  3. Use the .groupby() and .mean() methods to compute the mean occurrences by ecoregion and by month.
  4. Run the code – it will normalize the number of occurrences by month and ecoretion.
In [14]:
occurrence_df = (
    gbif_ecoregion_gdf
    # For each ecoregion, for each month...
    .groupby(['ecoregion', 'month'])
    # ...count the number of occurrences
    .agg(occurrences=('name', 'count'))
)

# Get rid of rare observations (possible misidentification?)
occurrence_df = occurrence_df[occurrence_df.occurrences>1]

# Take the mean by ecoregion
mean_occurrences_by_ecoregion = (
    occurrence_df
    .groupby(['ecoregion'])
    .mean()
)

# Take the mean by month
mean_occurrences_by_month = (
    occurrence_df
    .groupby(['month'])
    .mean()
)

# Normalize the observations by the monthly mean throughout the year
occurrence_df['norm_occurrences'] = (
    occurrence_df
    / mean_occurrences_by_ecoregion 
    / mean_occurrences_by_month
)
occurrence_df
Out[14]:
occurrences norm_occurrences
ecoregion month
57 6 16 0.052299
7 14 0.022974
8 6 0.008173
60 6 2 0.016343
7 3 0.012308
... ... ... ...
2528 8 2 0.016346
2545 6 4 0.015690
7 18 0.035446
8 15 0.024519
9 3 0.005624

879 rows × 2 columns

Plot the Danaus plexippus observations by month¶

Your task

  1. If applicable, replace any variable names with the names you defined previously.
  2. Replace column_name_used_for_ecoregion_color and column_name_used_for_slider with the column names you wish to use.
  3. Customize your plot with your choice of title, tile source, color map, and size.
In [16]:
from bokeh.models import HoverTool
import holoviews as hv
In [17]:
# Updating plot to remove scientific notation in hover tool

# Join the occurrences with the plotting GeoDataFrame
occurrence_gdf = ecoregion_plot.join(occurrence_df)

# Get the plot bounds so they don't change with the slider
xmin, ymin, xmax, ymax = occurrence_gdf.total_bounds

# Define slider widget
slider = pn.widgets.DiscreteSlider(
    name='month',
    options={calendar.month_name[i]: i for i in range(1,13)}
)

# Creating hover tool to show numbers as decimals and not in sci notation
hover = HoverTool(tooltips=[("norm_occurrences", "@norm_occurrences{'.0f'}")]) 

# Plot occurrence by ecoregion and month
migration_plot = (
    occurrence_gdf
    .hvplot(
        c='norm_occurrences',
        groupby='month',
        # Use background tiles
        geo=True, crs=ccrs.Mercator(), tiles='EsriWorldLightGrayBase',
        title="Monarch Butterfly Observations by Month",
        xlim=(xmin, xmax), ylim=(ymin, ymax),
        frame_height=550,
        widgets={'month': slider},
        widget_location='bottom',
        colormap='reds',
        yformatter='%.0f',
        tools= [hover]
    )
)

# Save the plot
migration_plot.save('monarch-migration_no_sci.html', embed=True)

# Show the plot
migration_plot

                                               
WARNING:bokeh.core.validation.check:W-1005 (FIXED_SIZING_MODE): 'fixed' sizing mode requires width and height to be set: figure(id='p11664', ...)









Out[17]:




BokehModel(combine_events=True, render_bundle={'docs_json': {'37debd06-2710-4609-b5b3-74de1e6e8542': {'version…




















In [18]:






%%capture
%%bash
jupyter nbconvert *.ipynb --to html

























::: {.content-visible when-format=“html”}

:::





Want an EXTRA CHALLENGE?


Notice that the month slider displays numbers instead of the month
name. Use pn.widgets.DiscreteSlider() with the options= parameter
set to give the months names. You might want to try asking ChatGPT how
to do this, or look at the documentation for
pn.widgets.DiscreteSlider(). This is pretty tricky!