Day 18: In-Class Assignment

✅  Put your name here

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✅  Put your group member names here

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To which switchgrass should we swiftly switch?¶

Credits: Missouri Department of Conservation

Learning goals of today’s assignment¶

• Compute confidence intervals via bootstrap and formula

• Recognize that the pre-class CI formula has pitfalls and tend to underestimate the true interval

• Practice matplotlib for confidence bands

Assignment instructions¶

Work with your group to complete this assignment. Instructions for submitting this assignment are at the end of the notebook. The assignment is due at the end of class.

Background¶

Switchgrass, a potential biofuel crop, is a genetically diverse species with phenotypic plasticity enabling it to grow in a range of environments and native to North American prairies. Two primary divergent ecotypes, uplands and lowlands, exhibit trait combinations representative of acquisitive and conservative growth allocation strategies, respectively. Whether these ecotypes respond differently to various types of environmental drivers remains unclear but is crucial to understanding how switchgrass varieties will respond to climate change.

This study grew two upland, two lowland, and two intermediate/hybrid cultivars of switchgrass on three states: Missouri, Illinois, and Texas. Over a 4-year period, the study measured plant functional traits and biomass yields and evaluated genotype-by-environment (G × E) interaction effects by analyzing switchgrass responses to soil and climate variables. Altogether, this research provides essential knowledge for improving the viability of switchgrass as a biofuel crop.

The end goal is to reproduce the results from Figure 2b in Ricketts et al (2023).

Ricketts, M. P., Heckman, R. W., Fay, P. A., Matamala, R., Jastrow, J. D., Fritschi, F. B., Bonnette, J., Juenger, T. E. (2023). Local adaptation of switchgrass drives trait relations to yield and differential responses to climate and soil environments. GCB Bioenergy, 15, 680–696.

Credits: Ricketts et al (2023)

✅  Question 1

Just focus on Figure (b)

• What is reflected on the x-axis?

• What is reflected on the y-axis?

• In your own words, what information do you get out of this figure?

✎ Put your answer here

1. Mean switchgrass yields¶

✅  Task 2

• Load the data set HARVEST.tsv with pandas

• Note that it is a TSV file: tab-separated file. What parameter of pd.read_csv do you need to specify to load the file correctly?

• Display the first few rows of the DataFrame to make sure it looks ok.

1.1 Wrangling with Series.str¶

Notice that the YEAR column is a string because it has a Y at the beginning of every entry. For reasons that will be clearer later, it will be much easier to have YEAR as an int instead.

• One way fix it is to convert the YEAR Series to an actual datetime datatype with pd.to_datetime and specifying the right format parameter.

  • We saw this strategy for Homework 3.

  • It works best when your data also has month or even day information.

• Another way is to remove the starting Y character with the .str.removepreffix function and the use .astype to convert the prefix-less strings to ints.

  • The .str tells pandas that your Series is all strings: there are plenty of things pandas can do with strings.

Important: both strategies only work for Series. Make sure you are working <your_dataframe>['YEAR'] (a Series) instead of <your_dataframe>.

✅  Task 2

• Convert the year column to an int datatype

• Replace the year column with the newly transformed Series

1.2 Summarizing the data¶

Columns to pay attention to for this assignment:

✅  Task 3

Compute the mean, standard error, and counts of biomass yield for switchgrass for each year, site, and genotype.

• Use groupby to group your row values by year-site-genotype and get the means and standard errors in a single line.

• Save the DataFrame as summary: it should be 72 rows by 6 columns.

Hint: pandas has a .count function.

1.4 Visualization¶

Let’s make sure that our data looks right. Instead of reproducing all of Figure 2b at once, let’s start small: one genotype at a time.

✅  Task 4

• Plot mean yield vs year for the 'Alamo'genotype

• Use different colors and markers for different sites

• Make sure your plot is labeled

• Add a grid to your plot

Hints:

• Define two lists: one with colors and another for markers

• Define a genotype string variable and make a subDataFrame out of summary only looking at data from that one genotype

• Then plot all the sites by looping through sites (list given below)

  • Make a sub-subDataFrame for yield values just for this site

  • Remember that .plot lets you draw both lines and markers by adding the parameter marker

2. Confidence intervals¶

Notice that in Figure 2b, the plot lines also come with shaded bands.

✅  Question 5

• According to 2b’s caption, what’s the meaning of these shaded areas?

• How many switchgrass measurements were collected per year-site-genotype?

✎ Put your answer here

2.1 Computing intervals with the formula¶

✅  Task 6

• Compute the lower and upper 95% confidence intervals for row in the summary dataframe.

• That is, get the width for the confidence interval from every set of measurements for each year, site, and genotype.

  $$\text{CI}_{\text{width}} = t_{(1+\alpha)/2,\;,n-1}\times\text{Standard Error}$$

  (1)

• Notice that you have almost all the information you need in the summary dataframe if you use the CI formula.

• Remember that you can compute $t$ quantiles with the stats.t.ppf function.

• Add the interval width value as a new column of summary.

Remember that you can easily add a new column to an existing dataframe by doing:

# Assuming that `new_column_values` has the same length as the dataframe
my_dataframe['new_column_name'] = new_column_values

2.2 Visualizing intervals¶

✅  Task 7

• Start by copy/pasting your matplotlib code from (1.4)

• Use the .fill_between function to draw shades—confidence intervals—that follow the lines and markers you already drew.

• Remember that the confidence interval is

  $$\text{Confidence Interval} = \text{Mean}\pm\text{CI}_{\text{width}}.$$

  (2)

• Make sure you have overlaid a grid!

Does your final plot look like Alamo in 2b? (Spoiler: it should be close but not equal).

3. Gear switch: Matplotlib pracice with Figure and Axis¶

Now let’s reproduce Figure 2b from Ricketts et al! Just a reminder on how the Axis interface initialization works for Matplotlib:

# Make six subplots, organized into 2 rows and 3 columns
# Make sure they all share the same x and y-axis scale so they are comparable
fig, ax = plt.subplots(2, 3, figsize=(12, 5), sharex=True, sharey=True)

The above will make ax a 2D array. Since we are still not too familiar with 2D arrays, we’ll force ax to be 1D.

# np.atleast_1d() makes sure ax is treated as an array in the first place
# .ravel() will a 2x3 two-dimensional array into a 6-length one-dimensional one.
ax = np.atleast_1d(ax).ravel()

The array ax is read left to right, up down. For example ax[0] corresponds to the top left plot, ax[1] is the top center one, etc. You can trean ax[i] almost the same way as plt.

✅  Task 8

• Run the cell below and add comments to the lines that are new to you

• Write new lines (in the appropriate place) to plot the average switchgrass yield for all years, sites, and genotypes.

• Add shades using the CI values you computed in (2.1)

• You can base your answer on what you already have from (2.2)

• Explore ax[i].text by toying with it:

  • Change 0.98, 0.98 for 0.02, 0.98 or 0.98, 0.5

  • Change ha to center or left

  • Change va to center or bottom

Further reading¶

• You can read more about the tranform parameter in .text() here: https://matplotlib.org/stable/users/explain/artists/transforms_tutorial.html

• Read more about text alignment (va and ha) here: https://matplotlib.org/stable/gallery/text_labels_and_annotations/text_alignment.html

Congratulations, you’re done!¶

Submit this assignment by uploading it to the course Canvas web page. Go to the “In-class assignments” folder, find the appropriate submission link, and upload it there.

See you next class!

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