Isotopic discrimination

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C3 and C4 plants assimilate the heavier atmospheric \(\ce{^{13}CO2}\) and \(\ce{^{14}CO2}\) molecules less easily than \(\ce{^{12}CO2}\), leading to a discrimination against carbon 13 and carbon 14 and alteration of the resulting isotopic composition of plant tissues. The isotopic discrimination and associated isotopic composition of a plant material depends on the photosynthetic pathway.

The pmodel module provides the CarbonIsotopes class, which takes the predicted optimal chi (\(\chi\)) and photosynthetic pathway from a fitted PModel instance and predicts various isotopic discrimination and composition values.

The predictions from the CarbonIsotopes class are driven by variation in \(\chi\). The examples below show predictions across a range of values of \(\chi\). The sequence of \(\chi\) values used is created by using the P Model to estimate \(\chi\) across a temperature gradient, giving the range of \(\chi\) values shown below for C3 and C4 plants.

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import numpy as np
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D

from pyrealm.pmodel.pmodel import PModel
from pyrealm.pmodel import PModelEnvironment, CarbonIsotopes

# Use a simple temperature sequence to generate a range of optimal chi values
n_pts = 31
tc_1d = np.linspace(-10, 40, n_pts)

# Fit models. Since only relative light use efficiency is needed,
# fAPAR and PPFD are set to unity.
env = PModelEnvironment(tc=tc_1d, patm=101325, co2=400, vpd=1000, fapar=1, ppfd=1)
mod_c3 = PModel(env, method_optchi="prentice14")
mod_c4 = PModel(env, method_optchi="c4")

plt.plot(tc_1d, mod_c3.optchi.chi.flatten(), label="C3", marker=".")
plt.plot(tc_1d, mod_c4.optchi.chi.flatten(), label="C4", marker=".")
plt.title(r"Variation in $\chi$ with temperature")
plt.xlabel("Temperature (°C)")
plt.ylabel(r"Predicted optimal $\chi$")
plt.legend(frameon=False)
plt.show()

/home/docs/checkouts/readthedocs.org/user_builds/pyrealm/checkouts/latest/pyrealm/pmodel/pmodel.py:481: UserWarning: 
    Pyrealm 2.0.0 uses a new default for the quantum yield of photosynthesis (phi0=1/8).
    You may need to change settings to duplicate results from pyrealm 1.0.0.
            
  warn(

Calculation of values

The CarbonIsotopes class takes a PModel instance, along with estimates of the atmospheric isotopic ratios for Carbon 13 (\(\delta13C\), permil) and Carbon 14 (\(\Delta14C\), permil) and calculates the following predictions:

• Delta13C_simple: discrimination against carbon 13 (\(\Delta\ce{^{13}C}\), permil) excluding photorespiration.

• Delta13C: discrimination against carbon 13 (\(\Delta\ce{^{13}C}\), permil) including photorespiration.

• Delta14C: discrimination against carbon 14 (\(\Delta\ce{^{14}C}\), permil) including photorespiration.

• d13C_leaf: isotopic ratio of carbon 13 in leaves (\(\delta\ce{^{13}C}\), permil).

• d14C_leaf: isotopic ratio of carbon 14 in leaves (\(\delta\ce{^{14}C}\), permil).

• d13C_wood: isotopic ratio of carbon 13 in wood (\(\delta\ce{^{13}C}\), permil), given a parameterized post-photosynthetic fractionation.

The calculations differ between C3 and C4 plants, and this is set by the selection of the method_optchi argument used for the PModel instance.

carb_c3 = CarbonIsotopes(mod_c3, d13CO2=-8.4, D14CO2=19.2)
carb_c3.summarize()

CarbonIsotopes(shape=(31,), method=False)
Attr               Mean     Min     Max    NaN  Units
---------------  ------  ------  ------  -----  -------
Delta13C_simple   19.42   11.25   26.17      0  permil
Delta13C          17.82   10.8    22.62      0  permil
Delta14C          35.65   21.6    45.23      0  permil
d13C_leaf        -25.75  -30.33  -19         0  permil
d14C_leaf        -15.83  -24.91   -2.35      0  permil
d13C_wood        -23.65  -28.23  -16.9       0  permil

carb_c4 = CarbonIsotopes(mod_c4, d13CO2=-8.4, D14CO2=19.2)
carb_c4.summarize()

CarbonIsotopes(shape=(31,), method=True)
Attr               Mean     Min    Max    NaN  Units
---------------  ------  ------  -----  -----  -------
Delta13C_simple    7.17    1.45  11.88      0  permil
Delta13C           7.17    1.45  11.88      0  permil
Delta14C          14.35    2.91  23.77      0  permil
d13C_leaf        -15.45  -20.04  -9.84      0  permil
d14C_leaf          4.83   -4.46  16.25      0  permil
d13C_wood        -13.35  -17.94  -7.74      0  permil

The plots below show how the calculated values alter with \(\chi\). The differences in the direction of these relationships between C3 and C4 pathways creates a predictable isotopic signature of relative contributions of the two pathways.

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# Create side by side subplots
fig, axes = plt.subplots(2, 3, figsize=(12, 8))

attrs = [
    "Delta13C_simple",
    "Delta13C",
    "Delta14C",
    "d13C_leaf",
    "d14C_leaf",
    "d13C_wood",
]

for attr, ax in zip(attrs, axes.flatten()):

    ax.plot(mod_c3.optchi.chi, getattr(carb_c3, attr), label="C3")
    ax.plot(mod_c4.optchi.chi, getattr(carb_c4, attr), label="C4")
    ax.set_title(attr)
    ax.set_ylabel(attr)
    ax.set_xlabel("Optimal Chi (-)")
    ax.legend(frameon=False)

fig.tight_layout()