Isotopic discrimination

The worked example from this page can be downloaded as Jupyter notebook here.

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 CalcCarbonIsotopes 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 CalcCarbonIsotopes 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.

Hide code cell source

 
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, CalcCarbonIsotopes

# 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()

pyrealm/pmodel.py:409: 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.
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Calculation of values

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

CalcCarbonIsotopes(shape=(31,), method=False)
Attr               Mean     Min     Max    NaN  Units
---------------  ------  ------  ------  -----  -------
Delta13C_simple   19.4    11.15   26.16      0  permil
Delta13C          17.81   10.71   22.61      0  permil
Delta14C          35.62   21.42   45.23      0  permil
d13C_leaf        -25.74  -30.33  -18.91      0  permil
d14C_leaf        -15.8   -24.9    -2.17      0  permil
d13C_wood        -23.64  -28.23  -16.81      0  permil

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

CalcCarbonIsotopes(shape=(31,), method=True)
Attr               Mean     Min    Max    NaN  Units
---------------  ------  ------  -----  -----  -------
Delta13C_simple    7.18    1.46  11.92      0  permil
Delta13C           7.18    1.46  11.92      0  permil
Delta14C          14.36    2.91  23.83      0  permil
d13C_leaf        -15.46  -20.08  -9.84      0  permil
d14C_leaf          4.81   -4.52  16.24      0  permil
d13C_wood        -13.36  -17.98  -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()
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