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Fit an A–Ci curve

Fit the Farquhar–von Caemmerer–Berry C3 model to A–Ci (and light and temperature) response data.

Inputs

A CSV, .xlsx or LI-6800 log with columns for A, Ci, light (Qabs or Q) and leaf temperature (Tleaf or T). Light should be absorbed light; PhytKit uses Qabs when both are present. Temperatures below 200 are read as °C.

Add a CurveID column if the file holds several curves. PhytKit then applies FvCB's per-curve constraints to each curve separately. LI-6800 logs merged with pk concat have one.

Steps

  1. Look at the model's parameters and defaults:

    pk describe fvcb

  2. Fit. This is an apparent fit (\(C_c = C_i\)), with mesophyll conductance fixed very high and alphaG held at zero:

    pk fit photosynthesis examples/aci.csv --model fvcb --set gm=1000000 --fix gm,alphaG

  3. Check the result before you use it:

    • warnings: did PhytKit use the columns and units you expected?
    • converged: false means it stopped at the iteration limit. Rerun with --max-iter 400 or more.
    • r2 and rmse: how closely the model follows the data.
    • params: values sitting exactly at a bound (pk describe fvcb) are poorly determined by the data.

  4. Add --predicted to get the model's prediction for every point next to the measured values, for plotting:

    pk fit photosynthesis examples/aci.csv --model fvcb --set gm=1000000 --fix gm,alphaG --predicted

Choosing what to fit

By default, every parameter not marked fixed by default in Models and parameters is fitted. That's 18 parameters, including the temperature responses. For a single curve at one temperature, that's far more than the data can determine. Fit only what the data constrains:

pk fit photosynthesis examples/aci.csv --model fvcb --set gm=1000000 --fit Vcmax25,Jmax25,TPU25,Rd25,alpha,theta

A single-temperature curve says nothing about the temperature parameters, so leaving them out of --fit keeps them at their defaults.

C4 leaves and the empirical model

pk fit photosynthesis examples/aci.csv --model fvcbC4
pk fit photosynthesis examples/aci.csv --model empiricalA

The sample data are C3, so these are for illustration only. See Photosynthesis models.

Constraints

FvCB's soft constraints are all on by default. To fit without them, or to weaken one:

pk fit photosynthesis examples/aci.csv --model fvcb --constraints none
pk fit photosynthesis examples/aci.csv --model fvcb --no-constraint ap_limits_high --weight vj_ratio=0.5

In Python

import phytkit as pk

fit = pk.fit("photosynthesis", "examples/aci.csv", model="fvcb", set={"gm": 1e6}, fix=["gm", "alphaG"], predicted=True)
print(fit["params"]["Vcmax25"], fit["params"]["Jmax25"])