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The phrase "evolution as a function of" is correct and usable in written English.
This phrase is used to discuss how a certain process or system evolves in relation to another factor. For example, you could say: "The evolution of language is a function of its environment." Here, the phrase is used to explain how language evolves in relation to its particular environment.
Exact(60)
Figure 1 Evolution as a function of mean grain size.
Figure 2 Evolution as a function of strain rate.
The damage mode and damage evolution as a function of fatigue deformation are identified.
Figure 8 Global mean signal power evolution as a function of longitude.
Figure 9 Au droplet evolution as a function of the DA.
The microstructural evolution as a function of sintering temperatures was shown in Figure 4.
The plug flow evolution as a function of time is described using DPIV.
The coatings' microstructure evolution, as a function of high-temperature exposure, was analysed by scanning and transmission electron microscopy.
To determine the mass evolution as a function of time, the samples were periodically removed from the oven and weighed.
Figure 5 PL peak position evolution as a function of dynamic viscosity for different liquids at 300 K.
A generalized equation that qualitatively matches the kinetics of gaseous product evolution as a function of pressure is given.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com