Evolution of phenotypic polymorphism in symbiont-pairing in plant-fungal symbiosis

Published Nov 11, 2025 on Dryad. https://doi.org/10.5061/dryad.6m905qgcs

Data files

Nov 11, 2025 version files 72.75 MB

evolution_simulations_alternate_pfix.wls

24.23 KB
evolution_simulations.wls

34.52 KB
evolution_times.csv

334.62 KB
model_and_analysis.wls

38.75 KB
phenotype_frequency_sims_alternate_method.csv

11.76 KB
phenotype_frequency_sims.csv

304 B
README.md

2.24 KB
root_allocation_sims.csv

72.30 MB

Abstract

This is Mathematica code to model the evolution of polyphenism in plants (i.e., the ability of a single genotype to randomly develop into individuals with different phenotypes). We are interested in the trait of roots allocated to two different fungal partners when the benefits of a particular ratio of partners vary with the environment. We use both an analytical model and a simulation to investigate the conditions for polyphenism to evolve and evolutionary endpoints -- the root allocation phenotypes that evolved to be expressed and the probability that each one is expressed. Along with the analytical model and simulation code, we also include saved simulation results as .csv files so that the results can be analyzed without needing to re-run the simulations. The saved simulation results include the evolved traits (root allocation and phenotype frequency) and the time it took for populations to evolve away from monophenism.

Dryad DOI: https://doi.org/10.5061/dryad.6m905qgcs

Authors: Alexandra L. Brown and Stephen Proulx
Contact: alexandra_brown (berkeley.edu)

This is Mathematica code that models the evolution of polyphenism in plants, in particular, polyphenism in the ratio of roots allocated to two different fungal partners in a variable environment. We use both an analytical model and a simulation to investigate the conditions for polyphenism to evolve and the endpoints of evolution. Along with the analytical model and simulation code, there are saved simulation results as .wdx files, which can be loaded from within evolution_simulations.wls and evolution_simulations_alternate_pfix.wls instead of running the simulations, if desired.

To produce the results in the manuscript, the code was run in Mathematica version 13.

Analytical model

model_and_analysis.wls contains the analytical model and its analysis. Produces Figures 2 and 3.

Code to run simulations

evolution_simulations.wls runs and plots the simulations with the fixation probability given in the main text. Produces Figures 4, 5, 6, and S1.
evolution_simulations_alternate_pfix.wls runs and plots simulations with an alternative method of calculating the fixation probability. Produces Figures S2 and S3.

Saved simulation results

root_allocation_sims.csv saved results for the simulated evolution of root allocation, assuming phenotype frequency is fixed and does not evolve (Figures 4 and S1). Shows the evolution of root allocation over time.
phenotype_frequency_sims.csv saved results for the simulated evolution of phenotype frequency and root allocation together (Figure 5). Shows the endpoint of evolution.
evolution_times.csv saved results for the timing of evolution (Figure 6). Shows the time it took for populations to move a certain distance away from the monophenic optimum.
phenotype_frequency_sims_alternate_method.csv saved results for the simulated evolution of phenotype frequency and root allocation together, using an alternate method of calculating the fixation probability (Figures S2 and S3). Shows the endpoint of evolution.