DOI: 10.5061/dryad.6m905qgcs
title: Evolution of phenotypic polymorphism in symbiont-pairing in plant-fungal symbiosis

description: 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.
description: # Evolution of phenotypic polymorphism in symbiont-pairing in plant-fungal
 symbiosis 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.