Functionally variable symbionts commonly co-occur including within the roots of individual plants, in spite of arguments from simple models of the stability of mutualism that predict competitive exclusion among symbionts. We explore this paradox by evaluating the dynamics generated by symbiont competition for plant resources, and the plant’s preferential allocation to the most beneficial symbiont, using a system of differential equations representing the densities of mutualistic and non-mutualistic symbionts and the level of preferentially allocated and non-preferentially allocated resources for which the symbionts compete. We find that host preferential allocation and costs of mutualism generate resource specialization that makes the coexistence of beneficial and non-beneficial symbionts possible. Furthermore, coexistence becomes likely due to negative physiological feedbacks in host preferential allocation. We find that biologically realistic models of plant physiology and symbiont competition predict that the coexistence of beneficial and non-beneficial symbionts should be common in root symbioses, and that the density and relative abundance of mutualists should increase in proportion to the needs of the host.

The zipped folder is the repository of analyses: Preferential allocation of benefits and resource competition among recipients allows coexistence of symbionts within hosts

This theoretical study is carried out by solving a four-variable ordinary differential model that represents two carbon resources and two consumers (i.e. mutualist and non-mutualist symbionts on plant's root). No empirical dataset is used. Codes are written using open-source software (i.e. R, FORTRAN). Analytical derivations are given in the related manuscript with details in the appendix.

Introduction

All analyses can be reproduced using the given codes.

Dependencies

• R, R studio
• latex, any tex compiler
• FORTRAN 77, ifort compiler
• Origin pro/ any other data drawing tool, e.g., Adobe illustrator (if necessary)

How to compile

The main manuscript is written using standard Microsoft word and Endnotes (for citations), Appendix can be compiled using any tex compiler (SG used Texmaker) from Appendix.tex. First, all numerical simulations from the model analysis were carried out using FORTRAN 77 and ifort compiler (source code ARMN.f) and results were stored as .dat files in ARMN_Results/ARMN_dat/ folders. For convenience, we already provided the .dat files, so one can skip this step. Alternatively, for someone who is not used to FORTRAN, an alternative R-script is provided as "ARMN.R". The file ARMN.R will execute the same task and can generate the same data files as we stored as .dat files. The only difference is in the computation time, FORTRAN is much faster for long-term simulation. Next, one needs to run the Master.R script to get all the plots to be saved as pdfs in ARMN_Results/ folder.

Short summary for each file

• ARMN.R: R script solving 4 variable ODE, arguments are explained in that script.
• ARMN.f: equivalent FORTRAN code doing the same things as the R script ARMN.R does but in a much faster way.
• ARMN.in: input file for ARMN.f.
• ARMN_plotter.R: plotter function related to output from ARMN.f and generates Figs (1 - 4) for the manuscript.
• eigenval_analysis.R: R script with the function to compute eigenvalues at equilibrium. If the maximum of the real part of eigenvalues is negative, that means the equilibrium is stable.
• get_fmax.R: R script that generates data plotted in Fig 5, i.e., regime of co-existence for different combinations of parameters s, aM, aN. It makes some additional plots for the range of fidelity vs. s given other parameters.
• get_MNAR_eqm_analytical.R: R script with the function to get equilibrium of the ODE model used in ARMN.f using the analytical expression which is derived in the manuscript.
• LookAtStability_cleaned.r: R script to check stability within the fidelity range (f_min,f_max) given all possible combinations of other parameters used in the model.
• Appendix.tex: supplementary latex file used for the manuscript.
• ARMN_alternative.R: a solver for 4 variable ODE with the different functional form of F(M, N) used in the appendix.
• Master.R: R script to generate all figures for the main manuscript, a master file.

NOTE: within the script, inputs for each function are well explained and commented out.