https://doi.org/10.5061/dryad.0rxwdbrzs

MATLAB script, which provides a numerical solution of the stability analysis and gives the evolutionary trait evolution by solving the ODE of the canonical equation.

1. Workflow

Run the iso2aniso_main_230718_dryad.m file with MATLAB (version 2022b or later), according to one of the following three alternatives

1) Run iso2aniso_main_230718_dryad without input arguments solves the evolutionary path for a predefined parameter combination*

2) Run with adjusted parameter: iso2aniso_main_230718_dryad(fmc,Kg,Kz,d,am,ar)

Where

and

The model parameter values will be adjusted to the closest tested value (see below).

3) Run with free parameters: iso2aniso_main_230718_dryad(fmc,Kg,Kz,d,am,ar,adjust)

Where adjust=true, the model parameter values are adjusted to the closest tested value, while adjust=false, the specified model parameters are unaltered.

Explanation:
The numerical solutions of the ODE can get unstable, especially for parameter regions being exactly between two regions of different evolutionary behaviour, or for extreme parameter values. The following code is adapted to handle the specific parameter combinations run for the figures produced in the manuscript (Fig. 4-5 and Fig S1-S2). Any other parameter combination could generate errors. By adjusting the chosen parameters to match the tested parameters, we can guarantee no errors.

Feel free to set adjust=false, but be aware that the numerical solutions might not work as intended. You can choose your own model parameters by specifying them as input arguments of the main function.

* Predefined parameter combination:

Examples of other parameter combinations:

iso2aniso_main_230718_dryad(1,0.1,1e4,1e2 ,1,0) % Yields isogamy
iso2aniso_main_230718_dryad(1,0.1,1e4,1e-2,1,0) % Yields female bias
iso2aniso_main_230718_dryad(1,0.1,1e4,0.5 ,1,0) % Yields male bias
iso2aniso_main_230718_dryad(1,0.1,1e4,1.5 ,1,0) % Yields oscillations

2. Brief description of all files

1) iso2aniso_main_230718_dryad.m

Main file, determines the model scenario and parameters, as described above.

Performs all numerical analysis, solves ODE and plots the ODE-solution by running the remaining files in the given order below:

1.1) iso2aniso_eq_fmc_230615.m

With an input of 1, 0 or -1, the function will output a structure array with all equation needed for the scenario of motility competition, fusion partner capture competition or chemoattraction, respectively. The function will load all equations needed, if the corresponding MAT-file for the scenario is present. Otherwise, it will generate all equations, and then save them as a MAT-file, before returning them as a structure array.

1.1.1) iso2aniso_eq_fmc_230615_1.mat

MAT-file that contains all equations for the motility competition scenario.

1.1.2) iso2aniso_eq_fmc_230615_0.mat

MAT-file that contains all equations for the fusion partner capture competition scenario.

1.1.2) iso2aniso_eq_fmc_230615_-1.mat

MAT-file that contains all equations for the chemoattraction scenario.

1.2) iso2aniso_stabanalysis_iso_230718.m

Solves for the isogamic singular points and derives the stability properties of the evolutionary dynamics.

1.3) iso2aniso_odesolve_230626.m

Solves for the ODE, first under the isogamic constraint until attractor reached, and then for unconstrained evolution until anisogamic attractor is reached.

1.4) iso2aniso_stabanalysis_aniso_230615.m

Derives the stability properties of the evolutionary dynamics of the anisogamic attractor.

1.5) iso2aniso_plot_220921.m

Plots the ODE-solution.

1.5.1) breakxaxis.m

Function that split the data on the x-axis, such that is has a left and right range.

1.5.1) sfigure.m

Function that creates new figure window without cause a focus on the new figure.

1.5.1) sigdig.m

Function that rounds numbers to certain significance

2.1 Naming convention

A prefix of iso2aniso_ indicates that the function was created for this specific project. The six numbers in a row indicated year month and date of last edit _YYMMDD.