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This dataset contains results of simulations of a discrete signaling game. Results for two main experiments are given.

One experiment allowed agents to play the signalling game starting at a nonsignaling or honest signaling state in order to determine which equilibria they reach after 1,000,000 generations. The other experiment focuses on trajectories of these simulations, studying how differential mutation rates for senders and receivers affects oscillations in strategies through time.

Description of the data and file structure (in Data.zip)

Equilibria_Honest Start and Equilibria_No Signaling Start folders:

These folder contain raw data for simulations used to make figure 3 in the manuscript and supplementary figures 1-2.

Simulations initialized at an honest signaling state (Equilibria_Honest Start folder) or a no signaling state (Equilibrai_No Signaling Start folder).

The *_equilibs.csv files give the equilibrium reached by each simulation, calculated using the tolerance value in the file name (eg 0.01).

Differential mutation rates: This folder contains raw data for simulations with different mutation rates and sizes (used to make figure 6 in the manuscript and supplementary figures 3-6).

In all folders:

• *params_json files are used as inputs when running simulations
• *summaryStats_Exper...* files store average values of strategy variables every 100 generations for a single simulation
• summaryStats.csv stores summarized data for all simulations in this folder

The numerical suffix to each file name corresponds across summary stat, parameter, and trajectory files.

Structure of data files:

Summary stats files (raw): [numerical code]_summaryStats_[name of experiment].csv

Each summaryStats file records population mean values every 100 generations for one replicate of a simulation

These summary statistics are computed and exported by the C++ simulaiton. They are used to track how strategies evolve through time and which equilibria are reached. These files are used to show population trajectories through time (eg Figure 5). These files are combined and collated into the summaryStats.csv files to produce figures concering evolved population strategies (eg figure 3).

Variables in these data (columns of the .csv) are as follows:

• "rep": Used if one file stores data for multiple replicates
• "gen": Generation which this row shows data for
• "indType": Does this row show data for senders or receivers?
• "strat01": Average population value for s01 or r01 at this generation (depending on value in indType; s01 if 'Sender' and r01 if 'Receiver' shown in indType)
• "strat11": Average population value for s11 or r11 at this generation (depending on indType)
• "meanFit": Average fitness of senders or reveivers at this generation (depending on indType)
• "expAlphaBeta": Expected value of alpha or beta (depending on indType) for a hybrid or honest equilibrium (whichever is predicted analytically for the parameters)
• "seed": User-input seed for random number generator
• "N": User-input number of signalers and receivers
• "G": User-input number of generations to run simiulations for
• "c1": User-input cost to consonant individuals ('c1' in paper)
• "c2": User-input cost to dissonant individuals ('c0' in paper)
• "v1": User-input benefit to consonant individuals (1 in paper)
• "v2": User-input benefit to dissonant individuals (1 in paper)
• "w1": User-input receiver benefit - play r = 1 to q = 1
• "w2": User-input receiver benefit - play r = 0 to q = 1
• "w3": User-input receiver benefit - play r = 0 to q = 1
• "w4": User-input receiver benefit - play r = 0 to q = 0
• "m": User-input percent of consonant signalers
• "mCorrected": Actual percent of consonant signalers in population (considers deviations from m due to integer number of consonant individuals)
• "interactionPartners": User-input number of individuals each sender and receiver plays the signaling game with
• "mutRateS": User-input mutation rate for sender strategies (s01, s11)
• "mutStepS": User-input mutation size for sender strategies (s01, s11)
• "mutRateR": User-input mutation rate for receiver strategies (r01, r11)
• "mutStepR": User-input mutation size for receivers strategies (r01, r11)
• "init01": User-input initial value for s01 or r01 (depending on indType)
• "init11": User-input initial value for s11 or r11 (depending on indType)
• "replicates": User-input number of replicates this data depicts
• "cauchyDist": User-input boolean value for whether a cauchy or normal distriubtion is used for mutations. 0 normal, 1 cauchy

Summary stats file (combined): 'summaryStats.csv'

Only for the 'Differential mutations rates' experiments

This is a file combining some data from all individual raw summaryStats files (which each hold data for one simulation) for an experiment. It shows the mean values of the final 200 000 generations of each raw summaryStat file.

Variables in these data (columns of the .csv) are as follows:

• "it": A number giving a unique identifying integer to each row
• "rep": Not relevant for this file: ignore
• "gen": Not relevant for this file: ignore
• "indType": Not relevant for this file: ignore
• "strat01": Not relevant for this file: ignore
• "strat11": Not relevant for this file: ignore
• "meanFit": Average population fitness over
• "expAlphaBeta": See above
• "seed": User input parameter, see above
• "N": User input parameter, see above
• "G": User input parameter, see above
• "c1": User input parameter, see above
• "c2": User input parameter, see above
• "v1": User input parameter, see above
• "v2": User input parameter, see above
• "w1": User input parameter, see above
• "w2": User input parameter, see above
• "w3": User input parameter, see above
• "w4": User input parameter, see above
• "m": User input parameter, see above
• "mCorrected": See above
• "interactionPartners": User input parameter, see above
• "mutRateS": User input parameter, see above
• "mutStepS": User input parameter, see above
• "mutRateR": User input parameter, see above
• "mutStepR": User input parameter, see above
• "init01": User input parameter, see above
• "init11": User input parameter, see above
• "replicates": User input parameter, see above
• "cauchyDist": User input parameter, see above
• "fileName": Raw data file which this row shows holds data from
• "ss01_mean": Average s01 value over the last 200 000 generations of the raw data file referred to in fileName
• "ss01_sd": Standard deviation of s01 values over the last 200 000 generations of the raw data
• "ss01_var": Variance of s01 values over the last 200 000 generations of the raw data
• "ss01_max": Maximum s01 value in the last 200 000 generations of the raw data
• "ss01_min": Minimum s01 value in the last 200 000 generations of the raw data
• "ss11_mean": Same as above, but for s11
• "ss11_sd": Same as above, but for s11
• "ss11_var": Same as above, but for s11
• "ss11_max": Same as above, but for s11
• "ss11_min": Same as above, but for s11
• "rs01_mean": Same as above, but for r01
• "rs01_sd": Same as above, but for r01
• "rs01_var": Same as above, but for r01
• "rs01_max": Same as above, but for r01
• "rs01_min": Same as above, but for r01
• "rs11_mean": Same as above, but for r11
• "rs11_sd": Same as above, but for r11
• "rs11_var": Same as above, but for r11
• "rs11_max": Same as above, but for r11
• "rs11_min": Same as above, but for r11
• "ss01_amp_mean": Not used in analyses. This is an attempt to capture the size of oscillations around a hybrid equilibrium. It shows the average difference betwen the maximum and minimum values of s01 in an oscialltion
• "ss01_amp_sd": Not used in analyses. This shows the standard deviation of amplitude of oscialltions of s01 around a hybrid equilibrium
• "ss01_halfPer_mean": Not used in analyses. This shows half the period between peaks in oscialltions of s01 around a hybrid equilirim
• "ss01_halfPer_sd": Not used in analyses. This shows the standard deviation of the above.

Parameter files: [experiment name]_[integer]_params.json

These text files hold input parameters which were used to run simulations. See description of these files under ##Code/Software below.

Summary files for equilibrium experiments: _endDataAll_11_noSig.csv and _endDataAll_11_honest.csv

Only for 'Equilibria_no signaling start' and 'Equilibria_ honest start' experiments

These files have the same function as summaryStats.csv: they hold calculated average values over the last 200 000 generations of the raw data files. There is one .csv for all simulations with an honest start and and another for all simulations with a no signaling start

Variables in these data (columns of the .csv) are as follows:

• "rep": Replicate of the raw data file in fileName which this row holds data for
• "gen": unused
• "indType": unused
• "strat01": unused
• "strat11": unused
• "meanFit": unused
• "expAlphaBeta": unused
• "seed": User input parameter, see above
• "N": User input parameter, see above
• "G": User input parameter, see above
• "c1": User input parameter, see above
• "c2": User input parameter, see above
• "v1": User input parameter, see above
• "v2": User input parameter, see above
• "w1": User input parameter, see above
• "w2": User input parameter, see above
• "w3": User input parameter, see above
• "w4" User input parameter, see above
• "m": User input parameter, see above
• "mCorrected": See above
• "interactionPartners": User input parameter, see above
• "mutRate": Mutation rate for both sender and receiver strategies (s01, s11, r01, and r11)
• "mutStep": Mutation size for both sender and receiver strategies
• "init01": Initial s01 and r01, determining whether the simulation is an honest start or no signaling start.
• "init11": Initial s11 and r11, determining whether the simulation is an honest start or no signaling start.
• "replicates": User input parameter, see above
• "cauchyDist": User input parameter, see above
• "fileName": Raw data file this row holds collated data for
• "expAlpha": Expected value of alpha for a pooling, hybrid, or honest equilibrium (whichever is predicted analytically for the parameters, priority given to nonpooling equilibria)
• "expBeta": Expected value of beta for a pooling, hybrid, or honest equilibrium (whichever is predicted analytically for the parameters)
• "mean_S01": Average value of s01 for the last 200 000 generations of this simulation
• "mean_S11": Average value of s11 for the last 200 000 generations of this simulation
• "mean_R01": Average value of r01 for the last 200 000 generations of this simulation
• "mean_R11": Average value of r11 for the last 200 000 generations of this simulation
• "fileSuffix": Part of the file name used by some R scripts
• "fileNum": Used to associated different rows showing different replicates in the same raw data file

Equilibrium files: [tolerance]_equilibs.csv

Only for 'Equilibria_no signaling start' and 'Equilibria_ honest start' experiments

These files hold, for each raw data file, the equilibrium reached after 1 000 000 generations of evolution.

This is calculated by taking mean population strategy values over the last 200 000 generations of evolution and comparing them to expected values for pooling, hybrid, and honest equilibria.

If the values are within a percentage (tolerance) of the expected values, the simulation is said to have reached that equilibrium

Tolerances used are given at the beginning of the file name: 0.01, 0.02, 0.03, 0.04, 0.05, and 0.1 were used

All columns are the same as for endDataAll files above, except for the last 8:

• "alpha": The actual mean alpha (s01) value for the last 200 000 generations of the simulation
• "devAlpha": Deviation of actual alpha from expected
• "expAlphaFix": Expected alpha value at a honest or hybrid equiulibirum (whichever is predicted analytically), or pooling if neither hybrid or honest is predicted. The 'fix' accounts for negative costs or costs greater that 1, which caused the original calculation to be incorrect
• "expBetaFix": Expected beta value at a honest or hybrid equiulibirum (whichever is predicted analytically), or pooling if neither hybrid or honest is predicted. The 'fix' accounts for negative costs or costs greater that 1, which caused the original calculation to be incorrect
• "beta": The actual mean beta (r11) value for the last 200 000 generations of the simulation
• "devBeta": Deviation of actual beta from expected
• "equilibrium": The equilibrium the data is determined to have reached if it is within [tolerance] percent of the expected values. "Hybrid, strong" means that the data is within [tolerance] of the expcted alpha and beta for a hybird equilibrium with that combination of m, c1, and c0. 'Honest' means that the population is within [tolerance] of an honest signaling state. [Pooling] means the population is within [tolerance] percent of a nonsignaling state. 'Undefined' is assigned if none of the aforementioned apply.
• "tol": Tolerance used for equilibrium calculations in this file.

Sharing/Access information

This is data for "Exploring the Importance of Stochasticity to Hybrid Equilibria in a Discrete Signaling Game"

by Jacob Chisausky, Kevin Zollman, and Graeme Ruxton (2024).

Published in the Journal of Evolutionary Biology

Jacob Chisausky is responsible for writing code and analyzing data - email him with questions at jacob.chisausky@princeton.edu

Code/Software.

Code is uploaded in this repository (in Code_for_agent_based_signaling_model.zip)

CreateBat_SignallingModel_v1.R This is an R script in takes user-entered parameter values and creates a folder with Parameter.json files as well as a bash script to run the jobs in sequence The user can input a vector of values and parameter json files are written with all parameter combinations: this allows easy testing of questions For instance, one could enter N <- (100,1000,1000) and mutRateAlpha <- (0.01,0.001) and 6 files will be created, with each combination of N and mutRateAlpha

DataAnalysis.R This is an R script which creates a graph of the trajectory of a single replicate, for now. It shows strategy frequencies and alpha and beta through time for a selected simulation

rScriptTest_Parameters.json This is an example .json file which shows the format that .json files need to be to be read by the cpp program

Agent-based-signaling-game

Agent-based model for "Exploring the Importance of Stochasticity to Hybrid Equilibria in a Discrete Signaling Game" Chisausky Zollman & Ruxton 2024

How to run this code on Windows:

Download all files. Edit the 'example_params.json" file to your desired combination of parameters. In the command line, run "signalling_model.exe example_params.json". Data will be written to .csv files in the folder containing the executable.

A description of parameters is as follows (with values for example):

"seed": 16570320, ----------------- Seed for random number generator
"N": 1000, ------------------------ Number of signalers and receivers
"G": 1000, ------------------------ Number of generations
"c1": 0.1, ------------------------ Cost to consonant individuals ('c1' in paper)
"c2": 0.5, ------------------------ Cost to dissonant individuals ('c0' in paper)
"v1": 1, -------------------------- Benefit to consonant individuals (1 in paper)
"v2": 1, -------------------------- Benefit to dissonant individuals (1 in paper)
"w1": 1, -------------------------- Receiver benefit - play r = 1 to q = 1
"w2": 0, -------------------------- Receiver benefit - play r = 0 to q = 1
"w3": 0, -------------------------- Receiver benefit - play r = 0 to q = 1
"w4": 1, -------------------------- Receiver benefit - play r = 0 to q = 0
"m": 0.333333333333333, ----------- Fraction of individuals that are consonant
"interactionPartners": 10, -------- How many games are played against different partners per individual per generation?
"mutRateS": 0.001, ---------------- Mutation rate for signaler strategies
"mutStepS": 0.01, ----------------- Mutation size for signaler strategies
"mutRateR": 0.001, ---------------- Mutation rate for receiver strategies
"mutStepR": 0.01, ----------------- Mutation size for receiver strategies
"cauchyDist": false, -------------- Use a cauchy distribution rather than normal for mutations?
"initS01": 0.5, ------------------- Initial value for s01 for all iundividuals
"initS11": 1, --------------------- Initial value for s11 for all iundividuals
"initR01": 0, --------------------- Initial value for r01 for all iundividuals
"initR11": 0.5, ------------------- Initial value for r11 for all iundividuals
"replicates": 10, ------------------ How many replicates to run?
"reportFreq": 100, ---------------- How many times to export data during the simulation?
"dataFileName": "Local_test", ----- This will be part of the file name for .csv files
"dataFileFolder": ".", ------------ Where to save data. Leave this as "." to save data in same folder as executable
"computeMeansInCpp": true --------- If false, export data for all individuals without calculating means.