Fitness and Overfitness: Implicit Regularization in Evolutionary Dynamics

This repository contains code to reproduce simulations and generate plots from the manuscript:

Fitness and Overfitness: Implicit Regularization in Evolutionary Dynamics
Hagai Rappeport and Mor Nitzan

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Overview

This project implements a computational framework to study the evolution of biological complexity through the lens of implicit regularization in evolutionary dynamics. It leverages the mathematical analogy between the replicator equation and Bayesian inference to explore how organismal complexity evolves to match environmental complexity.

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Repository Contents

src/overfitness_paper/      # Python package (importable as `overfitness_paper`)
  simulation.py             # replicator dynamics + linear/polynomial classes
  invasion.py               # invasion-tensor analysis
  models/neural_net.py      # 2-layer ReLU NN model used in SI figures
  metrics_helpers.py        # run_with_metrics() — wraps run() + metric helpers
  config.py                 # canonical default parameters

experiments/                # one script per figure, saves to data/
  main_fig{2,3,4}_*.py      # main-text figures
  si_*.py                   # supplementary figures S1–S14

data/                       # cached simulation outputs (.npz / .pkl)
                            # ships empty; populated by experiments/

notebooks/
  main_figures.ipynb        # generates Fig 1–4 from data/
  supplementary_figures.ipynb  # generates Fig S1–S14 from data/

figures/                    # rendered PDFs
  main/
  supplementary/

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Reproducing the figures

Install dependencies:

pip install -r requirements.txt

For each figure, first regenerate the cached simulation output, then run the corresponding notebook cell:

# Main figures
python -m experiments.main_fig2_stable_env
python -m experiments.main_fig3_transients
python -m experiments.main_fig4_env_change
jupyter nbconvert --to notebook --execute notebooks/main_figures.ipynb

# Supplementary figures
python -m experiments.si_mean_fitness_curves    # S1
python -m experiments.si_neural_network         # S2, S4
python -m experiments.si_polynomial             # S3
python -m experiments.si_ar1_environments       # S5
python -m experiments.si_correlated_cues        # S6
python -m experiments.si_class_size_sweep       # S7
python -m experiments.si_invasion               # S8
python -m experiments.si_mutations              # S9
python -m experiments.si_alt_fitness            # S10, S11
python -m experiments.si_alt_noise              # S12, S13
python -m experiments.si_param_sensitivity      # S14
jupyter nbconvert --to notebook --execute notebooks/supplementary_figures.ipynb

Each script is independent and idempotent. Wall-clock per script ranges from seconds to several hours depending on the size of the parameter sweep. All scripts read defaults from overfitness_paper.config; figure-specific overrides (e.g. γ=0.01 for the NN simulations) are documented inline.

See data/README.md for a filename → figure mapping.

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Requirements

• Python 3.8+
• NumPy
• Matplotlib
• Seaborn
• SciPy
• PyTorch (for the neural-network experiments)
• Jupyter
• tqdm

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License

This project is released under the MIT License. See LICENSE for details.

Contact

For questions or collaboration inquiries, please contact:

Hagai Rappeport — [hagai.rappeport@huji.mail.ac.il] Mor Nitzan — [mor.nitzan@huji.mail.ac.il]