🧬 Evolutionary Population Dynamics Simulator

A web-based simulation tool that models the evolution of a population under environmental pressure. It demonstrates core biological concepts such as Natural Selection, Mutation, Genetic Drift, and Carrying Capacity using mathematical models.

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🚀 Features

• Real-time Visualization: Watch the population evolve generation by generation.
• Interactive Controls: Adjust mutation rates, population size, and environmental harshness on the fly.
• Scientific & Math Documentation: Includes dedicated pages explaining the underlying biology and mathematics.
• Dual Charts:
  • 📈 Population Size: Logistic growth dynamics.
  • 🧬 Average Fitness: Adaptation level of the population.

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🔬 Scientific Model

1. The Individual (Genotype)

Each individual is represented by a single continuous trait $x$ (e.g., body size, resistance).

• Genotype: A float value.
• Mutation: Modeled as a stochastic process using a Normal Distribution.

$$ x_{new} = x + \mathcal{N}(0, \sigma_m) $$

2. Fitness Function (Natural Selection)

Fitness determines an individual's probability of survival and reproduction. We use a Gaussian Function (Bell Curve) centered around an optimal environmental value ($x_{opt}$).

$$ f(x) = e^{-\frac{(x - x_{opt})^2}{2\sigma_{env}^2}} $$

• Individuals closer to $x_{opt}$ have higher fitness (max 1.0).
• $\sigma_{env}$ (Tolerance) determines how harsh the environment is.

3. Population Dynamics (Ecology)

The population size ($N$) is not static. It follows the Logistic Growth Model, constrained by the environment's Carrying Capacity ($K$).

$$ N_{t+1} = N_t + r N_t \left( 1 - \frac{N_t}{K} \right) $$

• If $N < K$, the population grows.
• If $N > K$, the population shrinks due to competition.

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🛠 Installation & Usage

Prerequisites

• Node.js (v14 or higher)

Steps

1. Clone the repository

   git clone https://github.com/YusufOztoprak/Evolutionary-Population-Dynamics-Simulator.git
   cd Evolutionary-Population-Dynamics-Simulator

2. Install dependencies

   npm install

3. Start the server

   npm start

4. Open the simulator Go to http://localhost:3000 in your browser.

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📂 Project Structure

Evolutionary-Population-Dynamics-Simulator/
├── src/
│   ├── engine/          # Simulation logic (Population, Individual)
│   └── server.js        # Express backend API
├── public/
│   ├── index.html       # Main Simulator UI
│   ├── science.html     # Biological Background Page
│   ├── math.html        # Mathematical Model Page
│   └── js/              # Frontend logic (Charts, API calls)
├── package.json
└── README.md

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📜 License

This project is licensed under the MIT License - see the LICENSE file for details.

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Developed by Yusuf Oztoprak 🎓