Simulation of Parochial Altruism by Multilevel Selection

This project implements the simulation model described in the paper "Evolution of Parochial Altruism by Multilevel Selection". It simulates the dynamics of altruism and parochialism in a population divided into multiple groups, exploring how these traits evolve under selective pressures from within-group and between-group interactions.

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Overview

The model represents an absorbing Markov chain where a mutant strategy (either altruistic or parochial) spreads or dies out in a population initially dominated by egoists. Key processes include:

1. Reproduction: Individuals duplicate based on fitness, migrate, or stay within their group.
2. Conflict: Groups engage in contests, and winners replace losing groups.
3. Splitting: Groups split into smaller groups once they exceed a maximum size.
4. Absorption: The simulation continues until the population is homogeneous (either all mutants or all incumbents).

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Key Features

• Fitness-Driven Selection: Reproduction depends on fitness values derived from interactions within and between groups.
• Dynamic Group Conflicts: Groups compete, and winners are determined probabilistically based on payoffs.
• Splitting Mechanism: Groups split when they exceed a defined size, maintaining structure and introducing assortment effects.
• Parameter Tuning: Flexible settings for group size, conflict frequency, migration rates, and interaction probabilities.
• Fixation Probability Calculation: Estimates the probability of mutant strategies reaching fixation compared to neutral drift.

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Model Parameters

Parameter	Range (Default)
κ (Average Frequency of Groups in Conflict)	0.0–0.1 (0.025)
q (Splitting Probability)	0–1 (0.01)
n (Group Size)	5–20 (10)
m (Number of Groups)	5–20 (10)
b/c (Benefit-Cost Ratio)	1.5–5 (2.0)
z (Steepness of Winning Probability Curve)	0–1 (0.5)
α (Ingroup Interaction Frequency)	0–1 (0.8)
λ (Migration Rate)	0–1 (0.0)
w (Selection Intensity)	0–1 (0.1)

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Payoff Matrices

Ingroup Payoffs

	A	P	E
A	b − c	b − c	−c
P	b − c	b − c	−c
E	b	b	0

Outgroup Payoffs

	A	P	E
A	b − c	−c	−c
P	b	0	0
E	b	0	0

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Installation

This project uses a bash script, manage.sh, to streamline common operations.

1. Clone the Repository

   ./manage.sh clone
   cd Learning-Dynamics

2. Set up a Python Environment

   ./manage.sh setup

3. Run the Simulation

   ./manage.sh run

4. Clean up the Python Environment

   ./manage.sh clean