piegy 1.1.3

Payoff-Driven Stochastic Spatial Model for Evolutionary Game Theory

piegy

The package full name is: Payoff-Driven Stochastic Spatial Model for Evolutionary Game Theory. "pi" refers to "payoff, and "egy" are taken from "Evolutionary Game Theory".

Provides a stochastic spatial model for simulating the interaction and evolution of two species in either 1D or 2D space, as well as analytic tools.

Installation

To install piegy, run the following in terminal:

pip install piegy

Documentation and Source

See source code at: piegy GitHub-repo. The piegy documentation at: piegy Documentation.

How the Model Works

Our model can be summarized as "classical evolutionary game theory endowed with spatial structure and payoff-driven migration rules". Consider two species, predators and preys (denoted by U and V), in a rectangular region. We divide the region into N by M patches and simulate their interaction within a patch by classical game theory (i.e., payoff matrices and carrying capacity). Interactions across patches are simulated by payoff-driven migration rules. An individual migrates to a neighboring patch with probability weighted by payoff in the neighbors.

We use the Gillepie algorithm as the fundamental event-selection algorithm. At each time step, one event is selected and let happen; and the step size is continuous, dependent on the current state in the space. Data are recorded every some specified time interval.

Analytic Tools

The piegy package also provides a wide range of analytic and supportive tools alongside the main model, such as plotting, numerical tools, data saving & reading, etc. We also provide the piegy.videos module for more direct visualizations such as how population distribution change over time.

Examples

To get started, simply get our demo model and run simulation:

from piegy import model, figures
import matplotlib.pyplot as plt

sim = model.demo_model()
model.run(sim)

fig1, ax1 = plt.subplots()
figures.UV_dyna(sim, ax1)
fig2, ax2 = plt.subplots(1, 2, figsize = (12.8, 4.8))
U_hmap, V_hmap = figures.UV_heatmap(sim, ax2[0], ax2[1])

The figures reveal population dynamics and steady state population distribution.

Acknowledgments

• Thanks Professor Daniel Cooney at University of Illinois Urbana-Champaign. This package is developed alongside a project with Prof. Cooney and received enormous help from him.
• Special thanks to the open-source community for making this package possible.