deploy: a14bc33

Author: mtomasini

.buildinfo

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+# Sphinx build info version 1
+# This file records the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: fef82a2252b5bbd75425279a18f9ab63
+tags: 645f666f9bcd5a90fca523b33c5a78b7

.doctrees/author.doctree

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+# About the author
+
+This repository is developed and maintained by Dr. Matteo Tomasini, research engineer at the Gothenburg Research Infrastructure in Digital Humanities and researcher within the project [Maritime Encounters](https://www.gu.se/en/research/maritime-encounters) at the University of Gothenburg. You can find more about him at his [personal webpage](https://mtomasini.github.io/).

.doctrees/environment.pickle

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+.. MetaPypulation documentation master file, created by
+   sphinx-quickstart on Tue Jul  9 12:12:46 2024.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+Welcome to MetaPypulation's documentation!
+==========================================
+
+.. toctree::
+   :maxdepth: 2
+   :caption: Contents:
+   
+   overview.md
+   modules
+   author.md
+
+
+Indices and tables
+==================
+
+* :ref:`genindex`
+* :ref:`modindex`
+* :ref:`search`

.doctrees/index.doctree

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+metapypulation package
+======================
+
+Submodules
+----------
+
+metapypulation.individual module
+--------------------------------
+
+.. automodule:: metapypulation.individual
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+metapypulation.metapopulation module
+------------------------------------
+
+.. automodule:: metapypulation.metapopulation
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+metapypulation.subpopulation module
+-----------------------------------
+
+.. automodule:: metapypulation.subpopulation
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+metapypulation.simulation module
+-----------------------------------
+
+.. automodule:: metapypulation.simulation
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: metapypulation
+   :members:
+   :undoc-members:
+   :show-inheritance:

.doctrees/metapypulation.doctree

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+metapypulation
+==============
+
+.. toctree::
+   :maxdepth: 4
+
+   metapypulation

.doctrees/modules.doctree

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+# Metapypulation: an overview
+
+Metapypulation is a package to simulate the spread of culture in a metapopulation. It supplies a set of tools partly inspired by other frameworks such as [Mesa](https://mesa.readthedocs.io/en/stable/overview.html) which are general-purpose methods to perform agent-based modelling with Python. The main reason to create my own package for this purpose is to change the focus of the tool - population-based simulations instead of individual-based.
+
+## Structure
+
+Metapypulation has three main classes:
+
+- an [`Individual`](https://mtomasini.github.io/MetapopulationsPython/metapypulation.html#module-metapypulation.individual) class, which represents each individual in the metapopulation.
+- a [`Subpopulation`](https://mtomasini.github.io/MetapopulationsPython/metapypulation.html#module-metapypulation.subpopulation) class, representing the different discrete subpopulations that compose the metapopulation;
+- finally, a [`Metapopulation`](https://mtomasini.github.io/MetapopulationsPython/metapypulation.html#module-metapypulation.metapopulation) class, which puts `Individual` and `Subpopulation` together and have individuals interacting in this world.
+
+In addition, I provide a [`Simulation`](https://mtomasini.github.io/MetapopulationsPython/metapypulation.html#module-metapypulation.simulation) class, which allows to run a simulation with several replicates, which outputs different measurements ([see below](#diversity-measures)). The class also provides some quick tools to plot the results of the simulation.
+
+## The spread of cultural traits
+
+Currently, each individual's culture is represented by a set of {math}`N` features. Each feature in turn can assume one of {math}`\nu` traits. These features represent different (assumed) independent facets of culture: one could be language, burial tradition, boat building features, *etc*. So each individual is currently represented by a vector of integers.
+
+### Neutral model
+
+The Neutral model follows loosely the set up selected by other authors working on the spread of cultural traits (_e.g._ *Patterns in space and time: simulating cultural transmission in archaeology*, Marko Porčić). We use the simplest model where one focal individual at random in each subpopulation and each time-step copies one trait at random from another individual in the same subpopulation. The model allows for copying errors with rate {math}`\mu`: if a copying error occurs, instead of copying a trait from another individual, the focal individual changes the trait at the feature in focus with a random trait between the available ones. 
+
+### Axelrod model
+
+While we plan on adding several different ways for individuals to interact and change their traits, as of July 2024 the only such way to interact is shaped upon the **Axelrod model of culture dissemination** (*The Dissemination of Culture: A Model with Local Convergence and Global Polarization*, Robert Axelrod (1997), The Journal of Conflict Resolution, vol. 41, no. 2). In this model, at each generation an individual is chosen at random to copy a trait from a neighboring source on a lattice; the copy occurs with a probability proportional to the total similarity of the two random individuals. This mimicks homophily - the principle by which two individuals that resemble each other have a higher chance of having an exchange than two individuals that are completely different. In the metapopulation model that I developed, for each subpopulation we pick two random individuals that will act as target and source of the copy. Here too, copying errors occur with rate {math}`\mu`.
+
+### Diversity measures
+
+Currently, we have implemented a few diversity measures at the level of both the subpopulation and the whole metapopulation (to avoid repeating "subpopulation / metapopulation", we refer to either as the "reference population" for the measure. 
+
+#### Count of sets
+The first measure that we implemented is the number of unique sets of traits, {math}`K`. In code, this is done through the function `np.unique(..., return_counts = True)`. 
+
+#### Shannon diversity
+The second diversity index that we have implemented is the Shannon diversity index, which measures the entropy in the reference population. For {math}`K` sets of traits,
+
+```{math}
+H^{\prime} = - \sum_{i = 1}^{K} p_i \ln p_i ,
+```
+
+where {math}`p_i` is the frequency of a type of individual {math}`i` in the subpopulation / metapopulation. Shannon is a measure of how "easy" it is, given an individual of type `j`, to predict the set of traits of another individual in the same reference population.
+
+#### Simpson index
+We also implemented the Simpson's diversity index, defined as 
+
+```{math}
+S = \sum_{i = 1}^{K} p^2_i .
+```
+
+The Simpson index is bound between 0 and 1, and represents the probability that two individuals in the same reference population have the same set of traits.
+
+#### Gini-Simpson index
+The Gini-Simpson index is simply the complement of the Simpson index, that is it measures the probability that two random indeividuals in the same reference population do not share a set of traits. This is calculated as
+
+```{math}
+G = 1 - \sum_{i = 1}^{K} p^2_i = 1 - S.
+```

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