An Introduction to Galton-Watson Processes

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Howdy! I’m Eric Eager, and I’m an associate professor of mathematical biology at the University of Wisconsin – La Crosse.  I’m also a data scientist for Pro Football Focus and Orca Pacific.  In my first post for Quantitative Dynamics, I’m going to discuss a topic near and dear to my heart: Branching processes (thanks Sebastian Schreiber for teaching me these five years ago).

Branching processes are a great bridge between the continuous-space population models that permeate the ecological literature (e.g. Caswell 2001, Ellner, Childs and Rees 2016) and the individual-based realities that drive ecological systems (Railsback and Grimm 2011). All branching process models specify an absorbing state (usually extinction in ecology) and model the probability of reaching the absorbing state by creating an iterative map from one generation to the next. This allows you to work with a model whose space is in a set of discrete values (individual-based), but with a resulting model that’s a difference equation (traditional ecological models).

The most famous example of a branching process is the Galton-Watson process. Francis Galton was concerned about the eventual fate of surnames (a quaint artifact of the past), especially among the aristocracy. Below are a couple of videos I made, one deriving the Galton-Watson process and one solving it. Enjoy!

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