Galton-Watson Branching Process

Stochastic population growth, extinction & supercriticality

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Mean offspring μ
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Extinction prob.
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Generations
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Final population
1.20
Poisson
20
The Galton-Watson process models population growth: each individual independently produces k offspring with distribution p_k. Critical parameter: mean offspring μ = Σk·p_k. For μ < 1 (subcritical): extinction certain. For μ = 1 (critical): extinction certain but slowly. For μ > 1 (supercritical): extinction probability q is the smallest solution to q = G(q) where G is the generating function. Left: single tree realization. Right: distribution of final population sizes.