Branching Process - Example of Extinction Problem

Example of Extinction Problem

Consider a parent can produce at most two offspring and the probabilities for the number produced are p₀=.1, p₁=.6, and p₂=.3. The extinction probability in each generation is

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with d₀=0. Here, the extinction probability is calculated from generation 1 to generation 20. The result is shown in the table.

For the ultimate extinction probability, we need to find d which satisfies d=p₀+p₁d+p₂d2. In this example, d=1/3. This is exactly what the probabilities in the table converges to.