Category: Statistics

Summary: Testing whether intermediate environmental memory creates a peak in finite-time extinction heterogeneity for branching processes with fixed average growth.

Branching processes in random environments are usually analyzed through asymptotic survival criteria, but finite-time variability can be equally revealing. This experiment asks whether a two-state Markov environment with fixed mean offspring rate can still produce especially heterogeneous extinction outcomes at intermediate persistence times.

The simulations compare offspring families and environment-memory strengths while tracking extinction distributions over finite time horizons. Rather than asking only whether the process is supercritical or subcritical, the experiment measures how strongly memory changes the spread of outcomes across realizations.

That targets a crossover question: whether memory breaks the near-universal behavior seen in memoryless critical branching. The result is a map of finite-time heterogeneity, not just a check of standard long-run criteria.

Method: Stochastic Galton-Watson simulations in two-state Markov environments across offspring families and persistence strengths.

What is measured: Finite-time extinction distributions, heterogeneity across realizations, dependence on environment memory, and crossover behavior across offspring laws.