Category: Statistics

Summary: Testing whether offspring overdispersion shifts or amplifies the intermediate-persistence peak in extinction-time variability for branching in a Markov environment.

Branching processes in random environments can show especially large outcome variability when environmental states persist for intermediate lengths of time. This experiment asks whether that finite-time resonance changes when offspring counts become more overdispersed, so that family-size variability is high even at fixed mean behavior.

The simulation combines a two-state Markov environment with offspring laws of different overdispersion and measures extinction-time heterogeneity across persistence levels. The target is not only whether the peak survives, but whether stronger family-size noise shifts its location or changes its height.

That distinction matters because asymptotic survival theory often compresses these ingredients into broad criteria. The project instead focuses on a finite-time variability question where environmental memory and offspring overdispersion may interact in a nontrivial way.

Method: Repeated branching-process simulations in a two-state Markov environment, comparing extinction-time statistics across offspring overdispersion levels.

What is measured: Extinction-time coefficient of variation, location and height of the intermediate-persistence peak, and dependence on offspring overdispersion.