Discuss Findings

across all 2195 numeric sanitized payloads, mean peak persistence is 0.63577 [0.63535, 0.63619] and the interior-peak rate is 0.52452 [0.52368, 0.52535]; at amplitude 0.24 the peak groups sit near p_stay approximately 0.535 to 0.537, with peak CV_tau 2.11837 [2.11431, 2.12244] for Poisson, 1.86309 [1.85870, 1.86747] for Binomial, and 2.31446 [2.31004, 2.31888] for NegBin versus edge CV_tau 1.73164, 1.55811, and 1.87681 respectively; the NegBin family retains the largest heterogeneity peak at every amplitude slice.

CONFIRMED Finite-time extinction heterogeneity is maximized at intermediate environment persistence rather than at either persistence extreme. The overdispersed negative-binomial offspring law consistently gives the largest peak, showing that offspring-count variance amplifies the temporal-memory effect instead of averaging it away. Mechanistically the crossover arises between two limiting regimes: fast switching self-averages the environment, while highly persistent environments become effectively quenched and reduce trajectory mixing. The interior regime is where lineages experience enough memory to separate strongly, but not so much that they are trapped in a single environmental history.