Ludwig-Maximilians University              32nd Arnold-Sommerfeld-Lectures                                January 15, 2026

Life of a Noisy Seascape: Extinction, Growth, and Diversity

Summary

I.     Population dynamics: Growth & saturation (logistic to Richards), migration and stochasticity (demographic and seascape)

II.    Mean field analysis: Self-consistent steady state distributions for a complete graph

III.   Extinction on a seascape: Two universality classes

IV.    Growth on a seascape: Richards equation & Taylor's power law

V.    Diversity-Stability: Random interaction matrix & Robert May

VI.  Coexistence of a seascape: Spatio-temporal noise-induced stability

VI.  Phase behavior: Coexistence requires sufficiently large fluctuations

 Emergent neutrality:Hubbell's unified netural theory of biodiversity   

    Bertrand Ottino-Loffler,              Daniel Swartz,      Amer Al-Hiyasat,                Jeff Gore                               

Next (Introduction) Outline Growth & saturation Mean field analysis Extinction on a seascape Growth on a seascape Diversity vs Stability Coexistence on a seascape Phase behavior Summary