Role of Spatiotemporal Noise in Growth and Stability of Ecosystems

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

Outline

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

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

V.   Coexistence on a seascape: Spatio-temporal noise-induced stability

VI.  Phase behavior: Coexistence requires sufficiently large fluctuations

VII. Summary

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

Populations and communities rarely evolve in static environments; their fitness landscapes fluctuate across space and time, forming what may be called a noisy seascape. This talk examines how such variability modifies classical models of population dynamics and community stability. Beginning from the logistic equation, I will show how spatiotemporal fluctuations in fitness lead naturally to power-law population statistics and, under certain conditions, to the empirical (fractional) Richards growth law. Extending these ideas to interacting species reveals that the combined effects of dispersal and environmental noise can stabilize large, diverse communities despite strong competitive interactions. The resulting framework connects extinction, growth, and coexistence within a unified view of life on a noisy seascape.