Growth on a seascape

 Variations at each node are governed by time-scales from growth, migration, and noise

 However, variations of the mean   take the simpler form

Assuming that the growth rate is always sufficiently slow to allow for a quasi-static state, such that

 '

provides a universal mechanism to the empirical Richards growth equation from spatio-temporal stochasticity:

.

Numerical simulations [D. Swartz, B. Ottino-Loffler, M. Kardar, PRE 105, 014417 (2022)] support this conclusion

 The anomalous scaling of population variance with mean is known in ecology as

  relating the scaling of variance of population to its mean (in space of time).

 A potentially testable link between local population distributions, and a global growth exponent.

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

 Numerical simulation of time evolution of the population density