Introduction

 Sigmoid curves abound in describing population growth

From https://www.slideshare.net/JackieAndrews/population-dynamics-presentation

  Logistic growth is the most natural model for population dynamics

            

 Many variants of generalized logistic growth  (Covid-19 application)

(from: https://www.researchgate.net/figure/The-generalized-logistic-curve-and-its-derivative-models_fig3_304619003)

(Roland) Fisher's equation allows for migration of a population distributed in space:

Stochasticity in birth/death events leads to demographic noise:

    †

 Leads to extinction via the Directed Percolation universality class  [Janssen+Tauber (2005), ...]

Another form of stochasticity is from environmental fluctuations, causing fitness variations, termed

 Seascape                     

†

The linear version (a=0) describes the evolving weight of directed polymers in random media (in the KPZ universality class).

[Tu+Grinstein+Munoz (1997); Munoz+Hwa (1998); ...]

Including both forms of stochasticity leads to:

  †

 † (Ito interpretation of multiplicative noise)

Next (Mean field approach) Outline Introduction Mean field approach Neutral landscape Extinction on a seascape Growth on seascape Summary