On the time and space scales of geological, climatic, and biological changes

It is commonplace to claim that the geo-, atmo-, and bio- spheres of the Earth are coupled, or that biodiversity depends on their interplays, but the implicit hypothesis on the time and space scales at which coupling holds are seldom envisioned. For instance, "deep time" is a convenient shortcut that loosely conveys the ideas of steady state and large spatial scales, but what are the limits? Observations often fall short because the geological record is fragmentary, but also because it is uncommon to access crucial informations such as rates of speciation, extinction, or migration. Recent advances in numerical landscape evolution models permit to explore the dynamic equilibrium between the spheres of the Earth. Based on a few examples at different time and space scales, we will browse settings where steady state holds (where biodiversity depends on the instantaneous states of the geology and climate, as for instance set by the Wilson cycle), where transient state prevails (where considering the time derivative of their states is needed, as for instance when the pace of landscape reshaping promotes biodiversification), and where dynamic equilibrium breaks down in some sort of metastable situations (as in the press-pulse theory that well applies to the mass extinction events).