Here, we give evidence that, even at the narrow timescale separating human populations, on the order of tens of thousands of years, differences appear to be detectable and to be correlated with genetic differentiation among populations.
We reasoned that fewer complex changes in cis-regulatory region organization are likely to have occurred over the timescales separating S. cerevisiae strains, allowing us to more readily correlate sequence and expression divergence.
Moreover, any model assuming a single ecological attractor will overlook the interesting behaviours modelled here, regardless of whether the timescales are separated or similar.
In both cases, we determine that timescales must remain separated into three distinct classes for the solutions of interest to arise.
As a first application, we illustrate these ideas on a class of nonlinear systems with a single unknown sigmoidal nonlinearity and two sharply separated timescales.
If most or all of the eigenvectors are localized, then different nodes show separated timescales in their dynamical response to external stimulation.
Although the mathematical study of evolutionary adaptation has a rich history, ecological and evolutionary timescales were traditionally separated (Ferrière et al. 2004; Bell 2013), resulting in a relative dearth of models incorporating simultaneous change and bidirectional feedback between demography and genetics.
A necessary and sufficient condition for timescale separation is that the timescales governing the decay of the transients in the average concentrations are well separated.
In contrast to analytical approaches to adaptive dynamics [ 17, 31- 33], and in accordance with observed rapid evolution of bacteria and phage [ 34], ecological and evolutionary timescales are not explicitly separated.
In the current case the timescales are so well separated that the value of TS is readily estimated by fitting the data to an exponential decay, omitting the first point.
Bistability, and permanent synaptic strengthening by tetani, were seen when ongoing activity consisted of brief periods of Ca2+ elevation separated by intervals (timescale of minutes) without activity.
