Problem:

Whenever I look at discussions of fitness landscapes (in particular, Kauffman's NK model) the questions tend to resemble:

The population is at a local equilibrium, but another equilibrium of higher fitness exists

Question: how will the population cross the fitness valley between these equilibria?

These sort of statements assume that the population has reached a local equilibrium. Although, the local equilibria must exist,

Question: why do the people working in this field believe that they can be found before environmental (or other external events) change the fitness function?

Question: Are the timescales required to go from a random initial population to one that is at a local equilibrium compatible with the typical time-scales on which a fixed fitness landscape is an appropriate approximation?

If we switch to the polar opposite model of complete frequency-dependent selection (say replicator dynamics in evolutionary game theory) then limit-cycles (think rock-paper scissors game) and chaotic-attractors are common and it is possible for the population genetics to be constantly changing and never at equilibrium.

In an experimental setting, it also seems like although beneficial point-mutations are much more rare than deleterious, they do exist. This would suggest that experimentally, organisms are not at a local equilibrium.

Question: Do model organisms tend to be at local fitness equilibria?

Question: Is the local equilibrium assumption in fitness landscapes research a reasonable assumption?