In Lewis Carroll's Alice through the looking glass, the Red Queen remarks

"here, you see, it takes all the running you can do, to keep in the same place".

The analogy for running is coevolutionary change.

Coevolution can be escalatory:

In the Red Queen mode of coevolution, natural selection continually operates on each species to keep up with improvements made by competing species; each species environment deteriorates as its competitors evolve new adaptations. Evolution is said to be escalatory.

Coevolution can also take other forms:

• contraction: a species lags behind its competitors and does not evolve fast enough to keep up with them, it will fall further behind until it goes extinct (see lag load)

• expansion: a species could be ahead of its competitors and out-evolving them; it could theoretically expand until it had an infinite number of descendants

Clearly, the expansionary mode could not continue for long. In real systems, the main possibility is that a species could alternate between periods of expansionary and contractionary evolution as their fortunes fluctuate.

• stationary: in it the competing species evolve to a set of optimal states and then stay there; the lag load reduces to zero, no species changes, and no species goes extinct.

Why should the rate of environmental deterioration be approximately constant?