The random and different rules models work to help us understand the uneven tempo of evolution. As environments change, sometimes radically, this leaves open space as varying numbers of species disappear. The surviving species increase in numbers as competitive pressures subside for at least a short time. As competition reappears, species begin the process of moving into unoccupied space and begin the process of speciation. Biologists think is terms of adaptive radiations as this occurs. The concept of adaptive radiation involves a whole series of different species evolving from a single species. As members of the founding group spread out into new environments, they tend to develop their own specialized existence. That is they adapt features that help them survive in the new environment.
Since populations grow geometrically, one expects that competitive pressures arise again relatively quickly and drive change in a burst as members of a species move outward looking for the competitive edge. Species tend to radiate into as many environmental niches as possible to avoid the competitive pressures. This is a process known as Adaptive Radiation. As long as an organism finds it is preadapted to move from one environment to another, it will tend to do so under pressure. This leads to periods of significant change in the natural world.
It appears that punctuated equilibrium associated with changes in the natural world, the random model, and the different rules model provides a context for understanding important evolutionary trends. It does not preclude the gradual change that arises because natural selection favors some traits over others resulting in change as a continuum. Since the causes for branching in the "tree of life" are so different from those of continuous transformation of a species, one can see the importance of understanding that change has several dimensions - both slow and gradual, and abrupt, uneven and punctuated.
Keep in mind that the geological time scale is constructed in millions and hundreds of millions of years. Stephen Jay Gould recently used a poem by Robert Herrick to underscore the magnitude of time that evolution has worked within:
Give me a kiss, and to that kiss
a score;
Then to that twenty, add
a hundred more:
A thousand to the hundred:
so kiss on,
To make that thousand up
a million.