I do not know enough about contemporary historians and their writings to know if there is a Darwinian model of history in common use.
Since I wrote about the two common models of history the other day, one being the Great Man theory and the other being the Hegelian-Marxist economic trends theory, I want to point out my own view of history. I know there is a French view of history from the point of view of the common man and I know there is the Gregory Clark view of history that only has two parts before and after modern commerce. There are many other minor historical theories some that focus on sexually and gender as well as race and botany.
None of these are of any interest to me nor convincing.
I see history as a Darwinian process. Darwin gets credit for the idea, justifiably, that there are long periods of random variation in a population interrupted by a significant environmental change and the survival of the fittingest then acts on the population.
This is clearly the case for commerce. This is clearly the case for the world of biology.
The reason I think that it is also the case for history is that many times similar phenomena reoccur. This repetition has the quality of random variation. For example there are hundreds of religions and thousands of schismogenic sects of those religions. Very few survive for long periods because they don't fit into the culture or the society in which they must function.
Similarly there are random variations in tribal and geographic governance systems and many variations in national systems of government but only a few highly fitting systems survive competition from neighbors and invaders.
It appears to me that history does not have a cyclical quality they way Indians think of it. History has a random variation quality. Calendars appear and disappear. Calendars get modified and change their base from 4 days to 7 days to 10 to 60. Calendars survive because they fit the culture and society. Most recently, in the world of commerce, the most successful has been a 7 day based calendar.
I am inclined toward a Darwinian model of history. It explains a great deal more than any other model I know of.