We're now getting numbers of a magnitude that are more accessible to us. Thirty-five thousand is a number that can have meaning for us (e.g. consider income tax calculations!).

How much diversity in organisms will 35,000 evolutionary units allow for? Let us take a very conservative approach and say that, instead of a large scale evolutionary change such as a elephant size change (with the consequent production of many intermediate species), an evolutionary unit only results in any single species splitting into 2 species. That is, for every species that exists at the start of an evolutionary unit there are 2 species emerging from the end of that unit. (Certainly, this oversimplistic assumption isn't true for many organisms. For example, some sharks, turtles and the coelacanth have remained unchanged for very many instants; fossils of these animals show very little difference from modern species. These are the so- called «living fossils». Of course, many other organisms will have undergone more than 1 species split or speciation event during 100,000 years. Also, the extinction of species is ignored. However for the purposes of this discussion, which is to get a very rough idea of how much diversity might have been allowed during the available geologic time, let's see how far we can go with it. We'll come back to it shortly.)

In this scenario, the number of species doubles with each evolutionary unit; after one unit there exists 2 species, after 2 units there exists 4 species, after 3 units there exists 8 species and so on. To calculate the diversity of any given evolutionary unit simply raise 2 to the power of that unit. For example, how much diversity was there after 10 evolutionary units? Raise 2 to the power of 10 to find the answer: 2¹⁰ = 1024 species.  

So then, how much diversity has been allowed in the 35,000 evolutionary units that have already occurred. From our assumptions this has allowed for 2^35,000 species to have evolved. (By the way, don't bother to try and calculate this number to base 10, it's much too large a number for your calculator!) (Edited in June, 2020. It's 10¹⁰⁵³⁵) We are now back to inaccessible numbers; 2^35,000 is a larger number than the number of protons in the known universe (about 10⁸⁰). It is astronomically larger than astronomically large numbers! Certainly it is greater than the actual diversification of life that has occurred.

However I hope, with this simplistic argument, that you've come to realize that the time that the evolutionary processes have had to operate within is more than sufficient to completely account for all the vast diversity of life, from prokaryotes such as bacteria, mycoplasmas and blue-green algae (or cyanobacteria) to eukaryotes such as slime molds, lichens, sequoias, sea cucumbers, lobsters, pterodactyls and you.  

Be aware that one major problem with our analysis is that extinction events were ignored. There have been many major extinction events in the history of life: look at the geological time scale on page 458 in Campbell and note all the subdivisions of the time scale into the various eras and periods. The borders of these subdivisions are defined by extinction events; the eras are defined by major extinction events and the periods are defined by minor extinction events. An extinction event will reduce diversity by a greater or lesser degree as whole limbs on the «tree of life» are pruned, leaving no descendents to continue adding diversity. Look at the boundary between the Paleozoic («Old Life») and Mesozoic («Middle Life») eras. The end of the Permian was one of the greatest extinction events in the history of life and resulted in a tremendous loss of diversity as 98% of all life went extinct then.

  Another problem with our estimation of allowed species diversity is that we didn't consider ecological «species space» or niche availability. Look again at the geological time scale on p. 458 of Campbell and read what is said about the Triassic period and the Paleocene epoch. Mammals first evolved in the Triassic along with the first dinosaurs yet it wasn't until the Paleocene, 180 million years later, that mammals started diversifying from small opposom-like ancestors to their modern day dominance. Why did the mammals wait so long? What prevented their evolutionary radiation during the 180 million years of the Mesozoic. The answer is that the dinosaurs were much more successful during the Mesozoic and their evolutionary radiation occupied the niches that mammals would have otherwise occupied. The success of the dinosaurs meant that there wasn't ecological space for mammals to occupy other than as small insectivores. It wasn't until the mass extinction at the end of the Cretaceous, when the non-avian dinosaurs went extinct, that the ecological opportunities became available to the mammals and they responded with a major evolutionary radiation. Thus the lack of available niches (by an inability to compete with their current occupants) will also limit diversity.

These considerations (and others) have acted to prevent the actual diversity of life from achieving the potential diversity that 3,500,000,000 years of evolution would have permitted.

There are a few questions that I'd like to leave you with. How good a definition of diversity is the number of species? Does it encompass what you think of as the diversity of life? What else should the definition of diversity encompass?