We have identified the five main processes to transform galaxies. Let us show now that galaxy evolution necessarily leads to more diversity.
a) simple objects, without interaction, appearing at the same epoch
Two identical stars evolve along very identical paths, whatever the time they formed. Stars are characterized by quite a simple physics which is thus quite predictive. Their evolution is mainly dictated by mass and chemical composition. A galaxy is an ensemble of stars. If we consider simple galaxies, with not too many stars and gas, and assume a very little probability for internal instabilities, then the fate of all such galaxies is probably identical. This means that if two galaxies are given the same state at the same epoch, they will reach a different state, identical for the two and possibly define a new class (this is just a matter of arbitrary definition), at the same time.
If the Universe is populated with only such galaxies, then at any time there is only one class of galaxies. But over the history of the Universe, several classes have existed, all being extinct except one at the time of observation. This shows that evolution generates diversity, and this diversity can be observed only by scanning several redshifts.
b) simple objects, without interaction, appearing at different epochs
Who believes that all galaxies were “created” at the same time, in exactly the same physical and chemical state? So even if they are assembled initially in the same class, they would not do so at the same time throughout the Universe. Hence, we have the same total number of classes, but at any given time more than one are not extinct. This means that diversity can be observed at a given redshift, including our neighborhood.
c) complex objects without interaction
Who can believe that galaxies are all identical at some time, and that they are simple objects? You probably know that an ensemble of three stars is unstable, so what about 10⁹ or 10¹² stars? And what forms stars? Gas and dust, that is the hydrodynamic component of galaxies, that is prone to shock waves and dissipation of angular momentum of stars. Internal instabilities are thus an obvious ingredient in the transformation of galaxies. This merely implies that any perfectly identical galaxies will not reach the same state at the same time and more probably will quickly diverge by following two distinct evolutionary lineages.
The probability that two ensembles of stars are identical in number and distribution of stars, mass, chemical composition and so forth, is quite weak. This may occur when a small cloud of gas becomes self-gravitating and condenses into some stars, especially at the very beginning of the Universe after the recombination, but this remains quite improbable.
Hence diversity is partly due to the formation of the very first state of galaxies, but it is exacerbated by evolution which in the cases of galaxies is a transformation process.
d) complex objects with interactions
Galaxies are not isolated, they live in a structured gravitational field with many other galaxies in general. Interactions are unavoidable, but their characteristics are random: masses of the two galaxies, their relative velocity, their angles with respect to the global rotation, their disk. There are an infinite set of possibilities to have to galaxies encounter each other. And so for the consequences. Interactions are thus a strong driver of diversity.
Sometimes, when the interaction is too close, two galaxies merge together. They disappear to form a new object, so different that it necessarily belongs to another class, new or not in the history of the Universe. But this new class could be viewed as an hybridization process that is known not to fit into a cladistic analysis because it creates a reticulation in the tree. I do not have the clear answer yet to these question, and it is good to know that this problem appears in biology as well and that tools to build reticulograms are being worked upon.
Since galaxies tend to merger all together, a possible scenario is that in some many Gigayears from now there could remain only one galaxy, a monstrous one. I have sometimes been told that merging of galaxies tend to decrease diversity. This is wrong, it may end up by decreasing the current “living” diversity, but what about all the extinct classes? If only one living species remain on Earth (guess which one), would you say that the evolution of life has not generated diversity?
Another important point is that galaxy diversification is expected to occur mainly in a branching pattern: each transformation process can give birth to a new species from an existing one. As a consequence, galaxy diversification can very probably be represented on a hierarchical diagram. Note that the Hubble diagram, in its original design, is such a branching graph: elliptical galaxies were supposed to be the common ancestor of two categories, the spirals or the barred spirals.
Unfortunately, we have reversed the meaning of the Hubble tuning fork, giving the curious impression that galaxy diversification should be a converging one. Even cosmologists have adopted this view by producing what is sometimes called “an upside-down tree” of Dark Matter Halos history: halos appear as very small entities just after the recombination, and merge together to build very massive halos (see e.g. http://hal.archives-ouvertes.fr/hal-00416733/en). So it gives the false idea that the very many small halos merged together to produce a very few number of very big halos, but this merely forgets that we do observe a lot of variety of halo sizes and masses around us and that in the course of the Universe evolution many kinds of halo masses have been produced
I do think that we confuse the fate of individuals with the fate of the populations. A converging tree can represent some physical evolution of individual objects, by a diverging tree must be used to depict the diversification of the whole population of either galaxies or Dark Matter halos.