I will share about sympatric speciation (evolution of one species into two when all populations live together in the same location) and how it ties into the process of evolution as a whole. It is a common misconception that for speciation to occur, populations need to be physically separated from each other. This need not be true, although it is correct that the process must be a result of some form of reproductive isolation there are subtle differences that lead to some methods being viable and others not. First I will define species as two populations that cannot interbreed to produce successful offspring. There are two forms of reproductive isolation, one is prezygotic isolation and the other is postzygotic isolation. Postzygotic reproductive isolation is the phenomena of two populations that are able to breed but always produce offspring that have significantly reduced fitness, and are thus unable to withstand the forces of natural selection over time. Examples of how this would look are: the outcome is lethal to the heterozygote offspring, they could come out sterile, or they may simply have reduced performance in the environment. Postzygotic reproductive isolation can only successfully evolve in populations that are physically separated from each other, this is because if a population is all together, the alleles leading to the reproductive isolation will be selected against because they result in individuals with decreased fitness and thus they will not ever rise to fixation. This is by the same process that two populations that continue to have postzygotic reproductive isolation will never successfully come together again, they are weeded out by natural selection.
Prezygotic reproductive isolation on the other hand is observed when individuals are physically incapable or preferentially driven away from mating outside of their group. These individuals are not selected against by natural selection because they do not end up cross breeding in the first place, thus they do not actually realize problems with heterozygotes having reduced fitness. Examples of this occur when different populations have different mating times so they never end up interbreeding, there may be gamete incompatibilities where the egg of one population rejects the sperm of another, and finally it could be due to the evolved mating preference of the individuals of each population. The fixation of allele frequencies that lead to prezygotic reproductive isolation usually occurs as a result of those alleles leading to an increase in fitness. One example of this in the wild is the stickleback which is a fish found in both lakes and oceans around the world. This fish is currently undergoing speciation due to prezygotic isolation. there are two emerging species of this fish, one typically lives away from the bottom of lakes, and the other is a bottom feeder. I specify that they are emerging species because even though the populations can interbreed, and sometimes do given the right environment, they have already evolved significant differences and inhabit separate niches. The one that lives away from the lakebed has spines and other things that help protect it from predation while the one that lives on the bottom doesn't have spines but does have features that allow it to feed better in that area. When the species are interbred the half-breed that is produced has less fitness than either of the two populations. Thus you can see how the development of mating preference would be advantageous to the survival of each of the sub-populations. It turns out that the probability of spawning between the bottom dwelling sticklebacks and the sticklebacks that live away from the bottom is much lower than within the populations. As a control the two groups were given the chance to breed with populations from separated lakes and it was seen that they do not mind matting with individuals from the other populations as long as they are of the same evolving subtype of stickleback.
From the example of sticklebacks you can see how, when given that the two fish interbreeding results in a half-breed with reduced fitness, you get strong natural selection favoring any genes that cause the two populations of sticklebacks to shy away from interbreeding. Another good example of this may be found on Galapagos island in their finch population. There are several sizes of finch that are each well adapted to feed on a specific type of food when food is scarce. There are finches with large strong beaks that are well suited for the hard nuts that smaller finches cannot crack open. There are finches with long beaks that are well suited for harvesting the seeds from cactus, and there are several others that are equally specialized. As you can imagine, if any two of those finch subtypes bread with each other, you would get offspring that are in between niches and aren’t as well suited to feed on either. Thus this is another example where evolution is being set up to take place. Although all of the finches are still able to breed, natural selection is favoring genes that cause them to not want to breed, because in doing so they reduce the fitness of their offspring. They in fact do exhibit preferential mating, and scientists have noticed that they have evolved different songs. Since birds attract each other for mating with their songs you can see how selection for that trait would end up increasing the birds fitness.
Now that I have described several examples of sympatric speciation known to evolutionary biologists that are currently taking place, I will attempt to concisely list all the steps involved in achieving evolution via sympatric speciation for the purpose of recapping the main points:
Populations need to have the opportunity to split into sub niches. For example there needs to be distinct niches that allow for the separating populations to fill them so that they aren’t forced into competition before they have gotten a chance to actually separate out into species.
Populations need to have some form of fitness advantage that goes along with developing preferential or physically impossible mating. This could be in the form of a less specialized heterozygote.
Populations need to maintain their lack of mating behavior until the process of natural selection has driven them to being fully incapable of cross breeding. At that point you have separate species.
Pre-zygotic reproductive isolation, post-zygotic reproductive isolation, and physical separation all simply set the stage for natural selection. The same process that drives the alleles conferring whatever form of reproductive isolation of two subpopulations to fixation eventually also drives the two populations into separate niches or perhaps direct competition with each other. In the first of the two possible outcomes you will get two similar seeming but distinct species. In the second example you have the potential for one population to wipe the other out, effectively erasing it from ever having existed. It is by this second process eliminating groups and the first pushing populations further and further apart that we do not see a more complete fan of species ranging from the simplest life forms to the most complex. Instead we see species with seemingly profound differences and wonder how they could have ever shared a common ancestor.