When certain members of a herd of something for instance start producing a strain that will eventually become a new species at what point do they break off and start breeding with one another and no longer the original type? Is it more than likely just a slow process, where certain types dominate an isolated herd and out compete the originals? Where the original type is still alive and well in other herds.
Most speciation involves the physical separation of subpopulations of the parent species - say on two sides of a river that grows to a size that it cannot be crossed. That’s called allopatric or parapatric speciation, and there is no conceptual difficulty.
What you’re alluding to is called sympatric speciation, and your question is a very good one. For a long time there was controversy over whether it was even possible for speciation to occur in a single population without any external physical obstacle to gene flow. Plausible mechanisms have been proposed, but it remains uncertain how often it actually happens. Most of the story involves quite technical genetics.
The best known theoretical mechanism for sympatric speciation is called disruptive selection, in which the environment favors extreme values of a trait and disfavors the intermediate. For example, a long thin beak can access one food source, a short stubby strong beak can access a different food source, but an intermediate beak is not much good for either.
It generally doesn’t work that way. Rather what usually happens is a “herd” gets split for some geographic reason, those two or more now separate populations no longer interbreed or do so increasingly rarely until they slowly diverge into two or more different things. Sometimes this is really spread out and clinal as with ring species.
There are certainly oddball exceptions like when two different species of whiptail lizards in the American Southwest interbreed and create a parthenogenetic hybrid that is effectively is its own new, self-replicating thing. And it may be remotely possible that a spontaneous mutation could lead to a sexual selection advantage, as critters can have preferences - witness the complicated sexual politics of white-throated sparrows. But in the latter case you would be far less likely to end up with multiple species than it would be for one morph to swamp out the others.
But oddities like that aside the vast majority of speciation is mediated by geography. Allopatric (population split), peripatric (founder effect) and parapatric (wide dispersal range) are all basically different versions of geographic speciation. Sympatric speciation, which is what you are asking about, is vanishingly rare and some argue that it may not exactly exist at all (whiptail speciation as above for example is a thorny philosophical and definitional problem).
Two good answers cover the main question well, but I think it’s worth to quibble with this part as it’s close to the “unchanged for millions of years” misconception. Though there is evolutionary pressure to preserve beneficial traits, all populations change over time. Every generation has a bunch of new mutations spread among the individuals. It’s possible that even the “original type” would be unable to breed with their ancestral population back at the point where the new strain could, and it is almost certain that it will be a different species at some later time.
That helps understanding why speciation usually requires some form of separation.
HoneyBadgerDC,
This may be of interest. It is a study of Astyanax mexicanus where a species does co-exist with it’s ancestor.
But strictly speaking no species coexists with its ancestor, by definition. In terms of the evolutionary dynamics, it’s still better to think of this situation as two daughter species with a common ancestor coexisting in the same place. It may be that one of the two daughter species has evolved major changes and doesn’t look much like the common ancestor; whereas the other daugher species has maintained the same evolutionary niche and still closely resembles the common ancestor. Paleobiologists might decide to classify the former as a new species and the latter as the same species as the common ancestor, but technically nobody really knows if the latter species could still interbreed with the common ancestor, because they do not coexist.
The changes in the two daughter species will be reflected also in the genome. In the species that has changed significantly, positive selection will have driven divergence in DNA sequence away from the common ancestor;
whereas in the species that still closely resembles the common ancestor, purifying selection will have maintained a DNA sequence similar to the ancestor.
But what’s interesting is that this applies only to the parts of the genome that code for proteins or have some other function. Large parts of the genome serve no apparent function, and are not subject to significant natural selection at all. At non-functional parts of the genome, mutations will continue to accumulate at the same rate in both daughter species. The degree of sequence divergence from the common ancestor will reflect only the time since speciation. This is a powerful principle in molecular evolution that allows us to infer evolutionary history.
You are correct. I mis-spoke.
Whatever it illustrates, Astyanax mexicanus is an interesting case.
Or more precisely, it’ll reflect the number of generations since speciation. If one of the differences between two daughter species is a change in the length of a generation, then of contemporary members of the two species, the longer-generation one will be closer to the ancestor. For instance, we humans are closer to the human-chimp common ancestor than chimps are.
The 13 year and 17 year cicadas are separated in time, not space. Are they separate species? They must come out together every 221 years. Can they interbreed and, if so, to what clan do the offspring belong?
Do both species emerge at the same time of the year? A few weeks would make a significant difference, as I understand it.
ETA: refering to the cicadas in the previous post.
One mechanism that occurs to me is cases where the genes are involved in mating behavior.
Suppose, for example, you had a species of parrots living in a region. The parrots have multi-colored feathers with no particular genetic effect.
Now assume a mutation occurs which causes a parent to have a new gene which creates a preference for mating with parrots that have blue feathers (call it the BP gene). This parrot will seek to mate with parrots that have blue feathers, which means they have a gene for blue feathers (call it the BF gene). So both the BP gene and the BF gene will be present in the parents and will be passed on to some of their offspring.
In future generations, birds with the BP gene will be seeking mates with the BF gene, which will pass on both the BP and BF genes. Birds with just the BF gene may not have a preference for mating with BP gene carriers but they will be more likely to mate with BP gene carriers because those birds will be seeking to mate with them. So the birds with just BF genes will be more likely to have offspring with both the BF and BP genes. You’ll end up with a population of parrots having both genes.
Meanwhile there will be a population of parrots having the old mix of genes existing right alongside these new BF/BP parrots. They have the old mix of genes because they’re neither seeking the BF gene parrots or being sought by the BP gene parrots.
Right, I mentioned that above 
. But as I noted the more likely outcome of such a development would be either a swamping out of the less competitive color morphs in the case of complete preference. Or simply a multi-morph species maintained in an equilibrium situation like the above cited white-throated sparrow.
But the concept of species is a human construct anyway, one imposed artificially on fluid and complicated situations. Take the Dark-Eyed Junco. Their ridiculous number of widely different morphs are currently now all synonymized but probably represent a snapshot in time of speciation in action.
However you can contrast them with the Rose-Breated Grosbeak vs the Black headed Grosbeak. The adult males look very different, but females are virtually indistinguishable from one another. It is a very closely-related species pair that split at some point at the Great Plains/Rockies. But they will in fact hybridize naturally where they meet. They just don’t most of the time so they get lumped as separate species. But it is a tight call between these and the morphs/sub-species that the junco is categorized as. So it kinda becomes a judgement call despite every attempt to define things in a consistent way. Though Ernst Mayr might shake his fist and disagree from his little corner of Heaven, strictly speaking they represent one of those holes in the biological species concept. Birds in general because of their enormous potential vagility can get messy like this - we probably shouldn’t even get into gulls and sapsuckers 
.
Well, now - it’s complicated. But the short answer is yes. The thing is there are multiple species of both . So for example Brood V (2016, 2033) consists of three different species of 17-year cicadas. But the same species will have multiple broods.