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And a fish decided to come out of the water so it laid an egg that turned into a small mammal. However, there was only one egg so the mammal had no mate so another fish laid another egg and a mate evolved.

Congratulations, you have a ridiculous grade-school notion of evolutionary biology. Wait, I take it back, most grade-schoolers know better than this. Instead, you have a ridiculous cartoon notion of evolutionary biology, on par with that of most anti-evolutionists.

First, evolution is not about what species "decide" to do. Where did you pick up *that* goofy idea, a creationist pamphlet?

Second, evolution does not proceed via anything as laughable as a fish laying an egg that hatched into a mammal -- is this another anti-evolution lie you read in a creationist tract? Did you somehow sleep through the parts of biology class that covered how the transition from fish to mammal took hundreds of millions of years, and progressed through a great number of intermediate stages (including fish with flipper-like feet, fish-like proto-amphibians, amphibians, reptile-like amphibians, reptiles, mammal-like amphibians of various degrees of transition, etc.), as detailed in overwhelming amounts of evidence including vast numbers of fossils and DNA evidence and more? Or do you "learn" everything you "know" about evolution from the know-nothing anti-evolutionists like the twits that write the articles at "Evolution News & Views"?

Finally, the notion that speciation occurs via a sudden extreme mutation that gives birth to a brand new species in a single generation which then has to find another of its kind to mate with is so idiotic it could only have come from the anti-evolutionists, because no one else could possibly be that stupid. Anyone who has bothered to learn the first thing about biology before they attempt to critique it (which, again, leaves out the clueless anti-evolutionists) or who has even bothered to read Darwin (anti-evolutionists are obviously 150 years behind on their reading and have a nineteenth-century "understanding" of biology) would know better than this kind of moronic idea. Here, learn something for a change (if you can), from previous posts of mine in response to other people who had their heads filled with nonsense by the anti-evolution propagandists:

I know evolutionists believe that the changes occurred gradually. My point was at some point man was fully man. Unless every single creature gained that full manness at the same time, he was mating with something that would have been less (even if it only slightly less) human than he was.
Okay, let's see if I can explain it this way...
First, part of your confusion (in this, and in a lot of other topics in this thread) comes from your insistence on declaring that things must be 100% A or 100% B. The living world is not so black and white. The range of living things is a continuum more often than it's either/or. And not just across time, either -- several people have asked you to ponder the existence of "ring species", but I haven't seen you tackle it yet.
Furthermore, creationists often fail to appreciate the significance of the "nested hierarchies" of living things. It's as incorrect to say that a specific creature must be *either* a human *or* an ape as it is to say that a creature must be *either* a lion *or* a cat. Ponder that one for a moment, and then you'll be ready to understand the point of the essay You Are an Ape. Please read it.
Finally, even if you cling to the view that there's some "required" combination of genetic differences which, as soon as they're acquired, turn a "mere ape" into a "human", *bang*, that still doesn't make the evolution of one into the other a problem, or create any "breeding impossibilities". Here's how it works...
First, keep in mind that even if the "special" combination of genes which make primate DNA be considered human DNA has to all be present before *you'd* finally agree to label the resulting organism "finally human", a creature with only, say, 99% of those genes would still look pretty darned human and not so "classicly" apelike, since it would consist of 99% of the things that "separate" humans from apes. It'd only be missing one little thing out of the full set, so only one part of it would still be "apish" -- for example maybe it'd have more of a protruding brow than most people but all other human characterstics.
The other thing to keep in mind is that any one (or five, or fifty, or...) genetic differences is usually not enough to prevent interbreeding. The genetic differences just "mix and match" in members of the popuation, in the same way that both the blue-eyed gene and the brown-eyed gene swirl through human populations without any big deal.
So now that you've got some of the background, the way in which an "ape" population would evolve into a "human" population is straightforward. At some time a mutation X1 appears in the birth of a member of the population which offers some small advantage by virtue of being a small improvement (which in this example happens to bring the individual slightly closer to the advantages of being "humanlike"). The change is likely to be barely noticeable to those around him, perhaps he stands just slightly more upright, or has a slightly larger brain, or his hands are just a bit more talented, or he can voice a slightly wider range of sounds -- whatever. It's due to a small DNA change within him which just happens, by luck, to make a biochemical improvement to a particular protein in his body in a way that makes some function in his body perform just a touch better than was possible without the change. So, unlike many other mutations in the population, which made no difference, or the ones which caused damage to the functioning of the affected individual and got weeded out by natural selection, the individual who was lucky enough to receive X1 does a little better than the others in his species, and passes on his new X1 gene when he has children.
But wait, you ask, he's a "mutant", wouldn't that prevent him from mating with all the rest of the population since they don't have X1? No, it wouldn't, any more than your brown-eyed gene would prevent you from having children with a blue-eyed man. The "owner" of X1 mates with a woman who has the original form of the gene, call it Q1. Due to ordinary genetics, each of their children will have 2 X1's, or 2 Q1's, or 1 X1 and 1 Q1, by random chance. But because X1 gives a survival boost, more of the children who drew X1's from the genetic deck will have their own children than those who missed out. And so on and so on across generations, causing X1 to become more and more prevalent in the population than the competing "obsolete" Q1. Statistically, eventually X1 will "fix" in the population by virtue of being the only variety of that gene existing in the population, the Q1's having gone extinct when the last few individuals who still had a Q1 either didn't manage to have children, or had children but their children drew X1's from their parents genetic "deck".
So now the whole population is made of individuals with X1 genes and no Q1 genes.
Repeat this process for X2, another gene change which is a step along the road from "apeness" to "humanness". Then for X3, and X4, and... Finally, at some point the population will have genes X1 through X(N-1) out of the N genes which you believe are required to make them "fully human". They already look and behave pretty much entirely human, since they have almost every genetic feature which makes a species human, but you're still unwilling to declare them human because they're missing X(N), the last gene of the set. Okay, fine -- repeat the process I described above about X1 to gene mutation X(N). The first individual which gets that mutation is now "fully human" in your book. Hooray for him. However, he really isn't noticeably different from the other members of his species, since he only varies from them by a single genetic difference. So other than being the guy (or girl) who loses that last tiny remnant of "apeness" which is barely even noticeable in the population (maybe jaws on average protrude just 3% more than his or his offspring will), he has no problem having children with the mate of his choice, because they only differ by a single mutation. And eventually his X(N) gene spreads through the population over the next fifty generations until the old-style Q(N) gene gets replaced by it, and all of his kind are now 100% human instead of 99.9% human as they had been before the X(N) mutation.
And note that all the above is *standard* population genetics, *extremely* well established as ordinary processes which occur all the time in nature. It's not just an "imagine if" story.

Also note that I've simplified it somewhat by implying that, for example, mutation X46 wouldn't happen until mutation X45 had finished "fixing" in the population. Instead, it's just as easy for it to occur and be spreading into the population *while* X45 is in the process of doing so as well, for example. But this just makes the process even *more* likely, not less. There are always multiple sets of alleles floating around in populations without ill effect -- if there weren't we'd all be identical and homozygous clones.
Frankly, though, I don't think we're fully human *yet* -- if nothing else, we really need to get rid of the ape genes we still carry that cause these damned wisdom teeth which fit nicely and were useful in the longer ape jaw but just get jammed up and cause health problems in the rear of our smaller more human jaw. It looks as if we're still waiting for X(N) and haven't quite gotten the "full human" transformation finished just yet...

And:

Oh my, where to start... At the top, I suppose. You start with, "The definition of a species is that it can't reproduce with anything outside the species." No, this is incorrect. While it's true that if two groups *can't* interbreed, they are necessarily separate species, the converse is not true. Groups that can interbreed to some degree can still be separate species. Consider lions and tigers, for example. A better definition is that species are groups that *don't* interbreed to any large degree. A more technical way to put it is that they are independent breeding populations. But there are exceptions and gray areas -- this is because nature itself does not recognize the "species" concept. It's a manmade label applied for convenience and utility to certain groups. If Darwin was right, there should not be clear-cut distinctions between groups as they are in the process of diverging evolutionarily. And indeed, this is exactly what we find, which is why there's no "one definition fits all situations" meaning for "species". Groups like "ring species" throw a monkeywrench into any "nice and neat" definition of "species" that humans might care to try to formulate, for example. Nature is nowhere near that tidy.
But even leaving that aside, your idea about how a population can split into two distinct species (even by your definition) is a wildly incorrect misconception about how it actually works.
You have two major misconceptions and wrapped them around each other.
The first is that species formation involves a sudden "freak" with a massive mutation that occurs in a single individual in one generation. Nope, wrong. This is widely snickered at in the biological community as the "hopeful monster" scenario. But it's not how evolution proceeds.
Your second misconception is that having a different number of chromosomes would prevent successful mating. It doesn't. Or at least it needn't, depending on the nature of the difference, and there are many known cases where it doesn't. For example, the Przewalski horse, which has 33 chromosomes, and the domestic horse, with 32 chromosomes (due to a fusion), are able to mate and produce fertile offspring.
A third misconception, a combination of your first two, is that speciation requires anything like an "extra" chromosome. It doesn't.
What actually happens (or at least in most cases -- as in my earlier discussion of the definition of "species", nature is flexible and abounds with variations, and refuses to follow any one "script" in every single case) is that accumulated small changes in a population diverge if from a parent population.
Note for example that there is no one "big mutation" separating humans from our nearest extant cousins, the chimps. There are *thousands* of genetic differences, as one would expect after five million years of divergent evolution between the two groups. Heck, there are hundreds of genetic differences between *human* groups, and we share common ancestors a lot more recently.
[Sidebar: However, the nature of any one specific difference considered by itself is minor and of the type one would expect to be produced by evolution. There are no portions of the human -- or chimp -- genome which are so different that they seem "completely rewritten", or "written fresh on the drawing table" when compared with the other group. Both the human genome and the chimp genome have been completely sequenced and are available on several online databases. I challenge any creationist to compare any portions of the two and look for any difference between them which are "unique", or are major minor variations from the other to be of the sort -- in both amount and kind -- which one would not statistically expect to result merely from five million years of evolutionary "drift". Good luck! None have been found so far by anyone, but hey, maybe you could be the first.]
One genetic mutation does not a new species make (again, usually). Often *hundreds* are not enough, as proven by the many genetic differences occurring even within human populations.
Instead, it takes *many*, *many* accumulated mutational differences to separate one population from another to a degree large enough to warrant describing the two as different species, and/or to interfere significantly with their ability/willingness to reliably interbreed.
So the answer to your question is simple: Speciation does not occur in a single generation by one mother suddently giving birth, *poof*, to an offspring so mutated that it's a "new species" from its mother, and unable to interbreed with the rest of its (sort of) kind. Instead, subpopulations of a larger population (often separated by distance, geography, or other barriers) each accumulate genetic differences apart from each other as new mutations accumulate separately in each subpopulation, each mutationoccurring originally in a single individual then spreading through the subpopulation in succeeding generations (while detrimental mutations get constantly weeded out by natural select, and beneficial mutations get "amplifed" by it), until eventually the two populations are different enough from each other in their overall genetic makeup so that morphologically they are obviously different "subtypes" of creatures even to the unaided eye, and no longer reliably interbreed with each other.
And yes, there are countless field studies and genetic studies and all sorts of other studies which have established the reality of this, it's not just a hypothetical scenario.

And:

I'm no expert (this will become obvious momentarily) so I've always been puzzled about one thing. At a certain point a mother gives birth to a child with a different genetic code, right? Fine, but let's say the child is a female. My question is; where does the male come from with the same genetic code to propagate this new species? Or is it a horse + donkey = mule type of thing where the species are similar enough to carry on. My ignorance on this is great so I would appreciate any answers you could provide?
You're asking the wrong person, allow me...
The answer is that it's not a matter of having "same" or "different" genetic code. Every human being has a different, unique genetic code (that's why DNA matching works in criminal cases). But obviously we can still interbreed.
No "exact match" of DNA is required to interbreed, just "close enough".
And the short answer to your question (there are all sorts of fascinating complicating details) is that when a population (usually, an isolated *subpopulation*) of species X is evolving towards becoming species Y, the amount of genetic change per generation is small enough that each member of the population can continue to interbreed with the rest of the population, even if it has a mutation that hasn't yet spread to the rest of the population.
Over several generations its novel mutation does spread through the population and becomes ubiquitous in the population, and thus when the next novel mutation pops up in the population, everyone's already on the same "page" with respect to the last one, and the new mutation is no more hindrance to interbreeding than the last one originally was.
Rinse, repeat, etc.
Eventually number of novel mutations in the population becomes so large that even though the population itself can still interbreed (because they all "evolved together" into species Y through genetic exchange), the population is "enough different" DNA-wise that it will no longer be able to interbreed with members of the *original* population of species X it split off from (which itself may be relatively unchanged, or evolved off in a different direction itself).
This is how one species splits into two (or more), each "daughter" species unable to mate with its "sister" species, yet always able to breed with itself at every stage along the way.
Look back a few posts for a discussion of "ring species", whereby each subgroup along a "ring" around a mountain or whatever is still able to interbreed with its "neighbor" subgroups on the ring, but when the far "arms" of the ring meet each arm has changed enough genetically that they are unable to mate at the point where they "meet up" on the other side of the geographic obstacle. This works in a way similar to my description above -- each subgroup is "not too different" from its neighbors to interbreed, but over the whole extent of the line/ring, the far "ends" have diverged enough from each other to be unable to mate. Same thing, basically.