If we don’t have one species changing into another, we still have evolution, because that’s merely change. The change is a consequence of small replication errors, i.e. mutations, during mitosis and other cellular activity.
I’m not my grandfather (or my grandmother), and that’s the consequence of dropping half of the chromosomes for just two generations. And since there are 23 chromosome pairs, I’m not getting an even number from each of my grandparents (iow, it’s not exactly one quarter from each grandparent). Each of us has 64 great-great-great-great-grandparents, which means that, unless there’s been a cousin marriage along one of the lines, at least 18 of those 64 ancestors passed down zero chromosomes to us. They are still the ancestors, because they had to have lived and had offspring, but their genetic information has vanished from at least some of their descendants.
At the 5th-great generation — 128 of them — 82 have left zero to the current generation’s individual. In the next generation back, 210 left nothing. In short, there are (for most of us) 46 lines going back. As genetic sequencing becomes cheaper and quicker, and many, many more are sampled, common ancestry will be easier to figure out (even if no name can be put on it) and each of the 23 chromosome pairs will be grouped by common origin, and the number of groups will probably be in the high teens, at least.
That is exactly how I was taught human genetics about forty years ago.
Have there been developments since then that describe a process whereby some information gets exchanged between the members of a pair of chromosomes before meiosis takes place? I think the process is perhaps not as simple as some of us were taught and that the math you describe, although correct for the simpler model we were taught, is not, in fact, what actually happens.
Perhaps there is a recently trained geneticist reading this thread who can clarify this.
Number of chromosome pairs is irrelevant to quantity of genetic material passed from one generation to the next. Meiosis and fertilization are important events to understand here.
You get exactly half (on average) of each parent’s genetic material. The same thing happened to them from their parents, which means you have exactly one fourth (on average) of genetic material from each grandparent.
As for speciation—if it doesn’t exist, there can be no such thing as descent with modification and evolution is therefore only a figment of our imaginations.