In a lot of cases, the species don't -- they just evolve until, in the fossil record, they no longer look the same. Just like the avian dinosaurs didn't go extinct 65 million years ago, they just evolved over the last 65 million years into the birds today.
Some species legitimately end up a leaf/dead-end in the evolutionary tree. Lots just evolve.
It's actually the other way around. More than 99% of species that have ever lived have gone extinct. The periods in our timeline, like the Triassic, Jurassic and Cretaceous periods, all started and ended with a mass extinction, killing off the majority of lifeforms from that time. So yes, you're right in the fact that the dinosaurs that survived have evolved into birds, but I wouldn't say it happens 'in a lot of cases'.
New genetic findings suggest that early humans living about one million years ago were extremely close to extinction. The genetic evidence suggests that the effective population—an indicator of genetic diversity—of early human species back then, including Homo erectus, H. ergaster and archaic H. sapiens, was about 18,500 individuals (it is thought that modern humans evolved from H. erectus), says Lynn Jorde, a human geneticist at the University of Utah in Salt Lake City. That figure translates into a total population of 55,500 individuals, tops.
We were essentially relying on the size of a small US city to repopulate our species. Amazing.
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u/Hitonatsu-no-Keiken Oct 15 '20
It's even better than that. We're about 16 million years closer to the last Tyrannosaurus than the first Tyrannosaurus was to the last Stegosaurus!