Are my ancient ancestors considered extinct?

If you go back far enough, some of my ancestors are fish. Are the species those fish belong to considered to be an extinct species?

On the one hand, nothing that looks like those fish are around today. On the other hand, those fish have plenty of living descendants.

How do scientists interpret the word “extinct” in this context?

There’s nothing incompatible between genetic descent and the species model used used by palaeontologists. Assuming we are all descended from Australopithecus africanus [we don’t actually know which australopithecine species begat H sapiens, but could have been one of several known or as yet-undiscovered, or our ancestors seem to have shagged everything that moved so we could have multiple antecedents], that species is defined as a suite of physical traits that in combination are distinct from other australopithecines (different A. species) or hominids (genus-level). For long-extinct species the expectations of interbreeding cannot be demonstrated.
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We have some of the same traits [e.g. no of teeth, facial symmetry, body form, the way the mandible connects to the skull etc]. Some of these originated with australopithecines, and others go way back into the primate / mammal / vertebrate line. However, we are not australopithecines because we do not possess some of the defining traits, we have the version found in Homo.

When we get to Homo, then its no longer comparing apples and oranges but different apple varieties, some of which are defined from single, partial examples and whose identification as separate species may not stand up when more intact specimens are found.

Back to the question - what is extinct is the defined species. We carry genes that relate to our ancestors right back up the line, but its all animals expressing the particular combination of traits which defines each species that is extinct. Great-granny is dead but you are 1/8th her genes.

Species can evolve to become one or more other species, due to changes in their characteristics. To this extent, I suppose you could say the originating species is extinct, as in there are no more in existence with that specific array of characteristics.

If an archaeologist looked at x-rays of my skull, he would not say, “That is an australopithecus.”

The australopiths are all extinct. We are hoser mutants.

Is this a yo great-great-great…great-grand-momma joke?

I believe if you want to distinguish between extinct species with no descendants and extinct species that have descendants that evolved into a different species, the latter is called pseudoextinction.

But so far as I’m aware nobody would consider it incorrect to use “extinct” for both, just add the pseudo if you want to emphasize that aspect.

Not mine, and I make no comment about yours, not having known her myself.

Its actually in homage to Imogene Coca, who played Shag in Its about Time, one of the stepping-stones towards my education as a wannabe archaeologist.

When you go far enough back, it’s a guarantee that the individual you’re referring to is either an ancestor of every single human now alive, or none of them.

Just as a slight nitpick, Australopithecus is a genus of hominin, and all of genus Homo (of which modern Sapiens is the only extant species) are derived from one specific lineage of Australopithecus.

A species is functionally extinct when there are no more populations capable of breeding to produce more members that would be identified as that species (rather than a hybrid). How species are delineated is somewhat subjective; there are numerous examples of separate species which are fully capable of interbreeding and producing viable offspring, which was certainly the case with various pre-Sapiens members of Homo. The unidentified fish species that we and (presumably) every other land vertebrate evolved from is undoubtedly extinct, as are the primordial species that branched off into Amniotes and subsequently led to all Sauropsida and Synapsid clades. In fact, all predecessor species to modern humans are extinct, and the same is largely true for the vast majority of animal species because evolution never rests.

Stranger

This is like asking if a language is extinct if there are languages descended from it that are currently the native language of some people. So is Latin a dead language? Italian, French, Portuguese, Spanish, Romanian, Catalan, Romansh, and some other languages are descended from Latin. So when did Latin quit being a living language and when did the languages descended from it become living languages? It’s an arbitrary choice. There’s no point at which the speakers suddenly realized that they’re speaking a different language. It’s just that over centuries or millennia the language slowly changes. Generally you have to look at important historical events to arbitrarily choose when one language ends and another begins.