what would you call this situation…suppose you have a car, and over time you replace parts, until eventually you have replaced so many parts that no part of the original car still exists.
or suppose you have a group of individuals, and over time as people join and leave the group, none of the members are the original members.
I always refer to things like that as “Abe Lincoln’s ax,” after a story I once heard about an old-timer bragging to a tourist that he had Abe Lincoln’s ax: “It’s in great shape, too! I’ve only had to replace the head twice and the handle three times.”
Probably not what you’re looking for.
Well, the Republican Party was formed in what 1858? so it’s probably safe to assume that the original founders are no longer around but it’s still the Republican Party. Likewise the Masonic Lodge, the DAR and numerous other organizations.
I guess I don’t understand the question.
Happens quite often in rock & roll. Renaissance, for example. By the time they hit it small, there wasn’t a single original member left in the band.
I, too, use an axe as the basis of a story about this phenomena. But it’s my uncle’s axe. 
A bonanza for the parts suppliers. 
It’s still the same group of different individuals. Isn’t it?
Individulals are identified by the group, it’s purpose, ideals, activities etc.
You call it a professional sports franchise.
You, yourself, are made up of atoms and molecules–none of which were present in “you” lo, these many years ago.
I don’t believe there is any English word of the precise definition you are looking for.
…This is the reason you see in magazines like Hot Rodding, where they build a custom hot-rod and they always start with a rusty frame from a (non-salvage title) car or truck from way-back-when, the 1920’s or 1930’s. Because back then there were very few safety regulations to meet, and so (in the US) you can re-build that car on that frame, and (because the frame you are using was made and registered with the government way back in the bronze age) you don’t have to meet current safety or environmental standards. . . . . -So you are free to do fun things like use no bumpers at all, you don’t have to use safety glass, you don’t need no stinkin seatbelts or airbags, you can use a carbureted engine, and you can put as big an engine in it as you wish.
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A/k/a “Washington’s hatchet.” (Same definition: multiple heads, multiple handles.)
The only way I have seen this referred to in technical publications is “gradual replacement”.
The most obvious actual (rather than hypothetical) example is the replacement of atoms in the human body. Every atom is turned over gradually such that the person you are at 50 contains no measurable part of the person that you were at 10. You have been gradually replaced bit by tiny bit without ever having ceased to exist.
We see the same thing in populations of organisms, as othertshave pointed out. Whether the republican party or the bears of Yellowstone the population entity exists and functions precisely the same way even though the individuals are replaced one at a time.
Kind of like how people say all your cells are turned over every 7 years…
Interesting, I bet proponents of life after death could use this scenario in their arguments.
Yeah, only it’s true. Cells are turned over on average every 7 years. That’s not the same at all as saying they are all turned over every 7 years. For every hundred or so intestinal lining cells that are turned over every 6 hours there is a nerve cell that is never replaced from the moment it forms pre-birth.
So all your cells aren’t turned over every 7 years. Some of them last oyur entire lifetime without ever being replaced, some last less than a day.
I bet they could too, it just wouldn’t make any sense.
For bands I too use the Washington’s axe metaphor. But I call them a “head & handle” band.
I remember it from that comedian/juggler guy whose name escapes me. He was really popular in the mid-eighties, on Carson, Letterman, SNL, HBO Young Comedians etc. He never came up with any new material so he kind of just faded away.
Anyway, he was famous for simultaneously juggling a knife, a meat cleaver and an axe and when he took the axe out he would say that this was the actual axe Washington cut down the cherry tree with, and that it had been in his family for so long that over the years he’s had to replace the head, and the handle.
I’m surprised to hear that others use this analogy too.
I’d call it “xollective entity” or “group continuity.” The collective has a distinct identity which is not dependent on whether any of the original parts are still in there.
I meant to write “collective.” I was not trying to invent some new word by substituting the x instead
Here’s the essence of the problem, from the source I linked above.
I experienced this sort of thing when I toured the HMS Victory. When asked how much of the ship was original, the guide had to explain that the ship had undergone a significant refit decades after it’s original construction. And there was the fact that much of the ship was newer material to replace battle damage. So it was sort of moot asking how original the ship was. His contention was that it might be better to ask how much of the ship was “historic.”
I don’t know of any term that refers to the process, but you can find lots of info by searching on the problem of material constitution.