"Indigenous" is to "native" as "still here" is to "began in one place, moved to another". For example: the flowering dogwood cornus florida is indigenous to the Northeastern US. An individual tree of that species might be native to Pennsylvania — that is, it sprouted from a seed there — but, dug up and transplanted to another part of the country suitable for its growth, it is not indigenous, but still a "native Pennsylvanian". To confuse the usage a bit: capital-n Native Americans are the indigenous population of the contiguous United States. With a few notable exceptions, however, they are no longer indigenous to the regions where their histories say they originated.
I have not lived in my native place for 40 years; then, four years ago, I began what became in hindsight a 5000-mile zig-zag from one coast to the other, then three-quarters through the width of the country at its center. When people ask me, "Where are you from?" I usually answer with the state where I spent most of my life, thus far… that is, when I don't answer "How far back do you want to go?"
Each time, as soon as possible after unpacking I've tried to learn about the place I think I'm settling into, which usually means going to the library for books on regional and local history (and, in one lucky find so far, prehistory). I keep my ears open for nuances in speech, both in pronunciation and usage. I take note of the highways mentioned in radio traffic reports, names of communities in the news, and local personages of note and notoriety. In short (remembering what it was like to transfer across country during high school), I don't want to stand out —— or worse, be singled out — as The New Kid.
The word assimilate has two uses, passive and active. One is by the way of absorption, as the Norman invaders of Britain were assimilated by the (Anglo-)Saxons, and they all became English together. The other use is as a deliberate process performed by immigrants in order to 'fit in', thereby to accelerate absorption.
I don't know much, if anything, about the history of other countries our readers find themselves native to (if not indigenous), so I hope they will excuse examples from American history. We are a nation of immigrants. Ofttimes, owing to conditions in 'the old country', waves of immigrants from specific places and cultures have arrived here en masse. The immediate reaction of everyone already here — even if they arrived in the previous wave! — is xenophobia: fear, mistrust, denigration and sometimes hatred of the stranger. The recent tsuris over immigration in (and to) the US is merely the latest incarnation of this cycle.
Historically, many brand new immigrants have tried to 'Americanize' as quickly as possible to avoid just that. Many others have done so in sheer joy of being out of their oppressive homeland, and in gratitude for America being the haven it was. Either way, it's become nearly a cliché, and certainly expected of all newer-comers. Immigrant populations who refuse to actively assimilate (such as the Amish), or who retain foreign cultural characteristics (such as the Hasidic Jews), never quite escape the suspicious prejudice of their neighbors, no matter how many generations have passed since their arrival.
Ultimately descended as we all are from tiny isolated tribes, we instinctually need to 'fit in' when circumstances take us from home, whether our motivation is fear or a desire to embrace the new. The other side of that coin is: once welcomed by the new community, we join them in 'defense' against the next strangers to wander into camp.
Involuntary immigrants are called refugees. If the high estimates of sea-level rise due to global warming eventually occur (sadly, we won't know until it will be too late to arrest their encroachment), many millions will be dislocated to higher ground as their homes are inundated. To the children of the 2050's I offer this advice: