The word "re-establish" appears only one time and it is not in his context.
Arth said "70% of the coral has returned after a nuclear blast" (citing the article). The word "re-establish" is found in the following sentence:
(Page 509 said:
[...]however, we show that five decades is a suitable timeframe for the majority of the Bikini Atoll Scleractinian coral assemblage to re-establish after a long-term, chronic localised anthropogenic disturbance.
English is not my first language, so maybe there are some cases where "X has returned" and "X has re-established", but to me, in this case, the contexts seem to be identical. In both cases, something has disappeared and then comes back. If nothing else, that is the way it is used by biologists -- I am one, and I assume the authors are as well -- as a population that has remained in an area over a given period of time does not "re-establish itself"; only when it is missing (at least as a breeding population) does that happen.
The word "replenished" appears twice by only one time in relation to his context, which supports my position.
It "supports" your position only because you are being dishonest with what you quote. The article mentions "self-seeding from brooded larvae from surviving adults" and "survival of fragments of branching corals" as two alternatives, and adds "migration of new propagules from neighbouring atolls" as the third. It then elaborates on this by stating that:
Page 509 said:
The patchy nature of impacts may have mitigated the effect of disturbance at Bikini Atoll, with some patches surviving after each impact.
That is, since not all of the atoll was affected at once, the areas (patches) outside the immediate blast areas
may have had surviving adults of fragments, perhaps sufficient enough to repopulate directly affected sites between impacts. It cannot be inferred from this that any corals or parts thereof survived a direct impact. This is one of three possibilities they offer. They add a fourth -- which may be considered a subset of the first -- when they continue:
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Corals living on deep exposed reefs on Bikini Atoll may also have escaped some of the direct impacts, and thus have played an integral role in mitigating the overall effects of the disturbance event.
To some extent, it is made clear which of these explanations the authors find most likely:
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We consider the extremely large and highly diverse Rongelap Atoll s likely to have contributed a significant proportion of new propagules to enable recovery of the Bikini coral community, as Bikini Atoll lies downstream of the prevailing surface current from Rongelap.
Further, the article stresses that the recovery "benefit[ed] from the post-testing absence of human disturbance, the presence of uninhabited and non-impacted neighbouring atolls, and a supportive prevailing hydrodynamic regime for larval import". Again: "the radioactive contamination of northern Marshall Island Atolls has enabled the recovery of the reefs of Bikini Atoll to take place in the absence of further anthropogenic pressure."
These two statements, to me, seem to indicate that the authors credit the lack of prolonged or repeated disturbance of the coral reefs for its success in returning.
The word "migration" appears only one time but it does not discredit my positon above.
Yes, it does, as that is one of the two explanations for the rapid recovery that you chose not to cite, while you cite the two that at least superficially support your conclusion. In no place does it say, indicate, assert, suggest, imply, claim, or refer to information elsewhere doing so, that the surviving adults or parts thereof were from the area immediately affected by the impacts.