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"In a study in the Bahamas, lionfish abundance was found to have increased rapidly between 2004 and 2010, by which time lionfish accounted for nearly 40% of the total predator biomass in the system."

I'm quite confused with the exact year or years that 'by which time' refers to. Does 'by which time' mean 'by 2010' or 'the period of 7 years from 2004 to 2010'?

Based on the connotation that the context shows, I guess it means the former but I'm not quite sure. If the sentence was written "from 2004 to 2010, by which time ...", I could have better understood. But what about "between 2004 and 2010, by which time..."?

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    I understand the confusion, but since the "by which time..." clause immediately follows the 2010, I would gather that you're correct in thinking the "time" in this case is 2010. Try googling "misplaced modifiers" for more info. – Kevin Workman Jan 28 '15 at 18:21
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by which time refers to a specific time that has previously been mentioned. It's typically the end of a process or event, so in your example 2010 would be the likely referent.

Had they intended to refer to the entire time period, they would more properly have used during which time.

Furthermore, the context makes it unlikely that lionfish accounted for the same percentage during the entire period. The sentence emphasizes an increase. While it's conceivable that the lionfish population increased proportionately with all the rest of the predators, so that the percentage stayed the same, it doesn't seem to fit with the sense of the sentence.

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    To show how dependent on context this is, it would be perfectly possible to say “Lionfish abundance increased significantly from the 1970s on, but then began to stagnate around the turn of the millennium and remained completely stable between 2004 and 2010, by which time lionfish accounted for nearly 40%”. In this context, though the words next to by which time are the same, it seems likely that it refers to the period from 2004 till 2010, rather than just the end point. – Janus Bahs Jacquet Feb 27 '15 at 21:44
  • @JanusBahsJacquet The phrase "accounted for 40% ..." refers to a single point in time, which is consistent with the use of "by which time". It would therefore make more sense in both the original and your extended version to identify that time with one specific date rather than an interval. – Lawrence Nov 25 '15 at 6:47
  • @Lawrence "accounted for 40%" can also be used with a period. For instance, The war on drugs has been going on since the 70's, during which time non-violent drug offenders have accounted for 40% of prison incarcerations (I'm just making up the number, so no debates on the politics). – Barmar Nov 25 '15 at 15:17

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