Speaking as a linguist (working on my Ph.D.) this is something of a tempest in a tea-pot. The most relevant use would be for glottochronology [wikipedia.org] - a field that's largely been abandoned by anyone seriously working on historical linguistics because of the various problems involved with that approach, including what the authors of the paper find, that the rate of word loss is not constant over time. They have a better idea of the rate of word loss, which could help improve glottochronology, but the method has a lot of flaws regardless.
Also, the question they're asking - how do words change over time, in terms of coining, becoming current, and becoming obsolete - really isn't a question historical linguists are that concerned about. Historical linguists are much more interested in how the forms of words change over time (phonological change), or how their function changes over time (grammaticalization), whereas the coinage and loss of words isn't often so important, especially on the large scale statistical level. Furthermore, this type of model probably handles languages with phenomena like avoidance speech [wikipedia.org] poorly, since that would change how and why words are kept or lost.
Their language sample is at heart a convenience sample - they happened to have access to lots of data in those three languages, and it is largely written data. Spanish and English are both related languages with very similar cultural contexts, while Hebrew is a strange choice in that is has an ancient history, but only quite recent revitalised usage. Whether most spoken interaction (which is what linguists tend to be more interested in) has even a tiny subset of the total number of words they are talking about is an open question and would be better tested against corpora with a large quantity of spoken data such as the British National Corpus or the International Corpus of English.
It's an interesting study, but if it hadn't been written by physicists I'm not sure if it would have ended up in Diachronica or the Journal of Historical Lingiustics, much less Science. Their "statistical rules" are interesting, but really not of any great use to wider linguistic inquiry. I think its import is really just exaggerated by the fact that science editors read Science and NOT most linguistics journals, and therefore they think it's really impressive.
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