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I once heard that if Israel has the largest Jewish population, it has a significant effect on certain Halachot.

What are the criteria for this, and what halachot are affected? (Shmita is the one most cited)

According to JewishVirtualLibrary, that seems to now be the case, or is it? (links hidden in the word 'JewishVirtualLibrary')

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It's actually if Israel has the majority of the world's Jewish population, not just a plurality. The figures in your second link have 42.5% in Israel vs. 57.5% outside of it - so we're not quite there yet. (There is also, of course, the difficulty of determining who is a halachic Jew, ואכמ"ל.)

Anyway, Yovel (and Shemittah, according to some posekim) depends not only on the majority of the Jews being in the Land of Israel, but also on their living in their designated tribal territories (Rambam, Hil. Shemittah ve-Yovel 10:8). With almost no one knowing which tribe they're from, though, that's not really possible before Moshiach comes, barring major improvements in DNA analysis.

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Improvements in DNA analysis or improvements in the rate and readiness at which such analyses are applied? –  WAF Aug 17 '11 at 17:49
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@WAF: both, I guess. Current Y-DNA analysis, as far as I know, can't distinguish between the descendants of paternal brothers unless one of them has a variant sequence; it's highly doubtful that each of Yaakov's sons did. –  Alex Aug 18 '11 at 5:39
    
Actually, after living in separate populations for hundreds of years (especially with Benyamin not being allowed to marry in at all) it's very likely that a variant does exist. What is the source for Majority vs Plurality. –  avi Aug 18 '11 at 8:23
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@avi: the situation with Binyamin isn't really relevant - that seems to have lasted for only a short time. But anyway, even supposing that for several centuries each shevet kept to itself and married endogamously - we still wouldn't really have a way to know now whether a particular genetic sequence stems, say, from Yehudah himself, or from his son Peretz, or from Peretz's son Ram... etc. - it's just not that fine-grained yet; the error bars are still too large. –  Alex Aug 18 '11 at 15:11
    
What about the different moms? Mitochondrial DNA? Splitting everyone up between Leah, Rachel, Bilhah, and Zilpah should at least help? –  Kinnard Hockenhull Jan 8 '13 at 8:58
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