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"The linguistic center of gravity principle states that a language family's most likely point of origin is in the area of its greatest diversity." (Wikipedia https://en.wikipedia.org/wiki/Out_of_India_theory)
Can you direct me to further discussion of this theory online? I haven't been able to find very much.
I think it is Joseph Greenberg who first used this notion (borrowed from biogeography/taxonomy) in his controversy with Malcolm Guthrie, a leading Bantuist in the 1960s, about the Bantu homeland. Guthrie believed it to have been in the center (somewhere in what is today the DR of Congo) of the huge Bantu area (roughly all Africa south of Equator save the Khoisan area in South Africa-Namibia-Botswana) because it was the lesser diversity area, erroneously taken as the original zone having best preserved the original language.
Greenberg convincingly demonstrated that, to the contrary, the original Bantu homeland ought to be somewhere around the Cameroon-Nigeria border, where Bantu languages are most divergent, because it is the place where they had the longest time to accumulate divergences.
This notion of maximal diversity area (not "center of gravity") may be corroborated by finding the location of the closest outgroup of the family. The closest outgroup of Bantu languages actually is in southwestern Nigeria, just besides the maximal internal diversity area, implying that their common ancestor also originated around there. (Guthrie believed these languages were not really related to the Bantu family but were instead "Bantuized" languages. Actually, they are all rather closely related members of a 5th- or 6th-order subbranch of the Niger-Congo family.)
Of course neither the "maximal diversity area" nor the "closest outgroup location" are absolute rules for a linguistic group's homeland. In exceptional cases, people may travel quite a long way from their original group (think of Apaches walking 3,000 miles south from the Na-Dené territory). However, each works well as a rule of thumb, and when the two coincide, as in the Bantu case, certitude is close to absolute.
For references you may look at: Joseph H. Greenberg, Linguistic Evidence Regarding Bantu Origins, The Journal of African History, Vol. 13, No. 2 (1972), pp. 189-216, and references therein.
