10 On the basis of these dates and linguistic evi- dence from Hardman of a closer linguistic relationship between Kawki and Aymara than between Jaqaru and Aymara, Torero has posited the following phases in the expansion of the language family: (1) a first split in the fifth century A. D. or before, (2) a second split in the ninth century, and (3) a proto-Aymara period a few cen-~- turies before the establishment of the Inca empire. Tying these in with archaeological evidence, Torero has identified the first phase with the beginning of Nazca influence in the region of Ayacucho and the second phase as occurring during the Vifiaque culture centered in the city of Huari, which controlled the area from Yauyos in Lima to southern Cuzco and Arequipa between A. D. 500 and 1000. The third phase coincided with the third stage of the Middle Horizon after the decline of the important Vifiaque centers (Torero 1972b:92,94,97). With respect to the expansion of Aymara on the altiplano, Torero has calculated the date of divergence between the dialect of Moho in the province of Huancané, department of Puno, and that spoken near La Paz, Bolivia as about A. D. 1550. While holding that a comparison of these dialects with one from southern Bolivia would show a longer period of separation, he has tentatively suggested that Aymara penetrated the area around Lake Titicaca during the 13th century A. D. in the latter part of his third phase (Torero 1972b:62-63).