Introduction:

Yucatec Maya is one of the Mayan languages that is currently spoken in the Mexican states of Campeche, Quintana Roo, and Yucatan, as well as in the northern districts of Belize, such as Corozal. Once the area was occupied by the Spaniards, Spanish was introduced in the 16th Century coexisting with the Yucatec Maya during the entire Colonial era. However, the proportion of Mayan speakers has been decreasing during recent years.

Method:

In this research, we modeled the competition between Yucatec Maya and Spanish using Minett-Wang differential equations with three principal approaches: a direct approach, a generational approach, and a geographical approach, fitting the parameters by using Gradient Descent + Momentum with the historical data provided by the census and intercensal surveys of the National Institute of Statistics and Geography (Instituto Nacional de Estadística y Geografía, INEGI) in the states of Campeche, Quintana Roo and Yucatan from 1930 to 2015. The population projection of the three states were done using Logistic Model.

Results:

In almost all approaches was observed that Yucatec Maya tends to extinction. The combined usage of a direct and geographical approaches yields that Yucatec Maya will be extinct in Quintana Roo in 2285 (in Felipe Carrillo Puerto-Tulum), 2390 in Campeche (in Calkini), and finally in 2524 in Yucatan (in the southern and eastern municipalities). However, there are two cases in Yucatan where coexistence is possible: Mayapan and Tahdziu.

Discussion or Conclusion:

The model of Minett-Wang described appropriately an uncertain scenario of linguistic competition since the Mayan language still is numerically significant in Yucatan Peninsula. The area South-West of Yucatan, Central Quintana Roo, and Northern Campeche have more resistance to the language shift, but the parametric estimations show that this language tends to a scenario of extinction in most Mexican municipalities. There are needed relevant measures to minimize this panorama in terms of language policy and apply new estimations with the results of the following census to update the parameters of the model and monitor the decay of the number of Mayan speakers.

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