Kia kaua te reo e rite ki te moa, ka ngaro: do not let the language suffer the same fate as the moa

More than a third of the world's languages are currently classified as endangered and more than half are expected to go extinct by 2100. Strategies aimed at revitalizing endangered languages have been implemented in numerous countries, with varying degrees of success. Here, we develop a new model regarding language transmission by dividing the population into defined proficiency categories and dynamically quantifying transition rates between categories. The model can predict changes in proficiency levels over time and, ultimately, whether a given endangered language is on a long-term trajectory towards extinction or recovery. We calibrate the model using data from Wales and show that the model predicts that the Welsh language will thrive in the long term. We then apply the model to te reo Māori, the indigenous language of New Zealand, as a case study. Initial conditions for this model are estimated using New Zealand census data. We modify the model to describe a country, such as New Zealand, where the endangered language is associated with a particular subpopulation representing the indigenous people. We conclude that, with current learning rates, te reo Māori is on a pathway towards extinction, but identify strategies that could help restore it to an upward trajectory.