Anyone Have an Estimate of the Pre-Contact Population of Kiribati?

Does anyone on here have a rough estimate of the pre-contact (ideally 16th-century but it doesn't really matter) population of Kiribati, or, even better, one of Nonouti in particular? I ask for a specific estimate for Nonouti because total figures for all the Gilberts will likely skew towards towards towards the lusher Northern Gilberts, especially Butaritari. I'm interesting because I need sources for a possible timeline where the Fernando de Grijalva expedition, which discovered the island (calling it Isla de los Pescadores-Isle of the Fishermen) ran aground on Nonouti, contacting the I-Kiribati two centuries ahead of schedule.