The researchers started with the latest estimate for a founding population of about 400 people, including 170-230 women. They then applied population growth rates in the range achieved by past and present populations and modelled the human population size through the moa hunter period and beyond.
Prof Holdaway and Mr Jacomb said when moa and seals were still available, the better diet likely fuelled higher population growth.
But the moa's total extinction most probably occurred within a decade either side of 1425. This was barely a century after East Polynesians settled the earliest well-dated site, at Wairau Bar near Blenheim.
The last known moa lived in the mountains of north-west Nelson. The researchers said it was often suggested that people could not have caused the extinction of megafauna such as the mammoths and giant sloths of North America and the giant marsupials of Australia, because the human populations when the extinctions happened were too small.
Prof Holdaway and Mr Jacomb said the extinction of the New Zealand terrestrial megafauna of moa, giant eagle, and giant geese showed that population size can no longer be used as an argument against human involvement in extinctions elsewhere.