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The Department of Conservation (Doc) said tahr were wrecking native alpine tussocks in their search for food and destroying the ecosystems.
It hoped that a renewed focus on tahr would help reduce the population.
Tahr control programme manager James Holborow said the only way to kill them was by shooting, either from a helicopter or on the ground.
He said Doc was in the early stages of developing a new plan to cull the pest.
"Probably likely to be two phases of planning. We will need to do some more tahr control next winter. So we’ll be working with our treaty partner Ngai Tahu to develop that plan with their tahr stakeholders. And then we’re also trying to make sure we can have a longer term plan that will run for, say, the next five or so years."
Doc ecologist Brian Rance said tussocks played a vital role in the alpine ecosystem.
"These snow tussocks, they are really like the trees in the forest. You know, they’re the canopy species. So they’re dominant in the vegetation here and also like a forest, they’re old, they’re very long lived. These species will grow and live for several hundred years."