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Ms Sage's sudden announcement of the high killing ratio may yet be challenged in court.
Killing of the tahr, which are related to goats and were introduced here in 1904, is to start within two weeks.
Ms Sage is proposing the Department of Conservation kill 10,000 animals in various areas in the Southern Alps over the next eight months because the animal's estimated 35,000 population was "three times" that permitted by the long established Himalayan Tahr Control Plan.
"Heavy browsing and trampling by mobs of tahr damages and can potentially wipe out the native plants they feed on, including tall tussocks and iconic species like the Aoraki-Mt Cook buttercup," she said.
Erosion of already thin soils at altitude was also increased, she said.
Other groups will also contribute by culling a further 7500 tahr, although not all agree outright with Ms Sage's views.
The minister says even after culling 17,500 from the total population of 35,600, there will be plenty of tahr to sustain guided hunting and tourism ventures.
The New Zealand Deerstalkers Association will join the culling but president Bill O'Leary said the 17,500 target was "rushed and based on slender evidence".
"It could spell the demise of a unique and valuable trophy herd," he said in a statement.
Trophy animals are male tahr which are at least eight years old but they would be indiscriminately killed alongside the tahr nannies and kids.
Mr O'Leary said Doc had admitted there could be a margin of error in population estimates of up to 9000 animals, although he conceded the overall number was above the number in tahr control plan (TCP).
"Some carefully planned, highly selective culling needs to be done, but better data and more detailed planning is needed, rather than killing so many tahr with undue haste," he said.
Of 10,000 animals left after unselective culling, Mr O'Leary estimated only 5000 would be male and only a "fraction" of those would be the highly sought-after trophy size.
Dunedin hunter and NZDA member Grant Dodson said the sweeping cull was "wasteful" and "an appalling move" by Ms Sage. He claimed she had not followed proper consultation process.
"If this goes ahead in its current form, a significant backlash to Doc and the minister can be expected, along with a legal challenge from affected parties," he said.
He suggested reducing the initial cull to 5000 animals while starting a review of the TCP, which at 25 years old was out of date and was never based on hard science.
Mr Dodson said the legal challenge was being considered as the 1993 tahr management plan required consultation, which had not happened.
Forest & Bird, for whom Ms Sage worked for 13 years and has life membership, said the "skyrocketing" tahr numbers proved hunting organisations could not adequately control the population.
Forest & Bird Canterbury regional manager Nicky Snoyink said instead of the permitted population of 10,000, tahr numbers were now over 35,000 and "probably closer to 50,000" when non-conservation land was included.
"Because of the past failures of recreational and commercial hunting we now need to reduce their numbers by 80%," she said.