There is kill return data from the ballot blocks. It's publicly available online for 2017. Note that about 50% of parties returned a diary, and the reported female:male kill ratio is about 1.5:1. These numbers are suspect as you say, because hunters have various motivations for lying to DOC, but it's all there is to go on. Because of the 50% reporting rate, you could perhaps double the number of kills from 500 and change to say 1000 over the whole ballot areas.
https://www.doc.govt.nz/pagefiles/21...ng-results.pdf
DOC tahr culling data is hard to find. It's not publicly published really, except for these numbers. https://www.doc.govt.nz/parks-and-re...hr/tahr-culls/
The most recent complete numbers from this are 2012-2013. 2013 is incomplete data.
From this, you can identify that from the Landsborough and Mahitahi/Jacobs sub-areas of the ballot blocks alone, DOC and AATH offsets culled 1375 tahr - more from part of the ballot blocks in 2012-2013 than all rec hunters at a best case of 1000 and change over the entire ballot areas did in 2017. For all culls in the 2012-2013 year, DOC and AATH offsets culled about 3,000 tahr. Note that these numbers are 5-6 years old, and given that the population has likely increased (I don't know; no-one does. There is no publicly available data to know what the population trend is over the last 5 years, just that it has increased since 1993) cull numbers have likely increased commensurate with that. In 2011-2012 DOC culled 2200 and change, the increase from 2200 to 3000 the next year may be indicative of an increasing population.
As stated, in 2011-2012 DOC culled 2200 and change tahr. TIG (Tahr interest group) culls appear to have been unusually active that year (there have been none this year and the one last year was postponed due to poor weather and ended up being fairly unproductive as I understand.) with culling in 5 areas totalling 707 tahr. The TIG cull in 2016 shot 196 tahr (I shot 19 of those). TIG organised culls in an unusually busy year for it totalled less than 1/4 of all tahr culled, at a presumably lower population level. It demonstrates that a massive effort would be required to make a more significant contribution to culling by foot hunters - 3x the participation or 3x the time hunted, to equal DOC culling - at a presumably lower population level.
Looking at those published figures, the majority of DOC and AATH offset culling recorded in the publicly available figures takes place in the Wilderness Areas, Westland national park and other areas where it is difficult for foot hunters to access (and the exclusion zones) - say 90% or more, with some bits and pieces on the East Coast - Godley/Macaulay etc - these may be locally high numbers or areas that are difficult for foot hunters to access, e.g. in behind Lilybank where numbers are massive on PCL but you can't walk there. DOC/AATH offset culling is a much greater reduction in tahr numbers in those areas where it has taken place than rec hunters during the ballot, and while some might hunt those areas outside the ballot, I doubt it's significant: when did any of you last walk into the Adams Wilderness area or the Landsborough?
Culling may now be occurring in other areas where tahr numbers are too high (per monitoring) and rec hunting is not doing the job to control them - there aren't any published figures yet to draw any conclusions besides wild speculation.
If monitoring shows that tahr numbers are declining towards or stable at the intervention densities, culling will be reduced (no need to spend the money, not justifiable). Given that culling is a significantly larger contributor to controlling tahr numbers than rec hunting, any reduction in culling would leave more than enough slack for rec hunters to have animals to shoot.
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