you have a deer herd of 100,000 and reduce it by 8% which leaves you with 92,000 deer. now if that population increases by just 10% due to fawn births it would put it at 101,200. Year two decrease of 8% would put it at 93,104 with a 10% birth rate putting it back at 102,414. Therefore after 4 years of an 8% decrease you population would be 104,887 deer. So even though it may help prove your point to just forget how math works in reality an 8% decrease when taking all the factors into consideration turns out to actually be a 4.8% increase. It's funny how numbers work when you know how to use them. By the way...an 8% decrease on a population over 4 years (without taking any other factors into consideration) would actually be a 28% decrease in case you wanted to know.
You are right that one can't add percentages decreases over 4 years and get the exact amount of total herd reduction. But, your example is flawed because you are using the wrong defintion of herd reduction. The 8% herd reduction in 2001 ,was a reduction of the OW herd by *%. It was not an 8% reduction of the PS herd.
Furthermore, in 2000 the PGC said that a anterless harvest of 301K ,kept the herd stable. Therefore, if the 2001 harvest of 283 K reduced the OW herd by 8% ,there was no increase in recruitment from 2000 to 2001 and therefore it follows that the 2002 harvest of 352k anterless would have reduced the herd by more than 8% as would the the 2003 and 2004 harvests.
Remember the old computer model projected a decrease of 40% ,which is in line with the 2004 buck harevest of 124K ,which is close to the buck harvest back in 1984 .