I wonder what the same 7 year math,would look like applied to protected hawks that have no natural predator.
No natural predators? I fully beg to differ, they do in fact have predators... There are predators that will raid the nest of eggs and young like raccoons, owls and crows... Owls and hawks are also known to fight over nesting locations destroying each others eggs and killing each others chicks... Great Horned owls will even kill adult hawks over territory disputes or food... And young hawks learning to fly spend a great deal of time on the ground and during this ground time they face multiple ground predator threats as well... Read the article linked bellow, it says that 37% of red-tailed hawk perish in the first 10 days of flight training due to predators...
You are really trying to compare apples to pineapples, especially if you ignore that they do have natural predators just like rabbits that keep their population in check...
There are also other HUGE differences that need to be taken into account...
Lets take a look at red-tailed hawks for example...
Hawks only produce one generation of offspring a year...
A female red-tailed hawk only lays/hatches 1-4 eggs a year, when healthy one could estimate 2 babies per pair per year... But, based on the study bellow it appears on average a pair of red-tailed hawks is only producing 0.9 babies a year, so it takes 2+ years to just double the population if there was zero predator loss, now factor in the 37% loss in the first 10 days of flight training and it takes even more years to just double the population...
It also takes those babies 3 years to reach sexual maturity, so there is not going to be any babies from the offspring until the 3rd or 4th year...
The above are night and day differences in reproductive rates and sexual maturity times between rabbits and hawks, as well as offspring numbers per breeding as well as breeding cycles per year...
So lets work the math ignoring the factual predator loss, while basing the reproductive rate of roughly 1 baby a year per pair as found in the study bellow... We will also assume a 50/50 split of male/females... Parenthesis indicate year born...
Year 1 ~ M/F pair
Year 2 ~ M/F pair + F(2) offspring
Year 3 ~ M/F pair + F(2) offspring + M(3) offspring
Year 4 ~ M/F pair + F(2) offspring + M(3) offspring + F(4) offspring
Year 5 ~ M/F pair + F(2) offspring + M(3) offspring + F(4) offspring + M(5) offspring
** At this point the first Female offspring is reaching sexual maturity...
Year 6 ~ M/F pair + F(2) offspring + M(3) offspring + F(4) offspring + M(5) offspring + the F(2) female's F(2)(1) offspring
Year 7 ~ M/F pair + F(2) offspring + M(3) offspring + F(4) offspring + M(5) offspring + F(6) offspring + the F(2) female's F(2)(1) + M(2)(1) offspring
** At this point the second Female offspring is reaching sexual maturity...
Year 8 ~ M/F pair + F(2) offspring + M(3) offspring + F(4) offspring + M(5) offspring + F(6) offspring M(7) + the F(2) female's F(2)(1) + M(2)(1) offspring + F(2)(2) + the F(4) females F(4)(1)
So after 8 years we have a grand total of about 14 hawks 2 originals and 12 offspring (assuming my quick math is right)... Now if we plug in predator loss, say taking the 37% as the study found in the first 10 days of flight and assume lets say another 13% loss from other predators, we end up with give or take about 2 originals and maybe 6 offspring in the 7-8 year breeding cycle period... And that doesn't account for additional loss due to food shortages for example...
Now of course the numbers would be higher if we used the median 2 babies per breeding pair, but then again we only factored in the predator loss from babies in flight training, not those taken as eggs or chicks at other times...
In the end it's really a far fetched and silly analogy to try and make...
http://news.nationalgeographic.com/news/2001/08/0809_redtailedhawks_2.html