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Yes, Fibonacci made certain assumptions, as we all do when figuring out what to expect. But is it fair of Rachel to describe them as a "highly unbelievable breeding process"?
True, he ignores potential in-breeding problems and mortality, but this isn't unduly optimistic given that he asked what quantity of rabbits could be expected at the end of only 12 months. And the birth of two babies of the same sex to one adult pair could be offset by two of the opposite sex being born to another.
What Fibonacci does refrain from assuming is a geometric population expansion such as 1 pair the first month, 2 the second, 4 the third, and so on. At 12 months this would lead to 2048 pairs of rabbits, compared to Fibonacci's much more modest 144. This is because he builds in a highly realistic maturation delay right from the start: 1 pair the first month, and still just one pair the second month. Only with the third do we have two pairs (two adults and two babies), 3 pairs the fourth month (the first pair of adults with another pair of babies, but the second generation still without issue). That second generation first produces its own pair in the fifth month along with yet another pair from the first two rabbits, making 5 pairs altogether, and so on.
Asking how many pairs after 12 months seems reasonable given our custom of yearly progress reviews. However the answer 144 must have intrigued Fibonacci the mathematician, as it does us today, since it is of course 12 squared.
I investigate this matter of powers in the Fibonacci sequence a bit more in my two previous comments, Fib 5 and Hitting that Square.