Fibonacci sequence and rabbits

Question

In my calculus book by James Stewart it is mentioned that the Fibonacci sequence arose from studying breeding among rabbits. Now, I don't know what kind of rabbits those were, but I have seen rabbit breeders keep them tight and stacked several rabbits like twenty one above the other in a metal cage. There I would guess they could do nothing but breed randomly. Not sure if this is how it would happen as well, or whether they would each have their own families. Not sure how those rabbits feel.

In any case, if the population is skewed towards females, and number of females is on the left side of the plus sign and number of makes on the left and females totaling after gestation on the right hand side of the equals sign is what the right have side is, breeding in whatever way by its members, in the Fibonacci sequence would yield:

1+1=2 (one female and one male produce one female on average yielding two females) 2+1=3 (two females and one male produce one female and one male on average yielding three females) 3+2=5 (three females and two males produce two females and one male on average yielding females) ...

Sounds a bit perverted, considering who the male has sex with from step one to step two, but whatever, it's a rabbit world, and I've seen them caged.

Anyhow, not sure I'm getting what this "the Fibonacci sequence arose from a problem of rabbits breeding" is all about.

My question is, is this what it is? What?

Thanks.

Answer 1

Stewart doesn't quite say that the Fibonacci sequence arose from a "study" of breeding among rabbits. What he actually says is "This sequence arose when the $13$-th century Italian mathematician known as Fibonacci solved a problem concerning the breeding of rabbits (see Exercise $71$)" (p.$676$ in the $6$-th edition of $2008$. The page and exercise number will almost certainly differ from one edition to another).

If you consult Exercise $71$ (on p.$686$), however, you'll see that the problem has very little to do with the actual breeding behaviour of rabbits:

Fibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair which becomes productive at age $2$ months. If we start with one newborn pair, how many pairs of rabbits will we have in the $n$th month?

In fact, Stewart got two minor details wrong in his description of the problem posed originally by Fibonacci (in his now famous Liber abaci, first published in $1202$). In Fibonacci's original problem, the initial pair was not a newborn pair , but a productive pair, so the sequence in Liber abaci actually goes $1,2,3,5,\dots\ $ rather than $1,1,2,3,\dots\ $, and Fibonacci merely asks how many pairs there will be after a year (which he gives, correctly as $377$), not for a general formula for the number of pairs after an arbitrary number of months.