ABSTRACT
The study of population dynamics — the changing population of a specie, or of species within an ecosystem — has a very long history. As human societies grew and people aggregated in denser and denser towns, cities and conurbations, the natural and vital question became “How many people will there be?”. In the year 1202 ad , in his Latin text Liber Abaci [32], Leonardo of Pisa (aka Leonardo Pisano Bogolio or Leonardo Bonacci, or simply Fibonacci) asked the same question of rabbits: Suppose on the first day, I have one pair of adult rabbits. On each day, each pair of adults beget two infants. Infants grow to adulthood in one day, and all rabbits live forever. (Actually, the constraints proposed in 1202 ad were slightly different; This version is equivalent and conceptually easier to deal with.) With modern algebra it is trivial to arrive at a solution. Let Ft be the
number of pairs of rabbits (both adults and infants) on day t. Now the number of pairs of adults present on day t is given by Ft−1 (remember that rabbits grow to adulthood in one day, and therefore those rabbits present on day t − 1, will be adults by day t — if not sooner). So on day t + 1 we will have all the pairs alive on day t, Ft (since all rabbits are immortal) plus a number of pairs of new babies equal to the number of adults on day t, Ft−1. Hence,
Ft+1 = Ft + Ft−1.
