Evolution of an animal population - Colegiul National Mihail Eminescu (Satu Mare - Roumanie)

We intend studying the evolution of pairs of animals. Hypotheses are as follows:
On each step of time n, we suppose that:
-every pair of young animals from the previous step becomes a pair of adults;
-every pair of adults from the previous step has a pair of young.
The questions are:
-Is it possible to describe the evolution of the population?
-Is it possible to give a direct estimate of the total number of animals of each time n, without calculating the population of all preceding times?
-How can we introduce mortality in the example? (we can, for instance, study the case in which 50% of the parents die, and then the case in which 50% of the grandparents die.
The most common case is to begin with the study of an only pair of young. This subject is linked to the sequences (of whole numbers), to polynomials of degree 2, to the golden ratio, and even to polynomials of degree 3.