  In this paper we consider a mathematical model for the evolution and collapse
of the Easter Island society, starting from the fifth century until the last
period of the society collapse (fifteen century). Based on historical reports,
the available primary sources consisted almost exclusively on the trees. We
describe the inhabitants and the resources as an isolated system and both
considered as dynamic variables. A mathematical analysis about why the
structure of the Easter Island community collapse is performed. In particular,
we analyze the critical values of the fundamental parameters driving the
interaction humans-environment and consequently leading to the collapse. The
technological parameter, quantifying the exploitation of the resources, is
calculated and applied to the case of other extinguished civilization (Cop\'an
Maya) confirming, with a sufficiently precise estimation, the consistency of
the adopted model.
