  To use evolution algebras to model population dynamics that both allow
extinction and introduction of certain gametes in finite generations,
nilpotency must be built into the algebraic structures of these algebras with
the entire algebras not to be nilpotent if the populations are assumed to
evolve for a long period of time. To adequately address this need, evolution
algebras over rings with nilpotent elements must be considered instead of
evolution algebras over fields. This paper develops some criteria, which are
computational in nature, about the nilpotency of these algebras, and shows how
to construct finitely generated evolution algebras which are nil but not
nilpotent.
