  We present an alternative domain concerning mathematics to investigate
universal evolution mechanisms by focusing on large cycles theory (LCT) - a
simplified version of well-known hamiltonian graph theory. LCT joins together a
number of $NP$-complete cycle problems in graph theory. $NP$-completeness is
the kay factor insuring (by conjecture of Cook) the generation of endless
developments and great diversity around large cycles problems. Originated about
60 years ago, the individuals (claims, propositions, lemmas, conjectures,
theorems, and so on) in LCT continually evolve and adapt to their environment
by an iterative process from primitive beginnings to best possible theorems
based on inductive reasoning. LCT evolves much more rapidly than biosphere and
has a few thousand pronounced species (theorems). Recall that life on earth
with more than 2 million species was originated about 3.7 billion years ago and
evolves extremely slowly. We show that all theorems in LCT have descended from
some common primitive propositions such as "every complete graph is
hamiltonian" or "every graph contains a cycle of length at least one" via
improvements, modifications and three kinds of generalizations - closing,
associating and extending. It is reasonable to review Darwinian mechanisms in
light of LCT evolution mechanisms (especially inductive reasoning) including
the origin and macroevolution disputable phenomena in the biosphere.
