  Q-conditional (nonclassical) symmetries of the known three-component
reaction-diffusion system [K. Aoki et al Theor. Pop. Biol. 50(1) (1996)]
modeling interaction between farmers and hunter-gatherers are constructed for
the first time. A wide variety of Q-conditional symmetries are found in an
explicit form and it is shown that these symmetries are not equivalent to the
Lie symmetries. Some operators of Q-conditional (nonclassical) symmetry are
applied for finding exact solutions of the reaction-diffusion system in
question. Properties of the exact solutions (in particular, their asymptotic
behaviour) are identified and possible biological interpretation is discussed.
