A hunter-gatherer-farmer population model: new conditional symmetries and exact solutions with biological interpretation

New Q-conditional (nonclassical) symmetries and exact solutions of the hunter-gatherer-farmer population model proposed by Aoki, Shida and Shigesada (Theor. Popul. Biol. 1996;50:1-17) are constructed. The main method used for the aforementioned purposes is an extension of the nonclassical method for system of partial differential equations. An analysis of properties of the exact solutions obtained and their biological interpretation are carried out. New results are compared with those derived in recent studies devoted to the same model.