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Lie and Q-conditional symmetries of the classical three-component diffusiveLotka - Volterra system in the case of one space variable are studied. Thegroup-classification problems for finding Lie symmetries and Q-conditionalsymmetries of the first type are completely solved. Notably, non-Lie symmetries(Q-conditional symmetry operators) for a multi-component non-linearreaction-diffusion system are constructed for the first time. An example ofnon-Lie symmetry reduction for solving a biologically motivated problem ispresented.

Lie and conditional symmetries of the three-component diffusive Lotka - Volterra system