Abstract
For the equations of population dynamics, this note presents three symmetries: a coordinate symmetry, an additive symmetry and an exchange symmetry. Among them, additive symmetry is a new one that should be held in equations of population dynamics particularly those for quasispecies. The distinguishability between species is also stressed to obtain the stability condition of 2-dim Lotka-Volterra model that satisfies the additive symmetry.
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