They developed a mathematical model of operational competition on a linear range. The model is represented by an initial-boundary problem for the system of evolution equations. It is shown that the competition on the recovered trophic resource does not lead to the disappearance of one of the populations. The estimation of small population propagation rates in the range is given. They obtained the conditions for the existence of an autowave solution on an infinite straight line. The solution of nonlinear differential equations is based on numerical method use.