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Gause's principle of competition between two species is studied when one ofthem is sterile. We study the condition for total extinction in the niche,namely, when the sterile population exterminates the native one by an optimaluse of resources. A mathematical Lotka-Volterra non linear model of interactionbetween a native and sterile species is proposed. The condition for totalextinction is related to the initial number $M_{o}$ of sterile individualsreleased in the niche. In fact, the existence of a critical sterile-populationvalue $M_{c}$ is conjectured from numerical analysis and an analyticalestimation is found. When spatial diffusion (migration) is considered acritical size territory is found and, for small territory, total extinctionexist in any case. This work is motived by the extermination agricultureproblem of fruit flies in our region.Comment: 11 pages. Published in Jour.Phys.A Math.Gen. 33, 4877 (2000

Gause's exclusion principle revisited: artificial modified species and competition