  Gause's principle of competition between two species is studied when one of
them is sterile. We study the condition for total extinction in the niche,
namely, when the sterile population exterminates the native one by an optimal
use of resources. A mathematical Lotka-Volterra non linear model of interaction
between a native and sterile species is proposed. The condition for total
extinction is related to the initial number $M_{o}$ of sterile individuals
released in the niche. In fact, the existence of a critical sterile-population
value $M_{c}$ is conjectured from numerical analysis and an analytical
estimation is found. When spatial diffusion (migration) is considered a
critical size territory is found and, for small territory, total extinction
exist in any case. This work is motived by the extermination agriculture
problem of fruit flies in our region.
