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

Cause'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 opti mal use of resources. A mathematical Lotka-Volterra nonlinear model of inte raction between a native and sterile species is proposed. The condition for total extinction is related to the initial number M-O of sterile individua ls released in the niche. In fact, the existence of a critical sterile-popu lation value M-C is conjectured from numerical analysis and an analytical e stimation is found. When spatial diffusion (migration) is considered a crit ical size territory is found and, for small territory, total extinction exi st in any case. This work is motivated by the extermination agriculture pro blem of fruit flies in our region.