Qualitative theory of the spread of a new gene into a resident population

This work addresses the problems that arise in the estimation of the risk of invader/unwanted GMO spread and the optimal release of desired genes into a population through the release of transgenic individuals. On the basis of a general model of the propagation of an advantageous allele through a population we analyze the thresholds and critical aggregations in gene frequency necessary for the spread of new gene carriers. It is shown that if the invader appears at one place in the ecosystem then it will not spread throughout the ecosystem unless it exceeds some critical threshold, where the critical threshold is defined in terms of both the amount and distribution of the invader. The value of the critical threshold will depend on the fitness of the invader relative to the fitness of the resident organisms in the ecosystem and the mechanism of its dispersion. It is also shown that typically an invader will not spread symmetrically, even if the environment is isotropic, but rather develops clusters that form filaments within the ecosystem. We also demonstrate that if the invader aggregation is sufficiently large then after an initial period the advance of the invader into the resident population takes the form of a traveling wave. The speed of this wave tends to a speed characteristic of the relative fitness and dispersive mechanisms of the invader.