AN APPROACH TO PRACTICAL PERSISTENCE

A basic problem in community ecology is determining whether a communit y of interacting species will survive in the long term. A criterion en suring this is that of permanence (or uniform persistence), which is b ased on the idea that species densities for large time are above minim um non-zero levels. There are various mathematical techniques for inve stigating permanence, but they do not yield an estimate for the minimu m levels, and these may lie below minimum viability levels in the biol ogical sense of 'Practical Persistence'. Here we study a technique for obtaining explicit expressions for the minimum levels when one specie s is 'slow'. This is illustrated for a predator-prey problem governed by difference equations, and we note that the technique is applicable even when the dynamics is chaotic.