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.