Species that live in stable environments are likely to be
-selected, and have stable population sizes around carrying
capacity.

The rate that would change would be the  searching efficiency/attack rate. there are only two other rates in this model: the  growth rate of prey, and the  predator or consumer mortality rate.the  searching efficiency/attack rate is what indicates how effectively can a predator capture its prey whether in the searching process or actual capturing/attacking process. 

The last option water because it is slow