a farmer sprays his crops once a week with pesticides to kill beetles. he noticed that the pesticide he used last year is not killing the beetles this year . the beetles have evolved which strategies would best way to stop the evolution of pesticide resistant beetles?

The best way to stop is to use different forms of pesticide (stronger ones and then weaker ones). Or even use different form is terms of liquid or pebbles etc etc. This is because the beetles would not get used to one thing over and over again (natural selection) and hence stops the evolution.

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.