Atapeworm and a cat have this type of relationship
competition
mutualism
commensalism
parasitism

1.fossils 2.analogous organs 3.homologous organs

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.