Predator–prey interactions between swimming animals of the zooplankton are studied in a mathematical model. The assumptions are: 1) the animals are points in a 1-m3homogeneous space, 2) the animals move at random and are randomly distributed, and 3) the predator animal has an encounter radius given by its sensory system. The mathematics of encounter probabilities are developed for a 3-dimensional space. The results show two optimal strategies: 1) cruising predators which prey upon slow moving animals (herbivores), and 2) ambush (nonmoving) predators which prey upon fast cruising prey. Of the variables used (population densities, speeds of the two animal species, and encounter radius) the encounter radius has the greatest influence on the encounter probabilities. The results suggest a simple community structure and point to the importance of studies on live zooplankton.