The population size of a predator species is directly controlled by the population cycle of parasites the population cycle of producers the population size of decomposers the population size of its prey

population size of its prey

Explanation:

A predator can be define as an organism which kills another organisms so as to obtain them as food. The organism which is killed is called as prey. Generally, in a food chain the predator is more superior and powerful than the prey, therefore, it is capable of capturing and killing the prey.

According to the given situation, the population size of the predators is directly controlled by the population size of it's prey. This is because of the fact that prey is the source of food for the predators. In anyway if the population size of the prey decreases the population size of the predator will also decrease.  

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