The wolf is a consumer. (secondary consumer specifically)
Consumer means the animals in a food chain which eats other animal / plant at a lower tropic level (position in food chain) for energy.
Detritivore are organisms that decomposes dead organic matter, and returning the broken down nutrients and matter back to the start of a food chain, which is for the producers.
Producers are usually green plants which make their own food from sunlight, by the process of photosynthesis, and we call the organisms that uses this kind of feeding (making food on their own) as autotroph.
Therefore, since the wolf feeds on rabbits for energy, and not carrying out photosynthesis nor decomposing other organisms for food, so the answer is consumer.
Interspecific competition (i.e. <span>competition among individuals in a population )</span> is most likely to occur when: MATING (i.e. seeking a partner of the opposite sex to reproduce with).
If the producer were to disappear then all the other organisms will either go extinct, survival of the fittest, or have to adapt to the change.