A tick that is sucking blood from an elephant is an example of parasitism in the savanna. The tick is a parasite that is taking advantage of its host, and using its host for nutrients.
A parasite is an organism that feeds off of another organism. Parasitism is not a symbiotic relationship because the parasite benefits from the relationship but the host does not. Parasites can either use the body of its host as a place to live and reproduce, or simply use the host as a source of nutrition. Similarly, some parasites ultimately kill the host, while others feed off the host but do not cause any real damage. Parasites are usually very small in size, and many can go completely undetected throughout their entire lifetime.
There are examples of parasites in almost every biome. Specifically in the savanna, ticks attach themselves to any animal they can and drink that animal's blood for nutrients. While parasites can cause direct harm to the host organism, ticks, like many other parasites, can cause severe damage to their host not because the parasite itself damages the host, but instead because diseases arise from such close contact between organisms. For example, ticks can carry the bacterium that causes Lyme disease in humans and dogs. There are many examples of how parasitism causes indirect effects to the host organism.