Plants and animals do live on their own. They live among other plants and animals. Most are food for one another, making what scientists call a food chain. But even though some do become food, enough live on to breed and so continue their species.
At the bottom of this food chain are the plants. What kinds of plants grow depends on the climate and the soil. So places with different climates have different kinds of plant growing. Because animals depend on plants, they tend to vary with the plants, too. But they are also affected by the climate. Some animals can survive drought and heat, others can find food in deep snow, or they can go to sleep (hibernate) to see winter through.
This is true on land, and also in rivers, lakes and ponds. It is also true in the great oceans. In fact, everywhere you look, you will find communities of plants and animals. We sometimes give them names, like desert and mountain, coral reef and rainforest. One example is on the video below.