Climate
The topography of a specific region has a direct affect on the climate of that region. The climate, in turn, affects which animal species live in the region. For example, the flat topography of desert regions contributes to the hot, dry desert climate. These regions are not appropriate areas for animals that require a lot of water for survival. The harsh rays of sunlight also cause sunburns on animals not equipped with mechanisms to prevent them from getting sunburned.
Food
Animals need to live in areas where they can find food or they will not survive. The topography of a region dictates which species of plants and animals inhabit a region. If a specific region has none of the food sources for a specific animal species, you will not find that animal species in that area. This same principle can be conversely applied to predators of a specific species. If no predators are present, but prey is, an animal species will thrive. If too many predator species exist in a specific topographical area, the animal species in question runs the risk of being killed off by predators.
Barriers
Topographical elements, both natural and man-made, often pose as barriers to animal species. Mountains, for example, are often difficult for animals to traverse; therefore, you'll find certain species on one side of a mountain range but not on the other, even if the climate and vegetation are ideal on both sides of the mountain. While many barriers are permanent, such as cities and mountains, some barriers are temporary, including flooded areas.
Habitat
The habitat itself needs to be correct for an animal species to survive. Topographical differences tend to alter habitats, which could render a specific area inhospitable to a certain animal species. A habitat may be inhospitable to an animal species in many ways, including elevation, oxygen concentration and the availability of ground cover. This also applies to aquatic species. Even if animals designed to survive in saltwater could get around topographical changes and get to a freshwater source, their bodies are not designed to live in freshwater, and so they would die.