What animals became extinct due to Natural Selection and why?

the mean reson why animals become extinct due to natural selection is the never ending stuggle for food, for examlpe lets say a deer was liveing in Africa and the trees was to high. for the deer to get any leaf's (food) the animal would have to go thew phisical and mental change's.(due to a mutacion in the dna) if not the deer would die because their would be no possible way for the animal to get any food.