Equidae is a family in the order Perissodactyla in class Mammalia. It includes horses, donkeys, zebras, burros, and asses. It also included quagga but they went extinct in 1883. They are in the order Perissodactyla becuase they have an odd number of toes with the center of weight traveling through the 3rd or middle digit. In this case, those in family Equidae have a single functional toe. The single toe, or hoof, makes Equidae the most cursorial, or most adapted for running, Perissodactyla in the modern age. Equidae are grazers meaning their diet consists of grass and they are hindgut fermentors in order to digest grass. They are also polygnous. A single male stallion controls the access to multiple females. The stallions can get agressive and if another approaches, they can bite and kick with their powerful legs to ward them off.
Evolutionaryly, horses developed in present day North America, Europe, and Asia. They were small, dog sized animals that lived in forests and had more toes. Over time, as the global climate was changing and North America became more grassland, the horses grew in size and reduced the number of digits to adapt. Eventually, modern horses became extinct in the Americas and were not reintroduced until the Europeans travelled there.
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third sentence
In the third sentence you say "they", I am not sure if this is referring to the existing species or the extinct one. Restating the species it is referring to would be more clear.
Comments
"It also included quagga..." I think you should put this at the end of the previous sentence in parentheses, and say (quagga were included but went extinct in 1883), or think how necessary this peace of information is to your reader. Try to stay away from excess use of transition words like also. I think you don't need the word "evolutionarily" in the second paragraph. Also, when saying they were dog sized animals, perhaps say they were the size of a modern day wolf or coyote to make it less ambiguous. No need for the phrases "over time" and "eventually".
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I noticed a few times throughout your paragraph you used the word "they." I would try to refrain from using that and be more descriptive with who/what exactly you are talking about.