The facts:
1. Some animals aren't exactly the same as others.
2. Some of those differences are inheritable.
3. Some of those differences affect the probability that the animal will reproduce.
4. In the case where both 2 and 3 apply, a circular effect is set up in which a difference affects the probability of the animal reproducing, which in turn affects the probability that the difference will show up in the next generation, which means the difference affects the probability of itself existing.
5. In case 4, the differences which decrease the probability of reproduction will create feedback loop which tends to eliminate them from the population. The differences that increase the probability, a feedback loop is created which tends to cause them to spread through the population.
6. As a result, animals tend to have properties that help them reproduce.
7. With the introduction of mutation, the possibilty exists for one species to slowly turn into another.
Note that in 4, the circularity is often attacked as a fallacy, with such inanities as it's a "tautology". There is nothing fallacious about a circular effect.
All species are intermediate.