First of all, 'determinist' and 'compatibilist' is not an opposition. A compatibilist is a determinist, per definition. What you probably mean is what usually is called a 'hard determinist'; but I find this also a wrong term. The determinism of a compatibilist and a determinist is just as hard. Compatibilism is not determinism mixed with just a 'little free will'. So the best term is 'incompatibilist determinist'.
The compatibilist claims that, how hard the determinism might be, that there is a meaningful concept of free will that covers all necessary concepts that presuppose free will, such as blaming, praising, responsibility, punishment, etc, except a few wrong ideas that people have about free will. The basic idea is that all is needed is that people can act according their own wishes and believes, i.e. that their own wishes and believes are part of the causal fabric of the universe. That also means that the concept of free will that the compatibilist has, needs determinism. Without determinism, free will would be impossible, what people do would be random. It is difficult to see how random actions can be a basis for responsibility.
The biological basis of free will is the capability of animals to anticipate the future. Depending on what they expect, they act. They need to be able to see how their own future actions influence the future. Simple example: my cat says 'mow' when he is hungry, knowing that I will notice him and fill his top.
But the biological basis on its own is not enough: we need insight in our reasons for actions. Having such insights might evolutionary have arisen by the capability to have a 'folk psychology': to assign reasons to other animals. The next step is to assign reasons to yourself, and being able to evaluate them. At this moment 'free will is born'.
I think that the clearest sign in other species is behaviour that only can be reasonably be explained by animals that try to manipulate on the basis of what they think that other individuals think. So if we recognise compassion with other animals that are in pain, trying to hide food when nobody looks, cheating and mobbing, then these might be indications that we are justified to assign free will to them. So that would mean: certain crows, apes, whales and dolphins, and elephants can be assigned free will.
One important aspect of having free will is the capability to limit the free will of other individuals: one can coerce other individuals by creating a situation in which he does something that he normally would never do; or let him believe something to be true, which in fact is not true. Then this individual does not follow its own wishes or believes, but of somebody else. Seeing this should clarify the whole free will discussion: the opposite of free will is coercion; the opposite of determinism is randomness.
There is no opposition between free will and determinism.