An argument from authority (argumentum ab auctoritate), also called an appeal to authority, or argumentum ad verecundiam, is a form of defeasible argument in which a claimed authority's support is used as evidence for an argument's conclusion. It is well known as a fallacy, though some consider that it is used in a cogent form when all sides of a discussion agree on the reliability of the authority in the given context. Other authors consider it a fallacy to cite an authority on the discussed topic as the primary means of supporting an argument.
But the *primary* means of supporting evolution is NOT the argument from authority. It is the argument from observation.
The problem is that to understand what the observations mean requires training and education. So, the authorities are convinced, not by other authorities, but by the observational evidence. Others, who do not have the training to understand that evidence in detail, have to rely on the authorities.
As an example, I am a mathematician. If I doubt a particular mathematical claim, I look to the source and see if the proof is good or not. But I have been trained by decades of experience how to read and analyze mathematical proofs. Others without that training wouldn't even be able to understand the first line of most research articles in math.
So, if you are interested in a particular math result, you have two options: either get the training to evaluate the articles yourself, or rely on an authority to let you know. Since the training is expensive and difficult, most people rely on the authorities.
The same is true for other subjects. You *can* train in biology and do the relevant labs or field work yourself. But that takes a lot of time, money, and hard work. Unless you want to go through that, the next best option is to rely on an authority that *has* done that work.
Ultimately, though, the basis of their authority is that they have done the lab or field work and analyzed the data. And that is a legitimate basis for their authority.