Becoming a referee if authoring mostly in large collaborations
Being asked to be a reviewer means that people think your scientific opinion is likely to be valuable. 

Authoring papers in an area is only one of several ways to be noticed in this way (and, in my experience, not the best way). Other ways of being noticed include:


letting people in your professional network know that you are interested in reviewing papers
asking your supervisors to delegate sub-reviews to you
participating in conferences and workshops
organizing scientific events
giving seminars or other talks


In most areas, there is always a need for more prompt, thorough, and constructive reviewers. Thus, if you are at an appropriate point in your career to begin reviewing (e.g., at least a senior graduate student or postdoc), then people who know you will likely be interested to start delegating work to you as soon as you express interest, and performing a few good reviews will start more and more people looking your way to provide input, as your reputation spreads through the network.