Software ecosystems (SECOs) and open innovation processes have been claimed as a way forward for the software industry. A proper understanding of requirements is as important for these IT-systems as for more traditional ones. This paper presents a mapping study on the issues of requirements engineering and quality aspects in SECOs and analyzes emerging ideas. Our findings indicate that among the various phases or subtasks of requirements engineering, most of the SECO specific research has been accomplished on elicitation, analysis, and modeling. On the other hand, requirements selection, prioritization, verification, and traceability has attracted few published studies. Among the various quality attributes, most of the SECOs research has been performed on security, performance and testability. On the other hand, reliability, safety, maintainability, transparency, usability attracted few published studies. The paper provides a review of the academic literature about SECO-related requirements engineering activities, modeling approaches, and quality attributes, positions the source publications in a taxonomy of issues and identifies gaps where there has been little research.