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In a space-air-ground integrated network (SAGIN), managing resources for the growing number of highly-dynamic and heterogeneous radios is a challenging task. Symbiotic communication (SC) is a novel paradigm, which leverages the analogy of the natural ecosystem in biology to create a radio ecosystem in wireless networks that achieves cooperative service exchange and resource sharing, i.e., service/resource trading, among numerous radios. As a result, the potential of symbiotic communication can be exploited to enhance resource management in SAGIN. Despite the fact that different radio resource bottlenecks can complement each other via symbiotic relationships, unreliable information sharing among heterogeneous radios and multi-dimensional resources managing under diverse service requests impose critical challenges on trusted trading and intelligent decision-making. In this article, we propose a secure and smart symbiotic SAGIN (S^4) framework by using blockchain for ensuring trusted trading among heterogeneous radios and machine learning (ML) for guiding complex service/resource trading. A case study demonstrates that our proposed S^4 framework provides better service with rational resource management when compared with existing schemes. Finally, we discuss several potential research directions for future symbiotic SAGIN.