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Cognitive radio is the promising radio technology, which aims to detect and utilize the temporally unused spectrum bands by sensing its radio environment in order to enhance spectrum utilization. However, these objectives bring significant challenges and required functionalities such as spectrum sensing, sharing, management and mobility for the realization of cognitive radio networks (CRN). In particular, efficient spectrum sharing problem in cognitive radio communication is one of the most important problem which must be addressed in order to enhance the overall spectrum utilization in dynamic spectrum access environments. In this paper, we introduce a new BIOlogically-inspired spectrum sharing (BIOSS) algorithm which is based on the adaptive task allocation model in insect colonies. Without need for any coordination among the unlicensed users, BIOSS enables each unlicensed user to distributively determine the appropriate channel(s) over which it can communicate. Performance evaluations clearly reveal that BIOSS achieves efficient dynamic spectrum sharing with high spectrum utilization and without any coordination among the users and hence yielding no spectrum handoff latency overhead due to coordination.