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In multiagent systems that require coordination, agents must learn diverse policies that enable them to achieve their individual and team objectives. Multiagent Quality-Diversity methods partially address this problem by filtering the joint space of policies to smaller sub-spaces that make the diversification of agent policies tractable. However, in teams of asymmetric agents (agents with different objectives and capabilities), the search for diversity is primarily driven by the need to find policies that will allow agents to assume complementary roles required to work together in teams. This work introduces Asymmetric Island Model (AIM), a multiagent framework that enables populations of asymmetric agents to learn diverse complementary policies that foster teamwork via dynamic population size allocation on a wide variety of team tasks. The key insight of AIM is that the competitive pressure arising from the distribution of policies on different team-wide tasks drives the agents to explore regions of the policy space that yield specializations that generalize across tasks. Simulation results on multiple variations of a remote habitat problem highlight the strength of AIM in discovering robust synergies that allow agents to operate near-optimally in response to the changing team composition and policies of other agents.