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Teams are central to human accomplishment. Over the past half-century, psychologists have identified the Big-Five cross-culturally valid personality variables: Neuroticism, Extraversion, Openness, Conscientiousness, and Agreeableness. The first four have shown consistent relationships with team performance. Agreeableness (being harmonious, altruistic, humble, and cooperative), however, has demonstrated a non-significant and highly variable relationship with team performance. We resolve this inconsistency through computational modelling. An agent-based model (ABM) is used to predict the effects of personality traits on teamwork and a genetic algorithm is then used to explore the limits of the ABM in order to discover which traits correlate with best and worst performing teams for a problem with different levels of uncertainty (noise). New dependencies revealed by the exploration are corroborated by analyzing previously-unseen data from one the largest datasets on team performance to date comprising 3,698 individuals in 593 teams working on more than 5,000 group tasks with and without uncertainty, collected over a 10-year period. Our finding is that the dependency between team performance and Agreeableness is moderated by task uncertainty. Combining evolutionary computation with ABMs in this way provides a new methodology for the scientific investigation of teamwork, making new predictions, and improving our understanding of human behaviors. Our results confirm the potential usefulness of computer modelling for developing theory, as well as shedding light on the future of teams as work environments are becoming increasingly fluid and uncertain., Comment: Final version (open access) as published in journal