Mobility in spatial biodiversity models through recurrence quantification analysis

Abstract Recurrence plots (RPs) and their associated quantifiers provide a robust framework for detecting and characterizing complex patterns in non-linear time-series. We employ recurrence quantification analysis (RQA) to investigate the dynamics of the cyclic, non-hierarchical May–Leonard model (rock–paper–scissors), which captures competitive interactions among three species. A crucial control parameter is the species’ mobility m , which governs spatial displacement and strongly shapes the dynamics. By systematically varying m and constructing RPs from numerical simulations, we examine how recurrence quantifiers reflect distinct dynamical features associated with different ecological states. We then introduce an ensemble-based approach that leverages statistical distributions of quantifiers across many independent realizations to identify dynamical outliers, defined as significant deviations from typical system behaviour. Detailed numerical analyses show that these outliers correspond to divergent ecological regimes at specific mobility values and provide a robust route to infer m from observed data. Overall, our results highlight recurrence-based methods as effective diagnostics for spatial ecological systems, enabling the extraction of ecologically relevant information from non-linear dynamical patterns.