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Counterintuitive dynamics of various biological phenomena occur when composite system dynamics differ qualitatively from that of their component systems. Such composite systems typically arise when modelling situations with time-varying biotic or abiotic conditions, and examples range from metapopulation dynamics to population genetic models. These biological, and related physical, phenomena can often be modelled as simple financial games, wherein capital is gained and lost through gambling. Such games have been developed and used as heuristic devices to elucidate the processes at work in generating seemingly paradoxical outcomes across a spectrum of disciplines, albeit in a field-specific, ad hoc fashion. Here, we propose that studying these simple games can provide a much deeper understanding of the fundamental principles governing paradoxical behaviours in models from a diversity of topics in evolution and ecology in which fluctuating environmental effects, whether deterministic or stochastic, are an essential aspect of the phenomenon of interest. Of particular note, we find that, for a broad class of models, the ecological concept of equilibrium reactivity provides an intuitive necessary condition that must be satisfied in order for environmental variability to promote population persistence. We contend that further investigations along these lines promise to unify aspects of the study of a range of topics, bringing questions from genetics, species persistence and coexistence and the evolution of bet-hedging strategies, under a common theoretical purview.

Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology