From Individual Interactions to Collective Dynamics — and Back: Why Timing Matters
Tatjana Petrov
Collective systems—from biochemical regulatory networks to animal groups, robotic swarms, and artificial multi-agent systems—are fascinating because relatively simple, local interaction rules can give rise to rich, robust, and adaptive collective behaviour. Understanding how microscopic interaction mechanisms shape collective dynamics can reveal design principles in natural systems and guide the construction of engineered ones. Conversely, collective observations may provide clues about the individual mechanisms that generated them. This gives rise to two complementary problems: how can we predict collective dynamics from microscopic interactions, and how much can we infer about individual mechanisms from partial observations of the collective?
I will discuss these questions through stochastic population models of interacting agents. First, with examples inspired by gene regulation, I will illustrate how finite-size effects and multiple time scales can produce unexpected transient dynamics. I will then discuss formal and computational approaches for analysing and quantifying such behaviour, drawing on recent results on consensus robustness in stochastic swarms. On the inference side, I will consider how (sparse) observations of collective behaviour can be used to identify plausible models of individual interactions, drawing on our recent result on honeybee collective decision-making.
I will conclude with open questions on scalable prediction, inference, and robustness in stochastic interacting systems, and on how these challenges extend to increasingly adaptive and strategic artificial multi-agent systems.