Understanding Social Feedback in Biological Collectives with Smoothed Model Checking

Biological groups exhibit fascinating collective dynamics without centralised control, through only local interactions between individuals. Desirable group behaviours are typically linked to a certain fitness function, which the group robustly performs under different perturbations in, for instance, group structure, group size, noise, or environmental factors. Deriving this fitness function is an important step towards understanding the collective response, yet it easily becomes non-trivial in the context of complex collective dynamics. In particular, understanding the social feedback - how the collective behaviour adapts to changes in the group size - requires dealing with complex models and limited experimental data. In this work, we assume that the collective response is experimentally observed for a chosen, finite set of group sizes. Based on such data, we propose a framework which allows to: (i) predict the collective response for any given group size, and (ii) automatically propose a fitness function. We use Smoothed Model Checking, an approach based on Gaussian Process Classification, to develop a methodology that is scalable, flexible, and data-efficient; We specify the fitness function as a template temporal logic formula with unknown parameters, and we automatically infer the missing quantities from data. We evaluate the framework over a case study of a collective stinging defence mechanism in honeybee colonies.