Forward and inverse methods for inferring interactions in natural swarms

Many group-living animals are capable of impressive collective coordination phenomena ranging from flocking to collective decision-making and structure building. Inferring the individual-level rules of interaction that lead to the emergence of these phenomena is a complex scientific endeavour. It requires observing the system over two different scales (the individual and the collective) and describing it both empirically from real world data and theoretically with mathematical and computational models.
A common approach involves multiple iterations of the following "modelling cycle" (Sumpter, Mann, Perna, J. Roy. Soc. Interface 2012): (1) Characterise the interactions of individual animals with other group members (2) Implement the observed rules of interaction in an agent-based simulation model (3) Collect measures that characterise the collective-level pattern produced by the model and (4) validate the model by comparing the measures collected with empirical collective-level data. This approach allows identifying interaction rules that are biologically realistic (because they were observed from data) and are also sufficient to explain the observed collective phenomenon (because the model effectively reproduces it). Typically, however, this approach does not allow concluding that the observed rules of interaction are also "necessary": other animal species could implement completely different rules of interaction that lead to the same collective outcome. Identifying necessary (and hence universal) individual-level interaction rules can be achieved by running the modelling cycle in a reverse way: by modelling directly the collective-level outcome and by inferring the individual-level interaction directly from the model. I will bring some examples of both the forward and inverse methods based on my recent research.