Drivers of Variation in the Optimal Spatial Structure of Collective Information Gatherers.

Collective systems that self-organise to maximise the group's ability to collect and distribute information can be successful in environments with high spatial and temporal variation. Such organisations are abundant in nature, as sharing information is a key benefit of many biological collective systems, and have been influential in the design of many artificial collectives such as swarm robotics. Understanding how these systems may be spatially distributed to optimise their collective potential is therefore of importance in both ecology and in collective systems design. Here, we develop a mathematical model which uses an optimisation framework to determine the higher-order spatial structure of a collective that optimises group-level knowledge transfer. The domain of the objective function is a set of weighted hypergraphs, which can fully represent the spatial structure from a topological perspective. By varying the parameters within the objective function and the constraints, we determine how the optimal spatial structure may vary when individuals differ in their information gathering ability and how this variation differs in the context of resource constraints. Our key findings are that the amount of resources in the environment can lead to specific subgroup sizes being optimal for the group as a whole when individuals are homogeneous in their information gathering abilities. Further, when there is variation in information gathering abilities, our model implies that the sharing of space between smaller subgroups of the population, rather than the whole population, is optimal for collective knowledge sharing. Our results have applications across diverse contexts from behavioural ecology to bio-inspired collective systems design.