Accuracy, rationality and specialization in a generalized model of collective navigation.

Animal navigation is a key behavioural process, from localized foraging to global migration. Within groups, individuals may improve their navigational accuracy by following those with more experience or knowledge, by pooling information from many directional estimates ('many wrongs') or some combination of these strategies. Previous agent-based simulations have highlighted that homogeneous leaderless groups can improve their collective navigation accuracy when individuals preferentially copy the movement directions of their neighbours while giving a low weighting to their own navigational knowledge. Meanwhile, other studies have demonstrated how specialized leaders may emerge, and that a small number of such individuals can improve group-level navigation performance. However, in general, these earlier results either lack a full mathematical grounding or do not fully consider the effect of individual self-interest. Here we derive and analyse a mathematically tractable model of collective navigation. We demonstrate that collective navigation is compromised when individuals seek to optimize their own accuracy in both homogeneous groups and those with differing navigational abilities. We further demonstrate how heterogeneous navigational strategies (specialized leaders and followers) may evolve within the model. Our results thus unify different lines of research in collective navigation and highlight the importance of individual selection in determining group composition and performance.