Stigmergy as a mechanism to produce collective vortex behaviours: a study case in shoveler duck

Ant mill, caterpillar circle, bat donut, bacteria vortex, duck swirl and fish torus are different names for rotating circular formations of animals, where individuals turn around a common centre. Even if the ubiquity of this behavioural phenomenon might have suggested common causes or fundamental underlying principles across contexts, a variety of proximate mechanisms can give rise to vortex behaviours. Here, we investigate if stigmergic process (mechanism of self-organisation wit hout direct communication or interaction between individuals) is able to produce different collective behaviours, notably collective vortices. We present an individual-based simulation model for the movement of populations in a resource landscape that allows us to vary the strength of the interactions mentioned above. The key assumption and novelty of our model is that individuals can cause the release of additional nutrients, as well as consuming them. Our model produces clear predictions. For example, we expect more tortuous individual movement paths and higher levels of aggregation in populations occupying homogeneous environments where individual movement makes more nutrients available. We also show how observed movement dynamics could change when local nutrient sources are depleted or when the population density increases. Our predictions are testable and qualitatively reproduce the different feeding behaviours observed in filter-feeding ducks (Anas clypeata), for example. We suggest that considering two-way interactions between feeding individuals and resource landscapes could help to explain fine-scale movement dynamics.