Randomness in the choice of neighbours promotes cohesion in mobile animal groups

Abstract

Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group-level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real organisms; for example, fish stochastically align towards only one randomly chosen neighbour and yet the schools are highly polarized. Here, we ask—how do organisms maintain group cohesion? Using a spatially explicit model, inspired from empirical investigations, we show that group cohesion can be achieved in finite groups even when organisms randomly choose only one neighbour to interact with. Cohesion is maintained even in the absence of local averaging that requires interactions with many neighbours. Furthermore, we show that choosing a neighbour randomly is a better way to achieve cohesion than interacting with just its closest neighbour. To understand how cohesion emerges from these random pairwise interactions, we turn to a graph-theoretic analysis of the underlying dynamic interaction networks. We find that randomness in choosing a neighbour gives rise to well-connected networks that essentially cause the groups to stay cohesive. We compare our findings with the canonical averaging models (analogous to the Vicsek model). In summary, we argue that randomness in the choice of interacting neighbours plays a crucial role in achieving cohesion.

Collective responses of flocking sheep to a herding dog

“…It has also been shown that sheep select interaction neighbors [62]. To incorporate this cognitive constraint in our model, we introduce a key modification — sheep perceives a limited number of its nearest neighbors, among which only k have an impact on its behavior [63].…”

Data-driven discovery of stochastic dynamical equations of collective motion

“…In our model, each agent is characterised by its orientation, e i = (cos θ i , sin θ i ), position x i and moves at a constant speed, v. Agents move within a box of length L with periodic boundary conditions, and we update the positions of agents every ∆t. Recent studies have emphasised the role of the probabilistic nature of animal interactions on collective motion [44,69,70]. We incorporate this via asynchronous interactions among agents and choice of neighbours [70], as described below.…”

“…In other words, the schooling of fish is a consequence of the noise associated with small-sized groups, and hence is termed noise-induced schooling. Similarly, other group characteristics such as mechanical properties [38][39][40][41][42] and cohesion have also been identified as a consequence of stochastic effects [43,44]. Intrinsic noise could also be important in evolutionary dynamics that shapes collective motion of finite flocks [45,46].…”

Applying collective motion models to study discordant individual behaviours within a school of fish

“…Some models have been proposed that, by defining a set of interactions between the individuals comprising a school of fish, we are able to reproduce the collective behaviours of schools of fish that are most frequently observed in nature. Such models are commonly referred to as individual-based or agentbased models [5,[7][8][9]: in them, the evolution of position and velocity of each individual is governed by a set of differential equations [10][11][12][13][14][15][16][17] or a set of difference equations [4,[18][19][20][21][22][23][24][25][26][27][28][29][30] at discrete instants of time. Despite the simplicity of the interactions included in these models, they have been successful in replicating collective behaviours with good accuracy.…”

“…Indeed, there are models in which the collective behaviours already mentioned emerge even in the absence of orientation [11,12,14,16,44] or in the presence of attraction alone [16,23,25,27]. Finally, it is worth noting that in many works, the investigation was performed by restricting the school of fish to moving in one plane [9][10][11][12][13][14][15][16][17]22,23,26,27,29,30,45] and setting precise initial conditions to start its movement [10,12,13,29,45].…”