Senior Lecturer in Theoretical Biology


Life Sciences
Roehampton University
London SW15 5PJ


andrea.perna at

A "duality" between movements and positions

Animal groups produce characteristic formations that remain "similar" over time. Think for instance to a flock of geese flying in a V: the form of the flock stretches and contracts over time, but the V shaped formation remains recognizable over time. Within the group, each individual will typically maintain a relatively constant position relative to its nearest neighbour in spite of the fact that birds occasionally swap their positions and this nearest neighbour does not necessarily coincide with a particular individual.
Preserving a certain group configuration requires that each individual constantly and actively perform appropriate movements to restore the desired configuration whenever this is lost. This defines a minimal set of interactions responses that a group must perform, independently of more complex collective decision phenomena, such as the negotiation of a common direction of movement.

Preserving mutual positions

The movement of a focal individual with respect to a neighbour can be decomposed into an alignment response and an attraction-repulsion response by projecting it onto two different vectors (see figure). Alignment is the component of movement response that has the same bearing as the neighbour. Attraction and repulsion are the components of movement oriented towards the neighbour
Figure (a) illustrates the situation of an individual, in red, that has a preference for being directly behind its neighbour (target position indicated by a star); figure (b) illustrates a similar situation whereby the relative positions of the focal individual and of its neighbour are the same, but the focal individual aims at reaching a schooling configuration side by side with its neighbour. Both examples depict the same type of response (an attraction to the target), but we interpret them in terms of different alignment and attraction responses because we consider the other individual and not the target as the "point of attraction".

Animal interactions needed to maintain a stable relative position

Related scientific publications

  • Perna et al. "On the duality betweein interaction responses and mutual positions in flocking and schooling". Movement Ecology (2014) [Web]