  While moving, animals must frequently make decisions about their future
travel direction, whether they are alone or in a group. Here we investigate
this process for zebrafish (Danio rerio), which naturally move in cohesive
groups. Employing state-of-the-art virtual reality, we study how real fish
follow one or several moving, virtual conspecifics. These data are used to
inform, and test, a model of social response that includes a process of
explicit decision-making, whereby the fish can decide which of the virtual
conspecifics to follow, or to follow some average direction. This approach is
in contrast with previous models where the direction of motion was based on a
continuous computation, such as directional averaging. Building upon a
simplified version of this model [Sridhar et al. 2021], which was limited to a
one-dimensional projection of the fish motion, we present here a model that
describes the motion of the real fish as it swims freely in two-dimensions.
Motivated by experimental observations, the swim speed of the fish in this
model uses a burst-and-coast swimming pattern, with the burst frequency being
dependent on the distance of the fish from the followed conspecific(s). We
demonstrate that this model is able to explain the observed spatial
distribution of the real fish behind the virtual conspecifics in the
experiments. In particular, the model naturally explains the observed critical
bifurcations for a freely swimming fish, whenever the fish makes a decision to
follow only one of the virtual conspecifics, instead of following them as an
averaged group. This model can provide the foundation for modeling a cohesive
shoal of swimming fish, while explicitly describing their directional
decision-making process at the individual level
