Table 2.

Notation used and parameters of the model. An en dash (–) indicates a value that potentially varies in space and/or time.

	parameter	notation	description	value
characteristics	position	xi(t)	position of an agent at time t	–
	active swimming velocity	vi(t)	the velocity of an individual due to self-propulsion (active swimming)	–
	flow speed	u(xi(t), t)	the velocity of the background flow at time t and individual position xi(t)	–
	intended heading	θi(t)	the direction of active swimming	–
	actual heading	δi(t)	the actual direction of an individual after being affected by the background flow	–
velocity-jump random walk	active swim speed	s	the speed of swimming of an individual	1
	turning rate	λ	the mean time between successive reorientations of an individual	1
	number of agents	N	number of individuals simulated during a migration	100
goal	goal location	$x^{\star }$	the location of the destination that individuals are aiming for	(0, 0)
	goal tolerance	$\epsilon$	the distance from the goal location to be considered arrived	10
navigation	self-confidence	α	the weighting between inherent information and group information	1/2
	sensing range	R	when using fixed range selection, the maximum distance between individuals to be considered a neighbour	$\{0,2,5,10,20,50,500\}$
	number of neighbours	S	when using nearest neighbour selection, the fixed number of neighbours	$\{0,2,5,10,20,50,\text{all}\}$
	goal direction	ϕ	the direction towards the goal from the individual’s current position	–
	confidence in goal direction	κ	the inherent information, how confident the individual is in the direction towards the target	1*
	heading distribution concentration	κ′	the concentration parameter of the heading distribution, after accounting for the effect of group information	–
	neighbours of ith agent	${\mathcal{N}}_i^d(t)$	the set of neighbours the ith individual has at time t using distance measure $d\in \{\mathrm{N},\mathrm{F}\}$ (for $d=\mathrm{N},\hspace{0.17em}{\mathcal{N}}_i^{\mathrm{N}}(t)=S$ for all time)	–

*See electronic supplementary material C for simulations under variations to these values.