Figure 7.

Complications of drift compensation. One method to incorporate drift compensation would be to split the active swimming velocity (v) into two components v¹ and v², where v¹ is the active swimming velocity dedicated to swimming in the goal direction (ϕ), and v² is the portion of active swimming velocity dedicated to compensating for the flow, see (a). The model becomes $\mathrm{d}{x}_i(t)/\mathrm{d}t=(1-\chi )v_i^1(t)+\chi v_i^2(t)+u(x_i(t),t)$ where 0 ≤ χ ≤ 1 is a parameter controlling the amount of effort dedicated to compensating for the flow rather than seeking the goal. Consequently, this introduces further subtlety to communication, as it is now possible to communicate: ideal direction ($\text{arg}(v^1)$), intended direction ($\text{arg}(v^1+v^2)$) or actual direction ($\text{arg}(v^1+v^2+u)$), see (b). Panels (c–e) show the impact of these different communication types for a simple cross flow with $\zeta =0.2,\vartheta ={90}^{\circ }$. Blue trajectories are those for a navigating population with no drift compensation (χ = 0), while yellow trajectories are those under a slight compensation (χ = 0.2). All inset plots show the number of individuals yet to arrive at the goal against time.