Steer'n Roll: A Stereoscopic Flow-Sensing Strategy for Planktonic Prey Detection and Capture

TL;DR

This work addresses how planktonic predators, such as copepods, overcome the inherent symmetry of Stokes-flow disturbances to localize and capture prey. It introduces steer'n roll, a mechanism that couples stereoscopic hydrodynamic sensing with active rolling to triangulate prey direction and then steer toward it, producing robust three-dimensional trajectories. The approach is supported by a mathematical formulation based on a multipole expansion of the prey flow, analytical fixed-point and limit-cycle analysis, and numerical simulations demonstrating 100% success across initial conditions, plus quantitative robustness to sensory and motor noise and turbulence. The findings suggest a biologically plausible sensory–motor strategy for flow-mediated prey detection and have implications for understanding copepod navigation and the general design of distributed-flow sensing in micro-organisms.

Abstract

Planktonic organisms such as copepods sense swimming prey and sinking food particles through the hydrodynamic disturbances they generate. However, because these flow fields are often highly symmetric, they provide little directional information, making accurate localization of the source challenging. Here, we introduce the steer'n roll sensing and response strategy. This strategy combines stereoscopic flow sensing and a roll motion. Stereoscopic sensing allows plankton to disambiguate flow signals by integrating two spatially separated flow measurements, while a roll about the swimming axis enhances exploration of the three-dimensional space. We show that steer'n roll is efficient, achieving a 100% success rate, versatile across signal type, and robust to flow sensing noise, orientational diffusion, and turbulence. Together, these findings identify a biologically plausible mechanism for prey detection and capture via flow sensing, and offer testable insights into the sensory-motor strategies of planktonic organisms.

Figures (11)

• Figure 1: Overview of the predator--prey sensing problem and the steer'n roll strategy. (A) Schematic view of the predator-prey problem. The prey, swimming (or sinking) at speed $U$, generates a fluid disturbance that the predator detects through mechanosensors. The predator speed swims at constant speed $V$. (B) Reference frames: a prey-fixed Cartesian frame $(\boldsymbol{\hat{x}}, \boldsymbol{\hat{y}}, \boldsymbol{\hat{z}})$ and and a predator-fixed body frame $(\boldsymbol{\hat{n}}, \boldsymbol{\hat{b}}, \boldsymbol{\hat{t}})$. The vector $\boldsymbol{r}$ denotes the position of the predator in the prey's reference frame. (C) Streamlines (dark green) and velocity-magnitude contours (light green) of the stresslet flow field ( \ref{['eq:Stresslet']}) generated by a swimming prey . (D) Signal field $\mathbf{S}$ (red) ( \ref{['eq:dimensional_signal']}) measured by a predator with sensors aligned along $\boldsymbol{\hat{n}}$ (black). Prey-generated flow streamlines are shown in light green for reference. (E) Steer'n roll strategy: red arrows indicate local signal directions $\boldsymbol{\hat{s}}$; orange arrow $\boldsymbol{\hat{d}}$ denotes the inferred prey direction obtained from stereoscopic sensing ( \ref{['eq:triangulation_d']}). The angular velocity $\boldsymbol{\omega}_{\mathrm{steer}}$ steers the predator toward $\boldsymbol{\hat{d}}$, while $\boldsymbol{\omega}_{\mathrm{roll}}$ induces active rotation about the swimming direction $\boldsymbol{\hat{t}}$. The scalar $\xi$ (\ref{['eq:triangulation_sign']}) determines the funneling direction of the signal field.
• Figure 2: Predator trajectories. Trajectories obtained by integrating \ref{['Eq:Dynamics']} for a prey emitting a stresslet $\boldsymbol{v}_2(\boldsymbol{r})$. We simulate four different initial predator's positions, all with the same initial distance $r_0$ from the prey (green sphere) and same initial orientation. The predator speed is $V = 0.01r_0\omega_\mathrm{steer}$ and the prey is represented as a sphere of radius $a=0.04 r_0$. Four values of the roll speed $\omega_{\rm roll}$ are used as labeled. The trajectories are helices with a radius decreasing with $\omega_{\rm roll}$, but similar pitch angle. For two representative trajectories of panel B (red and yellow), the dynamics of the predator's orientation $\boldsymbol{\hat{t}}$ is shown in Fig. \ref{['fig:fig_3_t_trajectories']}A, and the dynamics of the predator's sensory antennae $\boldsymbol{\hat{n}}$ in Fig. \ref{['fig:Trajectories_vector_n']} in the Supporting Information.
• Figure 3: Predator's orientation dynamics. (A) Evolution of $\boldsymbol{\hat{t}}$ extracted from two of the trajectories shown in Fig. \ref{['fig:fig_2_trajectories']}B (red and yellow). The dynamics converges to an imperfect limit cycle. (B) Same as A, but in the absence of rotation ($V=0$), showing convergence to a perfect limit cycle. (C) Theoretical limit cycle predicted for $V=0$ and $\omega_\mathrm{roll} = 0$, by the fixed-point analysis (see \ref{['eq:fp']}).
• Figure 4: Performance of steer'n roll. The performance $P$ of the steer'n roll strategy for a predator detecting a stresslet flow field. (A) Direction of maximal strain $\boldsymbol{\hat{e}}_1$. The light green contour lines show the stresslet flow intensity. (B) Contour plot of the performance $P$ and average swimming direction $\boldsymbol{\hat{t}}$ for numerically integrated trajectories ($V=0$ and $\omega_\mathrm{roll} = 0.2\:\omega_\mathrm{steer}$). (C). Theoretical prediction of the performance $P$, and the mean predator's orientation $\braket{\boldsymbol{\hat{t}}} = \boldsymbol{\hat{e}}_1$, predicted from the fixed point analysis given in \ref{['eq:fp']}. There is no lengthscale in the plots because the problem is scale-free.
• Figure 5: Robustness to noise. (A) Performance metric $P$ and average trajectories when flow-sensing is noisy. The red line correspond to the distance $r=r_\mathrm{sens}$, as given by Eq. (\ref{['eq:r_sensory']}). (B) Performance $P$ when the predator’s rotational dynamics is affected by noise with $\omega_\mathrm{noise} = 0.5\, \omega_\mathrm{steer}$ (this noise does not introduce a scale in the problem and the strategy remains scale-free). (C) Performance $P$ in presence of a background flow modeling turbulence. The blue line represent the distance $r=r_\mathrm{turb}$, as given by Eq. (\ref{['eq:r_turbulent']}). All simulations are performed with $V = 0$ and $\omega_\mathrm{roll} = 0.2\,\omega_\mathrm{steer}$, similarly to Fig. \ref{['fig:fig_3_performancetheory']}B.