Collective predator evasion

Research summary

One paper, summarised for reference. Collective predator evasion: Putting the criticality hypothesis to the test — Pascal P. Klamser & Pawel Romanczuk, PLoS Comput. Biol. (2021) 17(3), e1008832. doi:10.1371/journal.pcbi.1008832.

The test

The criticality hypothesis holds that animal collectives self-organise near a critical point where collective computation (e.g. responsiveness to stimuli) is optimal. This paper puts it to a spatially-explicit test — most prior support came from non-spatial lattice models — and asks two things: does operating at criticality actually optimise predator evasion, and why; and can individual-level evolution self-tune the group there?

The model

Self-propelled prey (fixed speed $v_0$) with social forces — alignment (strength $\mu_{\text{alg}}$) and distance regulation (repulsion/attraction to a preferred spacing) over Voronoi (topological) neighbours — plus angular noise $D$ and a flee force $\mu_{\text{flee}}$ from a nearby predator. The predator is faster ($v_p = 2v_0$) and pursues the weighted centre of its frontal prey (catch probability decays with distance). The relevant transition is the directional order–disorder (symmetry-breaking) one, crossed by tuning $\mu_{\text{alg}}$ or $D$, with polarization the order parameter:

$$\Phi = \Big|\tfrac{1}{N}\textstyle\sum_i \vec u_i\Big|.$$

Result 1 — criticality is optimal, but not for the hypothesised reason

The two “criticality signatures” behave as predicted: the neighbour velocity-fluctuation correlation $C_{ij}=C(\delta\vec v_i,\delta\vec v_j)$ (directional information transfer) and the susceptibility

$$\chi = \frac{\partial \Phi}{\partial h} = N\big(\langle\Phi^2\rangle - \langle\Phi\rangle^2\big)$$

both peak at the transition, and the predator capture rate is minimal at criticality.

But varying the prey parameters also changes the spatial structure (e.g. inter-individual distance, strongly anti-correlated with capture rate, $C(\gamma_c,\mathrm{IID})\approx-0.69$). To separate structure from information, they add a non-fleeing control ($\mu_{\text{flee}}=0$): identical structure, no predator response. The escape ratio $R_{\text{esc}} = 1 - \gamma_c/\gamma_{c,\text{NF}}$ (and the raw capture-rate difference) shows no peak at criticality — it rises monotonically toward the ordered phase. So the minimal capture rate at criticality is due to the dynamic spatial structure (a passive effect), not the maximal responsiveness / information transfer; the active predator response actually improves deeper into the ordered phase.

Result 2 — criticality is evolutionarily unstable

Letting the individual alignment strength $\mu_{\text{alg}}$ evolve (fitness = fewer deaths), runs started below, above, and far above the transition all converge into the ordered phase (ESS $\mu_{\text{alg}}\approx 4.4$, well above the critical $\approx 0.9$). The critical region is not an attractor — it carries the steepest selection gradient. The driver is self-sorting: at the symmetry-breaking transition, small phenotype differences map onto systematic spatial positions (front/side/density), producing maximal assortative mixing; strongly-aligning agents form denser regions with a smaller “domain of danger” (dilution) and are attacked less. The ESS depends linearly on the flee strength $\mu_{\text{flee}}$, explained by prey balancing social vs. private predator information — social cues help when only your neighbours sense the predator, but conflict with private cues when you sense it directly — driving evolution toward over-weighting social information (“unresponsiveness”).

Why it matters

• Spatial self-organisation is decisive — fixed-lattice / rewiring models miss the structure↔dynamics feedback that both makes criticality optimal and makes it unstable.
• Individual-level selection is not a general self-tuning mechanism for criticality: unlike Hidalgo et al. (where each agent tunes its own transition), here the transition is a purely collective effect, so the group optimum and the individual ESS diverge (a social dilemma) — and multi-level selection cannot generally rescue it either.
• The result does not reject adaptive criticality in animal groups, but demands biologically plausible proximate mechanisms that account for spatial self-organisation and ecology.

References

Klamser & Romanczuk (2021), PLoS Comput. Biol. 17, e1008832 · Vicsek et al. (1995), Phys. Rev. Lett. 75, 1226 · Hidalgo et al. (2014), PNAS 111, 10095 · Couzin et al. (2002), J. Theor. Biol. 218, 1 · Calovi et al. (2015), J. R. Soc. Interface 12, 20141362 · Cavagna, Giardina & Grigera (2018), Phys. Rep. 728, 1 · Vanni, Lukovic & Grigolini (2011), Phys. Rev. Lett. 107, 078103 · Mora & Bialek (2011), J. Stat. Phys. 144, 268.