According to the criticality hypothesis, collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective behavior undergoes a qualitative change between different dynamical regimes. Critical systems exhibit unique properties, which may benefit collective information processing such as maximal responsiveness to external stimuli. Besides neuronal and gene-regulatory networks, recent empirical data suggests that also animal collectives may be examples of self-organized critical systems. However, open questions about self-organization mechanisms in animal groups remain: Evolutionary adaptation towards a group-level optimum (group-level selection), implicitly assumed in the “criticality hypothesis”, appears in general not reasonable for fission-fusion groups composed of non-related individuals. Furthermore, previous theoretical work relies on non-spatial models, which ignore potentially important self-organization and spatial sorting effects. Using a generic, spatially-explicit model of schooling prey being attacked by a predator, we show first that schools operating at criticality perform best. However, this is not due to optimal response of the prey to the predator, as suggested by the “criticality hypothesis”, but rather due to the spatial structure of the prey school at criticality. Secondly, by investigating individual-level evolution, we show that strong spatial self-sorting effects at the critical point lead to strong selection gradients, and make it an evolutionary unstable state. Our results demonstrate the decisive role of spatio-temporal phenomena in collective behavior, and that individual-level selection is in general not a viable mechanism for self-tuning of unrelated animal groups towards criticality.

Highlights d Field experiments investigated anti-predator benefits of fish collective behavior d Fish produced conspicuous, repetitive, and rhythmic surface waves for up to 2 min d Experimentally induced fish waves reduced attack frequency in predatory birds d The results further support an anti-predator function of fish collective behavior

Animals often face changing environments, and behavioral flexibility allows them to rapidly and adaptively respond to abiotic factors that vary more or less regularly. However, abiotic factors that affect prey species do not necessarily affect their predators. Still, the prey’s response might affect the predator indirectly, yet evidence from the wild for such a classical bottom-up effect of abiotic factors shaping several trophic levels remains sparse. In many aquatic environments, daily changes in oxygen concentrations occur frequently. When oxygen levels drop to hypoxic levels, many fishes respond with aquatic surface respiration (ASR), during which they obtain oxygen by skimming the upper, oxygenated surface layer. By increasing time at the surface, fish become more vulnerable to fish-eating birds. We explored these cascading effects in a sulfidic spring system that harbors the endemic sulphur molly (Poecilia sulphuraria) as prey species and several fish-eating bird species. Sulfide-rich springs pose harsh conditions as hydrogen sulfide (H2S) is lethal to most metazoans and reduces dissolved oxygen (DO). Field sampling during three daytimes indicated that water temperatures rose from morning to (after)noon, resulting in the already low DO levels to decrease further, while H2S levels showed no diurnal changes. The drop in DO levels was associated with a decrease in time spent diving in sulphur mollies, which corresponded with an increase in ASR. Interestingly, the laboratory-estimated threshold at which the majority of sulphur mollies initiate ASR (ASR50: <1.7 mg/L DO) was independent of temperature and this value was exceeded daily when hypoxic stress became more severe toward noon. As fish performed ASR, large aggregations built up at the water surface over the course of the day. As a possible consequence of fish spending more time at the surface, we found high activity levels of fish-eating birds at noon and in the afternoon. Our study reveals that daily fluctuations in water’s oxygen levels have the potential to alter predator-prey interactions profoundly and thus highlights the joined actions of abiotic and biotic factors shaping the evolution of a prey species.