  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.
