According to the criticality hypothesis, collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective dynamics 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 supports that also animal collectives may be examples of URLanized critical systems. However, open questions about URLanization mechanisms in animal groups remain: Evolutionary adaptation towards  group-level optima (group-level selection), often implicitly assumed in the criticality hypothesis, is in general not a reasonable mechanism in fission-fusion groups composed of non-related individuals. Furthermore, previous theoretical work relies on non-spatial models, which ignore potentially important spatial URLanization effects. Here, 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 the critical point is not an evolutionary stable state. On the contrary, strong spatial self-sorting effects increase the selection strength , and make it an evolutionary unstable state. Our results show that in collective behavior spatio-temporal dynamics are important , and that individual-level selection does not in general provide a robust proximate mechanism in support of the ``criticality hypothesis'' in animal groups .
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 URLanized critical systems. However, open questions about URLanization 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 URLanization 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 .
R
dynamics
behavior
R
supports
suggests
A
a
R
optima
optimum
D
often
R
criticality hypothesis, is
"criticality hypothesis", appears
R
a reasonable mechanism in
reasonable for
R
spatial URLanization effects. Here, using
URLanization and spatial sorting effects. Using
R
``criticality hypothesis''
"criticality hypothesis"
D
the critical point is not an evolutionary stable state. On the contrary,
R
increase the selection strength
at the critical point lead to strong selection gradients
R
show that
demonstrate the decisive role of spatio-temporal phenomena
D
spatio-temporal dynamics are important
R
does not in general provide a robust proximate mechanism in support of the ``criticality hypothesis'' in animal groups
is in general not a viable mechanism for self-tuning of unrelated animal groups towards criticality