Collective predator evasion: Putting the criticality hypothesis to the test.

Pascal P Klamser,Pawel Romanczuk,Nir Gov

doi:10.1371/journal.pcbi.1008832

Abstract

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

Distributed processing of information is at the core for the function of many complex systems in biology, such as neuronal networks [1], genetic regulatory networks [2] or animal collectives [3, 4]
Complex systems theory suggests that collective information processing is optimal at the border between order and disorder, i.e. at a critical point
Based on ideas initially developed in statistical physics and theoretical modeling it has been conjectured that such living systems operate in a special parameter region, in the vicinity of so-called critical points, where the system’s macroscopic dynamics undergo a qualitative change, and various aspects of collective computation become optimal [5,6,7,8,9,10,11]

Summary

Introduction

Distributed processing of information is at the core for the function of many complex systems in biology, such as neuronal networks [1], genetic regulatory networks [2] or animal collectives [3, 4]. In recent years some empirical support for the “criticality hypothesis” has been obtained from analysis of neuronal dynamics [10, 12, 13], gene regulatory networks [14, 15], and collective behaviors of animals [16,17,18,19,20,21] This evidence is often based on observation of characteristic features of critical behavior, such as power-law distribution or diverging correlation lengths in spatial systems. Open questions remain whether evolutionary, individual-level adaptation is a possible self-tuning mechanism for (i) biological collectives, where phase transitions are purely macroscopic phenomena, and (ii) animal groups characterized by spatial, dynamic interaction networks. It has been recently shown that even under strong group-level selection, as long as individual-level selection plays a non-negligible role, multi-level selection will result in evolution of sub-optimal collective behaviors [34, 35]

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