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Bak, P. & Snepen, K. Punctuated equilibrium and criticality in a simple model of evolution. Phys. Rev. Lett. 59, 381-384

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Abstract

A simple and robust model of biological evolution of an ecology of interacting species is introduced. The model self-organizes into a critical steady state with intermittent coevolutionary avalanches of all sizes; i.e., it exhibits ``punctuated equilibrium'' behavior. This collaborative evolution is much faster than non-cooperative scenarios since no large and coordinated, and hence prohibitively unlikely, mutations are involved.
... As an explanation for the occurrence of power law distributions, a number of hypotheses have therefore been formulated: Conjecture 1: (SOC) Nature generally self-organizes towards criticality; typical systems are slowly driven at nonequilibrium with many degrees of freedom and strongly nonlinear dynamics [50][51][52][53]. Conjecture 2: A classical model of self-sustained branching describes the avalanches of events in biology, in size S and in lifetime T as p(S) ∼ S −τ and p(T) ∼ T −a , where τ = 3/2 and a = 2 [22]. ...
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In the neighborhood of critical states, distinct materials exhibit the same physical behavior, expressed by common simple laws among measurable observables, hence rendering a more detailed analysis of the individual systems obsolete. It is a widespread view that critical states are fundamental to neuroscience and directly favor computation. We argue here that from an evolutionary point of view, critical points seem indeed to be a natural phenomenon. Using mammalian hearing as our example, we show, however, explicitly that criticality does not describe the proper computational process and thus is only indirectly related to the computation in neural systems.
... The Bak-Sneppen model [20] assumes that the average time taken to mutate across a fitness barrier goes exponentially with the height of the barrier as stated in the Arrhenius law of statistical mechanics. The model shows that a power-law distribution of coevolutionary avalanches might give rise in turn to a power-law distribution of extinction events. ...
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... is result, in general, is typical of critical phenomena, when a system responds to some minor event by a catastrophic change in its state. e SOC theory was used to interpret a wide variety of phenomena in nature and society, for instance, economics [101][102][103][104][105][106][107], biology [108][109][110][111], earthquakes [112], political science [113,114], sociology [115][116][117], brain functions (neural networks) [118][119][120][121][122][123], agriculture [124], and other fields. ...
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... In order to gain an understanding of the resulting complex coevolutionary dynamics in such systems, theoretic approaches have proven to be a powerful method. One of the most influential conceptual models of large-scale biological coevolution in this context is a model introduced by Bak and Sneppen (Bak and Sneppen, 1993), which directly assigns a new random value for the fitness of the least fit population and all interacting populations, mimicking the replacement of the former and the alteration of its interactions. Later, Solé and Manrubia proposed a similarly simple model of an ecological network, considering a more continuous drift of properties, and ancestral relations between populations (Solé, 1996;Solé and Manrubia, 1996). ...
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DOI:https://doi.org/10.1103/PhysRevLett.70.3833