Punctuated equilibrium and criticality in a simple model of evolution

On singular probability densities generated by extremal dynamics

“…Due to extremal dynamics, the BS model exhibits scale invariance in the stationary state, in which several quantites display power-law behaviour [1]. Simulations show that the stationary distribution of barriers follows a step function, being zero (in the infinite-size limit) for x < x * ≃ 0.66702 (8) [6].…”

“…Several quantities are known to display power-law behaviour in the BakSneppen model [1,6,18]. In particular, we studied the distribution P J (r) that sucessive updated sites are separated by a distance r. In the original model, P J (r) ∼ r −π , with π = 3.23(2) [18].…”

“…The Bak-Sneppen [1] model is a discrete-time Markov process on a ddimensional lattice of L d sites, with periodic boundaries. At each site we define a real-valued variable x i (0).…”

“…The Bak-Sneppen (BS) model was proposed as a possible explanation of mass extinctions observed in the fossil record [1], and was recently adapted to model experimental data on bacterial populations [2,3]. Independent of its biological interpretation, the model has atracted much attention as a prototype of self-organized criticality (SOC) under extremal dynamics [4,5].…”

Unified “micro”- and “macro-” evolution of eco-systems: self-organization of a dynamic network

“…The ecological models [9] that describe population dynamics using, for example, Lotka-Volterra type equations [10], usually ignore macroevolutionary changes in the eco-system. On the other hand, most of the macro-evolutionary models [11,12,13] do not explicitly explore the ageing and age-distributions of the populations of various species in the system. The models of ageing and dynamics of age-distributed populations [14], usually, focus on only one single species and do not incorporate the inter-species interactions that are, however, crucially important for their extinctions.…”