Self-Organized Criticality in Phylogenetic-Like Tree Growths

Kotrla

1999

Phys. Rev. Lett.

We investigate an extremal dynamics model of evolution with variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly concentrated in the largest cluster. The time dependence of the number of units exhibits intermittent structure. The self-organized criticality is manifested by a power-law distribution of forward avalanches, but two regimes with distinct exponents τ = 1.98±0.04 and τ ′ = 1.65 ± 0.05 are found. The distribution of extinction sizes obeys a power law with exponent 2.32 ± 0.05. [1,[6][7][8][9][10][11]). The dynamical system in question is composed of a large number of simple units, connected in a network. Each site of the network hosts one unit. The state of each unit is described by a dynamical variable b, called barrier. In each step, the unit with minimum b is mutated by updating the barrier. The effect of the mutation on the environment is taken into account by changing b also at all neighbors of the minimum site.General feature of ED models is the avalanche dynamics. The forward λ-avalanches are defined as follows [1]. For fixed λ we define active sites as those having barrier b < λ. Appearance of one active site can lead to avalanche-like proliferation of active sites in successive time steps. The avalanche stops, when all active sites disappear again. There is a value of λ, for which the probability distribution of avalanche sizes obeys a power law without any parameter tuning, so that the ED models are classified as a subgroup of self-organized critical models [12].The BS model was originally devised in order to explain the intermittent structure of the extinction events seen in the fossil record [13]. In various versions of the BS model it was found, that the avalanche exponent is 1 < τ ≤ 3/2, where the maximum value 3/2 holds in the mean-field universality class. On the other hand, in experimental data for the distribution of extinction sizes higher values of the exponent, typically around τ ≃ 2 are found [14]. The avalanche exponent close to 2 was also measured in ricepile experiments [15]. While there are several models of different kind, which give generic value τ = 2 [16,17], we are not aware of any ED model with such a big value of the exponent.The universality class a particular model belongs to, depends on the topology of the network on which the units are located. Usually, regular hypercubic networks [1] or Cayley trees [11] are investigated. For random neighbor networks, mean-field solution was found to be exact [18,7]. Also the tree models [11] were found to belong to the mean-field universality class. Recently, BS model on random networks, produced by bond percolation on fully connected lattice, was studied [19]. Two universality classes were found. Above the percolation threshold, the system belongs to the mean-field universality class, while exactly at the percolation threshold, the avalanche exponent is different. A dynamics changing the topology in order to dri...

“…Usually, regular hypercubic networks [1] or Cayley trees [11] are investigated. For random neighbor networks, mean-field solution was found to be exact [18,7].…”

mentioning

confidence: 99%

“…Among them, the Bak-Sneppen (BS) model [5] plays the role of a testing ground for various analytical as well as numerical approaches (see for example [1,[6][7][8][9][10][11]). The dynamical system in question is composed of a large number of simple units, connected in a network.…”

mentioning

confidence: 99%

Extremal Dynamics Model on Evolving Networks

Kotrla

1999

Phys. Rev. Lett.

“…The list of models studied starts with large-scale properties of the evolutionary process-massive global extinctions-and ends with the works which are aimed at following the replicative behavior of the chemical structures holding information, namely DNA molecules. A lot of effort has been devoted to this area recently [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] and still new fruitful ideas emerge [17,18,19].…”

Section: Introductionmentioning

confidence: 99%

Selective advantage of topological disorder in biological evolution

Kolář

The European Physical Journal B - Condensed Matter

2003

Abstract. We examine a model of biological evolution of Eigen's quasispecies in a so-called holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). The evolution dynamics is therefore determined by the topology of the genome space which is modelled by the random Bethe lattice. We use the effective medium and single-defect approximations to find the criteria under which the localized quasispecies cloud is created. We find that shorter genomes, which are more robust to random mutations than average, represent a selective advantage which we call "topological". A way of assessing empirically the relative importance of reproductive success and topological advantage is suggested.

“…Our strategy in the following will consist in calculating the free resolvent for various models of the genome space and then analysing the solution of the equation (4). To start with, we reexamine the previously obtained results on the hypercube.…”

Section: Introductionmentioning

confidence: 99%

How the quasispecies evolution depends on the topology of the genome space

Kolář

Physica A: Statistical Mechanics and its Applications

2002

We compared the properties of the error threshold transition in quasispecies evolution for three different topologies of the genome space. They are a) hypercube b) rugged landscape modelled by an ultrametric space, and c) holey landscape modelled by Bethe lattice. In all studied topologies the phase transition exists. We calculated the critical exponents in all the cases. For the critical exponent corresponding to appropriately defined susceptibility we found super-universal value.