Evolution and Extinction Dynamics in Rugged Fitness Landscapes

Abstract

After an introductory section summarizing the paleontological data and some of their theoretical descriptions, we describe the 'reset' model and its (in part analytically soluble) mean field version, which have been briefly introduced in Letters [1,2]. Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness landscapes. As a consequence, the average fitness in the system increases logarithmically with time, while the rate of extinction steadily decreases. This non-stationary dynamics is studied by numerical simulations and, in a simpler mean field version, analytically. We also consider the effect of externally added 'mass' extinctions. The predictions for various quantities of paleontological interest (life-time distribution, distribution of event sizes and behavior of the rate of extinction) are robust and in good agreement with available data.

Tempo and mode in quasispecies evolution

“…Adapting the results of Sibani and collaborators [36,37], for the case of record dynamics we find that P n is a Poisson distribution with parameter ln S,…”

“…A simple schematic analogue of the nonstationary (ever slowing) evolution process found in the quasispecies model is provided by the dynamics of records [34,35,36,39], which is equivalent to evolution by long-ranged random mutations known in the classical literature as the theory of "hopeful monsters" [23,30]. In the present context it reduces to the following rule for the motion of the master sequence σ * (t) in sequence space: At each time Figure 4: Comparison of the distribution of evolution times for exponentially distributed fitnesses (+) with an ensemble of landscapes for which neardegeneracies (small gaps) have been removed (×).…”

“…To avoid the complications due to a finite error threshold, we consider a strong selection limit (to be described in the next section), in which the population is localized at a single site in sequence space at all times. This allows a direct comparison with simple schematic models of evolutionary dynamics, such as adaptive walks [30,31,32,33] and record dynamics [34,35,36]. Adaptive walks describe the evolution of a genetically homogeneous population under the assumption that deleterious mutations (which decrease the fitness) are eliminated, while advantageous mutations spread instantaneously.…”

Optimal adaptive performance and delocalization in NK fitness landscapes

“…In order to simulate a population evolving in an NK landscape, we use the following algorithm, which has been used previously by Sibani and Pedersen [18], and is described in detail in Ref. [19].…”

<title>Extremal noise events, intermittency, and Log-Poisson statistics in non-equilibrium aging of complex systems</title>

“…The analysis of several specific examples [16][17][18][19][20][27][28][29] has shown the intimate connection between quakes and extremal, record-breaking, noise fluctuation within metastable attractors. Assuming that extremal fluctuations trigger the quakes enables one to translate the properties of record statistics into predictions of the statistical properties of the intermittent events, which are found to be in reasonable agreement with experimental and numerical results.…”