The tangled nature model as an evolving quasi-species model

Abstract

We show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold, consistent with the simulation results, that provides a valuable insight into how the microscopic dynamics of the model determine the observed macroscopic phenomena published previously. The dynamics of the Tangled Nature model is defined on the microevolutionary time scale via reproduction, with heredity, variation, and natural selection. Each organism reproduces with a rate that is linked to the individuals' genetic sequence and depends on the composition of the population in genotype space. Thus the microevolutionary dynamics of the fitness landscape is regulated by, and regulates, the evolution of the species by means of the mutual interactions. At low mutation rate, the macro evolutionary pattern mimics the fossil data: periods of stasis, where the population is concentrated in a network of coexisting species, is interrupted by bursts of activity. As the mutation rate increases, the duration and the frequency of bursts increases. Eventually, when the mutation rate reaches a certain threshold, the population is spread evenly throughout the genotype space showing that natural selection only leads to multiple distinct species if adaptation is allowed time to cause fixation.

Correlation, selection and the evolution of species networks

“…This version of the Tangled Nature model succeeded its predecessor (Collobiano, Christensen, & Jensen, 2003) (Anderson & Jensen, 2005) by introducing correlations into the inheritance process. Here, we shall present the construct of the model whilst summarising the correlative effects.…”

Punctuated equilibria and1/fnoise in a biological coevolution model with individual-based dynamics

“…An early attempt in this direction is the coupled N K model with population dynamics introduced by Kauffman and Johnsen [8,9], but thus far not many similar models have been studied. Recently, Hall, Christensen, and collaborators [10,11,12] introduced a model they called the "tanglednature" model, in which each individual lives in a dynamically evolving "fitness landscape" created by the populations of all the other species. Here we consider a simplified version of this model, in which no individual is allowed to live through more than one reproduction cycle.…”

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

“…Therefore, it is desirable to have a "unified" theoretical model that would unfold the natural continuous process while simulated on a computer. Very recently, attempts have been made by several groups to merge population dynamics and "macro"-evolution within a single mathematical framework [7,8,15,16,17,18]. These efforts may have been made feasible, at least in part, because of the availability of fast computers.…”