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.Comment: Paper submitted to Journal of Physics A. 13 pages, 4 figure
